Expression templates give you an easy way to enter math expressions in standard mathematical notation. When you insert a template, it appears on the entry line with small blocks at positions where you can enter elements. A cursor shows which element you can enter.

Use the arrow keys or press e

to move the cursor to each element’s position, and type a value or expression for the element. Press

/·

to evaluate the expression.

Fraction template /p

keys

Example:

Note: See also / (divide) , page 143.

Exponent template l

key

Example:

Note: Type the first value, press l

, and then type the exponent.

To return the cursor to the baseline, press right arrow (

Note: See also ^ (power) , page 144.

Square root template

Example:

Note: See also ‡ () (square root) , page 150.

keys

Nth root template

Note: See also root() , page 102.

Example:

TI-Nspire™ CAS Reference Guide 1

e exponent template

Example:

Natural exponential e

raised to a power

Note: See also e^() , page 40.

Log template

Example:

Calculates log to a specified base. For a default of base 10, omit the base.

Note: See also log() , page 71.

Piecewise template (2-piece)

Example:

Lets you create expressions and conditions for a two-piece piecewise function. To add a piece, click in the template and repeat the template.

Note: See also piecewise() , page 87.

keys

Catalog >

Piecewise template (N-piece)

Lets you create expressions and conditions for an N -piece piecewise function. Prompts for N .

Catalog >

Example:

See the example for Piecewise template (2-piece).

key

Note: See also piecewise() , page 87.

2 TI-Nspire™ CAS Reference Guide

System of 2 equations template

Catalog >

Example:

Creates a system of two equations. To add a row to an existing system, click in the template and repeat the template.

Note: See also system() , page 122.

System of N equations template

Lets you create a system of N equations. Prompts for N .

Catalog >

Example:

See the example for System of equations template (2-equation).

Note: See also system() , page 122.

Absolute value template

Note: See also abs() , page 7.

Example: dd°mm’ss.ss’’ template

Lets you enter angles in dd ° mm ’ ss.ss

’’ format, where dd is the number of decimal degrees, mm is the number of minutes, and ss.ss

is the number of seconds.

Example:

Matrix template (2 x 2)

Example:

Creates a 2 x 2 matrix.

Catalog >

TI-Nspire™ CAS Reference Guide 3

Matrix template (1 x 2)

Matrix template (2 x 1)

Example:

Matrix template (m x n)

The template appears after you are prompted to specify the number of rows and columns.

Example:

Catalog >

Note: If you create a matrix with a large number of rows and columns, it may take a few moments to appear.

Sum template ( G )

Example:

Note: See also G () ( sumSeq ), page 151.

Product template (

)

Example:

Note: See also

() ( prodSeq ), page 150.

4 TI-Nspire™ CAS Reference Guide

Catalog >

First derivative template

Example:

The first derivative template can also be used to calculate first derivative at a point.

Note: See also d() (derivative) , page 149.

Second derivative template

Example:

The second derivative template can also be used to calculate second derivative at a point.

Note: See also d() (derivative) , page 149.

Nth derivative template

Example:

The n th derivative template can be used to calculate the n th derivative.

Note: See also d() (derivative) , page 149.

Definite integral template

Example:

Note: See also ‰ () integral() , page 149.

Indefinite integral template

Note: See also ‰ () integral() , page 149.

Example:

Catalog >

TI-Nspire™ CAS Reference Guide 5

Limit template

Use N or ( N ) for left hand limit. Use + for right hand limit.

Note: See also limit() , page 63.

Example:

Catalog >

6 TI-Nspire™ CAS Reference Guide

Alphabetical listing

Items whose names are not alphabetic (such as +, !, and >) are listed at the end of this section, starting on page

142

. Unless otherwise specified, all examples in this section were performed in the default reset mode, and all variables are assumed to be undefined.

A

abs() abs(

Expr1

) abs(

List1

) abs(

Matrix1

)

⇒ expression

⇒ list

⇒ matrix

Returns the absolute value of the argument.

Note: See also Absolute value template , page 3.

If the argument is a complex number, returns the number’s modulus.

Note: All undefined variables are treated as real variables.

Catalog > amortTbl() amortTbl( NPmt , N , I , PV , [ Pmt ] , [ FV ] , [ PpY ] , [ CpY ] , [ PmtAt ] ,

[ roundValue

] )

⇒ matrix

Amortization function that returns a matrix as an amortization table for a set of TVM arguments.

NPmt is the number of payments to be included in the table. The table starts with the first payment.

Pmt

PpY

CpY

, and

PmtAt are described in the table of TVM arguments, page 131.

• If you omit Pmt , it defaults to

Pmt = tvmPmt( N , I , PV , FV , PpY , CpY , PmtAt ) .

• If you omit FV , it defaults to FV =0.

• The defaults for PpY , CpY , and PmtAt are the same as for the

TVM functions.

roundValue specifies the number of decimal places for rounding.

Default=2.

The columns in the result matrix are in this order: Payment number, amount paid to interest, amount paid to principal, and balance.

The balance displayed in row n is the balance after payment n .

You can use the output matrix as input for the other amortization functions G Int() and G Prn() , page 152, and bal() , page 13.

and

BooleanExpr1

and

BooleanExpr2

BooleanList1

and

BooleanList2

⇒ Boolean expression

⇒ Boolean list

BooleanMatrix1

and

BooleanMatrix2 ⇒ Boolean matrix

Returns true or false or a simplified form of the original entry.

Catalog >

TI-Nspire™ CAS Reference Guide 7

and

Integer1

and

Integer2 ⇒ integer

Compares two real integers bit-by-bit using an and operation.

Internally, both integers are converted to signed, 64-bit binary numbers. When corresponding bits are compared, the result is 1 if both bits are 1; otherwise, the result is 0. The returned value represents the bit results, and is displayed according to the Base mode.

You can enter the integers in any number base. For a binary or hexadecimal entry, you must use the 0b or 0h prefix, respectively.

Without a prefix, integers are treated as decimal (base 10).

In Hex base mode:

Important: Zero, not the letter O.

In Bin base mode:

In Dec base mode:

Catalog >

Note: A binary entry can have up to 64 digits (not counting the

0b prefix). A hexadecimal entry can have up to 16 digits.

angle() angle(

Expr1

)

⇒ expression

Returns the angle of the argument, interpreting the argument as a complex number.

Note: All undefined variables are treated as real variables.

In Degree angle mode:

In Gradian angle mode:

Catalog >

In Radian angle mode: angle(

List1

)

⇒ list angle(

Matrix1

)

⇒ matrix

Returns a list or matrix of angles of the elements in

List1

Matrix1

, interpreting each element as a complex number that represents a two-dimensional rectangular coordinate point.

ANOVA

List1

List2

[ ,

List3

, ...

List20

][ ,

Flag

]

Performs a one-way analysis of variance for comparing the means of two to 20 populations. A summary of results is stored in the stat.results

variable. (See page 119.)

Flag

=0 for Data,

Flag

=1 for Stats

Output variable stat.

F stat.PVal

stat.df

stat.SS

Description

Value of the

statistic

Smallest level of significance at which the null hypothesis can be rejected

Degrees of freedom of the groups

Sum of squares of the groups

8 TI-Nspire™ CAS Reference Guide

Catalog >

Output variable stat.MS

stat.dfError

stat.SSError

stat.MSError

stat.sp

stat.xbarlist

stat.CLowerList

stat.CUpperList

Description

Mean squares for the groups

Degrees of freedom of the errors

Sum of squares of the errors

Mean square for the errors

Pooled standard deviation

Mean of the input of the lists

95% confidence intervals for the mean of each input list

ANOVA2way

List1

List2

[ ,

List3

, … ,

List10

][ , levRow

]

Computes a two-way analysis of variance for comparing the means of two to 10 populations. A summary of results is stored in the stat.results

variable. (See page 119.)

LevRow =0 for Block

LevRow =2,3,..., Len -1, for Two Factor, where

Len =length( List1 )=length( List2 ) = … = length( List10 ) and

Len / LevRow ∈ {2,3,…}

Outputs: Block Design

Output variable stat.

F stat.PVal

stat.df

stat.SS

stat.MS

stat.

F Block stat.PValBlock

stat.dfBlock

stat.SSBlock

stat.MSBlock

stat.dfError

stat.SSError

stat.MSError

stat.s

Description

statistic of the column factor

Smallest level of significance at which the null hypothesis can be rejected

Degrees of freedom of the column factor

Sum of squares of the column factor

Mean squares for column factor

F statistic for factor

Least probability at which the null hypothesis can be rejected

Degrees of freedom for factor

Sum of squares for factor

Mean squares for factor

Degrees of freedom of the errors

Sum of squares of the errors

Mean squares for the errors

Standard deviation of the error

Catalog >

TI-Nspire™ CAS Reference Guide 9

COLUMN FACTOR Outputs

Output variable stat.

F col stat.PValCol

stat.dfCol

stat.SSCol

stat.MSCol

Description

F statistic of the column factor

Probability value of the column factor

Degrees of freedom of the column factor

Sum of squares of the column factor

Mean squares for column factor

ROW FACTOR Outputs

Output variable stat.

F Row stat.PValRow

stat.dfRow

stat.SSRow

stat.MSRow

Description

F statistic of the row factor

Probability value of the row factor

Degrees of freedom of the row factor

Sum of squares of the row factor

Mean squares for row factor

INTERACTION Outputs

Output variable stat.

F Interact stat.PValInteract

stat.dfInteract

stat.SSInteract

stat.MSInteract

Description

F statistic of the interaction

Probability value of the interaction

Degrees of freedom of the interaction

Sum of squares of the interaction

Mean squares for interaction

ERROR Outputs

Output variable stat.dfError

stat.SSError

stat.MSError

Description

Degrees of freedom of the errors

Sum of squares of the errors

Mean squares for the errors

Standard deviation of the error

10 TI-Nspire™ CAS Reference Guide

Ans

⇒ value

Returns the result of the most recently evaluated expression.

approx() approx(

Expr1

)

⇒ expression

Returns the evaluation of the argument as an expression containing decimal values, when possible, regardless of the current Auto or

Approximate mode.

This is equivalent to entering the argument and pressing

approx(

List1

)

⇒ list approx(

Matrix1

)

⇒ matrix

Returns a list or matrix where each element has been evaluated to a decimal value, when possible.

4 approxFraction()

Expr 4 approxFraction( [ Tol ] )

⇒ expression

List 4 approxFraction( [

Tol

] )

⇒ list

Matrix 4 approxFraction( [

Tol

] )

⇒ matrix

Returns the input as a fraction, using a tolerance of Tol . If Tol is omitted, a tolerance of 5.E-14 is used.

Note: You can insert this function from the computer keyboard by typing @>approxFraction( ...

) .

keys

Catalog >

Catalog > approxRational() approxRational(

Expr

[ ,

Tol

] ) approxRational(

List

[ ,

Tol

] )

⇒ expression

⇒ list approxRational(

Matrix

[ ,

Tol

] )

⇒ matrix

Returns the argument as a fraction using a tolerance of

Tol

. If

Tol

is omitted, a tolerance of 5.E-14 is used.

arccos()

Catalog >

See cos / (), page 23.

TI-Nspire™ CAS Reference Guide 11

arccosh() arccot() arccoth() arccsc() arccsch() arcLen() arcLen(

Expr1

Var

Start

End

)

⇒ expression

Returns the arc length of Expr1 from Start to End with respect to variable

Var

Arc length is calculated as an integral assuming a function mode definition.

arcLen(

List1 , Var , Start , End

)

⇒ list

Returns a list of the arc lengths of each element of List1 from Start to

End with respect to Var .

arcsec() arcsech() arcsin() arcsinh() arctan() arctanh() augment() augment(

List1, List2

)

⇒ list

Returns a new list that is

List2

appended to the end of

List1

12 TI-Nspire™ CAS Reference Guide

See cosh / (), page 24.

See cot / (), page 25.

See coth / (), page 25.

See csc / (), page 27.

See csch / (), page 27.

Catalog >

See sec / (), page 105.

See sech / (), page 106.

See sin / (), page 112.

See sinh / (), page 113.

See tan / (), page 124.

See tanh / (), page 125.

Catalog >

augment() augment(

Matrix1

Matrix2

)

⇒ matrix

Returns a new matrix that is

Matrix2

appended to

Matrix1

. When the “,” character is used, the matrices must have equal row dimensions, and

Matrix2

is appended to

Matrix1

as new columns.

Does not alter Matrix1 or Matrix2 .

Catalog > avgRC() avgRC(

Expr1

Var

[

=Value

] [ ,

Step

] ) avgRC(

Matrix1

Var

[

=Value

] [ ,

Step

] )

⇒ expression avgRC(

Expr1

Var

[

=Value

] [ ,

List1

] ) avgRC(

List1

Var

[

=Value

] [ ,

Step

] )

⇒ list

⇒ matrix

Returns the forward-difference quotient (average rate of change).

Expr1 can be a user-defined function name (see Func ).

When

Value

is specified, it overrides any prior variable assignment or any current “with” substitution for the variable.

Step

is the step value. If

Step

is omitted, it defaults to 0.001.

Note that the similar function centralDiff() uses the centraldifference quotient.

B

bal() bal(

NPmt

, [

Pmt

] , [

PpY

] , [

CpY

] , [

PmtAt

] ,

[ roundValue

] )

⇒ value bal(

NPmt

, amortTable

)

⇒ value

Amortization function that calculates schedule balance after a specified payment.

Pmt

PpY

CpY

, and

PmtAt are described in the table of TVM arguments, page 131.

NPmt specifies the payment number after which you want the data calculated.

Pmt

PpY

CpY

, and

PmtAt are described in the table of TVM arguments, page 131.

• If you omit Pmt , it defaults to

Pmt

= tvmPmt(

PpY

CpY

PmtAt

) .

• If you omit FV , it defaults to FV =0.

• The defaults for

PpY

CpY

, and

PmtAt

are the same as for the

TVM functions.

roundValue

specifies the number of decimal places for rounding.

Default=2.

bal(

NPmt

, amortTable

) calculates the balance after payment number

NPmt , based on amortization table amortTable . The amortTable argument must be a matrix in the form described under amortTbl() , page 7.

Note: See also G Int() and G Prn() , page 152.

Catalog >

TI-Nspire™ CAS Reference Guide 13

4 Base2

Integer1 4

Base2

⇒ integer

Note: You can insert this operator from the computer keyboard by typing @>Base2 .

Converts Integer1 to a binary number. Binary or hexadecimal numbers always have a 0b or 0h prefix, respectively.

Zero, not the letter O, followed by b or h.

0b binaryNumber

0h hexadecimalNumber

A binary number can have up to 64 digits. A hexadecimal number can have up to 16.

Without a prefix,

Integer1

is treated as decimal (base 10). The result is displayed in binary, regardless of the Base mode.

Negative numbers are displayed in “two's complement” form. For example,

N 1 is displayed as

0hFFFFFFFFFFFFFFFF in Hex base mode

0b111...111 (64 1’s) in Binary base mode

N 2

is displayed as

0h8000000000000000 in Hex base mode

0b100...000 (63 zeros) in Binary base mode

If you enter a decimal integer that is outside the range of a signed,

64-bit binary form, a symmetric modulo operation is used to bring the value into the appropriate range. Consider the following examples of values outside the range.

becomes N 2

and is displayed as

0h8000000000000000 in Hex base mode

0b100...000 (63 zeros) in Binary base mode

becomes 0 and is displayed as

0h0 in Hex base mode

0b0 in Binary base mode

N 2

63 N 1 becomes 2

63 N 1 and is displayed as

0h7FFFFFFFFFFFFFFF in Hex base mode

0b111...111 (64 1’s) in Binary base mode

4 Base10

Integer1 4

Base10

⇒ integer

Note: You can insert this operator from the computer keyboard by typing @>Base10 .

Converts Integer1 to a decimal (base 10) number. A binary or hexadecimal entry must always have a 0b or 0h prefix, respectively.

0b binaryNumber

0h hexadecimalNumber

Zero, not the letter O, followed by b or h.

A binary number can have up to 64 digits. A hexadecimal number can have up to 16.

Without a prefix, Integer1 is treated as decimal. The result is displayed in decimal, regardless of the Base mode.

14 TI-Nspire™ CAS Reference Guide

Catalog >

4 Base16

Integer1 4

Base16

⇒ integer

Note: You can insert this operator from the computer keyboard by typing @>Base16 .

Converts Integer1 to a hexadecimal number. Binary or hexadecimal numbers always have a 0b or 0h prefix, respectively.

0b binaryNumber

0h hexadecimalNumber

Zero, not the letter O, followed by b or h.

A binary number can have up to 64 digits. A hexadecimal number can have up to 16.

Without a prefix,

Integer1

is treated as decimal (base 10). The result is displayed in hexadecimal, regardless of the Base mode.

If you enter a decimal integer that is too large for a signed, 64-bit binary form, a symmetric modulo operation is used to bring the value into the appropriate range. For more information, see 4

Base2 , page 14.

binomCdf() binomCdf( n

, p

)

⇒ number binomCdf( n

, p

, lowBound

, upBound

)

⇒ number

if lowBound and upBound

are numbers,

list

if lowBound

and upBound

are lists binomCdf( n

, p

, upBound

) for P(0

{

{ upBound

)

⇒ number

if upBound

is a number,

list

if upBound

is a list

Computes a cumulative probability for the discrete binomial distribution with n number of trials and probability p of success on each trial.

For P(X { upBound ), set lowBound =0 binomPdf() binomPdf( n

, p

)

⇒ number binomPdf( n

, p

XVal

)

⇒ number

XVal

is a number, list

XVal

is a list

Computes a probability for the discrete binomial distribution with n number of trials and probability p of success on each trial.

C

ceiling() ceiling(

Expr1

)

⇒ integer

Returns the nearest integer that is | the argument.

The argument can be a real or a complex number.

Note: See also floor() .

ceiling(

List1

)

⇒ list ceiling(

Matrix1

)

⇒ matrix

Returns a list or matrix of the ceiling of each element.

Catalog >

TI-Nspire™ CAS Reference Guide 15

centralDiff() centralDiff(

Expr1

Var

[

=Value

][ ,

Step

] )

⇒ expression centralDiff(

Expr1

Var

[ ,

Step

] )| Var=Value centralDiff(

Expr1

Var

[

=Value

][ ,

List

] )

⇒ expression

⇒ list centralDiff(

List1

Var

[

=Value

][ ,

Step

] )

⇒ list centralDiff(

Matrix1

Var

[

=Value

][ ,

Step

] )

⇒ matrix

Returns the numerical derivative using the central difference quotient formula.

When Value is specified, it overrides any prior variable assignment or any current “with” substitution for the variable.

Step is the step value. If Step is omitted, it defaults to 0.001.

When using

List1

Matrix1

, the operation gets mapped across the values in the list or across the matrix elements.

Note: See also avgRC() and d() .

Catalog > cFactor() cFactor(

Expr1

[ ,

Var

] ) cFactor(

List1

[ ,

Var

] )

⇒ expression

⇒ list cFactor(

Matrix1

[ ,

Var

] )

⇒ matrix cFactor( Expr1 ) returns Expr1 factored with respect to all of its variables over a common denominator.

Expr1 is factored as much as possible toward linear rational factors even if this introduces new non-real numbers. This alternative is appropriate if you want factorization with respect to more than one variable.

cFactor( Expr1 , Var ) returns Expr1 factored with respect to variable

Var .

Expr1 is factored as much as possible toward factors that are linear in Var , with perhaps non-real constants, even if it introduces irrational constants or subexpressions that are irrational in other variables.

The factors and their terms are sorted with Var as the main variable.

Similar powers of Var are collected in each factor. Include Var if factorization is needed with respect to only that variable and you are willing to accept irrational expressions in any other variables to increase factorization with respect to Var . There might be some incidental factoring with respect to other variables.

For the Auto setting of the Auto or Approximate mode, including Var also permits approximation with floating-point coefficients where irrational coefficients cannot be explicitly expressed concisely in terms of the built-in functions. Even when there is only one variable, including Var might yield more complete factorization.

Note: See also factor() .

Catalog >

To see the entire result, press

and then use

and

to move the cursor.

16 TI-Nspire™ CAS Reference Guide

char() char(

Integer

)

⇒ character

Returns a character string containing the character numbered Integer from the handheld character set. The valid range for

Integer

is 0–

65535.

charPoly() charPoly( squareMatrix,Var

)

⇒ polynomial expression charPoly( squareMatrix,Expr

)

⇒ polynomial expression charPoly( squareMatrix1,Matrix2

)

⇒ polynomial expression

Returns the characteristic polynomial of squareMatrix . The characteristic polynomial of n

× n

matrix

, denoted by p

( l ), is the polynomial defined by p

( l ) = det( l • I N A ) where

denotes the n

× n

identity matrix.

squareMatrix1 and squareMatrix2 must have the equal dimensions.

c 2

2way c 2

2way obsMatrix chi22way obsMatrix

Computes a c 2 test for association on the two-way table of counts in the observed matrix obsMatrix . A summary of results is stored in the stat.results

variable. (See page 119.)

For information on the effect of empty elements in a matrix, see

“Empty (void) elements” on page 159.

Output variable stat.

c 2 stat.PVal

stat.df

stat.ExpMat

stat.CompMat

Description

Chi square stat: sum (observed - expected)

/expected

Smallest level of significance at which the null hypothesis can be rejected

Degrees of freedom for the chi square statistics

Matrix of expected elemental count table, assuming null hypothesis

Matrix of elemental chi square statistic contributions c 2

Cdf() c 2

Cdf( lowBound

, upBound

, df

)

⇒ number

if lowBound

and upBound

are numbers, list

if lowBound

and upBound

are lists chi2Cdf( lowBound

, upBound

, df

)

⇒ number

if lowBound

and upBound

are numbers, list

if lowBound

and upBound

are lists

Computes the c 2 distribution probability between lowBound and upBound for the specified degrees of freedom df .

For P(

X { upBound

), set lowBound

= 0.

For information on the effect of empty elements in a list, see “Empty

(void) elements” on page 159.

Catalog >

TI-Nspire™ CAS Reference Guide 17

c 2

GOF c 2

GOF obsList

, expList

, df chi2GOF obsList

, expList

, df

Performs a test to confirm that sample data is from a population that conforms to a specified distribution. obsList is a list of counts and must contain integers. A summary of results is stored in the stat.results

variable. (See page 119.)

For information on the effect of empty elements in a list, see “Empty

(void) elements” on page 159.

Output variable stat.

c 2 stat.PVal

stat.df

stat.CompList

Description

Chi square stat: sum((observed - expected)

/expected

Smallest level of significance at which the null hypothesis can be rejected

Degrees of freedom for the chi square statistics

Elemental chi square statistic contributions c 2

Pdf() c 2

Pdf(

XVal

, df

) list

⇒ chi2Pdf(

XVal

, df

) a list

⇒ number

XVal

is a number, list

XVal

is a number

XVal

is a number, list

XVal

Computes the probability density function (pdf) for the c 2

distribution at a specified XVal value for the specified degrees of freedom df .

For information on the effect of empty elements in a list, see “Empty

(void) elements” on page 159.

ClearAZ

Clears all single-character variables in the current problem space.

If one or more of the variables are locked, this command displays an error message and deletes only the unlocked variables. See unLock , page 134.

Catalog >

18 TI-Nspire™ CAS Reference Guide

ClrErr

Catalog >

ClrErr

Clears the error status and sets system variable errCode to zero.

The Else clause of the Try...Else...EndTry

block should use ClrErr or PassErr . If the error is to be processed or ignored, use ClrErr . If what to do with the error is not known, use PassErr to send it to the next error handler. If there are no more pending Try...Else...EndTry

error handlers, the error dialog box will be displayed as normal.

For an example of ClrErr , See Example 2 under the Try command, page 129 .

Note: See also PassErr , page 87, and Try , page 129.

Note for entering the example: In the Calculator application on the handheld, you can enter multi-line definitions by pressing

@ instead of

at the end of each line. On the computer keyboard, hold down Alt and press Enter .

colAugment() colAugment(

Matrix1

Matrix2

)

⇒ matrix

Returns a new matrix that is Matrix2 appended to Matrix1 . The matrices must have equal column dimensions, and Matrix2 is appended to Matrix1 as new rows. Does not alter Matrix1 or

Matrix2 .

Catalog > colDim() colDim( Matrix )

⇒ expression

Returns the number of columns contained in

Matrix

Note: See also rowDim() .

colNorm() colNorm(

Matrix

)

⇒ expression

Returns the maximum of the sums of the absolute values of the elements in the columns in Matrix .

Note: Undefined matrix elements are not allowed. See also rowNorm() .

comDenom() comDenom(

Expr1

[ ,

Var

] ) comDenom(

List1

[ ,

Var

] )

⇒ expression

⇒ list comDenom(

Matrix1

[ ,

Var

] )

⇒ matrix comDenom(

Expr1

) returns a reduced ratio of a fully expanded numerator over a fully expanded denominator.

Catalog >

TI-Nspire™ CAS Reference Guide 19

comDenom() comDenom( Expr1 , Var ) returns a reduced ratio of numerator and denominator expanded with respect to Var . The terms and their factors are sorted with Var as the main variable. Similar powers of

Var are collected. There might be some incidental factoring of the collected coefficients. Compared to omitting Var , this often saves time, memory, and screen space, while making the expression more comprehensible. It also makes subsequent operations on the result faster and less likely to exhaust memory.

Var

does not occur in

Expr1

, comDenom(

Expr1

Var

) returns a reduced ratio of an unexpanded numerator over an unexpanded denominator. Such results usually save even more time, memory, and screen space. Such partially factored results also make subsequent operations on the result much faster and much less likely to exhaust memory.

Even when there is no denominator, the comden function is often a fast way to achieve partial factorization if factor() is too slow or if it exhausts memory.

Hint: Enter this comden() function definition and routinely try it as an alternative to comDenom() and factor() .

completeSquare() completeSquare( ExprOrEqn , Var )

⇒ expression or equation completeSquare( ExprOrEqn , Var^Power )

⇒ expression or equation completeSquare( ExprOrEqn , Var1, Var2 [,...] ) equation

⇒ expression or completeSquare( ExprOrEqn , { Var1, Var2 [,...] } )

⇒ expression or equation

Converts a quadratic polynomial expression of the form a·x

+b·x+c into the form a·(x-h)

- or -

Converts a quadratic equation of the form a·x

+b·x+c=d into the form a·(x-h)

The first argument must be a quadratic expression or equation in standard form with respect to the second argument.

The Second argument must be a single univariate term or a single univariate term raised to a rational power, for example x, y

, or z

(1/3)

The third and fourth syntax attempt to complete the square with respect to variables Var1 , Var2 [,… ]).

20 TI-Nspire™ CAS Reference Guide

Catalog >

conj() conj(

Expr1

) conj(

List1

)

⇒ expression

⇒ list conj(

Matrix1

)

⇒ matrix

Returns the complex conjugate of the argument.

Note: All undefined variables are treated as real variables.

constructMat() constructMat(

Expr

Var1

Var2

, numRows

, numCols

)

⇒ matrix

Returns a matrix based on the arguments.

Expr is an expression in variables Var1 and Var2 . Elements in the resulting matrix are formed by evaluating Expr for each incremented value of Var1 and Var2 .

Var1 is automatically incremented from 1 through numRows . Within each row, Var2 is incremented from 1 through numCols.

CopyVar

Var1

Var2

CopyVar

Var1 .

Var2 .

CopyVar Var1 , Var2 copies the value of variable Var1 to variable

Var2

, creating

Var2

if necessary. Variable

Var1

must have a value.

If Var1 is the name of an existing user-defined function, copies the definition of that function to function

Var2

. Function

Var1

must be defined.

Var1

must meet the variable-naming requirements or must be an indirection expression that simplifies to a variable name meeting the requirements.

CopyVar

Var1 .

Var2 .

copies all members of the

Var1 .

variable group to the

Var2 .

group, creating

Var2 .

if necessary.

Var1 .

must be the name of an existing variable group, such as the statistics stat .

results, or variables created using the

LibShortcut() function. If

Var2 .

already exists, this command replaces all members that are common to both groups and adds the members that do not already exist. If one or more members of Var2 .

are locked, all members of Var2 .

are left unchanged.

Catalog >

TI-Nspire™ CAS Reference Guide 21

corrMat() corrMat(

List1

List2

[ , …[ ,

List20

]] )

Computes the correlation matrix for the augmented matrix [

List1,

List2 , ..., List20 ].

4 cos

Expr 4 cos

Note: You can insert this operator from the computer keyboard by typing @>cos .

Represents Expr in terms of cosine. This is a display conversion operator. It can be used only at the end of the entry line.

4 cos reduces all powers of sin(...) modulo 1 N cos(...)^2 so that any remaining powers of cos(...) have exponents in the range

(0, 2). Thus, the result will be free of sin(...) if and only if sin(...) occurs in the given expression only to even powers.

Note: This conversion operator is not supported in Degree or

Gradian Angle modes. Before using it, make sure that the Angle mode is set to Radians and that

Expr

does not contain explicit references to degree or gradian angles. cos() cos(

Expr1

) cos(

List1

)

⇒ expression

⇒ list cos( Expr1 ) returns the cosine of the argument as an expression.

cos(

List1

) returns a list of the cosines of all elements in

List1

Note: The argument is interpreted as a degree, gradian or radian angle, according to the current angle mode setting. You can use ¡ , or R to override the angle mode temporarily.

In Degree angle mode:

In Gradian angle mode:

In Radian angle mode:

Catalog >

key

22 TI-Nspire™ CAS Reference Guide

cos() cos( squareMatrix1

)

⇒ squareMatrix

Returns the matrix cosine of squareMatrix1 . This is not the same as calculating the cosine of each element.

When a scalar function f(A) operates on squareMatrix1 (A), the result is calculated by the algorithm:

Compute the eigenvalues ( l i

) and eigenvectors (V i

) of A.

squareMatrix1 must be diagonalizable. Also, it cannot have symbolic variables that have not been assigned a value.

Form the matrices:

In Radian angle mode:

key

Then A = X B X

/ and f(A) = X f(B) X

. For example, cos(A) = X cos(B)

where: cos(B) =

All computations are performed using floating-point arithmetic.

cos / () cos

(

Expr1

)

⇒ expression cos

(

List1

)

⇒ list

In Degree angle mode:

μ cos / ( Expr1 ) returns the angle whose cosine is Expr1 as an expression.

cos

( List1 ) returns a list of the inverse cosines of each element of

List1 .

Note: The result is returned as a degree, gradian or radian angle, according to the current angle mode setting.

Note: You can insert this function from the keyboard by typing arccos( ...

) .

In Gradian angle mode:

In Radian angle mode: cos

( squareMatrix1

)

⇒ squareMatrix

Returns the matrix inverse cosine of squareMatrix1 . This is not the same as calculating the inverse cosine of each element. For information about the calculation method, refer to cos() . squareMatrix1 must be diagonalizable. The result always contains floating-point numbers.

In Radian angle mode and Rectangular Complex Format:

key

To see the entire result, press

and then use

and

to move the cursor.

TI-Nspire™ CAS Reference Guide 23

cosh() cosh(

Expr1

) cosh(

List1

)

⇒ expression

⇒ list cosh( Expr1 ) returns the hyperbolic cosine of the argument as an expression.

cosh ( List1 ) returns a list of the hyperbolic cosines of each element of

List1

cosh ( squareMatrix1

)

⇒ squareMatrix

Returns the matrix hyperbolic cosine of squareMatrix1

. This is not the same as calculating the hyperbolic cosine of each element. For information about the calculation method, refer to cos() .

squareMatrix1 must be diagonalizable. The result always contains floating-point numbers.

In Radian angle mode:

Catalog > cosh

() cosh

(

Expr1

)

⇒ expression cosh

(

List1

)

⇒ list

Catalog > cosh / ( Expr1 ) returns the inverse hyperbolic cosine of the argument as an expression.

cosh

(

List1

) returns a list of the inverse hyperbolic cosines of each element of List1 .

Note: You can insert this function from the keyboard by typing arccosh( ...

) .

cosh

( squareMatrix1

)

⇒ squareMatrix

Returns the matrix inverse hyperbolic cosine of squareMatrix1

. This is not the same as calculating the inverse hyperbolic cosine of each element. For information about the calculation method, refer to cos() .

squareMatrix1 must be diagonalizable. The result always contains floating-point numbers.

In Radian angle mode and In Rectangular Complex Format:

To see the entire result, press

and then use

and

to move the cursor.

key cot() cot(

Expr1

) cot(

List1

)

⇒ expression

⇒ list

Returns the cotangent of Expr1 or returns a list of the cotangents of all elements in List1 .

Note: The argument is interpreted as a degree, gradian or radian angle, according to the current angle mode setting. You can use or R to override the angle mode temporarily.

¡ ,

In Degree angle mode:

In Gradian angle mode:

In Radian angle mode:

24 TI-Nspire™ CAS Reference Guide

cot / () cot

(

Expr1

)

⇒ expression cot

(

List1

)

⇒ list

Returns the angle whose cotangent is

Expr1

or returns a list containing the inverse cotangents of each element of List1 .

Note: The result is returned as a degree, gradian or radian angle, according to the current angle mode setting.

Note: You can insert this function from the keyboard by typing arccot( ...

) .

In Degree angle mode:

In Gradian angle mode:

In Radian angle mode:

key coth() coth(

Expr1

) coth(

List1

)

⇒ expression

⇒ list

Returns the hyperbolic cotangent of

Expr1

or returns a list of the hyperbolic cotangents of all elements of List1 .

Catalog > coth

() coth

(

Expr1

)

⇒ expression coth

(

List1

)

⇒ list

Returns the inverse hyperbolic cotangent of Expr1 or returns a list containing the inverse hyperbolic cotangents of each element of

List1 .

Note: You can insert this function from the keyboard by typing arccoth( ...

) .

Catalog > count()

Catalog > count(

Value1orList1

Value2orList2

[,...]] )

⇒ value

Returns the accumulated count of all elements in the arguments that evaluate to numeric values.

Each argument can be an expression, value, list, or matrix. You can mix data types and use arguments of various dimensions.

For a list, matrix, or range of cells, each element is evaluated to determine if it should be included in the count.

Within the Lists & Spreadsheet application, you can use a range of cells in place of any argument.

Empty (void) elements are ignored. For more information on empty elements, see page 159.

In the last example, only 1/2 and 3+4* i are counted. The remaining arguments, assuming x is undefined, do not evaluate to numeric values.

TI-Nspire™ CAS Reference Guide 25

countif()

Catalog > countif(

List

Criteria

)

⇒ value

Returns the accumulated count of all elements in List that meet the specified

Criteria

Criteria can be:

Counts the number of elements equal to 3.

• A value, expression, or string. For example, 3 counts only those elements in List that simplify to the value 3.

• A Boolean expression containing the symbol ?

as a placeholder for each element. For example, ?<5 counts only those elements in

List

that are less than 5.

Counts the number of elements equal to “def.”

Within the Lists & Spreadsheet application, you can use a range of cells in place of

List

Empty (void) elements in the list are ignored. For more information on empty elements, see page 159.

Note: See also sumIf() , page 122, and frequency() , page 51.

Counts the number of elements equal to x

; this example assumes the variable x is undefined.

Counts 1 and 3.

Counts 3, 5, and 7.

cPolyRoots() cPolyRoots(

Poly

Var

)

⇒ list cPolyRoots(

ListOfCoeffs

)

⇒ list

The first syntax, cPolyRoots(

Poly

Var

) , returns a list of complex roots of polynomial Poly with respect to variable Var .

Poly

must be a polynomial in one variable.

The second syntax, cPolyRoots( ListOfCoeffs ) , returns a list of complex roots for the coefficients in

ListOfCoeffs.

Note: See also polyRoots() , page 91.

Counts 1, 3, 7, and 9.

Catalog > crossP() crossP(

List1

List2

)

⇒ list

Returns the cross product of

List1

and

List2

as a list.

List1 and List2 must have equal dimension, and the dimension must be either 2 or 3.

crossP(

Vector1

Vector2

)

⇒ vector

Returns a row or column vector (depending on the arguments) that is the cross product of Vector1 and Vector2 .

Both Vector1 and Vector2 must be row vectors, or both must be column vectors. Both vectors must have equal dimension, and the dimension must be either 2 or 3.

26 TI-Nspire™ CAS Reference Guide

Catalog >

csc() csc(

Expr1

) csc(

List1

)

⇒ expression

⇒ list

Returns the cosecant of

Expr1

or returns a list containing the cosecants of all elements in List1 .

In Degree angle mode:

In Gradian angle mode:

In Radian angle mode:

key csc

() csc csc

(

Expr1

)

⇒ expression

(

List1

)

⇒ list

Returns the angle whose cosecant is

Expr1

or returns a list containing the inverse cosecants of each element of List1 .

Note: The result is returned as a degree, gradian or radian angle, according to the current angle mode setting.

Note: You can insert this function from the keyboard by typing arccsc( ...

) .

In Degree angle mode:

In Gradian angle mode:

In Radian angle mode: csch() csch(

Expr1

)

⇒ expression csch(

List1

)

⇒ list

Returns the hyperbolic cosecant of Expr1 or returns a list of the hyperbolic cosecants of all elements of List1 .

Catalog >

key csch / () csch

(

Expr1

)

⇒ expression csch

(

List1

)

⇒ list

Returns the inverse hyperbolic cosecant of

Expr1

or returns a list containing the inverse hyperbolic cosecants of each element of List1 .

Note: You can insert this function from the keyboard by typing arccsch( ...

) .

Catalog >

TI-Nspire™ CAS Reference Guide 27

cSolve() cSolve(

Equation

Var

)

⇒

Boolean expression cSolve(

Equation

Var=Guess

) cSolve(

Inequality

Var

)

⇒ Boolean expression

⇒

Boolean expression

Returns candidate complex solutions of an equation or inequality for

Var . The goal is to produce candidates for all real and non-real solutions. Even if Equation is real, cSolve() allows non-real results in Real result Complex Format.

Although all undefined variables that do not end with an underscore

(_) are processed as if they were real, cSolve() can solve polynomial equations for complex solutions. cSolve() temporarily sets the domain to complex during the solution even if the current domain is real. In the complex domain, fractional powers having odd denominators use the principal rather than the real branch. Consequently, solutions from solve() to equations involving such fractional powers are not necessarily a subset of those from cSolve() .

Catalog > cSolve() starts with exact symbolic methods. cSolve() also uses iterative approximate complex polynomial factoring, if necessary.

Note: See also cZeros() , solve() , and zeros() .

Note: If Equation is non-polynomial with functions such as abs() , angle() , conj() , real() , or imag() , you should place an underscore

(press

) at the end of Var . By default, a variable is treated as a real value.

In Display Digits mode of Fix 2:

To see the entire result, press

and then use

and

to move the cursor.

z is treated as real: If you use var _ , the variable is treated as complex.

You should also use var

_ for any other variables in

Equation

that might have unreal values. Otherwise, you may receive unexpected results.

z_ is treated as complex: cSolve(

Eqn1

and

Eqn2

[ and

…

] ,

VarOrGuess1

VarOrGuess2

[ ,

…

] )

⇒ Boolean expression cSolve( SystemOfEqns , VarOrGuess1 ,

VarOrGuess2 [ ,

…

] )

⇒

Boolean expression

Returns candidate complex solutions to the simultaneous algebraic equations, where each varOrGuess specifies a variable that you want to solve for.

Optionally, you can specify an initial guess for a variable. Each varOrGuess

must have the form: variable

– or – variable = real or non-real number

For example, x is valid and so is x=3+ i

If all of the equations are polynomials and if you do NOT specify any initial guesses, cSolve() uses the lexical Gröbner/Buchberger elimination method to attempt to determine all complex solutions.

Note: The following examples use an underscore (press

) so that the variables will be treated as complex.

28 TI-Nspire™ CAS Reference Guide

cSolve()

Complex solutions can include both real and non-real solutions, as in the example to the right.

Catalog >

Simultaneous polynomial equations can have extra variables that have no values, but represent given numeric values that could be substituted later.

To see the entire result, press

and then use

and

to move the cursor.

To see the entire result, press

and then use

and

to move the cursor.

You can also include solution variables that do not appear in the equations. These solutions show how families of solutions might contain arbitrary constants of the form c k, where k is an integer suffix from 1 through 255.

For polynomial systems, computation time or memory exhaustion may depend strongly on the order in which you list solution variables.

If your initial choice exhausts memory or your patience, try rearranging the variables in the equations and/or varOrGuess

list.

If you do not include any guesses and if any equation is nonpolynomial in any variable but all equations are linear in all solution variables, cSolve() uses Gaussian elimination to attempt to determine all solutions.

To see the entire result, press

and then use

and

to move the cursor.

If a system is neither polynomial in all of its variables nor linear in its solution variables, cSolve() determines at most one solution using an approximate iterative method. To do so, the number of solution variables must equal the number of equations, and all other variables in the equations must simplify to numbers.

A non-real guess is often necessary to determine a non-real solution.

For convergence, a guess might have to be rather close to a solution.

To see the entire result, press

and then use

and

to move the cursor.

TI-Nspire™ CAS Reference Guide 29

CubicReg

[ , [

Freq

] [ ,

Category

Include

]]

Computes the cubic polynomial regression y = a · x

+b · x

+c · x+d on lists X and Y with frequency Freq . A summary of results is stored in the stat.results

variable. (See page 119.)

All the lists must have equal dimension except for Include .

X and Y are lists of independent and dependent variables.

Freq is an optional list of frequency values. Each element in Freq specifies the frequency of occurrence for each corresponding X and Y data point. The default value is 1. All elements must be integers | 0.

Category is a list of category codes for the corresponding X and Y data.

Include is a list of one or more of the category codes. Only those data items whose category code is included in this list are included in the calculation.

For information on the effect of empty elements in a list, see “Empty

(void) elements” on page 159.

cumulativeSum() cumulativeSum(

List1

)

⇒ list

Returns a list of the cumulative sums of the elements in List1 , starting at element 1. cumulativeSum(

Matrix1

)

⇒ matrix

Returns a matrix of the cumulative sums of the elements in Matrix1 .

Each element is the cumulative sum of the column from top to bottom.

An empty (void) element in List1 or Matrix1 produces a void element in the resulting list or matrix. For more information on empty elements, see page 159.

Catalog >

Output variable stat.RegEqn

stat.a, stat.b, stat.c, stat.d

stat.R

2 stat.Resid

stat.XReg

stat.YReg

stat.FreqReg

Description

Regression equation: a · x 3 +b · x 2 +c · x+d

Regression coefficients

Coefficient of determination

Residuals from the regression

List of data points in the modified X List actually used in the regression based on restrictions of Freq ,

Category List , and Include Categories

List of data points in the modified Y List actually used in the regression based on restrictions of Freq ,

Category List , and Include Categories

List of frequencies corresponding to stat.XReg

and stat.YReg

Catalog >

30 TI-Nspire™ CAS Reference Guide

Cycle

Catalog >

Cycle

Transfers control immediately to the next iteration of the current loop

( For , While , or Loop ).

Function listing that sums the integers from 1 to 100 skipping

50.

Cycle is not allowed outside the three looping structures ( For ,

While , or Loop ).

Note for entering the example: In the Calculator application on the handheld, you can enter multi-line definitions by pressing

@ instead of

at the end of each line. On the computer keyboard, hold down Alt and press Enter .

4 Cylind

Vector 4

Cylind

Note: You can insert this operator from the computer keyboard by typing @>Cylind .

Displays the row or column vector in cylindrical form [r, ±q , z].

Vector must have exactly three elements. It can be either a row or a column.

Catalog > cZeros()

Catalog > cZeros(

Expr

Var

)

⇒ list

Returns a list of candidate real and non-real values of

Var

that make

Expr =0. cZeros() does this by computing exp 4 list(cSolve(

Expr

=0,

Var

) ,

Var

) . Otherwise, cZeros() is similar to zeros() .

In Display Digits mode of Fix 3:

Note: See also cSolve() , solve() , and zeros() .

To see the entire result, press

and then use

and

to move the cursor.

Note: If

Expr

is non-polynomial with functions such as abs() , angle() , conj() , real() , or imag() , you should place an underscore

(press

) at the end of

Var

. By default, a variable is treated as a real value. If you use var_ , the variable is treated as complex.

You should also use var_

for any other variables in

Expr

that might have unreal values. Otherwise, you may receive unexpected results.

z is treated as real: z_ is treated as complex: cZeros({

Expr1

Expr2

[ , … ] },

{

VarOrGuess1

VarOrGuess2

[ , … ] })

⇒ matrix

Returns candidate positions where the expressions are zero simultaneously. Each

VarOrGuess

specifies an unknown whose value you seek.

Optionally, you can specify an initial guess for a variable. Each

VarOrGuess

must have the form: variable

– or – variable = real or non-real number

For example, x is valid and so is x=3+ i

TI-Nspire™ CAS Reference Guide 31

cZeros()

Catalog >

If all of the expressions are polynomials and you do NOT specify any initial guesses, cZeros() uses the lexical Gröbner/Buchberger elimination method to attempt to determine all complex zeros.

Complex zeros can include both real and non-real zeros, as in the example to the right.

Each row of the resulting matrix represents an alternate zero, with the components ordered the same as the VarOrGuess list. To extract a row, index the matrix by [ row

Note: The following examples use an underscore _ (press

) so that the variables will be treated as complex.

Simultaneous polynomials can have extra variables that have no values, but represent given numeric values that could be substituted later.

Extract row 2:

You can also include unknown variables that do not appear in the expressions. These zeros show how families of zeros might contain arbitrary constants of the form c k, where k is an integer suffix from 1 through 255.

For polynomial systems, computation time or memory exhaustion may depend strongly on the order in which you list unknowns. If your initial choice exhausts memory or your patience, try rearranging the variables in the expressions and/or VarOrGuess list.

If you do not include any guesses and if any expression is nonpolynomial in any variable but all expressions are linear in all unknowns, cZeros() uses Gaussian elimination to attempt to determine all zeros.

If a system is neither polynomial in all of its variables nor linear in its unknowns, cZeros() determines at most one zero using an approximate iterative method. To do so, the number of unknowns must equal the number of expressions, and all other variables in the expressions must simplify to numbers.

A non-real guess is often necessary to determine a non-real zero. For convergence, a guess might have to be rather close to a zero.

32 TI-Nspire™ CAS Reference Guide

D

dbd() dbd( date1,date2

)

⇒ value

Returns the number of days between date1

and date2

using the actual-day-count method.

date1

and date2

can be numbers or lists of numbers within the range of the dates on the standard calendar. If both date1 and date2 are lists, they must be the same length.

date1 and date2 must be between the years 1950 through 2049.

You can enter the dates in either of two formats. The decimal placement differentiates between the date formats.

MM.DDYY (format used commonly in the United States)

DDMM.YY (format use commonly in Europe)

4 DD

Expr1 4

List1 4

⇒ value

⇒ list

Matrix1 4

⇒ matrix

In Degree angle mode:

Note: You can insert this operator from the computer keyboard by typing @>DD .

Returns the decimal equivalent of the argument expressed in degrees.

The argument is a number, list, or matrix that is interpreted by the

Angle mode setting in gradians, radians or degrees.

In Gradian angle mode:

In Radian angle mode:

4 Decimal

Expression1 4 Decimal

⇒ expression

List1 4 Decimal

⇒ expression

Matrix1 4 Decimal

⇒ expression

Note: You can insert this operator from the computer keyboard by typing @>Decimal .

Displays the argument in decimal form. This operator can be used only at the end of the entry line.

Catalog >

TI-Nspire™ CAS Reference Guide 33

Define

Var

Expression

Define

Function

(

Param1

Param2

, ...

) =

Expression

Defines the variable Var or the user-defined function Function .

Parameters, such as Param1 , provide placeholders for passing arguments to the function. When calling a user-defined function, you must supply arguments (for example, values or variables) that correspond to the parameters. When called, the function evaluates

Expression using the supplied arguments.

Var and Function cannot be the name of a system variable or built-in function or command.

Note: This form of Define is equivalent to executing the expression: expression & Function ( Param1,Param2 ) .

Define

Function

(

Param1

Param2

, ...

) = Func

Block

EndFunc

Define

Program

(

Param1

Param2

, ...

) = Prgm

Block

EndPrgm

In this form, the user-defined function or program can execute a block of multiple statements.

Block

can be either a single statement or a series of statements on separate lines. Block also can include expressions and instructions

(such as If , Then , Else , and For ).

Note for entering the example: In the Calculator application on the handheld, you can enter multi-line definitions by pressing

@ instead of

at the end of each line. On the computer keyboard, hold down Alt and press Enter .

Note: See also Define LibPriv , page 34, and Define LibPub , page 35.

Define LibPriv

Var

Expression

Define LibPriv

Function

(

Param1

Param2

, ...

) =

Expression

Define LibPriv Function ( Param1 , Param2 , ...

) = Func

Block

EndFunc

Define LibPriv Program ( Param1 , Param2 , ...

) = Prgm

Block

EndPrgm

Operates the same as Define , except defines a private library variable, function, or program. Private functions and programs do not appear in the Catalog.

Note: See also Define , page 34, and Define LibPub , page 35.

34 TI-Nspire™ CAS Reference Guide

Catalog >

Define LibPub

Var

Expression

Define LibPub

Function

(

Param1

Param2

, ...

) =

Expression

Define LibPub Function ( Param1 , Param2 , ...

) = Func

Block

EndFunc

Define LibPub Program ( Param1 , Param2 , ...

) = Prgm

Block

EndPrgm

Operates the same as Define , except defines a public library variable, function, or program. Public functions and programs appear in the Catalog after the library has been saved and refreshed.

Note: See also Define , page 34, and Define LibPriv , page 34.

deltaList() deltaTmpCnv()

DelVar

Var1

[ ,

Var2

] [ ,

Var3

] ...

DelVar

Var .

Deletes the specified variable or variable group from memory.

If one or more of the variables are locked, this command displays an error message and deletes only the unlocked variables. See unLock , page 134.

DelVar

Var .

deletes all members of the

Var .

variable group (such as the statistics stat .

results or variables created using the

LibShortcut() function)

The dot ( .

) in this form of the DelVar command limits it to deleting a variable group; the simple variable

Var is not affected.

Catalog >

See @ List() , page 67.

See @ tmpCnv() , page 128.

Catalog > delVoid() delVoid( List1 )

⇒ list

Returns a list that has the contents of List1 with all empty (void) elements removed.

For more information on empty elements, see page 159.

derivative()

Catalog >

See d (), page 149.

TI-Nspire™ CAS Reference Guide 35

deSolve() deSolve(

1stOr2ndOrderODE

Var

, depVar

)

⇒ a general solution

Returns an equation that explicitly or implicitly specifies a general solution to the 1st- or 2nd-order ordinary differential equation (ODE).

In the ODE:

• Use a prime symbol (press

) to denote the 1st derivative of the dependent variable with respect to the independent variable.

• Use two prime symbols to denote the corresponding second derivative.

The prime symbol is used for derivatives within deSolve() only. In other cases, use d() .

The general solution of a 1st-order equation contains an arbitrary constant of the form c k, where k is an integer suffix from 1 through

255. The solution of a 2nd-order equation contains two such constants.

Apply solve() to an implicit solution if you want to try to convert it to one or more equivalent explicit solutions.

When comparing your results with textbook or manual solutions, be aware that different methods introduce arbitrary constants at different points in the calculation, which may produce different general solutions.

deSolve(

1stOrderODE

and initCond

Var

, depVar

)

⇒ a particular solution

Returns a particular solution that satisfies 1stOrderODE and initCond . This is usually easier than determining a general solution, substituting initial values, solving for the arbitrary constant, and then substituting that value into the general solution.

initCond is an equation of the form: depVar ( initialIndependentValue ) = initialDependentValue

The initialIndependentValue and initialDependentValue can be variables such as x0 and y0 that have no stored values. Implicit differentiation can help verify implicit solutions.

deSolve(

2ndOrderODE

and initCond1

and initCond2

Var

, depVar

)

⇒ a particular solution

Returns a particular solution that satisfies 2nd Order ODE and has a specified value of the dependent variable and its first derivative at one point.

For initCond1 , use the form: depVar ( initialIndependentValue ) = initialDependentValue

For initCond2

, use the form: depVar ( initialIndependentValue ) = initial1stDerivativeValue

36 TI-Nspire™ CAS Reference Guide

Catalog >

deSolve() deSolve(

2ndOrderODE

and bndCond1

and bndCond2

Var

, depVar

)

⇒ a particular solution

Returns a particular solution that satisfies 2ndOrderODE and has specified values at two different points.

det() det( squareMatrix

[ ,

Tolerance

] )

⇒ expression

Returns the determinant of squareMatrix

Optionally, any matrix element is treated as zero if its absolute value is less than

Tolerance

. This tolerance is used only if the matrix has floating-point entries and does not contain any symbolic variables that have not been assigned a value. Otherwise,

Tolerance

is ignored.

• If you use

/·

or set the Auto or Approximate mode to Approximate, computations are done using floatingpoint arithmetic.

• If Tolerance is omitted or not used, the default tolerance is calculated as:

5E M 14 · max(dim( squareMatrix rowNorm( squareMatrix )

)) · diag() diag(

List

)

⇒ matrix diag( rowMatrix

)

⇒ matrix diag( columnMatrix

)

⇒ matrix

Returns a matrix with the values in the argument list or matrix in its main diagonal.

diag( squareMatrix

)

⇒ rowMatrix

Returns a row matrix containing the elements from the main diagonal of squareMatrix .

squareMatrix must be square.

dim() dim(

List

)

⇒ integer

Returns the dimension of List .

dim(

Matrix

)

⇒ list

Returns the dimensions of matrix as a two-element list {rows, columns}.

dim(

String

)

⇒ integer

Returns the number of characters contained in character string

String

Catalog >

TI-Nspire™ CAS Reference Guide 37

Disp

Disp [ exprOrString1

] [ , exprOrString2

] ...

Displays the arguments in the Calculator history. The arguments are displayed in succession, with thin spaces as separators.

Useful mainly in programs and functions to ensure the display of intermediate calculations.

Note for entering the example: In the Calculator application on the handheld, you can enter multi-line definitions by pressing

@ instead of

at the end of each line. On the computer keyboard, hold down Alt and press Enter .

Catalog >

4 DMS

Expr 4

DMS

List 4

DMS

Matrix 4

DMS

Note: You can insert this operator from the computer keyboard by typing @>DMS .

Interprets the argument as an angle and displays the equivalent DMS

(DDDDDD ¡ MM ' SS.ss

'' ) number. See ¡ , ', '' on page 154 for DMS

(degree, minutes, seconds) format.

Note:

4 DMS will convert from radians to degrees when used in radian mode. If the input is followed by a degree symbol ¡ , no conversion will occur. You can use 4 DMS only at the end of an entry line.

In Degree angle mode:

Catalog >

38 TI-Nspire™ CAS Reference Guide

dominantTerm() dominantTerm(

Expr1

Var

[ ,

Point

] )

⇒ expression dominantTerm(

Expr1

Var

[ ,

Point

] ) |

Var

Point

⇒ expression dominantTerm(

Expr1

Var

[ ,

Point

] ) |

Var

Point

⇒ expression

Returns the dominant term of a power series representation of Expr1 expanded about

Point

. The dominant term is the one whose magnitude grows most rapidly near Var = Point . The resulting power of (

Var N Point

) can have a negative and/or fractional exponent. The coefficient of this power can include logarithms of (

Var N Point

) and other functions of

Var

that are dominated by all powers of (

Var

Point

) having the same exponent sign.

Point defaults to 0. Point can be ˆ or Nˆ , in which cases the dominant term will be the term having the largest exponent of Var rather than the smallest exponent of

Var

dominantTerm(…) returns “ dominantTerm(…) ” if it is unable to determine such a representation, such as for essential singularities such as sin( 1/ z

) at z

=0, e

N 1/z

at z=0, or e z

at z = ˆ or Nˆ .

If the series or one of its derivatives has a jump discontinuity at Point , the result is likely to contain sub-expressions of the form sign(…) or abs(…) for a real expansion variable or (-1) floor(…angle(…)…) for a complex expansion variable, which is one ending with “_”. If you intend to use the dominant term only for values on one side of Point , then append to dominantTerm( ...

) the appropriate one of “| Var >

Point ”, “| Var < Point ”, “| “ Var | Point ”, or “ Var { Point ” to obtain a simpler result.

dominantTerm() distributes over 1st-argument lists and matrices.

dominantTerm() is useful when you want to know the simplest possible expression that is asymptotic to another expression as

Var " Point . dominantTerm() is also useful when it isn’t obvious what the degree of the first non-zero term of a series will be, and you don’t want to iteratively guess either interactively or by a program loop.

Note: See also series() , page 108.

dotP() dotP(

List1

List2

)

⇒ expression

Returns the “dot” product of two lists.

dotP(

Vector1

Vector2

)

⇒ expression

Returns the “dot” product of two vectors.

Both must be row vectors, or both must be column vectors.

Catalog >

TI-Nspire™ CAS Reference Guide 39

E

e ^() e ^(

Expr1

)

⇒ expression

Returns e raised to the Expr1 power.

Note: See also e exponent template , page 2.

Note: Pressing u

to display e^( is different from pressing the character

on the keyboard.

You can enter a complex number in re i q

polar form. However, use this form in Radian angle mode only; it causes a Domain error in Degree or Gradian angle mode.

e ^(

List1

)

⇒ list

Returns e raised to the power of each element in

List1

e ^( squareMatrix1

)

⇒ squareMatrix

Returns the matrix exponential of squareMatrix1 . This is not the same as calculating e raised to the power of each element. For information about the calculation method, refer to cos() .

squareMatrix1 must be diagonalizable. The result always contains floating-point numbers.

key eff() eff( nominalRate,CpY

)

⇒ value

Financial function that converts the nominal interest rate nominalRate to an annual effective rate, given CpY as the number of compounding periods per year.

nominalRate must be a real number, and CpY must be a real number

> 0.

Note: See also nom() , page 82.

Catalog > eigVc()

Catalog > eigVc( squareMatrix

)

⇒ matrix

Returns a matrix containing the eigenvectors for a real or complex squareMatrix

, where each column in the result corresponds to an eigenvalue. Note that an eigenvector is not unique; it may be scaled by any constant factor. The eigenvectors are normalized, meaning that if V = [x

, x

, … , x n

], then: x

+ x

+ … + x n

= 1 squareMatrix is first balanced with similarity transformations until the row and column norms are as close to the same value as possible.

The squareMatrix is then reduced to upper Hessenberg form and the eigenvectors are computed via a Schur factorization.

In Rectangular Complex Format:

To see the entire result, press

and then use

and

to move the cursor.

40 TI-Nspire™ CAS Reference Guide

EndFor

EndFunc

EndIf

EndLoop

EndPrgm

EndTry eigVl() eigVl( squareMatrix

)

⇒ list

Returns a list of the eigenvalues of a real or complex squareMatrix .

squareMatrix

is first balanced with similarity transformations until the row and column norms are as close to the same value as possible.

The squareMatrix

is then reduced to upper Hessenberg form and the eigenvalues are computed from the upper Hessenberg matrix.

In Rectangular complex format mode:

Catalog >

Else

To see the entire result, press

and then use

and

to move the cursor.

See If, page 57.

ElseIf

If BooleanExpr1 Then

Block1

ElseIf BooleanExpr2 Then

Block2

ElseIf BooleanExprN Then

BlockN

EndIf

Note for entering the example: In the Calculator application on the handheld, you can enter multi-line definitions by pressing

@ instead of

at the end of each line. On the computer keyboard, hold down Alt and press Enter .

Catalog >

See For, page 49.

See Func, page 52.

See If, page 57.

See Loop, page 73.

See Prgm, page 92.

See Try, page 129.

TI-Nspire™ CAS Reference Guide 41

EndWhile See While, page 135.

euler()

Catalog > euler( Expr , Var , depVar , { Var0, VarMax } , depVar0 , VarStep

[ , eulerStep ] )

⇒ matrix euler( SystemOfExpr , Var , ListOfDepVars , { Var0 , VarMax } ,

ListOfDepVars0

VarStep

[ , eulerStep

] )

⇒ matrix euler(

ListOfExpr

Var

ListOfDepVars

, {

Var0

VarMax

} ,

ListOfDepVars0 , VarStep [ , eulerStep ] )

⇒ matrix

Differential equation: y'=0.001*y*(100-y) and y(0)=10 d

Uses the Euler method to solve the system depVar d Var

= Expr ( Var , depVar ) with depVar ( Var0 )= depVar0 on the interval [ Var0 , VarMax ]. Returns a matrix whose first row defines the Var output values and whose second row defines the value of the first solution component at the corresponding Var values, and so on.

To see the entire result, press move the cursor.

and then use

and

Compare above result with CAS exact solution obtained using deSolve() and seqGen():

Expr is the right-hand side that defines the ordinary differential equation (ODE).

SystemOfExpr is the system of right-hand sides that define the system of ODEs (corresponds to order of dependent variables in

ListOfDepVars ).

ListOfExpr is a list of right-hand sides that define the system of ODEs

(corresponds to the order of dependent variables in ListOfDepVars ).

Var is the independent variable.

ListOfDepVars is a list of dependent variables.

{ Var0 , VarMax } is a two-element list that tells the function to integrate from Var0 to VarMax .

ListOfDepVars0 is a list of initial values for dependent variables.

System of equations:

VarStep is a nonzero number such that sign( VarStep ) = sign( VarMax Var0 ) and solutions are returned at Var0 +i· VarStep for all i=0,1,2,… such that Var0 +i· VarStep is in [ var0 , VarMax ] (there may not be a solution value at VarMax ).

with y1 (0)=2 and y2 (0)=5 eulerStep is a positive integer (defaults to 1) that defines the number of euler steps between output values. The actual step size used by the euler method is VarStep à eulerStep .

exact() exact(

Expr1

[ ,

Tolerance

] ) exact(

List1

[ ,

Tolerance

] )

⇒ expression

⇒ list exact(

Matrix1

[ ,

Tolerance

] )

⇒ matrix

Uses Exact mode arithmetic to return, when possible, the rationalnumber equivalent of the argument.

Tolerance specifies the tolerance for the conversion; the default is 0

(zero).

Catalog >

42 TI-Nspire™ CAS Reference Guide

Exit

Exits the current For , While , or Loop block.

Exit is not allowed outside the three looping structures ( For , While , or Loop ).

Note for entering the example: In the Calculator application on the handheld, you can enter multi-line definitions by pressing

@ instead of

at the end of each line. On the computer keyboard, hold down Alt and press Enter .

Function listing:

Catalog >

4 exp

Expr 4 exp

Represents Expr in terms of the natural exponential e . This is a display conversion operator. It can be used only at the end of the entry line.

Note: You can insert this operator from the computer keyboard by typing @>exp .

exp() exp(

Expr1

)

⇒ expression

Returns e raised to the Expr1 power.

Note: See also e exponent template, page 2.

You can enter a complex number in re i q

polar form. However, use this form in Radian angle mode only; it causes a Domain error in Degree or Gradian angle mode.

exp(

List1

)

⇒ list

Returns e raised to the power of each element in List1 .

exp( squareMatrix1 )

⇒ squareMatrix

Returns the matrix exponential of squareMatrix1

. This is not the same as calculating e raised to the power of each element. For information about the calculation method, refer to cos() .

squareMatrix1 must be diagonalizable. The result always contains floating-point numbers.

Catalog > u

key

TI-Nspire™ CAS Reference Guide 43

exp 4 list() exp

4 list(

Expr

Var

)

⇒ list

Examines Expr for equations that are separated by the word “or,” and returns a list containing the right-hand sides of the equations of the form Var=Expr . This gives you an easy way to extract some solution values embedded in the results of the solve() , cSolve() , fMin() , and fMax() functions.

Note: exp 4 list() is not necessary with the zeros() and cZeros() functions because they return a list of solution values directly.

You can insert this function from the keyboard by typing exp@>list( ...

) .

expand() expand(

Expr1

[ ,

Var

] )

⇒ expression expand(

List1

[

, Var

] )

⇒ list expand(

Matrix1

[

, Var

] )

⇒ matrix expand(

Expr1

) returns

Expr1

expanded with respect to all its variables. The expansion is polynomial expansion for polynomials and partial fraction expansion for rational expressions.

The goal of expand() is to transform Expr1 into a sum and/or difference of simple terms. In contrast, the goal of factor() is to transform Expr1 into a product and/or quotient of simple factors.

expand( Expr1 , Var ) returns Expr1 expanded with respect to Var .

Similar powers of Var are collected. The terms and their factors are sorted with Var as the main variable. There might be some incidental factoring or expansion of the collected coefficients. Compared to omitting

Var

, this often saves time, memory, and screen space, while making the expression more comprehensible.

Even when there is only one variable, using Var might make the denominator factorization used for partial fraction expansion more complete.

Hint: For rational expressions, propFrac() is a faster but less extreme alternative to expand() .

Note: See also comDenom() for an expanded numerator over an expanded denominator.

Catalog >

44 TI-Nspire™ CAS Reference Guide

expand() expand( Expr1 ,

[ Var ] ) also distributes logarithms and fractional powers regardless of Var . For increased distribution of logarithms and fractional powers, inequality constraints might be necessary to guarantee that some factors are nonnegative.

expand( Expr1 ,

[ Var ] ) also distributes absolute values, sign() , and exponentials, regardless of

Var

Note: See also tExpand() for trigonometric angle-sum and multiple-angle expansion.

expr() expr(

String

)

⇒ expression

Returns the character string contained in String as an expression and immediately executes it.

Catalog >

ExpReg

ExpReg X, Y [ , [ Freq ] [ , Category, Include ]]

Computes the exponential regression y = a · (b) x on lists

and

Y with frequency Freq . A summary of results is stored in the stat.results

variable. (See page 119.)

All the lists must have equal dimension except for Include .

and

are lists of independent and dependent variables.

Freq is an optional list of frequency values. Each element in Freq specifies the frequency of occurrence for each corresponding

and

Y data point. The default value is 1. All elements must be integers | 0.

Category is a list of category codes for the corresponding X and Y data.

Include is a list of one or more of the category codes. Only those data items whose category code is included in this list are included in the calculation.

For information on the effect of empty elements in a list, see “Empty

(void) elements” on page 159.

Output variable stat.RegEqn

stat.a, stat.b

stat.r

Description

Regression equation: a · (b) x

Regression coefficients

Coefficient of linear determination for transformed data

Catalog >

TI-Nspire™ CAS Reference Guide 45

Output variable stat.r

stat.Resid

stat.ResidTrans

stat.XReg

stat.YReg

stat.FreqReg

Description

Correlation coefficient for transformed data (x, ln(y))

Residuals associated with the exponential model

Residuals associated with linear fit of transformed data

List of data points in the modified X List actually used in the regression based on restrictions of Freq ,

Category List , and Include Categories

List of data points in the modified

Y List

actually used in the regression based on restrictions of

Freq

Category List , and Include Categories

List of frequencies corresponding to stat.XReg

and stat.YReg

F

factor() factor(

Expr1

[ ,

Var

] ) factor(

List1

[

⇒ expression

, Var

] )

⇒ list factor(

Matrix1

[

, Var

] )

⇒ matrix factor( Expr1 ) returns Expr1 factored with respect to all of its variables over a common denominator.

Expr1 is factored as much as possible toward linear rational factors without introducing new non-real subexpressions. This alternative is appropriate if you want factorization with respect to more than one variable.

Catalog > factor( Expr1 , Var ) returns Expr1 factored with respect to variable

Var .

Expr1 is factored as much as possible toward real factors that are linear in

Var

, even if it introduces irrational constants or subexpressions that are irrational in other variables.

The factors and their terms are sorted with

Var

as the main variable.

Var

. There might be some incidental factoring with respect to other variables.

For the Auto setting of the Auto or Approximate mode, including

Var

permits approximation with floating-point coefficients where irrational coefficients cannot be explicitly expressed concisely in terms of the built-in functions. Even when there is only one variable, including Var might yield more complete factorization.

Note: See also comDenom() for a fast way to achieve partial factoring when factor() is not fast enough or if it exhausts memory.

Note: See also cFactor() for factoring all the way to complex coefficients in pursuit of linear factors.

46 TI-Nspire™ CAS Reference Guide

factor() factor( rationalNumber

) returns the rational number factored into primes. For composite numbers, the computing time grows exponentially with the number of digits in the second-largest factor.

For example, factoring a 30-digit integer could take more than a day, and factoring a 100-digit number could take more than a century.

To stop a calculation manually,

• Windows®: Hold down the F12 key and press Enter repeatedly.

• Macintosh®: Hold down the F5 key and press Enter repeatedly.

• Handheld: Hold down the c

key and press

· repeatedly.

If you merely want to determine if a number is prime, use isPrime() instead. It is much faster, particularly if rationalNumber is not prime and if the second-largest factor has more than five digits.

Cdf()

Cdf( lowBound

, upBound

, dfNumer

, dfDenom

)

⇒ number

if lowBound

and upBound

are numbers,

list

if lowBound

and upBound

are lists

FCdf( lowBound

, upBound

, dfNumer

, dfDenom

)

⇒ number

if lowBound

and upBound

are numbers,

list

if lowBound

and upBound

are lists

Computes the upBound for the specified dfNumer

(degrees of freedom) and dfDenom .

distribution probability between lowBound

and

For P(

X { upBound

), set lowBound

= 0.

Fill

Expr, matrixVar ⇒ matrix

Replaces each element in variable matrixVar with Expr .

matrixVar must already exist.

Fill Expr, listVar

⇒ list

Replaces each element in variable listVar with Expr .

listVar must already exist.

Catalog >

TI-Nspire™ CAS Reference Guide 47

FiveNumSummary

FiveNumSummary X

[ , [

Freq

][ ,

Category

Include

]]

Provides an abbreviated version of the 1-variable statistics on list

A summary of results is stored in the stat.results

variable. (See page

119.)

X represents a list containing the data.

Freq

is an optional list of frequency values. Each element in

Freq specifies the frequency of occurrence for each corresponding X and Y data point. The default value is 1.

Category is a list of numeric category codes for the corresponding X data.

Include is a list of one or more of the category codes. Only those data items whose category code is included in this list are included in the calculation.

An empty (void) element in any of the lists

Freq

, or

Category results in a void for the corresponding element of all those lists. For more information on empty elements, see page 159.

Output variable stat.MinX

stat.Q

X stat.MedianX

stat.Q

X stat.MaxX

Description

Minimum of x values.

1st Quartile of x.

Median of x.

3rd Quartile of x.

Maximum of x values.

floor() floor(

Expr1

)

⇒ integer

Returns the greatest integer that is { the argument. This function is identical to int() .

The argument can be a real or a complex number.

floor(

List1

)

⇒ list floor(

Matrix1

)

⇒ matrix

Returns a list or matrix of the floor of each element.

Note: See also ceiling() and int() .

fMax() fMax( Expr, Var )

⇒

Boolean expression fMax(

Expr

Var

, lowBound

) fMax( Expr , Var , lowBound , upBound ) fMax( Expr , Var ) | lowBound < Var < upBound

Returns a Boolean expression specifying candidate values of Var that maximize Expr or locate its least upper bound.

48 TI-Nspire™ CAS Reference Guide

Catalog >

fMax()

You can use the “|” operator to restrict the solution interval and/or specify other constraints.

For the Approximate setting of the Auto or Approximate mode, fMax() iteratively searches for one approximate local maximum. This is often faster, particularly if you use the “|” operator to constrain the search to a relatively small interval that contains exactly one local maximum.

Note: See also fMin() and max() .

fMin() fMin(

Expr, Var

)

⇒ Boolean expression fMin(

Expr

Var

, lowBound

) fMin(

Expr

Var

, lowBound

, upBound

) fMin(

Expr

Var

) | lowBound

Var

< upBound

Returns a Boolean expression specifying candidate values of

Var

that minimize Expr or locate its greatest lower bound.

You can use the “|” operator to restrict the solution interval and/or specify other constraints.

For the Approximate setting of the Auto or Approximate mode, fMin() iteratively searches for one approximate local minimum. This is often faster, particularly if you use the “|” operator to constrain the search to a relatively small interval that contains exactly one local minimum.

Note: See also fMax() and min() .

For

Var

Low

High

[ ,

Step

]

Block

EndFor

Executes the statements in Block iteratively for each value of Var , from

Low

High

, in increments of

Step

Var must not be a system variable.

Step

can be positive or negative. The default value is 1.

Block can be either a single statement or a series of statements separated with the “:” character.

Note for entering the example: In the Calculator application on the handheld, you can enter multi-line definitions by pressing

@ instead of

at the end of each line. On the computer keyboard, hold down Alt and press Enter .

Catalog >

TI-Nspire™ CAS Reference Guide 49

format() format(

Expr

[

, formatString

] )

⇒ string

Returns Expr as a character string based on the format template.

Expr

must simplify to a number.

formatString is a string and must be in the form: “F[n]”, “S[n]”,

“E[n]”, “G[n][c]”, where [ ] indicate optional portions.

F[n]: Fixed format. n is the number of digits to display after the decimal point.

S[n]: Scientific format. n is the number of digits to display after the decimal point.

E[n]: Engineering format. n is the number of digits after the first significant digit. The exponent is adjusted to a multiple of three, and the decimal point is moved to the right by zero, one, or two digits.

G[n][c]: Same as fixed format but also separates digits to the left of the radix into groups of three. c specifies the group separator character and defaults to a comma. If c is a period, the radix will be shown as a comma.

[Rc]: Any of the above specifiers may be suffixed with the Rc radix flag, where c is a single character that specifies what to substitute for the radix point.

fPart() fPart(

Expr1

) fPart(

List1

)

⇒ expression

⇒ list fPart(

Matrix1

)

⇒ matrix

Returns the fractional part of the argument.

For a list or matrix, returns the fractional parts of the elements.

The argument can be a real or a complex number.

F Pdf()

Pdf( XVal , dfNumer , dfDenom )

⇒ number if XVal is a number, list if XVal is a list

Computes the F distribution probability at XVal for the specified dfNumer (degrees of freedom) and dfDenom .

freqTable 4 list() freqTable

4 list(

List1

, freqIntegerList

)

⇒ list

Returns a list containing the elements from

List1

expanded according to the frequencies in freqIntegerList . This function can be used for building a frequency table for the Data & Statistics application.

List1 can be any valid list.

freqIntegerList

must have the same dimension as

List1

and must contain non-negative integer elements only. Each element specifies the number of times the corresponding

List1

element will be repeated in the result list. A value of zero excludes the corresponding

List1

element.

Note: You can insert this function from the computer keyboard by typing freqTable@>list( ...

) .

Empty (void) elements are ignored. For more information on empty elements, see page 159.

50 TI-Nspire™ CAS Reference Guide

Catalog >

frequency()

Catalog > frequency(

List1,binsList

)

⇒ list

Returns a list containing counts of the elements in List1 . The counts are based on ranges (bins) that you define in binsList

If binsList is {b(1), b(2), …, b(n)}, the specified ranges are { ?

{ b(1), b(1)< ?

{ b(2),…,b(n-1)< ?

{ b(n), b(n)> ?

}. The resulting list is one element longer than binsList .

Each element of the result corresponds to the number of elements from List1 that are in the range of that bin. Expressed in terms of the countIf() function, the result is { countIf(list, ?

{ b(1)), countIf(list, b(1)< ?

{ b(2)), …, countIf(list, b(n-1)< ?

{ b(n)), countIf(list, b(n)> ?

)}.

Elements of

List1

that cannot be “placed in a bin” are ignored.

Empty (void) elements are also ignored. For more information on empty elements, see page 159.

Explanation of result:

2 elements from Datalist are { 2.5

4 elements from Datalist are >2.5 and { 4.5

3 elements from Datalist are >4.5

The element “hello” is a string and cannot be placed in any of the defined bins.

Within the Lists & Spreadsheet application, you can use a range of cells in place of both arguments.

Note: See also countIf() , page 26.

Test_2Samp

List1

List2

[ ,

Freq1

[ ,

Freq2

[ ,

Hypoth

]]]

FTest_2Samp

List1

List2

[ ,

Freq1

[ ,

Freq2

[ ,

Hypoth

]]]

(Data list input)

Test_2Samp sx1

, n1

, sx2

, n2

[ ,

Hypoth

]

FTest_2Samp sx1

, n1

, sx2

, n2

[ ,

Hypoth

]

(Summary stats input)

Performs a two-sample F test. A summary of results is stored in the stat.results

variable. (See page 119.)

For H a

: s 1 > s 2, set

Hypoth

For H a

: s 1 ƒ s 2 (default), set Hypoth =0

For H a

: s 1 < s 2, set Hypoth <0

For information on the effect of empty elements in a list, see “Empty

(void) elements” on page 159.

Catalog >

Output variable stat.

F stat.PVal

stat.dfNumer

stat.dfDenom

stat.sx1, stat.sx2

stat.x1_bar

stat.x2_bar

stat.n1, stat.n2

Description

Calculated

statistic for the data sequence

Smallest level of significance at which the null hypothesis can be rejected numerator degrees of freedom = n1-1 denominator degrees of freedom = n2-1

Sample standard deviations of the data sequences in List 1 and List 2

Sample means of the data sequences in List 1 and List 2

Size of the samples

TI-Nspire™ CAS Reference Guide 51

Func

Block

EndFunc

Template for creating a user-defined function.

Block

can be a single statement, a series of statements separated with the “:” character, or a series of statements on separate lines.

The function can use the Return instruction to return a specific result.

Define a piecewise function:

Note for entering the example: In the Calculator application on the handheld, you can enter multi-line definitions by pressing

@ instead of

at the end of each line. On the computer keyboard, hold down Alt and press Enter .

Result of graphing g(x)

Catalog >

G

gcd() gcd(

Number1, Number2

)

⇒ expression

Returns the greatest common divisor of the two arguments. The gcd of two fractions is the gcd of their numerators divided by the lcm of their denominators.

In Auto or Approximate mode, the gcd of fractional floating-point numbers is 1.0.

gcd(

List1, List2

)

⇒ list

Returns the greatest common divisors of the corresponding elements in List1 and List2 .

gcd(

Matrix1, Matrix2

)

⇒ matrix

Returns the greatest common divisors of the corresponding elements in Matrix1 and Matrix2 .

geomCdf() geomCdf( p

, lowBound

, upBound

)

⇒ number

if lowBound

and upBound

are numbers,

list

if lowBound

and upBound

are lists geomCdf( p , upBound ) for P(1

{

{ upBound upBound

is a number,

list

if upBound

is a list

)

⇒ number if

Computes a cumulative geometric probability from lowBound to upBound

with the specified probability of success p

For P(X { upBound ), set lowBound = 1.

Catalog >

52 TI-Nspire™ CAS Reference Guide

geomPdf() geomPdf( p

XVal

) is a list

⇒ number

XVal

is a number,

list

XVal

Computes a probability at XVal , the number of the trial on which the first success occurs, for the discrete geometric distribution with the specified probability of success p.

getDenom() getDenom(

Expr1

)

⇒ expression

Transforms the argument into an expression having a reduced common denominator, and then returns its denominator.

getLangInfo() getLangInfo()

⇒ string

Returns a string that corresponds to the short name of the currently active language. You can, for example, use it in a program or function to determine the current language.

English = “en”

Danish = “da”

German = “de”

Finnish = “fi”

French = “fr”

Italian = “it”

Dutch = “nl”

Belgian Dutch = “nl_BE”

Norwegian = “no”

Portuguese = “pt”

Spanish = “es”

Swedish = “sv” getLockInfo() getLockInfo (

Var

)

⇒ value

Returns the current locked/unlocked state of variable Var .

value

= 0 :

Var

is unlocked or does not exist.

value = 1 : Var is locked and cannot be modified or deleted.

See Lock , page 70, and unLock , page 134.

Catalog >

TI-Nspire™ CAS Reference Guide 53

getMode() getMode(

ModeNameInteger

) getMode(0)

⇒ list

⇒ value getMode(

ModeNameInteger

) returns a value representing the current setting of the ModeNameInteger mode.

getMode(0) returns a list containing number pairs. Each pair consists of a mode integer and a setting integer.

For a listing of the modes and their settings, refer to the table below.

If you save the settings with getMode(0) & var , you can use setMode( var ) in a function or program to temporarily restore the settings within the execution of the function or program only. See setMode() , page 109.

getNum() getNum(

Expr1

)

⇒ expression

Transforms the argument into an expression having a reduced common denominator, and then returns its numerator.

Catalog >

Mode

Name

Display Digits

Angle

Exponential Format

Real or Complex

Auto or Approx.

Vector Format

Base

Unit system

Mode

Integer

Setting Integers

1 =Float, 2 =Float1, 3 =Float2, 4 =Float3, 5 =Float4, 6 =Float5, 7 =Float6, 8 =Float7,

9 =Float8, 10 =Float9, 11 =Float10, 12 =Float11, 13 =Float12, 14 =Fix0, 15 =Fix1,

16 =Fix2, 17 =Fix3, 18 =Fix4, 19 =Fix5, 20 =Fix6, 21 =Fix7, 22 =Fix8, 23 =Fix9,

24 =Fix10, 25 =Fix11, 26 =Fix12

1 =Radian, 2 =Degree, 3 =Gradian

1 =Normal, 2 =Scientific, 3 =Engineering

1 =Real, 2 =Rectangular, 3 =Polar

1 =Auto, 2 =Approximate, 3 =Exact

1 =Rectangular, 2 =Cylindrical, 3 =Spherical

1 =Decimal, 2 =Hex, 3 =Binary

1 =SI, 2 =Eng/US

Catalog >

54 TI-Nspire™ CAS Reference Guide

getType() getType( var

)

⇒ string

Returns a string that indicates the data type of variable var .

If var

has not been defined, returns the string "NONE".

getVarInfo() getVarInfo()

⇒ matrix or string getVarInfo(

LibNameString

)

⇒ matrix

or string getVarInfo() returns a matrix of information (variable name, type, library accessibility, and locked/unlocked state) for all variables and library objects defined in the current problem.

If no variables are defined, getVarInfo() returns the string

"NONE".

getVarInfo( LibNameString ) returns a matrix of information for all library objects defined in library LibNameString . LibNameString must be a string (text enclosed in quotation marks) or a string variable.

If the library LibNameString does not exist, an error occurs.

Note the example to the left, in which the result of getVarInfo() is assigned to variable vs . Attempting to display row 2 or row 3 of vs returns an “Invalid list or matrix” error because at least one of elements in those rows (variable b , for example) revaluates to a matrix.

This error could also occur when using Ans to reevaluate a getVarInfo() result.

The system gives the above error because the current version of the software does not support a generalized matrix structure where an element of a matrix can be either a matrix or a list.

Catalog >

TI-Nspire™ CAS Reference Guide 55

Goto

Goto labelName

Transfers control to the label labelName

labelName must be defined in the same function using a Lbl instruction.

Note for entering the example: In the Calculator application on the handheld, you can enter multi-line definitions by pressing

@ instead of

at the end of each line. On the computer keyboard, hold down Alt and press Enter .

Catalog >

4 Grad

Expr1 4

Grad

⇒ expression

Converts Expr1 to gradian angle measure.

Note: You can insert this operator from the computer keyboard by typing @>Grad .

In Degree angle mode:

In Radian angle mode:

I

identity() identity(

Integer

)

⇒ matrix

Returns the identity matrix with a dimension of Integer .

Integer must be a positive integer.

Catalog >

56 TI-Nspire™ CAS Reference Guide

BooleanExpr

Statement

If BooleanExpr Then

Block

EndIf

If BooleanExpr evaluates to true, executes the single statement

Statement or the block of statements Block before continuing execution.

If BooleanExpr evaluates to false, continues execution without executing the statement or block of statements.

Block can be either a single statement or a sequence of statements separated with the “:” character.

Note for entering the example: In the Calculator application on the handheld, you can enter multi-line definitions by pressing

@ instead of

at the end of each line. On the computer keyboard, hold down Alt and press Enter .

BooleanExpr

Then

Block1

Else

Block2

EndIf

If BooleanExpr evaluates to true, executes Block1 and then skips

Block2 .

If BooleanExpr evaluates to false, skips Block1 but executes

Block2 .

Block1 and Block2 can be a single statement.

BooleanExpr1

Then

Block1

ElseIf

BooleanExpr2

Then

Block2

ElseIf

BooleanExprN

Then

BlockN

EndIf

Allows for branching. If

BooleanExpr1

evaluates to true, executes

Block1 . If BooleanExpr1 evaluates to false, evaluates

BooleanExpr2

, and so on.

Catalog >

TI-Nspire™ CAS Reference Guide 57

ifFn()

Catalog > ifFn(

BooleanExpr

Value_If_true

[ ,

Value_If_false

[ ,

Value_If_unknown

]] )

⇒ expression, list, or matrix

Evaluates the boolean expression

BooleanExpr

(or each element from BooleanExpr ) and produces a result based on the following rules:

• BooleanExpr can test a single value, a list, or a matrix.

• If an element of

BooleanExpr evaluates to true, returns the corresponding element from Value_If_true .

• If an element of

BooleanExpr evaluates to false, returns the corresponding element from Value_If_false . If you omit

Value_If_false

, returns undef

• If an element of BooleanExpr is neither true nor false, returns the corresponding element

Value_If_unknown

. If you omit

Value_If_unknown , returns undef.

• If the second, third, or fourth argument of the ifFn() function is a single expression, the Boolean test is applied to every position in

BooleanExpr

Note: If the simplified BooleanExpr statement involves a list or matrix, all other list or matrix arguments must have the same dimension(s), and the result will have the same dimension(s).

Test value of 1 is less than 2.5, so its corresponding

Value_If_True

element of 5 is copied to the result list.

Test value of 2 is less than 2.5, so its corresponding

Value_If_True element of 6 is copied to the result list.

Test value of 3 is not less than 2.5, so its corresponding

Value_If_False

element of 10 is copied to the result list.

Value_If_true is a single value and corresponds to any selected position.

Value_If_false

is not specified. Undef is used.

imag() imag(

Expr1

)

⇒ expression

Returns the imaginary part of the argument.

Note: All undefined variables are treated as real variables. See also real() , page 98 imag(

List1

)

⇒ list

Returns a list of the imaginary parts of the elements.

imag(

Matrix1

)

⇒ matrix

Returns a matrix of the imaginary parts of the elements.

One element selected from Value_If_true . One element selected from Value_If_unknown .

Catalog > impDif() impDif(

Equation

Var

, dependVar

[ ,

Ord

] )

⇒ expression where the order Ord defaults to 1.

Computes the implicit derivative for equations in which one variable is defined implicitly in terms of another.

Indirection

Catalog >

See #() , page 153 .

58 TI-Nspire™ CAS Reference Guide

inString() inString( srcString

, subString

[ ,

Start

] )

⇒ integer

Returns the character position in string srcString at which the first occurrence of string subString

begins.

Start , if included, specifies the character position within srcString where the search begins. Default = 1 (the first character of srcString

If srcString does not contain subString or Start is > the length of srcString

, returns zero.

int() int(

Expr

) int (

List1

)

⇒ integer

⇒ list int (

Matrix1

)

⇒ matrix

Returns the greatest integer that is less than or equal to the argument. This function is identical to floor() .

The argument can be a real or a complex number.

For a list or matrix, returns the greatest integer of each of the elements.

intDiv() intDiv( Number1 , Number2 ) intDiv( List1 , List2 ) intDiv( Matrix1 , Matrix2 )

⇒ integer

⇒ list

⇒ matrix

Returns the signed integer part of ( Number1 ÷ Number2 ).

For lists and matrices, returns the signed integer part of

(argument 1 ÷ argument 2) for each element pair.

integral

Catalog >

See ‰ () , page 149 .

TI-Nspire™ CAS Reference Guide 59

interpolate()

Catalog > interpolate( xValue , xList , yList , yPrimeList )

⇒ list

This function does the following:

Differential equation: y '=-3· y +6· t +5 and y (0)=5

Given xList , yList = f( xList ) , and yPrimeList = f'( xList ) for some unknown function f , a cubic interpolant is used to approximate the function f at xValue . It is assumed that xList is a list of monotonically increasing or decreasing numbers, but this function may return a value even when it is not. This function walks through xList looking for an interval [ xList [i], xList [i+1]] that contains xValue . If it finds such an interval, it returns an interpolated value for f( xValue ) ; otherwise, it returns undef .

xList , yList , and yPrimeList must be of equal dimension | 2 and contain expressions that simplify to numbers.

To see the entire result, press move the cursor.

and then use

and

Use the interpolate() function to calculate the function values for the xvaluelist: xValue can be an undefined variable, a number, or a list of numbers.

inv c 2

() inv c 2

(

Area

, df

) invChi2( Area , df )

Computes the Inverse cumulative c 2

(chi-square) probability function specified by degree of freedom, df

for a given

Area

under the curve.

inv F () inv

( Area , dfNumer , dfDenom ) invF(

Area

, dfNumer

, dfDenom

) computes the Inverse cumulative

distribution function specified by dfNumer and dfDenom for a given Area under the curve.

invNorm() invNorm(

Area

[ , m

[ , s

]] )

Computes the inverse cumulative normal distribution function for a given Area under the normal distribution curve specified by m and s .

invt() invt(

Area

, df

)

Computes the inverse cumulative student-t probability function specified by degree of freedom, df for a given Area under the curve.

60 TI-Nspire™ CAS Reference Guide

Catalog >

iPart() iPart(

Number

) iPart (

List1

) iPart (

Matrix1

)

⇒ integer

⇒ list

⇒ matrix

Returns the integer part of the argument.

For lists and matrices, returns the integer part of each element.

The argument can be a real or a complex number.

irr() irr(

CF0

CFList

CFFreq

] )

⇒ value

Financial function that calculates internal rate of return of an investment.

CF0 is the initial cash flow at time 0; it must be a real number.

CFList

is a list of cash flow amounts after the initial cash flow CF0.

CFFreq is an optional list in which each element specifies the frequency of occurrence for a grouped (consecutive) cash flow amount, which is the corresponding element of CFList . The default is

1; if you enter values, they must be positive integers < 10,000.

Note: See also mirr() , page 77.

Catalog >

Catalog > isPrime()

Catalog > isPrime(

Number

)

⇒ Boolean constant expression

Returns true or false to indicate if number is a whole number | 2 that is evenly divisible only by itself and 1.

If Number exceeds about 306 digits and has no factors { 1021, isPrime( Number ) displays an error message.

If you merely want to determine if Number is prime, use isPrime() instead of factor() . It is much faster, particularly if Number is not prime and has a second-largest factor that exceeds about five digits.

Function to find the next prime after a specified number:

Note for entering the example: In the Calculator application on the handheld, you can enter multi-line definitions by pressing

@ instead of

at the end of each line. On the computer keyboard, hold down Alt and press Enter .

isVoid() isVoid(

Var

) isVoid(

Expr

) isVoid(

List

)

⇒

Boolean constant expression

⇒

Boolean constant expression

⇒ list of Boolean constant expressions

Returns true or false to indicate if the argument is a void data type.

For more information on void elements, see page 159.

Catalog >

TI-Nspire™ CAS Reference Guide 61

L

Lbl

Lbl labelName

Defines a label with the name labelName within a function.

You can use a Goto labelName

instruction to transfer control to the instruction immediately following the label.

labelName

must meet the same naming requirements as a variable name.

Note for entering the example: In the Calculator application on the handheld, you can enter multi-line definitions by pressing

@ instead of

at the end of each line. On the computer keyboard, hold down Alt and press Enter .

lcm() lcm(

Number1

Number2

) lcm(

List1

List2

) lcm(

Matrix1

Matrix2

)

⇒ expression

⇒ list

⇒ matrix

Returns the least common multiple of the two arguments. The lcm of two fractions is the lcm of their numerators divided by the gcd of their denominators. The lcm of fractional floating-point numbers is their product.

For two lists or matrices, returns the least common multiples of the corresponding elements.

left() left( sourceString

[ ,

Num

] )

⇒ string

Returns the leftmost Num characters contained in character string sourceString .

If you omit Num , returns all of sourceString .

left( List1 [ , Num ] )

⇒ list

Returns the leftmost Num elements contained in List1 .

If you omit Num , returns all of List1 .

left(

Comparison

)

⇒ expression

Returns the left-hand side of an equation or inequality.

Catalog >

62 TI-Nspire™ CAS Reference Guide

libShortcut()

Catalog > libShortcut(

LibNameString

ShortcutNameString

[ ,

LibPrivFlag

] )

⇒ list of variables

Creates a variable group in the current problem that contains references to all the objects in the specified library document libNameString

. Also adds the group members to the Variables menu.

You can then refer to each object using its ShortcutNameString .

Set

LibPrivFlag

= 0 to exclude private library objects (default)

Set LibPrivFlag = 1 to include private library objects

This example assumes a properly stored and refreshed library document named linalg2 that contains objects defined as clearmat , gauss1 , and gauss2 .

To copy a variable group, see CopyVar on page 21.

To delete a variable group, see DelVar on page 35.

limit() or lim() limit(

Expr1

Var

Point

[ ,

Direction

] ) limit(

List1

Var

Point

[ ,

Direction

] )

⇒ expression

⇒ list limit(

Matrix1

Var

Point

[ ,

Direction

] )

⇒ matrix

Returns the limit requested.

Note: See also Limit template , page 6.

Direction : negative=from left, positive=from right, otherwise=both.

(If omitted, Direction defaults to both.)

Catalog >

Limits at positive ˆ and at negative ˆ are always converted to onesided limits from the finite side.

Depending on the circumstances, limit() returns itself or undef when it cannot determine a unique limit. This does not necessarily mean that a unique limit does not exist. undef means that the result is either an unknown number with finite or infinite magnitude, or it is the entire set of such numbers.

limit() uses methods such as L’Hopital’s rule, so there are unique limits that it cannot determine. If Expr1 contains undefined variables other than

Var

, you might have to constrain them to obtain a more concise result.

Limits can be very sensitive to rounding error. When possible, avoid the Approximate setting of the Auto or Approximate mode and approximate numbers when computing limits. Otherwise, limits that should be zero or have infinite magnitude probably will not, and limits that should have finite non-zero magnitude might not.

TI-Nspire™ CAS Reference Guide 63

LinRegBx

LinRegBx X , Y

[ , [

Freq

][ , Category , Include

]]

Computes the linear regression y = a+b · x on lists X and Y with frequency

Freq

. A summary of results is stored in the stat.results

variable. (See page 119.)

All the lists must have equal dimension except for

Include

X and Y are lists of independent and dependent variables.

Freq

is an optional list of frequency values. Each element in

Freq specifies the frequency of occurrence for each corresponding X and Y data point. The default value is 1. All elements must be integers | 0.

Category

is a list of category codes for the corresponding

and

Y data.

Include

is a list of one or more of the category codes. Only those data items whose category code is included in this list are included in the calculation.

For information on the effect of empty elements in a list, see “Empty

(void) elements” on page 159.

Catalog >

Output variable stat.RegEqn

stat.a, stat.b

stat.r

2 stat.r

stat.Resid

stat.XReg

stat.YReg

stat.FreqReg

Description

Regression Equation: a+b · x

Regression coefficients

Coefficient of determination

Correlation coefficient

Residuals from the regression

List of data points in the modified X List actually used in the regression based on restrictions of Freq ,

Category List , and Include Categories

List of data points in the modified

Y List

actually used in the regression based on restrictions of

Freq

Category List , and Include Categories

List of frequencies corresponding to stat.XReg

and stat.YReg

LinRegMx

[ , [

Freq

][ ,

Category

Include

]]

Computes the linear regression y = m · x+b on lists X and Y with frequency

Freq

. A summary of results is stored in the stat.results

variable. (See page 119.)

All the lists must have equal dimension except for

Include

X and Y are lists of independent and dependent variables.

Freq

is an optional list of frequency values. Each element in

Freq specifies the frequency of occurrence for each corresponding X and Y data point. The default value is 1. All elements must be integers | 0.

Category

is a list of category codes for the corresponding

and

Y data.

Include

is a list of one or more of the category codes. Only those data items whose category code is included in this list are included in the calculation.

For information on the effect of empty elements in a list, see “Empty

(void) elements” on page 159.

64 TI-Nspire™ CAS Reference Guide

Catalog >

Output variable stat.RegEqn

stat.m, stat.b

stat.r

2 stat.r

stat.Resid

stat.XReg

stat.YReg

stat.FreqReg

Description

Regression Equation: y = m · x+b

Regression coefficients

Coefficient of determination

Correlation coefficient

Residuals from the regression

List of data points in the modified X List actually used in the regression based on restrictions of Freq ,

Category List , and Include Categories

List of data points in the modified Y List actually used in the regression based on restrictions of Freq ,

Category List , and Include Categories

List of frequencies corresponding to stat.XReg

and stat.YReg

LinRegtIntervals

[ ,

[ ,0 [ ,

CLev

]]]

For Slope. Computes a level C confidence interval for the slope.

LinRegtIntervals

[ ,

[ ,1,

Xval

[ ,

CLev

]]]

For Response. Computes a predicted y-value, a level C prediction interval for a single observation, and a level C confidence interval for the mean response.

A summary of results is stored in the stat.results

variable. (See page

119.)

All the lists must have equal dimension.

and

are lists of independent and dependent variables.

F is an optional list of frequency values. Each element in F specifies the frequency of occurrence for each corresponding

and

data point. The default value is 1. All elements must be integers | 0.

For information on the effect of empty elements in a list, see “Empty

(void) elements” on page 159.

Catalog >

Output variable stat.RegEqn

stat.a, stat.b

stat.df

stat.r

2 stat.r

stat.Resid

Description

Regression Equation: a+b · x

Regression coefficients

Degrees of freedom

Coefficient of determination

Correlation coefficient

Residuals from the regression

TI-Nspire™ CAS Reference Guide 65

For Slope type only

Output variable

[stat.CLower, stat.CUpper] stat.ME

stat.SESlope

stat.s

Description

Confidence interval for the slope

Confidence interval margin of error

Standard error of slope

Standard error about the line

For Response type only

Output variable

[stat.CLower, stat.CUpper] stat.ME

stat.SE

[stat.LowerPred, stat.UpperPred] stat.MEPred

stat.SEPred

stat.

Description

Confidence interval for the mean response

Confidence interval margin of error

Standard error of mean response

Prediction interval for a single observation

Prediction interval margin of error

Standard error for prediction a + b · XVal

LinRegtTest

[ ,

Freq

[ ,

Hypoth

]]

Computes a linear regression on the X and Y lists and a t test on the value of slope b and the correlation coefficient r for the equation y

= a + b x. It tests the null hypothesis H

: b =0 (equivalently, r =0) against one of three alternative hypotheses.

All the lists must have equal dimension.

and

are lists of independent and dependent variables.

Freq is an optional list of frequency values. Each element in Freq specifies the frequency of occurrence for each corresponding

and

Y data point. The default value is 1. All elements must be integers | 0.

Hypoth is an optional value specifying one of three alternative hypotheses against which the null hypothesis (H

: b = r =0) will be tested.

For H a

: bƒ 0 and rƒ 0 (default), set Hypoth =0

For H a

: b <0 and r <0, set

Hypoth

For H a

: b >0 and r >0, set

Hypoth

A summary of results is stored in the stat.results

variable. (See page

119.)

For information on the effect of empty elements in a list, see “Empty

(void) elements” on page 159.

66 TI-Nspire™ CAS Reference Guide

Catalog >

Output variable stat.RegEqn

stat.t

stat.PVal

stat.df

stat.a, stat.b

stat.s

stat.SESlope

stat.r

2 stat.r

stat.Resid

Description

Regression equation: a + b · x t -Statistic for significance test

Smallest level of significance at which the null hypothesis can be rejected

Degrees of freedom

Regression coefficients

Standard error about the line

Standard error of slope

Coefficient of determination

Correlation coefficient

Residuals from the regression linSolve() linSolve(

SystemOfLinearEqns

Var1

Var2

...

) linSolve(

LinearEqn1 and

LinearEqn2 and

...

Var1

Var2

...

)

⇒ list

⇒ list linSolve({

LinearEqn1

LinearEqn2

...

Var1

Var2

...

)

⇒ list linSolve(

SystemOfLinearEqns

, {

Var1

Var2

...

})

⇒ list linSolve(

LinearEqn1 and

LinearEqn2 and

...

{

Var1

Var2

...

})

⇒ list linSolve({

LinearEqn1

LinearEgn2

, ...

}, {

Var1

Var2

, ...

})

⇒ list

Returns a list of solutions for the variables Var1

Var2

The first argument must evaluate to a system of linear equations or a single linear equation. Otherwise, an argument error occurs.

For example, evaluating linSolve ( x=1 and x=2,x ) produces an

“Argument Error” result.

@ List()

List(

List1

)

⇒ list

Note: You can insert this function from the keyboard by typing deltaList( ...

) .

Returns a list containing the differences between consecutive elements in List1 . Each element of List1 is subtracted from the next element of

List1

. The resulting list is always one element shorter than the original List1 .

Catalog >

TI-Nspire™ CAS Reference Guide 67

list 4 mat() list

4 mat(

List

[ , elementsPerRow

] )

⇒ matrix

Returns a matrix filled row-by-row with the elements from List .

elementsPerRow

, if included, specifies the number of elements per row. Default is the number of elements in List (one row).

List

does not fill the resulting matrix, zeros are added.

Note: You can insert this function from the computer keyboard by typing list@>mat( ...

) .

4 ln

Expr 4 ln

⇒ expression

Causes the input

Expr

to be converted to an expression containing only natural logs (ln).

Note: You can insert this operator from the computer keyboard by typing @>ln .

ln() ln(

Expr1

) ln (

List1

)

⇒ expression

⇒ list

Returns the natural logarithm of the argument.

For a list, returns the natural logarithms of the elements.

If complex format mode is Real:

Catalog >

keys

If complex format mode is Rectangular: ln( squareMatrix1

)

⇒ squareMatrix

Returns the matrix natural logarithm of squareMatrix1 . This is not the same as calculating the natural logarithm of each element. For information about the calculation method, refer to cos() on.

squareMatrix1 must be diagonalizable. The result always contains floating-point numbers.

In Radian angle mode and Rectangular complex format:

To see the entire result, press

and then use

and

to move the cursor.

68 TI-Nspire™ CAS Reference Guide

LnReg

[ , [

Freq

] [ ,

Category

Include

]]

Computes the logarithmic regression y = a+b · ln(x) on lists

and

Y with frequency Freq . A summary of results is stored in the stat.results

variable. (See page 119.)

All the lists must have equal dimension except for Include .

and

are lists of independent and dependent variables.

Freq is an optional list of frequency values. Each element in Freq specifies the frequency of occurrence for each corresponding

and

Y data point. The default value is 1. All elements must be integers | 0.

Category is a list of category codes for the corresponding X and Y data.

Include is a list of one or more of the category codes. Only those data items whose category code is included in this list are included in the calculation.

For information on the effect of empty elements in a list, see “Empty

(void) elements” on page 159.

Catalog >

Output variable stat.RegEqn

stat.a, stat.b

stat.r

2 stat.r

stat.Resid

stat.ResidTrans

stat.XReg

stat.YReg

stat.FreqReg

Description

Regression equation: a+b · ln(x)

Regression coefficients

Coefficient of linear determination for transformed data

Correlation coefficient for transformed data (ln(x), y)

Residuals associated with the logarithmic model

Residuals associated with linear fit of transformed data

List of data points in the modified

X List

actually used in the regression based on restrictions of

Freq

Category List , and Include Categories

List of data points in the modified Y List actually used in the regression based on restrictions of Freq ,

Category List

, and

Include Categories

List of frequencies corresponding to stat.XReg

and stat.YReg

TI-Nspire™ CAS Reference Guide 69

Local

Var1

[ ,

Var2

] [ ,

Var3

] ...

Declares the specified vars

as local variables. Those variables exist only during evaluation of a function and are deleted when the function finishes execution.

Note: Local variables save memory because they only exist temporarily. Also, they do not disturb any existing global variable values. Local variables must be used for For loops and for temporarily saving values in a multi-line function since modifications on global variables are not allowed in a function.

Note for entering the example: In the Calculator application on the handheld, you can enter multi-line definitions by pressing

@ instead of

at the end of each line. On the computer keyboard, hold down Alt and press Enter .

Lock

Var1

[ ,

Var2

] [ ,

Var3

] ...

Lock

Var .

Locks the specified variables or variable group. Locked variables cannot be modified or deleted.

You cannot lock or unlock the system variable Ans , and you cannot lock the system variable groups stat .

or tvm .

Note: The Lock command clears the Undo/Redo history when applied to unlocked variables.

See unLock , page 134, and getLockInfo() , page 53.

Catalog >

70 TI-Nspire™ CAS Reference Guide

log() log (

Expr1

[ ,

Expr2

] ) log (

List1

[ ,

Expr2

] )

⇒ expression

⇒ list

Returns the base -Expr2 logarithm of the first argument.

Note: See also Log template , page 2.

For a list, returns the base -Expr2 logarithm of the elements.

If the second argument is omitted, 10 is used as the base.

If complex format mode is Real:

keys

If complex format mode is Rectangular: log ( squareMatrix1

[ ,

Expr

] )

⇒ squareMatrix

Returns the matrix baseExpr logarithm of squareMatrix1 . This is not the same as calculating the base-

Expr

logarithm of each element.

For information about the calculation method, refer to cos() .

squareMatrix1

must be diagonalizable. The result always contains floating-point numbers.

In Radian angle mode and Rectangular complex format:

If the base argument is omitted, 10 is used as base.

To see the entire result, press

and then use

and

to move the cursor.

4 logbase

Expr 4 logbase(

Expr1

)

⇒ expression

Causes the input Expression to be simplified to an expression using base Expr1 .

Note: You can insert this operator from the computer keyboard by typing @>logbase( ...

) .

Catalog >

TI-Nspire™ CAS Reference Guide 71

Logistic

[ , [

Freq

] [ ,

Category

Include

]]

Computes the logistic regression y = (c/(1+a · e

-bx

)) on lists X and Y with frequency Freq . A summary of results is stored in the stat.results

variable. (See page 119.)

All the lists must have equal dimension except for Include .

X and Y are lists of independent and dependent variables.

Freq

is an optional list of frequency values. Each element in

Freq specifies the frequency of occurrence for each corresponding X and Y data point. The default value is 1. All elements must be integers | 0.

Category is a list of category codes for the corresponding X and Y data.

Include is a list of one or more of the category codes. Only those data items whose category code is included in this list are included in the calculation.

For information on the effect of empty elements in a list, see “Empty

(void) elements” on page 159.

Catalog >

Output variable stat.RegEqn

stat.a, stat.b, stat.c

stat.Resid

stat.XReg

stat.YReg

stat.FreqReg

Description

Regression equation: c/(1+a · e

-bx

)

Regression coefficients

Residuals from the regression

List of data points in the modified X List actually used in the regression based on restrictions of Freq ,

Category List , and Include Categories

List of data points in the modified Y List actually used in the regression based on restrictions of Freq ,

Category List , and Include Categories

List of frequencies corresponding to stat.XReg

and stat.YReg

LogisticD

[ , [

Iterations

] , [

Freq

] [ ,

Category

Include

] ]

Computes the logistic regression y = (c/(1+a · e

-bx

)+d) on lists X and

with frequency

Freq

, using a specified number of

Iterations

. A summary of results is stored in the stat.results

variable. (See page

119.)

All the lists must have equal dimension except for Include .

and

are lists of independent and dependent variables.

Freq is an optional list of frequency values. Each element in Freq specifies the frequency of occurrence for each corresponding

and

Y data point. The default value is 1. All elements must be integers | 0.

Category is a list of category codes for the corresponding X and Y data.

Include is a list of one or more of the category codes. Only those data items whose category code is included in this list are included in the calculation.

For information on the effect of empty elements in a list, see “Empty

(void) elements” on page 159.

Catalog >

72 TI-Nspire™ CAS Reference Guide

Output variable stat.RegEqn

stat.a, stat.b, stat.c, stat.d

stat.Resid

stat.XReg

stat.YReg

stat.FreqReg

Description

Regression equation: c/(1+a · e

-bx

)+d)

Regression coefficients

Residuals from the regression

List of data points in the modified X List actually used in the regression based on restrictions of Freq ,

Category List , and Include Categories

List of data points in the modified Y List actually used in the regression based on restrictions of Freq ,

Category List , and Include Categories

List of frequencies corresponding to stat.XReg

and stat.YReg

Loop

Block

EndLoop

Repeatedly executes the statements in

Block

. Note that the loop will be executed endlessly, unless a Goto or Exit instruction is executed within

Block

Block is a sequence of statements separated with the “:” character.

Note for entering the example: In the Calculator application on the handheld, you can enter multi-line definitions by pressing

@ instead of

at the end of each line. On the computer keyboard, hold down Alt and press Enter .

Catalog >

TI-Nspire™ CAS Reference Guide 73

Matrix

, lMatrix

, uMatrix

, pMatrix[,Tol]

Calculates the Doolittle LU (lower-upper) decomposition of a real or complex matrix. The lower triangular matrix is stored in lMatrix , the upper triangular matrix in uMatrix

, and the permutation matrix

(which describes the row swaps done during the calculation) in pMatrix

lMatrix · uMatrix = pMatrix · matrix

Optionally, any matrix element is treated as zero if its absolute value is less than Tol . This tolerance is used only if the matrix has floatingpoint entries and does not contain any symbolic variables that have not been assigned a value. Otherwise, Tol is ignored.

• If you use

/·

or set the Auto or Approximate mode to Approximate, computations are done using floatingpoint arithmetic.

• If Tol is omitted or not used, the default tolerance is calculated as:

5E M 14 · max(dim( Matrix )) · rowNorm( Matrix )

The LU factorization algorithm uses partial pivoting with row interchanges.

Catalog >

M

mat 4 list() mat

4 list( Matrix )

⇒ list

Returns a list filled with the elements in Matrix . The elements are copied from Matrix row by row.

Note: You can insert this function from the computer keyboard by typing mat@>list( ...

) .

74 TI-Nspire™ CAS Reference Guide

Catalog >

max() max(

Expr1

Expr2

) max (

List1

List2

)

⇒ expression

⇒ list max (

Matrix1

Matrix2

)

⇒ matrix

Returns the maximum of the two arguments. If the arguments are two lists or matrices, returns a list or matrix containing the maximum value of each pair of corresponding elements.

max(

List

)

⇒ expression

Returns the maximum element in list .

max(

Matrix1

)

⇒ matrix

Returns a row vector containing the maximum element of each column in

Matrix1

Empty (void) elements are ignored. For more information on empty elements, see page 159.

Note: See also fMax() and min() .

mean() mean(

List

[

, freqList

] )

⇒ expression

Returns the mean of the elements in List .

Each freqList element counts the number of consecutive occurrences of the corresponding element in List .

mean( Matrix1 [

, freqMatrix ] )

⇒ matrix

Returns a row vector of the means of all the columns in Matrix1 .

Each freqMatrix

element counts the number of consecutive occurrences of the corresponding element in Matrix1 .

Empty (void) elements are ignored. For more information on empty elements, see page 159.

In Rectangular vector format:

Catalog >

Catalog > median() median( List [

, freqList ] )

⇒ expression

Returns the median of the elements in

List

Each freqList element counts the number of consecutive occurrences of the corresponding element in

List

Catalog >

TI-Nspire™ CAS Reference Guide 75

median() median(

Matrix1

[

, freqMatrix

] )

⇒ matrix

Returns a row vector containing the medians of the columns in

Matrix1 .

Each freqMatrix element counts the number of consecutive occurrences of the corresponding element in Matrix1 .

Notes:

• All entries in the list or matrix must simplify to numbers.

• Empty (void) elements in the list or matrix are ignored. For more information on empty elements, see page 159.

MedMed

[ ,

Freq

] [ ,

Category

Include

]]

Computes the median-median line y = (m · x+b) on lists X and Y with frequency

Freq

. A summary of results is stored in the stat.results

variable. (See page 119.)

All the lists must have equal dimension except for

Include

X and Y are lists of independent and dependent variables.

Freq

is an optional list of frequency values. Each element in

Freq specifies the frequency of occurrence for each corresponding X and Y data point. The default value is 1. All elements must be integers | 0.

Category

is a list of category codes for the corresponding

and

Y data.

Include

is a list of one or more of the category codes. Only those data items whose category code is included in this list are included in the calculation.

For information on the effect of empty elements in a list, see “Empty

(void) elements” on page 159.

Catalog >

Output variable stat.RegEqn

stat.m, stat.b

stat.Resid

stat.XReg

stat.YReg

stat.FreqReg

Description

Median-median line equation: m · x+b

Model coefficients

Residuals from the median-median line

List of data points in the modified

X List

actually used in the regression based on restrictions of

Freq

Category List , and Include Categories

List of data points in the modified Y List actually used in the regression based on restrictions of Freq ,

Category List

, and

Include Categories

List of frequencies corresponding to stat.XReg

and stat.YReg

mid() mid( sourceString

Start

[ ,

Count

] )

⇒ string

Returns Count characters from character string sourceString , beginning with character number Start .

If Count is omitted or is greater than the dimension of sourceString , returns all characters from sourceString , beginning with character number Start .

Count must be | 0. If Count = 0, returns an empty string.

76 TI-Nspire™ CAS Reference Guide

Catalog >

mid() mid( sourceList

Start

[ ,

Count

] )

⇒ list

Returns

Count

elements from sourceList

, beginning with element number Start .

Count

is omitted or is greater than the dimension of sourceList

, returns all elements from sourceList , beginning with element number

Start

Count must be | 0. If Count = 0, returns an empty list.

mid( sourceStringList , Start

[

, Count

] )

⇒ list

Returns Count strings from the list of strings sourceStringList , beginning with element number

Start

min() min(

Expr1

Expr2

) min(

List1, List2

)

⇒ expression

⇒ list min(

Matrix1, Matrix2

)

⇒ matrix

Returns the minimum of the two arguments. If the arguments are two lists or matrices, returns a list or matrix containing the minimum value of each pair of corresponding elements.

min(

List

)

⇒ expression

Returns the minimum element of List .

min(

Matrix1

)

⇒ matrix

Returns a row vector containing the minimum element of each column in

Matrix1

Note: See also fMin() and max() .

mirr() mirr( financeRate

, reinvestRate

CF0

CFList

[ ,

CFFreq

] )

Financial function that returns the modified internal rate of return of an investment.

financeRate

is the interest rate that you pay on the cash flow amounts.

reinvestRate

is the interest rate at which the cash flows are reinvested.

CF0 is the initial cash flow at time 0; it must be a real number.

CFList is a list of cash flow amounts after the initial cash flow CF0.

CFFreq is an optional list in which each element specifies the frequency of occurrence for a grouped (consecutive) cash flow amount, which is the corresponding element of CFList . The default is

1; if you enter values, they must be positive integers < 10,000.

Note: See also irr() , page 61.

Catalog >

TI-Nspire™ CAS Reference Guide 77

mod() mod(

Expr1

Expr2

) mod(

List1

List2

)

⇒ expression

⇒ list mod(

Matrix1

Matrix2

)

⇒ matrix

Returns the first argument modulo the second argument as defined by the identities: mod(x,0) = x mod(x,y) = x y floor(x/y)

When the second argument is non-zero, the result is periodic in that argument. The result is either zero or has the same sign as the second argument.

If the arguments are two lists or two matrices, returns a list or matrix containing the modulo of each pair of corresponding elements.

Note: See also remain() , page 99 mRow() mRow(

Expr

Matrix1

Index

)

⇒ matrix

Returns a copy of Matrix1 with each element in row Index of

Matrix1

multiplied by

Expr

mRowAdd() mRowAdd(

Expr

Matrix1

Index1

Index2

)

⇒ matrix

Returns a copy of Matrix1 with each element in row Index2 of

Matrix1 replaced with:

Expr · row Index1 + row Index2

MultReg

[ ,

,… [ ,

X10

]]]

Calculates multiple linear regression of list Y on lists X1 , X2 , … , X10 .

A summary of results is stored in the stat.results

variable. (See page

119.)

All the lists must have equal dimension.

For information on the effect of empty elements in a list, see “Empty

(void) elements” on page 159.

Output variable stat.RegEqn

stat.b0, stat.b1, ...

stat.R

2 stat.

List stat.Resid

Description

Regression Equation: b0+b1 · x1+b2 · x2+ ...

Regression coefficients

Coefficient of multiple determination y

List = b0+b1 · x1+ ...

Residuals from the regression

78 TI-Nspire™ CAS Reference Guide

Catalog >

MultRegIntervals

[ ,

,… [ ,

X10

]]] ,

XValList

[ ,

CLevel

]

Computes a predicted y-value, a level C prediction interval for a single observation, and a level C confidence interval for the mean response.

A summary of results is stored in the stat.results

variable. (See page

119.)

All the lists must have equal dimension.

For information on the effect of empty elements in a list, see “Empty

(void) elements” on page 159.

Output variable stat.RegEqn

stat.

Description

Regression Equation: b0+b1 · x1+b2 · x2+ ...

A point estimate: y

= b0 + b1 · xl + ... for

XValList stat.dfError

Error degrees of freedom stat.CLower, stat.CUpper

Confidence interval for a mean response stat.ME

stat.SE

stat.LowerPred, stat.UpperrPred

Confidence interval margin of error

Standard error of mean response

Prediction interval for a single observation stat.MEPred

stat.SEPred

stat.bList

stat.Resid

Prediction interval margin of error

Standard error for prediction

List of regression coefficients, {b0,b1,b2,...}

Residuals from the regression

MultRegTests

[ ,

,… [ ,

X10

]]]

Multiple linear regression test computes a multiple linear regression on the given data and provides the global

test statistic and t

test statistics for the coefficients.

A summary of results is stored in the stat.results

variable. (See page

119.)

For information on the effect of empty elements in a list, see “Empty

(void) elements” on page 159.

Outputs

Output variable stat.RegEqn

stat.F

stat.PVal

stat.R

Description

Regression Equation: b0+b1 · x1+b2 · x2+ ...

Global F test statistic

P-value associated with global F statistic

Coefficient of multiple determination

Catalog >

TI-Nspire™ CAS Reference Guide 79

Output variable stat.AdjR

2 stat.s

stat.DW

stat.dfReg

stat.SSReg

stat.MSReg

stat.dfError

stat.SSError

stat.MSError

stat.bList

stat.tList

stat.PList

stat.SEList

stat.

List stat.Resid

stat.sResid

stat.CookDist

stat.Leverage

Description

Adjusted coefficient of multiple determination

Standard deviation of the error

Durbin-Watson statistic; used to determine whether first-order auto correlation is present in the model

Regression degrees of freedom

Regression sum of squares

Regression mean square

Error degrees of freedom

Error sum of squares

Error mean square

{b0,b1,...} List of coefficients

List of t statistics, one for each coefficient in the bList

List P-values for each t statistic

List of standard errors for coefficients in bList y

List = b0+b1 · x1+ . . .

Residuals from the regression

Standardized residuals; obtained by dividing a residual by its standard deviation

Cook’s distance; measure of the influence of an observation based on the residual and leverage

Measure of how far the values of the independent variable are from their mean values

N

nCr() nCr(

Expr1

Expr2

)

⇒ expression

For integer

Expr1

and

Expr2

with

Expr1 | Expr2 | 0, nCr() is the number of combinations of Expr1 things taken Expr2 at a time. (This is also known as a binomial coefficient.) Both arguments can be integers or symbolic expressions.

nCr(

Expr ,

0 )

⇒

1 nCr(

Expr , negInteger )

⇒

0 nCr( Expr , posInteger )

⇒

Expr · ( Expr N

1 )...

(

Expr N posInteger

+1)/ posInteger

nCr(

Expr , nonInteger

)

⇒ expression

((

Expr N nonInteger

· nonInteger

!) nCr(

List1

List2

)

⇒ list

Returns a list of combinations based on the corresponding element pairs in the two lists. The arguments must be the same size list.

Catalog >

80 TI-Nspire™ CAS Reference Guide

nCr() nCr(

Matrix1

Matrix2

)

⇒ matrix

Returns a matrix of combinations based on the corresponding element pairs in the two matrices. The arguments must be the same size matrix.

nDerivative() nDerivative(

Expr1

Var=Value

[ ,

Order

] )

⇒ value nDerivative(

Expr1

Var

[ ,

Order

] ) |

Var=Value ⇒ value

Returns the numerical derivative calculated using auto differentiation methods.

When

Value

is specified, it overrides any prior variable assignment or any current “with” substitution for the variable.

Order

of the derivative must be 1 or 2 .

newList() newList( numElements )

⇒ list

Returns a list with a dimension of numElements . Each element is zero.

newMat() newMat( numRows

, numColumns

)

⇒ matrix

Returns a matrix of zeros with the dimension numRows by numColumns .

nfMax() nfMax(

Expr

Var

)

⇒ value nfMax(

Expr

Var

, lowBound

)

⇒ value nfMax(

Expr

Var

, lowBound , upBound

)

⇒ value nfMax(

Expr, Var

) | lowBound

Var

< upBound ⇒ value

Returns a candidate numerical value of variable Var where the local maximum of Expr occurs.

If you supply lowBound and upBound , the function looks between those values for the local maximum.

Note: See also fMax() and d() .

nfMin() nfMin(

Expr

Var

)

⇒ value nfMin(

Expr

Var

, lowBound

) nfMin(

Expr

Var

, lowBound

⇒ value

, upBound

)

⇒ value nfMin( Expr, Var ) | lowBound < Var < upBound

⇒ value

Returns a candidate numerical value of variable Var where the local minimum of Expr occurs.

If you supply lowBound and upBound , the function looks between those values for the local minimum.

Note: See also fMin() and d() .

Catalog >

TI-Nspire™ CAS Reference Guide 81

nInt() nInt(

Expr1, Var, Lower, Upper

)

⇒ expression

If the integrand Expr1 contains no variable other than Var , and if

Lower

and

Upper

are constants, positive ˆ , or negative ˆ , then nInt() returns an approximation of ‰ ( Expr1 , Var , Lower , Upper ) .

This approximation is a weighted average of some sample values of the integrand in the interval Lower < Var < Upper .

The goal is six significant digits. The adaptive algorithm terminates when it seems likely that the goal has been achieved, or when it seems unlikely that additional samples will yield a worthwhile improvement.

A warning is displayed (“Questionable accuracy”) when it seems that the goal has not been achieved.

Nest nInt() to do multiple numeric integration. Integration limits can depend on integration variables outside them.

Note: See also ‰ () , page 149.

nom() nom( effectiveRate,CpY

)

⇒ value

Financial function that converts the annual effective interest rate effectiveRate to a nominal rate, given CpY as the number of compounding periods per year.

effectiveRate must be a real number, and CpY must be a real number

> 0.

Note: See also eff() , page 40.

norm() norm(

Matrix

) norm(

Vector

)

⇒ expression

Returns the Frobenius norm.

Catalog >

82 TI-Nspire™ CAS Reference Guide

normalLine() normalLine(

Expr1

Var

Point

) normalLine(

Expr1

Var

Point

)

⇒ expression

Returns the normal line to the curve represented by

Expr1

at the point specified in Var = Point .

Make sure that the independent variable is not defined. For example,

If f1(x):=5 and x:=3, then normalLine( f1(x),x,2 ) returns “false.”

Catalog > normCdf() normCdf( lowBound

, upBound

[ , m

[ , s

]] )

⇒ number

if lowBound and upBound

are numbers,

list

if lowBound

and upBound

are lists

Computes the normal distribution probability between lowBound and upBound

for the specified m (default=0) and s (default=1).

For P(X {Å upBound

), set lowBound

= .ˆ .

normPdf() normPdf( XVal [ , m

[ , s

]] )

⇒ number if XVal is a number, list if

XVal is a list

Computes the probability density function for the normal distribution at a specified XVal value for the specified m and s .

not not

BooleanExpr ⇒ Boolean expression

Returns true, false, or a simplified form of the argument.

Catalog >

Catalog > not

Integer1 ⇒ integer

Returns the one’s complement of a real integer. Internally,

Integer1

is converted to a signed, 64-bit binary number. The value of each bit is flipped (0 becomes 1, and vice versa) for the one’s complement.

Results are displayed according to the Base mode.

In Hex base mode:

Important: Zero, not the letter O.

You can enter the integer in any number base. For a binary or hexadecimal entry, you must use the 0b or 0h prefix, respectively.

Without a prefix, the integer is treated as decimal (base 10).

If you enter a decimal integer that is too large for a signed, 64-bit binary form, a symmetric modulo operation is used to bring the value into the appropriate range. For more information, see 4

Base2 , page 14.

In Bin base mode:

To see the entire result, press

and then use

and

to move the cursor.

Note: A binary entry can have up to 64 digits (not counting the

0b prefix). A hexadecimal entry can have up to 16 digits.

TI-Nspire™ CAS Reference Guide 83

nPr() nPr(

Expr1

Expr2

)

⇒ expression

For integer

Expr1

and

Expr2

with

Expr1 | Expr2 | 0, nPr() is the number of permutations of Expr1 things taken Expr2 at a time. Both arguments can be integers or symbolic expressions.

nPr(

Expr

, 0)

⇒

1 nPr(

Expr

, negInteger

)

⇒

1/((

Expr

+1) · (

Expr

+2) ...

( expression N negInteger

)) nPr(

Expr

, posInteger

)

⇒ Expr · (

Expr N

1)...

(

Expr N posInteger

+1) nPr(

Expr

, nonInteger

)

⇒ Expr

! / (

Expr N nonInteger

nPr( List1 , List2 )

⇒ list

Returns a list of permutations based on the corresponding element pairs in the two lists. The arguments must be the same size list.

nPr(

Matrix1

Matrix2

)

⇒ matrix

Returns a matrix of permutations based on the corresponding element pairs in the two matrices. The arguments must be the same size matrix.

Catalog > npv() npv(

InterestRate

CFO

CFList

CFFreq

] )

Financial function that calculates net present value; the sum of the present values for the cash inflows and outflows. A positive result for npv indicates a profitable investment.

InterestRate is the rate by which to discount the cash flows (the cost of money) over one period.

CF0 is the initial cash flow at time 0; it must be a real number.

CFList is a list of cash flow amounts after the initial cash flow CF0 .

CFFreq

is a list in which each element specifies the frequency of occurrence for a grouped (consecutive) cash flow amount, which is the corresponding element of CFList . The default is 1; if you enter values, they must be positive integers < 10,000.

nSolve() nSolve(

Equation

Var

Guess

])

⇒ number or error_string nSolve(

Equation

Var

Guess

], lowBound

)

⇒ number or error_string nSolve(

Equation

Var

Guess

], lowBound

, upBound

)

⇒ number or error_string nSolve(

Equation

Var

Guess

]) | lowBound

Var

< upBound

⇒ number or error_string

Iteratively searches for one approximate real numeric solution to

Equation

for its one variable. Specify the variable as: variable

– or – variable = real number

For example, x is valid and so is x=3.

Catalog >

Note: If there are multiple solutions, you can use a guess to help find a particular solution.

84 TI-Nspire™ CAS Reference Guide

nSolve() nSolve() is often much faster than solve() or zeros() , particularly if the “|” operator is used to constrain the search to a small interval containing exactly one simple solution.

nSolve() attempts to determine either one point where the residual is zero or two relatively close points where the residual has opposite signs and the magnitude of the residual is not excessive. If it cannot achieve this using a modest number of sample points, it returns the string “no solution found.”

Note: See also cSolve() , cZeros() , solve() , and zeros() .

O

OneVar

OneVar [ 1, ]

[ , [

Freq

][ ,

Category

Include

]]

OneVar [ n

, ]

[

[ , …[ ,

X20

]]]

Calculates 1-variable statistics on up to 20 lists. A summary of results is stored in the stat.results

variable. (See page 119.)

All the lists must have equal dimension except for Include .

Category is a list of numeric category codes for the corresponding X values.

Include is a list of one or more of the category codes. Only those data items whose category code is included in this list are included in the calculation.

An empty (void) element in any of the lists X , Freq , or Category results in a void for the corresponding element of all those lists. An empty element in any of the lists X1 through X20 results in a void for the corresponding element of all those lists. For more information on empty elements, see page 159.

Output variable stat.

v stat.

G x stat.

G x

2 stat.sx

stat.

s x stat.n

stat.MinX

stat.Q

X stat.MedianX

stat.Q

X stat.MaxX

Description

Mean of x values

Sum of x values

Sum of x

values

Sample standard deviation of x

Population standard deviation of x

Number of data points

Minimum of x values

1st Quartile of x

Median of x

3rd Quartile of x

Maximum of x values

Catalog >

TI-Nspire™ CAS Reference Guide 85

Output variable stat.SSX

Description

Sum of squares of deviations from the mean of x or

BooleanExpr1

BooleanExpr2

⇒ Boolean expression

Returns true or false or a simplified form of the original entry.

Returns true if either or both expressions simplify to true. Returns false only if both expressions evaluate to false.

Note: See xor .

Note for entering the example: In the Calculator application on the handheld, you can enter multi-line definitions by pressing

@ instead of

at the end of each line. On the computer keyboard, hold down Alt and press Enter .

Catalog >

Integer1

Integer2 ⇒ integer

You can enter the integers in any number base. For a binary or hexadecimal entry, you must use the 0b or 0h prefix, respectively.

Without a prefix, integers are treated as decimal (base 10).

In Hex base mode:

Compares two real integers bit-by-bit using an or operation.

Internally, both integers are converted to signed, 64-bit binary numbers. When corresponding bits are compared, the result is 1 if either bit is 1; the result is 0 only if both bits are 0. The returned value represents the bit results, and is displayed according to the Base mode.

Important: Zero, not the letter O.

In Bin base mode:

Note: A binary entry can have up to 64 digits (not counting the

0b prefix). A hexadecimal entry can have up to 16 digits.

If you enter a decimal integer that is too large for a signed, 64-bit binary form, a symmetric modulo operation is used to bring the value into the appropriate range. For more information, see 4

Base2 , page 14.

Note: See xor .

ord() ord(

String

) ord(

List1

)

⇒ integer

⇒ list

Returns the numeric code of the first character in character string

String

, or a list of the first characters of each list element.

Catalog >

86 TI-Nspire™ CAS Reference Guide

P

P 4 Rx()

Rx( rExpr

, q Expr

)

⇒ expression

Rx( rList

, q List

)

⇒ list

Rx( rMatrix

, q Matrix

)

⇒ matrix

Returns the equivalent x-coordinate of the

(r, q ) pair.

Note: The q argument is interpreted as either a degree, gradian or radian angle, according to the current angle mode. If the argument is an expression, you can use setting temporarily.

¡ ,

or R to override the angle mode

Note: You can insert this function from the computer keyboard by typing P@>Rx( ...

) .

In Radian angle mode:

P 4 Ry()

Ry( rExpr

, q Expr

)

⇒ expression

Ry( rList

, q List

)

Ry( rMatrix

, q

⇒ list

Matrix

)

⇒ matrix

Returns the equivalent y-coordinate of the (r, q ) pair.

Note: The q argument is interpreted as either a degree, radian or gradian angle, according to the current angle mode. If the argument is an expression, you can use setting temporarily.

¡ ,

or R to override the angle mode

Note: You can insert this function from the computer keyboard by typing P@>Ry( ...

) .

In Radian angle mode:

Catalog >

PassErr

Catalog >

PassErr

Passes an error to the next level.

If system variable errCode is zero, PassErr does not do anything.

The Else clause of the Try...Else...EndTry

error handlers, the error dialog box will be displayed as normal.

For an example of PassErr , See Example 2 under the Try command, page 129 .

Note: See also ClrErr , page 19 , and Try , page 129.

Note for entering the example: In the Calculator application on the handheld, you can enter multi-line definitions by pressing

@ instead of

at the end of each line. On the computer keyboard, hold down Alt and press Enter .

piecewise() piecewise(

Expr1

[ ,

Cond1

[ ,

Expr2

[ ,

Cond2

[ , … ]]]] )

Returns definitions for a piecewise function in the form of a list. You can also create piecewise definitions by using a template.

Note: See also Piecewise template , page 2.

Catalog >

TI-Nspire™ CAS Reference Guide 87

poissCdf() poissCdf( l

, lowBound

, upBound

)

⇒ number

if lowBound

and upBound

are numbers,

list

if lowBound

and upBound

are lists poissCdf( l

, upBound

) for P(0

{

{ upBound

) upBound

is a number, list if upBound

is a list

⇒ number

Computes a cumulative probability for the discrete Poisson distribution with specified mean l .

For P(X { upBound ), set lowBound =0 poissPdf() poissPdf( l

XVal

)

⇒ number

XVal

is a number,

list

XVal

is a list

Computes a probability for the discrete Poisson distribution with the specified mean l .

4 Polar

Vector 4

Polar

Note: You can insert this operator from the computer keyboard by typing @>Polar .

Displays vector

in polar form [r ±q ]. The vector must be of dimension 2 and can be a row or a column.

Note:

4 Polar is a display-format instruction, not a conversion function. You can use it only at the end of an entry line, and it does not update ans

Note: See also 4 Rect , page 98.

complexValue 4

Polar

Displays complexVector

in polar form.

• Degree angle mode returns (r ±q ).

• Radian angle mode returns re i q

complexValue can have any complex form. However, an re i q

entry causes an error in Degree angle mode.

Note: You must use the parentheses for an (r ±q ) polar entry.

In Radian angle mode:

In Gradian angle mode:

In Degree angle mode:

Catalog >

88 TI-Nspire™ CAS Reference Guide

polyCoeffs() polyCoeffs(

Poly

Var

] )

⇒ list

Returns a list of the coefficients of polynomial Poly with respect to variable

Var

Poly must be a polynomial expression in Var . We recommend that you do not omit

Var

unless

Poly

is an expression in a single variable.

Catalog >

Expands the polynomial and selects x

for the omitted

Var

polyDegree() polyDegree(

Poly

Var

] )

⇒ value

Returns the degree of polynomial expression Poly with respect to variable Var . If you omit Var , the polyDegree() function selects a default from the variables contained in the polynomial Poly .

Poly must be a polynomial expression in Var . We recommend that you do not omit Var unless Poly is an expression in a single variable.

Constant polynomials

Catalog > polyEval() polyEval(

List1

Expr1

) polyEval(

List1

List2

)

⇒ expression

Interprets the first argument as the coefficient of a descending-degree polynomial, and returns the polynomial evaluated for the value of the second argument.

The degree can be extracted even though the coefficients cannot. This is because the degree can be extracted without expanding the polynomial.

Catalog >

TI-Nspire™ CAS Reference Guide 89

polyGcd() polyGcd(

Expr1

Expr2

)

⇒ expression

Returns greatest common divisor of the two arguments.

Expr1

and

Expr2

must be polynomial expressions.

List, matrix, and Boolean arguments are not allowed.

polyQuotient() polyQuotient(

Poly1

Poly2

Var

] )

⇒ expression

Returns the quotient of polynomial Poly1 divided by polynomial

Poly2 with respect to the specified variable Var .

Poly1 and Poly2 must be polynomial expressions in Var . We recommend that you do not omit Var unless Poly1 and Poly2 are expressions in the same single variable.

Catalog >

Catalog > polyRemainder() polyRemainder( Poly1 , Poly2 [, Var ] )

⇒ expression

Returns the remainder of polynomial Poly1 divided by polynomial

Poly2 with respect to the specified variable Var .

Poly1 and Poly2 must be polynomial expressions in Var . We recommend that you do not omit Var unless Poly1 and Poly2 are expressions in the same single variable.

Catalog >

90 TI-Nspire™ CAS Reference Guide

polyRoots() polyRoots(

Poly

Var

)

⇒ list polyRoots(

ListOfCoeffs

)

⇒ list

The first syntax, polyRoots(

Poly

Var

) , returns a list of real roots of polynomial Poly with respect to variable Var . If no real roots exist, returns an empty list: { }.

Poly must be a polynomial in one variable.

The second syntax, polyRoots(

ListOfCoeffs

) , returns a list of real roots for the coefficients in ListOfCoeffs.

Note: See also cPolyRoots() , page 26.

Catalog >

PowerReg

[ ,

Freq

] [ ,

Category

Include

]]

Computes the power regression y = (a · (x) b

) on lists

and

with frequency Freq . A summary of results is stored in the stat.results

variable. (See page 119.)

All the lists must have equal dimension except for Include .

and

are lists of independent and dependent variables.

Freq is an optional list of frequency values. Each element in Freq specifies the frequency of occurrence for each corresponding

and

Y data point. The default value is 1. All elements must be integers | 0.

Category is a list of category codes for the corresponding X and Y data.

Include is a list of one or more of the category codes. Only those data items whose category code is included in this list are included in the calculation.

For information on the effect of empty elements in a list, see “Empty

(void) elements” on page 159.

Catalog >

Output variable stat.RegEqn

stat.a, stat.b

stat.r

2 stat.r

stat.Resid

stat.ResidTrans

stat.XReg

stat.YReg

stat.FreqReg

Description

Regression equation: a · (x) b

Regression coefficients

Coefficient of linear determination for transformed data

Correlation coefficient for transformed data (ln(x), ln(y))

Residuals associated with the power model

Residuals associated with linear fit of transformed data

List of data points in the modified X List actually used in the regression based on restrictions of Freq ,

Category List , and Include Categories

List of data points in the modified Y List actually used in the regression based on restrictions of Freq ,

Category List , and Include Categories

List of frequencies corresponding to stat.XReg

and stat.YReg

TI-Nspire™ CAS Reference Guide 91

Prgm

Catalog >

Prgm

Block

EndPrgm

Template for creating a user-defined program. Must be used with the

Define , Define LibPub , or Define LibPriv command.

Block can be a single statement, a series of statements separated with the “:” character, or a series of statements on separate lines.

Note for entering the example: In the Calculator application on the handheld, you can enter multi-line definitions by pressing

@ instead of

at the end of each line. On the computer keyboard, hold down Alt and press Enter .

Calculate GCD and display intermediate results.

prodSeq()

Product (PI) product() product( List [

, Start [

, End ]] )

⇒ expression

Returns the product of the elements contained in

List

Start

and

End are optional. They specify a range of elements.

product(

Matrix1

[

, Start

[

, End

]] )

⇒ matrix

Returns a row vector containing the products of the elements in the columns of Matrix1 . Start and end are optional. They specify a range of rows.

Empty (void) elements are ignored. For more information on empty elements, see page 159.

92 TI-Nspire™ CAS Reference Guide

See

( ) , page 150.

See

( ) , page 150.

Catalog >

propFrac() propFrac(

Expr1

[ ,

Var

] )

⇒ expression propFrac( rational_number ) returns rational_number as the sum of an integer and a fraction having the same sign and a greater denominator magnitude than numerator magnitude.

propFrac( rational_expression , Var ) returns the sum of proper ratios and a polynomial with respect to

Var

. The degree of

Var

in the denominator exceeds the degree of Var in the numerator in each proper ratio. Similar powers of

Var

are collected. The terms and their factors are sorted with Var as the main variable.

Var

is omitted, a proper fraction expansion is done with respect to the most main variable. The coefficients of the polynomial part are then made proper with respect to their most main variable first and so on.

For rational expressions, propFrac() is a faster but less extreme alternative to expand() .

You can use the propFrac() function to represent mixed fractions and demonstrate addition and subtraction of mixed fractions.

Catalog >

Q

Catalog >

Matrix

, qMatrix

, rMatrix

[ ,

Tol

]

Calculates the Householder QR factorization of a real or complex matrix. The resulting Q and R matrices are stored to the specified

Matrix . The Q matrix is unitary. The R matrix is upper triangular.

The floating-point number (9.) in m1 causes results to be calculated in floating-point form.

• If you use

/·

or set the Auto or Approximate mode to Approximate, computations are done using floatingpoint arithmetic.

• If Tol is omitted or not used, the default tolerance is calculated as:

5E L 14 · max(dim( Matrix )) · rowNorm( Matrix )

TI-Nspire™ CAS Reference Guide 93

The QR factorization is computed numerically using Householder transformations. The symbolic solution is computed using Gram-

Schmidt. The columns in qMatName

are the orthonormal basis vectors that span the space defined by matrix .

Catalog >

QuadReg

[ ,

Freq

] [ ,

Category

Include

]]

Computes the quadratic polynomial regression y = a the stat.results

variable. (See page 119.)

· x

+b · x+c on lists

and

with frequency

Freq

. A summary of results is stored in

All the lists must have equal dimension except for

Include

X and Y are lists of independent and dependent variables.

Category

is a list of category codes for the corresponding

and

Y data.

Include

is a list of one or more of the category codes. Only those data items whose category code is included in this list are included in the calculation.

For information on the effect of empty elements in a list, see “Empty

(void) elements” on page 159.

Catalog >

Output variable stat.RegEqn

stat.a, stat.b, stat.c

stat.R

2 stat.Resid

stat.XReg

stat.YReg

stat.FreqReg

Description

Regression equation: a · x

+b · x+c

Regression coefficients

Coefficient of determination

Residuals from the regression

List of data points in the modified X List actually used in the regression based on restrictions of Freq ,

Category List , and Include Categories

List of data points in the modified Y List actually used in the regression based on restrictions of Freq ,

Category List , and Include Categories

List of frequencies corresponding to stat.XReg

and stat.YReg

94 TI-Nspire™ CAS Reference Guide

QuartReg

[ ,

Freq

] [ ,

Category

Include

]]

Computes the quartic polynomial regression y = a · x

+b · x

+c · x

+d · x+e on lists X and Y with frequency Freq .

A summary of results is stored in the stat.results

variable. (See page

119.)

All the lists must have equal dimension except for Include .

X and Y are lists of independent and dependent variables.

Category is a list of category codes for the corresponding X and Y data.

Include is a list of one or more of the category codes. Only those data items whose category code is included in this list are included in the calculation.

For information on the effect of empty elements in a list, see “Empty

(void) elements” on page 159.

Catalog >

Output variable stat.RegEqn

stat.a, stat.b, stat.c, stat.d, stat.e

stat.R

2 stat.Resid

stat.XReg

stat.YReg

stat.FreqReg

Description

Regression equation: a · x

+b · x

+c · x

+d · x+e

Regression coefficients

Coefficient of determination

Residuals from the regression

List of data points in the modified X List actually used in the regression based on restrictions of Freq ,

Category List , and Include Categories

List of data points in the modified Y List actually used in the regression based on restrictions of Freq ,

Category List , and Include Categories

List of frequencies corresponding to stat.XReg

and stat.YReg

TI-Nspire™ CAS Reference Guide 95

R

R 4 P q ()

P q

( xExpr

, yExpr

)

⇒ expression

P q

( xList

, yList

)

⇒ list

P q

( xMatrix

, yMatrix

)

⇒ matrix

Returns the equivalent

( x,y

) pair arguments.

q -coordinate of the

Note: The result is returned as a degree, gradian or radian angle, according to the current angle mode setting.

Note: You can insert this function from the computer keyboard by typing R@>Ptheta( ...

) .

In Degree angle mode:

In Gradian angle mode:

In Radian angle mode:

Catalog >

R 4 Pr()

Pr ( xExpr

, yExpr

)

⇒ expression

Pr ( xList , yList )

⇒ list

Pr ( xMatrix , yMatrix )

⇒ matrix

Returns the equivalent r-coordinate of the ( x,y ) pair arguments.

Note: You can insert this function from the computer keyboard by typing R@>Pr( ...

) .

In Radian angle mode:

Catalog >

4 Rad

Expr1 4

Rad

⇒ expression

Converts the argument to radian angle measure.

Note: You can insert this operator from the computer keyboard by typing @>Rad .

In Degree angle mode:

In Gradian angle mode: rand() rand()

⇒ expression rand(

#Trials

)

⇒ list rand() returns a random value between 0 and 1.

rand( #Trials ) returns a list containing #Trials random values between 0 and 1.

96 TI-Nspire™ CAS Reference Guide

Catalog >

Sets the random-number seed.

Catalog >

randBin() randBin( n , p

)

⇒ expression randBin( n , p , #Trials

)

⇒ list randBin( n , p

) returns a random real number from a specified

Binomial distribution.

randBin( n , p , #Trials

) returns a list containing #Trials random real numbers from a specified Binomial distribution.

randInt() randInt( lowBound

, upBound

)

⇒ expression randInt( lowBound

, upBound

#Trials

)

⇒ list randInt( lowBound

, upBound

) returns a random integer within the range specified by lowBound and upBound integer bounds.

randInt( lowBound

, upBound

#Trials

) returns a list containing

#Trials random integers within the specified range.

randMat() randMat( numRows

, numColumns

)

⇒ matrix

Returns a matrix of integers between -9 and 9 of the specified dimension.

Both arguments must simplify to integers.

Catalog >

Note: The values in this matrix will change each time you press

randNorm() randNorm( m

, s

)

⇒ expression randNorm( m

, s

#Trials

)

⇒ list randNorm( m

, s

) returns a decimal number from the specified normal distribution. It could be any real number but will be heavily concentrated in the interval [ mN 3 · s , m +3 · s ].

randNorm( m

, s

#Trials

) returns a list containing #Trials decimal numbers from the specified normal distribution.

randPoly() randPoly(

Var

Order

)

⇒ expression

Returns a polynomial in Var of the specified Order . The coefficients are random integers in the range L 9 through 9. The leading coefficient will not be zero.

Order must be 0–99.

randSamp() randSamp(

List

#Trials

[ , noRepl

] )

⇒ list

Returns a list containing a random sample of #Trials trials from List with an option for sample replacement ( noRepl =0), or no sample replacement ( noRepl =1). The default is with sample replacement.

Catalog >

TI-Nspire™ CAS Reference Guide 97

RandSeed

Number

= 0, sets the seeds to the factory defaults for the randomnumber generator. If Number ƒ 0, it is used to generate two seeds, which are stored in system variables seed1 and seed2.

real() real(

Expr1

)

⇒ expression

Returns the real part of the argument.

Note: All undefined variables are treated as real variables. See also imag() , page 58.

real(

List1

)

⇒ list

Returns the real parts of all elements.

real(

Matrix1

)

⇒ matrix

Returns the real parts of all elements.

Catalog >

4 Rect

Vector 4

Rect

Note: You can insert this operator from the computer keyboard by typing @>Rect .

Displays Vector in rectangular form [x, y, z]. The vector must be of dimension 2 or 3 and can be a row or a column.

Note:

4 Rect is a display-format instruction, not a conversion function. You can use it only at the end of an entry line, and it does not update ans .

Note: See also 4 Polar , page 88.

complexValue 4

Rect

Displays complexValue in rectangular form a+bi. The complexValue can have any complex form. However, an re i q

entry causes an error in

Degree angle mode.

In Radian angle mode:

Note: You must use parentheses for an (r ±q ) polar entry.

In Gradian angle mode:

Catalog >

In Degree angle mode:

Note: To type ± , select it from the symbol list in the Catalog.

98 TI-Nspire™ CAS Reference Guide

ref() ref(

Matrix1

[ ,

Tol

] )

⇒ matrix

Returns the row echelon form of Matrix1 .

• If you use

/·

or set the Auto or Approximate mode to Approximate, computations are done using floatingpoint arithmetic.

• If Tol is omitted or not used, the default tolerance is calculated as:

5E L 14 · max(dim( Matrix1 )) · rowNorm( Matrix1 )

Avoid undefined elements in Matrix1 . They can lead to unexpected results.

For example, if a is undefined in the following expression, a warning message appears and the result is shown as:

The warning appears because the generalized element 1/ a

would not be valid for a =0.

You can avoid this by storing a value to a

beforehand or by using the

“|” substitution mechanism, as shown in the following example.

Note: See also rref() , page 104.

remain() remain(

Expr1

Expr2

) remain(

List1

List2

)

⇒ expression

⇒ list remain(

Matrix1

Matrix2

)

⇒ matrix

Returns the remainder of the first argument with respect to the second argument as defined by the identities: remain(x,0)  x remain(x,y)  x N y · iPart(x/y)

As a consequence, note that remain( N x,y )  N remain( x,y ) . The result is either zero or it has the same sign as the first argument.

Note: See also mod() , page 78.

Catalog >

TI-Nspire™ CAS Reference Guide 99

Request

Catalog >

Request promptString

var

[ ,

DispFlag

[ , statusVar ]]

Request promptString

func

( arg1

...argn

)

[ ,

DispFlag

[ , statusVar ]]

Programming command: Pauses the program and displays a dialog box containing the message promptString

and an input box for the user’s response.

When the user types a response and clicks OK , the contents of the input box are assigned to variable var .

Define a program:

Define request_demo()=Prgm

Request “Radius: ”,r

Disp “Area = “,pi*r

EndPrgm

Run the program and type a response: request_demo()

If the user clicks Cancel , the program proceeds without accepting any input. The program uses the previous value of var if var was already defined.

The optional DispFlag argument can be any expression.

• If

DispFlag

is omitted or evaluates to 1 , the prompt message and user’s response are displayed in the Calculator history.

• If

DispFlag

evaluates to 0 , the prompt and response are not displayed in the history.

Result after selecting

Radius: 6/2

Area= 28.2743

OK :

The optional statusVar argument gives the program a way to determine how the user dismissed the dialog box. Note that statusVar requires the DispFlag argument.

Define a program:

Define polynomial()=Prgm

Request "Enter a polynomial in x:",p(x)

Disp "Real roots are:",polyRoots(p(x),x)

EndPrgm • If the user clicked OK or pressed Enter or Ctrl+Enter , variable statusVar is set to a value of 1 .

• Otherwise, variable statusVar is set to a value of 0 .

Run the program and type a response: polynomial()

The func () argument allows a program to store the user’s response as a function definition. This syntax operates as if the user executed the command:

Define func

( arg1

, ...

argn

) = user’s response

The program can then use the defined function func (). The promptString

should guide the user to enter an appropriate user’s response that completes the function definition.

Note: You can use the Request program but not within a function.

command within a user-defined

Result after selecting OK :

Enter a polynomial in x: x^3+3x+1

Real roots are: {-0.322185}

To stop a program that contains a Request command inside an infinite loop:

• Windows®: Hold down the F12 key and press Enter repeatedly.

• Macintosh®: Hold down the F5 key and press Enter repeatedly.

• Handheld: Hold down the c

key and press

· repeatedly.

Note: See also RequestStr , page 101.

100 TI-Nspire™ CAS Reference Guide

RequestStr

Catalog >

RequestStr promptString

var

[ ,

DispFlag

]

Programming command: Operates identically to the first syntax of the

Request command, except that the user’s response is always interpreted as a string. By contrast, the Request command interprets the response as an expression unless the user encloses it in quotation marks (““).

Define a program:

Define requestStr_demo()=Prgm

RequestStr “Your name:”,name,0

Disp “Response has “,dim(name),” characters.”

EndPrgm

Run the program and type a response: requestStr_demo()

Note: You can use the RequestStr command within a userdefined program but not within a function.

To stop a program that contains a RequestStr command inside an infinite loop:

• Windows®: Hold down the F12 key and press Enter repeatedly.

• Macintosh®: Hold down the F5 key and press Enter repeatedly.

• Handheld: Hold down the c

key and press

· repeatedly.

Note: See also Request , page 100.

Result after selecting OK (Note that the DispFlag argument of

0 omits the prompt and response from the history): requestStr_demo()

Response has 5 characters.

Return

Return [

Expr

]

Returns

Expr

as the result of the function. Use within a

Func ...

EndFunc block.

Note: Use Return without an argument within a Prgm ...

EndPrgm block to exit a program.

Note for entering the example: In the Calculator application on the handheld, you can enter multi-line definitions by pressing

@ instead of

at the end of each line. On the computer keyboard, hold down Alt and press Enter .

Catalog > right() right(

List1

[ ,

Num

] )

⇒ list

Returns the rightmost Num elements contained in List1 .

If you omit Num , returns all of List1 .

right( sourceString

[

, Num

] )

⇒ string

Returns the rightmost Num characters contained in character string sourceString .

If you omit Num , returns all of sourceString .

right(

Comparison

)

⇒ expression

Returns the right side of an equation or inequality.

Catalog >

TI-Nspire™ CAS Reference Guide 101

rk23()

Catalog > rk23( Expr , Var , depVar , { Var0 , VarMax }, depVar0 , VarStep

[, diftol ] )

⇒ matrix rk23( SystemOfExpr , Var , ListOfDepVars , { Var0 , VarMax } ,

ListOfDepVars0 , VarStep [ , diftol ] )

⇒ matrix rk23( ListOfExpr , Var , ListOfDepVars , { Var0 , VarMax } ,

ListOfDepVars0 , VarStep [ , diftol ] )

⇒ matrix d

Uses the Runge-Kutta method to solve the system depVar d Var

= Expr ( Var , depVar ) with depVar ( Var0 )= depVar0 on the interval [ Var0 , VarMax ]. Returns a matrix whose first row defines the Var output values as defined by

VarStep . The second row defines the value of the first solution component at the corresponding Var values, and so on.

Differential equation: y'=0.001*y*(100-y) and y(0)=10

To see the entire result, press move the cursor.

and then use

and

Same equation with diftol set to 1.

E •6

Expr is the right hand side that defines the ordinary differential equation (ODE).

SystemOfExpr is a system of right-hand sides that define the system of ODEs (corresponds to order of dependent variables in

ListOfDepVars ).

ListOfExpr is a list of right-hand sides that define the system of ODEs

(corresponds to order of dependent variables in ListOfDepVars ).

Compare above result with CAS exact solution obtained using deSolve() and seqGen():

Var is the independent variable.

ListOfDepVars is a list of dependent variables.

{ Var0 , VarMax } is a two-element list that tells the function to integrate from Var0 to VarMax .

ListOfDepVars0 is a list of initial values for dependent variables.

If VarStep evaluates to a nonzero number: sign( VarStep ) = sign( VarMax Var0 ) and solutions are returned at Var0 +i* VarStep for all i=0,1,2,… such that Var0 +i* VarStep is in [ var0 , VarMax ] (may not get a solution value at VarMax ).

if VarStep evaluates to zero, solutions are returned at the "Runge-

Kutta" Var values.

diftol is the error tolerance (defaults to 0.001).

System of equations: with y1 (0)=2 and y2 (0)=5 root() root( Expr )

⇒ root root(

Expr1

Expr2

)

⇒ root root( Expr ) returns the square root of Expr .

root(

Expr1

Expr2

) returns the Expr2 root of Expr1 . Expr1 can be a real or complex floating point constant, an integer or complex rational constant, or a general symbolic expression.

Note: See also Nth root template , page 1.

102 TI-Nspire™ CAS Reference Guide

Catalog >

rotate()

Catalog > rotate(

Integer1

[ ,

#ofRotations

] )

⇒ integer

Rotates the bits in a binary integer. You can enter Integer1 in any number base; it is converted automatically to a signed, 64-bit binary form. If the magnitude of Integer1 is too large for this form, a symmetric modulo operation brings it within the range. For more information, see 4

Base2 , page 14.

In Bin base mode:

If #ofRotations is positive, the rotation is to the left. If #ofRotations is negative, the rotation is to the right. The default is L 1 (rotate right one bit).

To see the entire result, press

and then use

and

to move the cursor.

In Hex base mode:

For example, in a right rotation:

Each bit rotates right.

0b00000000000001111010110000110101

Rightmost bit rotates to leftmost.

produces:

0b10000000000000111101011000011010

Important: To enter a binary or hexadecimal number, always use the 0b or 0h prefix (zero, not the letter O).

The result is displayed according to the Base mode.

rotate(

List1

[ ,

#ofRotations

] )

⇒ list

Returns a copy of List1 rotated right or left by #of Rotations elements. Does not alter List1 .

If #ofRotations is positive, the rotation is to the left. If #of Rotations is negative, the rotation is to the right. The default is L 1 (rotate right one element).

rotate(

String1

[ ,

#ofRotations

] )

⇒ string

Returns a copy of String1 rotated right or left by #ofRotations characters. Does not alter String1 .

If #ofRotations is positive, the rotation is to the left. If #ofRotations is negative, the rotation is to the right. The default is L 1 (rotate right one character).

In Dec base mode: round() round(

Expr1

[ , digits

] )

⇒ expression

Returns the argument rounded to the specified number of digits after the decimal point.

digits must be an integer in the range 0–12. If digits is not included, returns the argument rounded to 12 significant digits.

Note: Display digits mode may affect how this is displayed.

round(

List1

[ , digits

] )

⇒ list

Returns a list of the elements rounded to the specified number of digits.

round(

Matrix1

[ , digits

] )

⇒ matrix

Returns a matrix of the elements rounded to the specified number of digits.

Catalog >

TI-Nspire™ CAS Reference Guide 103

rowAdd() rowAdd(

Matrix1

, rIndex1

, rIndex2

)

⇒ matrix

Returns a copy of Matrix1 with row rIndex2 replaced by the sum of rows rIndex1

and rIndex2

rowDim() rowDim( Matrix )

⇒ expression

Returns the number of rows in Matrix .

Note: See also colDim() , page 19.

rowNorm() rowNorm(

Matrix

)

⇒ expression

Returns the maximum of the sums of the absolute values of the elements in the rows in Matrix .

Note: All matrix elements must simplify to numbers. See also colNorm() , page 19.

rowSwap() rowSwap(

Matrix1

, rIndex1

, rIndex2

)

⇒ matrix

Returns Matrix1 with rows rIndex1 and rIndex2 exchanged.

rref() rref(

Matrix1

[ ,

Tol

] )

⇒ matrix

Returns the reduced row echelon form of Matrix1 .

Catalog >

104 TI-Nspire™ CAS Reference Guide

rref()

• If you use

/·

or set the Auto or Approximate mode to Approximate, computations are done using floatingpoint arithmetic.

• If Tol is omitted or not used, the default tolerance is calculated as:

5E L 14 · max(dim( Matrix1 )) · rowNorm( Matrix1 )

Note: See also ref() , page 99.

S

sec() sec(

Expr1

) sec(

List1

)

⇒ expression

⇒ list

Returns the secant of Expr1 or returns a list containing the secants of all elements in

List1

Note: The argument is interpreted as a degree, gradian or radian angle, according to the current angle mode setting. You can use ¡ , or R to override the angle mode temporarily.

In Degree angle mode: sec / () sec

(

Expr1

)

⇒ expression sec

(

List1

)

⇒ list

Returns the angle whose secant is

Expr1

or returns a list containing the inverse secants of each element of List1 .

Note: The result is returned as a degree, gradian or radian angle, according to the current angle mode setting.

Note: You can insert this function from the keyboard by typing arcsec( ...

) .

In Degree angle mode:

In Gradian angle mode:

In Radian angle mode:

Catalog >

key

key sech() sech(

Expr1

) sech(

List1

)

⇒ expression

⇒ list

Returns the hyperbolic secant of Expr1 or returns a list containing the hyperbolic secants of the List1 elements.

Catalog >

TI-Nspire™ CAS Reference Guide 105

sech / () sech

(

Expr1

)

⇒ expression sech

(

List1

)

⇒ list

Returns the inverse hyperbolic secant of Expr1 or returns a list containing the inverse hyperbolic secants of each element of List1 .

Note: You can insert this function from the keyboard by typing arcsech( ...

) .

Catalog >

In Radian angle and Rectangular complex mode: seq() seq(

Expr

Var

Low

High

[ ,

Step

] )

⇒ list

Increments Var from Low through High by an increment of Step , evaluates Expr , and returns the results as a list. The original contents of Var are still there after seq() is completed.

The default value for Step = 1.

Catalog >

Press Ctrl + Enter

/·

(Macintosh®: “ + Enter ) to evaluate:

106 TI-Nspire™ CAS Reference Guide

seqGen()

Catalog > seqGen( Expr , Var , depVar , { Var0 , VarMax }[ , ListOfInitTerms

[ , VarStep [ , CeilingValue ]]] )

⇒ list

Generates a list of terms for sequence depVar ( Var )= Expr as follows:

Increments independent variable Var from Var0 through VarMax by

VarStep , evaluates depVar ( Var ) for corresponding values of Var using the Expr formula and ListOfInitTerms , and returns the results as a list.

seqGen( ListOrSystemOfExpr , Var , ListOfDepVars , { Var0 , VarMax }

[ , MatrixOfInitTerms [ , VarStep [ , CeilingValue ]]] )

⇒ matrix

Generate the first 5 terms of the sequence u ( n ) = u ( n -1) with u (1)= 2 and VarStep = 1 .

/2,

Generates a matrix of terms for a system (or list) of sequences

ListOfDepVars

(

Var

ListOrSystemOfExpr

as follows: Increments independent variable Var from Var0 through VarMax by VarStep , evaluates

ListOfDepVars

(

Var

) for corresponding values of

Var

using

ListOrSystemOfExpr formula and MatrixOfInitTerms , and returns the results as a matrix.

The original contents of Var are unchanged after seqGen() is completed.

The default value for VarStep = 1 .

Example in which Var0=2:

Example in which initial term is symbolic:

System of two sequences:

Note: The Void (_) in the initial term matrix above is used to indicate that the initial term for u1(n) is calculated using the explicit sequence formula u1(n)=1/n.

seqn()

Catalog > seqn( Expr ( u , n [ , ListOfInitTerms [ , nMax

[ , CeilingValue ]]] )

⇒ list

Generates a list of terms for a sequence u

( n

Expr

( u

, n

) as follows:

Increments n from 1 through nMax by 1, evaluates u ( n ) for corresponding values of n

using the

Expr

( u

, n

) formula and

ListOfInitTerms , and returns the results as a list.

seqn( Expr ( n [ , nMax [ , CeilingValue ]] )

⇒ list

Generates a list of terms for a non-recursive sequence u

( n

Expr

( n

) as follows: Increments n from 1 through nMax by 1, evaluates u ( n ) for corresponding values of n

using the

Expr

( n

) formula, and returns the results as a list.

If nMax

is missing, nMax

is set to 2500

If nMax =0, nMax is set to 2500

Note: seqn() calls seqGen( ) with n0

= 1 and nstep

= 1

Generate the first 6 terms of the sequence u ( n ) = u ( n -1)/2, with u (1)= 2 .

TI-Nspire™ CAS Reference Guide 107

series() series(

Expr1

Var

Order

[ ,

Point

] )

⇒ expression series(

Expr1

Var

Order

[ ,

Point

] ) |

Var

Point series(

Expr1

Var

Order

[ ,

Point

] ) |

Var

Point

⇒ expression

Returns a generalized truncated power series representation of Expr1 expanded about Point through degree Order . Order can be any rational number. The resulting powers of ( Var N Point ) can include negative and/or fractional exponents. The coefficients of these powers can include logarithms of ( Var N Point ) and other functions of Var that are dominated by all powers of ( Var N Point ) having the same exponent sign.

Point defaults to 0. Point can be ˆ or Nˆ , in which cases the expansion is through degree Order in 1/( Var N Point ).

series(...) returns “ series(...) ” if it is unable to determine such a representation, such as for essential singularities such as sin( 1/ z ) at z

=0, e

N 1/z

at z=0, or e z

at z = ˆ or Nˆ .

If the series or one of its derivatives has a jump discontinuity at

Point

, the result is likely to contain sub-expressions of the form sign(…) or abs(…) for a real expansion variable or (-1) floor(…angle(…)…) for a complex expansion variable, which is one ending with “_”. If you intend to use the series only for values on one side of Point , then append the appropriate one of “|

Var

Point

”, “|

Var

Point

”, “|

“ Var | Point ”, or “ Var { Point ” to obtain a simpler result.

series() can provide symbolic approximations to indefinite integrals and definite integrals for which symbolic solutions otherwise can't be obtained.

series() distributes over 1st-argument lists and matrices.

series() is a generalized version of taylor() .

As illustrated by the last example to the right, the display routines downstream of the result produced by series(...) might rearrange terms so that the dominant term is not the leftmost one.

Note: See also dominantTerm() , page 39.

Catalog >

108 TI-Nspire™ CAS Reference Guide

setMode()

Catalog > setMode( modeNameInteger

, settingInteger

) setMode( list

)

⇒ integer list

⇒ integer

Valid only within a function or program.

setMode( modeNameInteger

, settingInteger

) temporarily sets mode modeNameInteger to the new setting settingInteger , and returns an integer corresponding to the original setting of that mode. The change is limited to the duration of the program/ function’s execution.

modeNameInteger specifies which mode you want to set. It must be one of the mode integers from the table below.

Display approximate value of p using the default setting for Display

Digits, and then display p with a setting of Fix2. Check to see that the default is restored after the program executes.

settingInteger specifies the new setting for the mode. It must be one of the setting integers listed below for the specific mode you are setting.

setMode( list

) lets you change multiple settings. list

contains pairs of mode integers and setting integers. setMode( list ) returns a similar list whose integer pairs represent the original modes and settings.

If you have saved all mode settings with getMode(0) & var you can use setMode( var

) to restore those settings until the

, function or program exits. See getMode() , page 54.

Note: The current mode settings are passed to called subroutines. If any subroutine changes a mode setting, the mode change will be lost when control returns to the calling routine.

Note for entering the example: In the Calculator application on the handheld, you can enter multi-line definitions by pressing

instead of

at the end of each line. On the computer keyboard, hold down Alt and press Enter .

Mode

Name

Display Digits

Angle

Exponential Format

Real or Complex

Auto or Approx.

Vector Format

Base

Unit system

Mode

Integer

Setting Integers

1 =Float, 2 =Float1, 3 =Float2, 4 =Float3, 5 =Float4, 6 =Float5, 7 =Float6, 8 =Float7,

9 =Float8, 10 =Float9, 11 =Float10, 12 =Float11, 13 =Float12, 14 =Fix0, 15 =Fix1,

16 =Fix2, 17 =Fix3, 18 =Fix4, 19 =Fix5, 20 =Fix6, 21 =Fix7, 22 =Fix8, 23 =Fix9, 24 =Fix10,

25 =Fix11, 26 =Fix12

1 =Radian, 2 =Degree, 3 =Gradian

1 =Normal, 2 =Scientific, 3 =Engineering

1 =Real, 2 =Rectangular, 3 =Polar

1 =Auto, 2 =Approximate, 3 =Exact

1 =Rectangular, 2 =Cylindrical, 3 =Spherical

1 =Decimal, 2 =Hex, 3 =Binary

1 =SI, 2 =Eng/US

TI-Nspire™ CAS Reference Guide 109

shift()

Catalog > shift(

Integer1

[ ,

#ofShifts

] )

⇒ integer

Shifts the bits in a binary integer. You can enter Integer1 in any number base; it is converted automatically to a signed, 64-bit binary form. If the magnitude of Integer1 is too large for this form, a symmetric modulo operation brings it within the range. For more information, see 4

Base2 , page 14.

If #ofShifts is positive, the shift is to the left. If #ofShifts is negative, the shift is to the right. The default is L 1 (shift right one bit).

In Bin base mode:

In Hex base mode:

In a right shift, the rightmost bit is dropped and 0 or 1 is inserted to match the leftmost bit. In a left shift, the leftmost bit is dropped and 0 is inserted as the rightmost bit.

For example, in a right shift:

Each bit shifts right.

0b0000000000000111101011000011010

Important: To enter a binary or hexadecimal number, always use the 0b or 0h prefix (zero, not the letter O).

Inserts 0 if leftmost bit is 0, or 1 if leftmost bit is 1.

produces:

0b00000000000000111101011000011010

The result is displayed according to the Base mode. Leading zeros are not shown.

shift(

List1

[ ,

#ofShifts

] )

⇒ list In Dec base mode:

Returns a copy of List1 shifted right or left by #ofShifts elements.

Does not alter List1 .

If #ofShifts is positive, the shift is to the left. If #ofShifts is negative, the shift is to the right. The default is L 1 (shift right one element).

Elements introduced at the beginning or end of list by the shift are set to the symbol “undef”.

shift( String1 [ , #ofShifts ] )

⇒ string

Returns a copy of

String1

shifted right or left by

#ofShifts

characters.

Does not alter String1 .

#ofShifts

is positive, the shift is to the left. If

#ofShifts

is negative, the shift is to the right. The default is L 1 (shift right one character).

Characters introduced at the beginning or end of string by the shift are set to a space.

sign() sign(

Expr1

) sign(

List1

)

⇒ expression

⇒ list sign(

Matrix1

)

⇒ matrix

For real and complex

Expr1

, returns

Expr1

/ abs(

Expr1

) when

Expr1 ƒ 0.

Returns 1 if

Expr1 is positive.

Returns L 1 if Expr1 is negative. sign(0) returns „ 1 if the complex format mode is Real; otherwise, it returns itself.

sign(0) represents the unit circle in the complex domain.

For a list or matrix, returns the signs of all the elements.

If complex format mode is Real:

Catalog >

110 TI-Nspire™ CAS Reference Guide

simult() simult( coeffMatrix

, constVector

[ ,

Tol

] )

⇒ matrix

Returns a column vector that contains the solutions to a system of linear equations.

Solve for x and y: x + 2y = 1

3x + 4y = L 1

Note: See also linSolve() , page 67.

coeffMatrix

must be a square matrix that contains the coefficients of the equations.

constVector

must have the same number of rows (same dimension) as coeffMatrix and contain the constants.

The solution is x=

Solve: ax + by = 1 cx + dy = 2

L 3 and y=2.

• If you set the Auto or Approximate mode to Approximate, computations are done using floating-point arithmetic.

• If

Tol

is omitted or not used, the default tolerance is calculated as:

5E L 14 · max(dim( coeffMatrix

)) · rowNorm( coeffMatrix

) simult( coeffMatrix

, constMatrix

[ ,

Tol

] )

⇒ matrix

Solves multiple systems of linear equations, where each system has the same equation coefficients but different constants.

Each column in constMatrix must contain the constants for a system of equations. Each column in the resulting matrix contains the solution for the corresponding system.

Solve: x + 2y = 1

3x + 4y = L 1 x + 2y = 2

3x + 4y = L 3

Catalog >

4 sin

Expr 4 sin

Note: You can insert this operator from the computer keyboard by typing @>sin .

Represents

Expr

in terms of sine. This is a display conversion operator. It can be used only at the end of the entry line.

4 sin reduces all powers of cos(...) modulo 1 N sin(...)^2 so that any remaining powers of sin(...) have exponents in the range

(0, 2). Thus, the result will be free of cos(...) if and only if cos(...) occurs in the given expression only to even powers.

Note: This conversion operator is not supported in Degree or

Gradian Angle modes. Before using it, make sure that the Angle mode is set to Radians and that Expr does not contain explicit references to degree or gradian angles.

For the first system, x= L 3 and y=2. For the second system, x= L 7 and y=9/2.

Catalog >

TI-Nspire™ CAS Reference Guide 111

sin() sin(

Expr1

) sin(

List1

)

⇒ expression

⇒ list sin(

Expr1

) returns the sine of the argument as an expression.

sin( List1 ) returns a list of the sines of all elements in List1 .

Note: The argument is interpreted as a degree, gradian or radian angle, according to the current angle mode. You can use ¡ ,

, or R to override the angle mode setting temporarily.

In Degree angle mode:

In Gradian angle mode:

In Radian angle mode: sin( squareMatrix1

)

⇒ squareMatrix

Returns the matrix sine of squareMatrix1 . This is not the same as calculating the sine of each element. For information about the calculation method, refer to cos() .

squareMatrix1

must be diagonalizable. The result always contains floating-point numbers.

In Radian angle mode: sin / () sin

(

Expr1

)

⇒ expression sin

(

List1

)

⇒ list sin / ( Expr1 ) returns the angle whose sine is Expr1 as an expression.

In Degree angle mode: sin / ( List1 ) returns a list of the inverse sines of each element of

List1 .

In Gradian angle mode:

Note: The result is returned as a degree, gradian or radian angle, according to the current angle mode setting.

Note: You can insert this function from the keyboard by typing arcsin( ...

) .

In Radian angle mode:

key

112 TI-Nspire™ CAS Reference Guide

sin / () μ

key sin

( squareMatrix1

)

⇒ squareMatrix

Returns the matrix inverse sine of squareMatrix1 . This is not the same as calculating the inverse sine of each element. For information about the calculation method, refer to cos() .

squareMatrix1

must be diagonalizable. The result always contains floating-point numbers.

In Radian angle mode and Rectangular complex format mode:

To see the entire result, press

and then use

and

to move the cursor.

sinh() sinh(

Expr1

) sinh(

List1

)

⇒ expression

⇒ list sinh (

Expr1

) returns the hyperbolic sine of the argument as an expression.

sinh (

List1

) returns a list of the hyperbolic sines of each element of

List1 .

sinh( squareMatrix1

)

⇒ squareMatrix

Returns the matrix hyperbolic sine of squareMatrix1 . This is not the same as calculating the hyperbolic sine of each element. For information about the calculation method, refer to cos() .

squareMatrix1

must be diagonalizable. The result always contains floating-point numbers.

In Radian angle mode:

Catalog > sinh / () sinh

( Expr1 )

⇒ expression sinh

( List1 )

⇒ list sinh

( Expr1 ) returns the inverse hyperbolic sine of the argument as an expression.

sinh / ( List1 ) returns a list of the inverse hyperbolic sines of each element of List1 .

Note: You can insert this function from the keyboard by typing arcsinh( ...

) .

sinh

( squareMatrix1

)

⇒ squareMatrix

Returns the matrix inverse hyperbolic sine of squareMatrix1 . This is not the same as calculating the inverse hyperbolic sine of each element. For information about the calculation method, refer to cos() .

squareMatrix1 must be diagonalizable. The result always contains floating-point numbers.

In Radian angle mode:

Catalog >

TI-Nspire™ CAS Reference Guide 113

SinReg

[ , [

Iterations

] , [

Period

] [ ,

Category

Include

] ]

Computes the sinusoidal regression on lists X and Y . A summary of results is stored in the stat.results

variable. (See page 119.)

All the lists must have equal dimension except for Include .

X and Y are lists of independent and dependent variables.

Iterations is a value that specifies the maximum number of times (1 through 16) a solution will be attempted. If omitted, 8 is used.

Typically, larger values result in better accuracy but longer execution times, and vice versa.

Period specifies an estimated period. If omitted, the difference between values in X should be equal and in sequential order. If you specify Period , the differences between x values can be unequal.

Category is a list of category codes for the corresponding X and Y data.

Include is a list of one or more of the category codes. Only those data items whose category code is included in this list are included in the calculation.

The output of SinReg is always in radians, regardless of the angle mode setting.

For information on the effect of empty elements in a list, see “Empty

(void) elements” on page 159.

Catalog >

Output variable stat.RegEqn

stat.a, stat.b, stat.c, stat.d

stat.Resid

stat.XReg

stat.YReg

stat.FreqReg

Description

Regression Equation: a · sin(bx+c)+d

Regression coefficients

Residuals from the regression

List of data points in the modified X List actually used in the regression based on restrictions of Freq ,

Category List , and Include Categories

List of data points in the modified Y List actually used in the regression based on restrictions of Freq ,

Category List , and Include Categories

List of frequencies corresponding to stat.XReg

and stat.YReg

solve() solve(

Equation

Var

) solve(

Inequality

Var

)

⇒

Boolean expression solve(

Equation

Var=Guess

)

⇒

Boolean expression

⇒

Boolean expression

Returns candidate real solutions of an equation or an inequality for

Var . The goal is to return candidates for all solutions. However, there might be equations or inequalities for which the number of solutions is infinite.

Solution candidates might not be real finite solutions for some combinations of values for undefined variables.

Catalog >

114 TI-Nspire™ CAS Reference Guide

solve()

For the Auto setting of the Auto or Approximate mode, the goal is to produce exact solutions when they are concise, and supplemented by iterative searches with approximate arithmetic when exact solutions are impractical.

Due to default cancellation of the greatest common divisor from the numerator and denominator of ratios, solutions might be solutions only in the limit from one or both sides.

For inequalities of types | , { , <, or >, explicit solutions are unlikely unless the inequality is linear and contains only Var .

For the Exact mode, portions that cannot be solved are returned as an implicit equation or inequality.

Catalog >

Use the “|” operator to restrict the solution interval and/or other variables that occur in the equation or inequality. When you find a solution in one interval, you can use the inequality operators to exclude that interval from subsequent searches.

In Radian angle mode: false is returned when no real solutions are found. true is returned if solve() can determine that any finite real value of Var satisfies the equation or inequality.

Since solve() always returns a Boolean result, you can use “and,”

“or,” and “not” to combine results from solve() with each other or with other Boolean expressions.

Solutions might contain a unique new undefined constant of the form n j with j being an integer in the interval 1–255. Such variables designate an arbitrary integer.

In Radian angle mode:

In Real mode, fractional powers having odd denominators denote only the real branch. Otherwise, multiple branched expressions such as fractional powers, logarithms, and inverse trigonometric functions denote only the principal branch. Consequently, solve() produces only solutions corresponding to that one real or principal branch.

Note: See also cSolve() , cZeros() , nSolve() , and zeros() .

solve(

Eqn1

and

Eqn2

[ and … ] ,

VarOrGuess1

VarOrGuess2

[ , … ] )

⇒ Boolean expression solve(

SystemOfEqns

VarOrGuess1

VarOrGuess2

[ , … ] )

⇒

Boolean expression solve( {

Eqn1

Eqn2

[,...]} {

VarOrGuess1

VarOrGuess2

[ , … ]} )

⇒ Boolean expression

Returns candidate real solutions to the simultaneous algebraic equations, where each VarOrGuess specifies a variable that you want to solve for.

You can separate the equations with the and operator, or you can enter a

SystemOfEqns

using a template from the Catalog. The number of VarOrGuess arguments must match the number of equations. Optionally, you can specify an initial guess for a variable.

Each VarOrGuess must have the form: variable

– or – variable

= real or non-real number

For example, x is valid and so is x=3.

TI-Nspire™ CAS Reference Guide 115

solve()

If all of the equations are polynomials and if you do NOT specify any initial guesses, solve() uses the lexical Gröbner/Buchberger elimination method to attempt to determine all real solutions.

For example, suppose you have a circle of radius r at the origin and another circle of radius r centered where the first circle crosses the positive x-axis. Use solve() to find the intersections.

Catalog >

As illustrated by r in the example to the right, simultaneous polynomial equations can have extra variables that have no values, but represent given numeric values that could be substituted later.

You can also (or instead) include solution variables that do not appear in the equations. For example, you can include z as a solution variable to extend the previous example to two parallel intersecting cylinders of radius r.

The cylinder solutions illustrate how families of solutions might contain arbitrary constants of the form c k, where k is an integer suffix from 1 through 255.

To see the entire result, press

and then use

and

to move the cursor.

For polynomial systems, computation time or memory exhaustion may depend strongly on the order in which you list solution variables.

If your initial choice exhausts memory or your patience, try rearranging the variables in the equations and/or varOrGuess list.

If you do not include any guesses and if any equation is nonpolynomial in any variable but all equations are linear in the solution variables, solve() uses Gaussian elimination to attempt to determine all real solutions.

If a system is neither polynomial in all of its variables nor linear in its solution variables, solve() determines at most one solution using an approximate iterative method. To do so, the number of solution variables must equal the number of equations, and all other variables in the equations must simplify to numbers.

To see the entire result, press

and then use

and

to move the cursor.

Each solution variable starts at its guessed value if there is one; otherwise, it starts at 0.0.

Use guesses to seek additional solutions one by one. For convergence, a guess may have to be rather close to a solution.

116 TI-Nspire™ CAS Reference Guide

SortA

List1

[ ,

List2

] [ ,

List3

] ...

SortA

Vector1

[ ,

Vector2

] [ ,

Vector3

] ...

Sorts the elements of the first argument in ascending order.

If you include additional arguments, sorts the elements of each so that their new positions match the new positions of the elements in the first argument.

All arguments must be names of lists or vectors. All arguments must have equal dimensions.

Empty (void) elements within the first argument move to the bottom.

For more information on empty elements, see page 159.

SortD

List1

[ ,

List2

] [ ,

List3

] ...

SortD

Vector1

[ ,

Vector2

] [ ,

Vector3

] ...

Identical to SortA , except SortD sorts the elements in descending order.

Empty (void) elements within the first argument move to the bottom.

For more information on empty elements, see page 159.

Catalog >

TI-Nspire™ CAS Reference Guide 117

4 Sphere

Vector 4

Sphere

Note: You can insert this operator from the computer keyboard by typing @>Sphere .

Displays the row or column vector in spherical form [ r ±q ±f ].

Vector must be of dimension 3 and can be either a row or a column vector.

Note:

4 Sphere is a display-format instruction, not a conversion function. You can use it only at the end of an entry line.

Press Ctrl + Enter evaluate:

/·

Catalog >

(Macintosh®: “ + Enter ) to

Press Ctrl + Enter

/·

(Macintosh®: “ + Enter ) to evaluate:

Press

· sqrt () sqrt( Expr1 ) sqrt( List1 )

⇒ expression

⇒ list

Returns the square root of the argument.

For a list, returns the square roots of all the elements in List1 .

Note: See also Square root template , page 1.

(ρ,θ,φ)

Catalog >

118 TI-Nspire™ CAS Reference Guide

stat.results

Displays results from a statistics calculation.

The results are displayed as a set of name-value pairs. The specific names shown are dependent on the most recently evaluated statistics function or command.

You can copy a name or value and paste it into other locations.

Note: Avoid defining variables that use the same names as those used for statistical analysis. In some cases, an error condition could occur. Variable names used for statistical analysis are listed in the table below.

Catalog > stat.a

stat.AdjR² stat.b

stat.b0

stat.b1

stat.b2

stat.b3

stat.b4

stat.b5

stat.b6

stat.b7

stat.b8

stat.b9

stat.b10

stat.bList

stat.

c ² stat.c

stat.CLower

stat.CLowerList

stat.CompList

stat.CompMatrix

stat.CookDist

stat.CUpper

stat.CUpperList

stat.d

stat.dfDenom

stat.dfBlock

stat.dfCol

stat.dfError

stat.dfInteract

stat.dfReg

stat.dfNumer

stat.dfRow

stat.DW

stat.e

stat.ExpMatrix

stat.

F stat.

F Block stat.

F col stat.

F Interact stat.FreqReg

stat.

F row stat.Leverage

stat.LowerPred

stat.LowerVal

stat.m

stat.MaxX

stat.MaxY

stat.ME

stat.MedianX

stat.MedianY

stat.MEPred

stat.MinX

stat.MinY

stat.MS

stat.MSBlock

stat.MSCol

stat.MSError

stat.MSInteract

stat.MSReg

stat.MSRow

stat.n

stat.

Ç stat.

Diff stat.PList

stat.PVal

stat.PValBlock

stat.PValCol

stat.PValInteract

stat.PValRow

stat.Q1X

stat.Q1Y

stat.Q3X

stat.Q3Y

stat.r

stat.r² stat.RegEqn

stat.Resid

stat.ResidTrans

stat.

s x stat.

s y stat.

s x1 stat.

s x2 stat.

G x stat.

G x² stat.

G xy stat.

G y stat.

G y

² stat.s

stat.SE

stat.SEList

stat.SEPred

stat.sResid

stat.SEslope

stat.sp

stat.SS

stat.SSBlock

Note: Each time the Lists & Spreadsheet application calculates statistical results, it copies the “stat .

” group variables to a “stat# .

” group, where # is a number that is incremented automatically. This lets you maintain previous results while performing multiple calculations.

stat.SSCol

stat.SSX

stat.SSY

stat.SSError

stat.SSInteract

stat.SSReg

stat.SSRow

stat.tList

stat.UpperPred

stat.UpperVal

stat.

v stat.

v 1 stat.

v 2 stat.

v Diff stat.

v List stat.XReg

stat.XVal

stat.XValList

stat.

w stat.

y stat.

List stat.YReg

TI-Nspire™ CAS Reference Guide 119

stat.values

Displays a matrix of the values calculated for the most recently evaluated statistics function or command.

Unlike stat.results

, stat.values

omits the names associated with the values.

You can copy a value and paste it into other locations.

See the stat.results

example.

stDevPop() stDevPop(

List

[

, freqList

] )

⇒ expression

Returns the population standard deviation of the elements in List .

Each freqList element counts the number of consecutive occurrences of the corresponding element in List .

Note:

List must have at least two elements. Empty (void) elements are ignored. For more information on empty elements, see page 159.

In Radian angle and auto modes:

Catalog >

Catalog > stDevPop(

Matrix1

[

, freqMatrix

] )

⇒ matrix

Returns a row vector of the population standard deviations of the columns in Matrix1 .

Each freqMatrix

element counts the number of consecutive occurrences of the corresponding element in Matrix1 .

Note:

Matrix1 must have at least two rows. Empty (void) elements are ignored. For more information on empty elements, see page 159.

stDevSamp() stDevSamp(

List

[

, freqList

] )

⇒ expression

Returns the sample standard deviation of the elements in List .

Each freqList element counts the number of consecutive occurrences of the corresponding element in List .

Note:

List must have at least two elements. Empty (void) elements are ignored. For more information on empty elements, see page 159.

Catalog >

120 TI-Nspire™ CAS Reference Guide

stDevSamp() stDevSamp(

Matrix1

[

, freqMatrix

] )

⇒ matrix

Returns a row vector of the sample standard deviations of the columns in Matrix1 .

Each freqMatrix element counts the number of consecutive occurrences of the corresponding element in Matrix1 .

Note:

Matrix1 must have at least two rows. Empty (void) elements are ignored. For more information on empty elements, see page 159.

Stop

Programming command: Terminates the program.

Stop is not allowed in functions.

Note for entering the example: In the Calculator application on the handheld, you can enter multi-line definitions by pressing

@ instead of

at the end of each line. On the computer keyboard, hold down Alt and press Enter .

Catalog >

Store string() string(

Expr

)

⇒ string

Simplifies

Expr

and returns the result as a character string.

subMat() subMat(

Matrix1

[ , startRow

] [ , startCol

] [ , endRow

] [ , endCol

] )

⇒ matrix

Returns the specified submatrix of

Matrix1

Defaults: startRow =1, startCol =1, endRow =last row, endCol =last column.

Sum (Sigma)

See & (store) , page 157 .

Catalog >

See G () , page 151 .

TI-Nspire™ CAS Reference Guide 121

sum() sum(

List

[

, Start

[

, End

]] )

⇒ expression

Returns the sum of all elements in List .

Start and End are optional. They specify a range of elements.

Any void argument produces a void result. Empty (void) elements in

List are ignored. For more information on empty elements, see page

159.

sum( Matrix1 [

, Start [

, End ]] )

⇒ matrix

Returns a row vector containing the sums of all elements in the columns in Matrix1 .

Start

and

End

are optional. They specify a range of rows.

Any void argument produces a void result. Empty (void) elements in

Matrix1

are ignored. For more information on empty elements, see page 159.

sumIf() sumIf(

List

Criteria

SumList

] )

⇒ value

Returns the accumulated sum of all elements in List that meet the specified Criteria . Optionally, you can specify an alternate list, sumList , to supply the elements to accumulate.

List can be an expression, list, or matrix. SumList , if specified, must have the same dimension(s) as List .

Criteria can be:

• A value, expression, or string. For example, 34 accumulates only those elements in List that simplify to the value 34.

• A Boolean expression containing the symbol ?

as a placeholder for each element. For example, ?<10 accumulates only those elements in List that are less than 10.

When a List element meets the Criteria , the element is added to the accumulating sum. If you include sumList , the corresponding element from sumList is added to the sum instead.

Within the Lists & Spreadsheet application, you can use a range of cells in place of List and sumList .

Empty (void) elements are ignored. For more information on empty elements, see page 159.

Note: See also countIf() , page 26.

sumSeq() system() system(

Eqn1

[ ,

Eqn2

[ ,

Eqn3

[ , ...]]] ) system(

Expr1

[ ,

Expr2

[ ,

Expr3

[ , ...]]] )

Returns a system of equations, formatted as a list. You can also create a system by using a template.

Note: See also System of equations , page 3.

122 TI-Nspire™ CAS Reference Guide

Catalog >

See G (), page 151.

Catalog >

T

T (transpose)

Matrix1 T

⇒ matrix

Returns the complex conjugate transpose of Matrix1 .

Note: You can insert this operator from the computer keyboard by typing @t .

tan() tan(

Expr1

) tan(

List1

)

⇒ expression

⇒ list tan( Expr1 ) returns the tangent of the argument as an expression.

tan( List1 ) returns a list of the tangents of all elements in List1 .

Note: The argument is interpreted as a degree, gradian or radian angle, according to the current angle mode. You can use override the angle mode setting temporarily.

¡ ,

In Degree angle mode:

In Gradian angle mode:

In Radian angle mode:

Catalog >

key tan( squareMatrix1

)

⇒ squareMatrix

Returns the matrix tangent of squareMatrix1

. This is not the same as calculating the tangent of each element. For information about the calculation method, refer to cos() .

squareMatrix1 must be diagonalizable. The result always contains floating-point numbers.

In Radian angle mode:

TI-Nspire™ CAS Reference Guide 123

tan / () tan

(

Expr1

)

⇒ expression tan

(

List1

)

⇒ list tan

(

Expr1

) returns the angle whose tangent is

Expr1

as an expression.

In Degree angle mode:

In Gradian angle mode: tan / ( List1 ) returns a list of the inverse tangents of each element of

List1 .

Note: The result is returned as a degree, gradian or radian angle, according to the current angle mode setting.

Note: You can insert this function from the keyboard by typing arctan( ...

) .

tan

( squareMatrix1

)

⇒ squareMatrix

Returns the matrix inverse tangent of squareMatrix1 . This is not the same as calculating the inverse tangent of each element. For information about the calculation method, refer to cos() .

squareMatrix1 must be diagonalizable. The result always contains floating-point numbers.

In Radian angle mode:

In Radian angle mode: tangentLine() tangentLine(

Expr1

Var

Point

) tangentLine(

Expr1

Var

Point

)

⇒ expression

Returns the tangent line to the curve represented by Expr1 at the point specified in

Var

Point

Make sure that the independent variable is not defined. For example,

If f1(x):=5 and x:=3, then tangentLine( f1(x),x,2 ) returns “false.”

Catalog >

key tanh() tanh(

Expr1

) tanh(

List1

)

⇒ expression

⇒ list tanh( Expr1 ) returns the hyperbolic tangent of the argument as an expression.

tanh( List1 ) returns a list of the hyperbolic tangents of each element of List1 .

tanh( squareMatrix1

)

⇒ squareMatrix

Returns the matrix hyperbolic tangent of squareMatrix1 . This is not the same as calculating the hyperbolic tangent of each element. For information about the calculation method, refer to cos() .

In Radian angle mode: squareMatrix1 must be diagonalizable. The result always contains floating-point numbers.

Catalog >

124 TI-Nspire™ CAS Reference Guide

tanh / ()

Catalog > tanh

(

Expr1

)

⇒ expression tanh

(

List1

)

⇒ list

In Rectangular complex format: tanh / ( Expr1 ) returns the inverse hyperbolic tangent of the argument as an expression.

tanh

(

List1

) returns a list of the inverse hyperbolic tangents of each element of

List1

Note: You can insert this function from the keyboard by typing arctanh( ...

) .

tanh

( squareMatrix1

)

⇒ squareMatrix

Returns the matrix inverse hyperbolic tangent of squareMatrix1

. This is not the same as calculating the inverse hyperbolic tangent of each element. For information about the calculation method, refer to cos() .

squareMatrix1

must be diagonalizable. The result always contains floating-point numbers.

In Radian angle mode and Rectangular complex format: taylor() taylor(

Expr1

Var

Order

[ ,

Point

] )

⇒ expression

Returns the requested Taylor polynomial. The polynomial includes non-zero terms of integer degrees from zero through

Order

in (

Var minus Point ). taylor() returns itself if there is no truncated power series of this order, or if it would require negative or fractional exponents. Use substitution and/or temporary multiplication by a power of ( Var minus Point ) to determine more general power series.

Point defaults to zero and is the expansion point.

As illustrated by the last example to the right, the display routines downstream of the result produced by taylor(...) might rearrange terms so that the dominant term is not the leftmost one.

To see the entire result, press

and then use

and

to move the cursor.

Catalog > tCdf() tCdf( lowBound

, upBound

, df

)

⇒ number

if lowBound

and upBound

are numbers,

list

if lowBound

and upBound

are lists

Computes the Studentt distribution probability between lowBound and

upBound

for the specified degrees of freedom

For P(X { upBound ), set lowBound = .ˆ .

Catalog >

TI-Nspire™ CAS Reference Guide 125

tCollect() tCollect(

Expr1

)

⇒ expression

Returns an expression in which products and integer powers of sines and cosines are converted to a linear combination of sines and cosines of multiple angles, angle sums, and angle differences. The transformation converts trigonometric polynomials into a linear combination of their harmonics.

Sometimes tCollect() will accomplish your goals when the default trigonometric simplification does not. tCollect() tends to reverse transformations done by tExpand() . Sometimes applying tExpand() to a result from tCollect() , or vice versa, in two separate steps simplifies an expression.

tExpand() tExpand(

Expr1

)

⇒ expression

Returns an expression in which sines and cosines of integer-multiple angles, angle sums, and angle differences are expanded. Because of the identity (sin(x))2+(cos(x))2=1, there are many possible equivalent results. Consequently, a result might differ from a result shown in other publications.

Sometimes tExpand() will accomplish your goals when the default trigonometric simplification does not. tExpand() tends to reverse transformations done by tCollect() . Sometimes applying tCollect() to a result from tExpand() , or vice versa, in two separate steps simplifies an expression.

Note: Degree-mode scaling by p /180 interferes with the ability of tExpand() to recognize expandable forms. For best results, tExpand() should be used in Radian mode.

Catalog >

Text

Catalog >

Text promptString

[ ,

DispFlag

]

Programming command: Pauses the program and displays the character string promptString

in a dialog box.

Define a program that pauses to display each of five random numbers in a dialog box.

Within the Prgm...EndPrgm template, complete each line by pressing

instead of

. On the computer keyboard, hold down Alt and press Enter .

When the user selects OK , program execution continues.

The optional flag

argument can be any expression.

• If DispFlag is omitted or evaluates to added to the Calculator history.

1 , the text message is

• If DispFlag evaluates to 0 , the text message is not added to the history.

Define text_demo()=Prgm

For i,1,5 strinfo:=”Random number “ & string(rand(i))

Text strinfo

EndPrgm

If the program needs a typed response from the user, refer to

Request , page 100, or RequestStr , page 101.

Note: You can use this command within a user-defined program but not within a function.

Run the program: text_demo()

Sample of one dialog box:

See If, page 57 .

Then

126 TI-Nspire™ CAS Reference Guide

tInterval tInterval

List

[ ,

Freq

[ ,

CLevel

]]

(Data list input) tInterval v

, sx

, n [ ,

CLevel ]

(Summary stats input)

Computes a t

confidence interval. A summary of results is stored in the stat.results

variable. (See page 119.)

For information on the effect of empty elements in a list, see “Empty

(void) elements” on page 159.

Output variable Description stat.CLower, stat.CUpper

Confidence interval for an unknown population mean stat.

x Sample mean of the data sequence from the normal random distribution stat.ME

stat.df

stat.

s x stat.n

Margin of error

Degrees of freedom

Sample standard deviation

Length of the data sequence with sample mean tInterval_2Samp tInterval_2Samp

List1

List2

[ ,

Freq1

[ ,

Freq2

[ ,

CLevel

[ ,

Pooled

]]]]

(Data list input) tInterval_2Samp v 1

, sx1

, n1

, v 2

, sx2

, n2

[ ,

CLevel

[ ,

Pooled

]]

(Summary stats input)

Computes a two-sample t confidence interval. A summary of results is stored in the stat.results

variable. (See page 119.)

Pooled = 1 pools variances; Pooled = 0 does not pool variances.

For information on the effect of empty elements in a list, see “Empty

(void) elements” on page 159.

Output variable Description stat.CLower, stat.CUpper

Confidence interval containing confidence level probability of distribution stat.

x 1 x 2 Sample means of the data sequences from the normal random distribution stat.ME

stat.df

stat.

x 1

, stat.

x 2 stat.

s x1, stat.

s x2

Margin of error

Degrees of freedom

Sample means of the data sequences from the normal random distribution

Sample standard deviations for List 1 and List 2 stat.n1, stat.n2

stat.sp

Number of samples in data sequences

The pooled standard deviation. Calculated when Pooled = YES

Catalog >

TI-Nspire™ CAS Reference Guide 127

tmpCnv() tmpCnv( Expr_ ¡ tempUnit ,

⇒ expression _ ¡ tempUnit2

¡ tempUnit2 )

Converts a temperature value specified by

Expr

from one unit to another. Valid temperature units are:

¡ C Celsius

¡ F Fahrenheit

¡ K Kelvin

¡ R Rankine

To type ¡ , select it from the Catalog symbols.

to type _ , press

For example, 100_ ¡ C converts to 212_ ¡ F.

To convert a temperature range, use @ tmpCnv() instead.

Catalog >

Note: You can use the Catalog to select temperature units.

@ tmpCnv()

Catalog >

@ tmpCnv(

Expr_ ¡ tempUnit

⇒ expression _ ¡ tempUnit2

_ ¡ tempUnit2

)

Note: You can insert this function from the keyboard by typing deltaTmpCnv( ...

) .

Converts a temperature range (the difference between two temperature values) specified by Expr from one unit to another. Valid temperature units are:

_ ¡ C Celsius

_ ¡ F Fahrenheit

_ ¡ K Kelvin

_ ¡ R Rankine

To enter ¡ , select it from the Symbol Palette or type @d .

Note: You can use the Catalog to select temperature units.

To type _ , press

1_ ¡ C and 1_ ¡ K have the same magnitude, as do 1_ ¡ F and 1_ ¡ R.

However, 1_ ¡ C is 9/5 as large as 1_ ¡ F.

For example, a 100_ ¡ C range (from 0_ ¡ C to 100_ ¡ C) is equivalent to a 180_ ¡ F range.

To convert a particular temperature value instead of a range, use tmpCnv() .

tPdf() tPdf( XVal , df ) list

⇒ number if XVal is a number, list if XVal is a

Computes the probability density function (pdf) for the Studentt distribution at a specified x value with specified degrees of freedom df

Catalog >

128 TI-Nspire™ CAS Reference Guide

trace() trace( squareMatrix

)

⇒ expression

Returns the trace (sum of all the elements on the main diagonal) of squareMatrix

Try

Try block1

Else block2

EndTry

Executes block1

unless an error occurs. Program execution transfers to block2 if an error occurs in block1 . System variable errCode contains the error code to allow the program to perform error recovery. For a list of error codes, see “ Error codes and messages ,” page 165.

block1 and block2 can be either a single statement or a series of statements separated with the “:” character.

Note for entering the example: In the Calculator application on the handheld, you can enter multi-line definitions by pressing

@ instead of

at the end of each line. On the computer keyboard, hold down Alt and press Enter .

Catalog >

Example 2

To see the commands Try , ClrErr , and PassErr in operation, enter the eigenvals() program shown at the right. Run the program by executing each of the following expressions.

Define eigenvals(a,b)=Prgm

Try

Disp "A= ",a

Disp "B= ",b

Disp " "

Disp "Eigenvalues of A·B are:",eigVl(a*b)

Else

If errCode=230 Then

Disp "Error: Product of A·B must be a square matrix"

ClrErr

Else

PassErr

EndIf

EndTry

EndPrgm

Note: See also ClrErr , page 19 , and PassErr , page 87 .

TI-Nspire™ CAS Reference Guide 129

tTest tTest m 0

List

[ ,

Freq

[ ,

Hypoth

]]

(Data list input) tTest m 0

, x

, sx

, n

, [

Hypoth

]

(Summary stats input)

Performs a hypothesis test for a single unknown population mean m when the population standard deviation s is unknown. A summary of results is stored in the stat.results

variable. (See page 119.)

Test H

: m = m 0, against one of the following:

For H a

: m < m 0, set

Hypoth

For H a

: m ƒ m 0 (default), set Hypoth =0

For H a

: m > m 0, set Hypoth >0

For information on the effect of empty elements in a list, see “Empty

(void) elements” on page 159.

Output variable stat.t

stat.PVal

stat.df

stat.

x stat.sx

stat.n

Description

( x N m 0) / (stdev / sqrt(n))

Smallest level of significance at which the null hypothesis can be rejected

Degrees of freedom

Sample mean of the data sequence in List

Sample standard deviation of the data sequence

Size of the sample tTest_2Samp tTest_2Samp

List1

List2

[ ,

Freq1

[ ,

Freq2

[ ,

Hypoth

[ ,

Pooled

]]]]

(Data list input) tTest_2Samp v 1

, sx1

, n1

, v 2

, sx2

, n2

[ ,

Hypoth

[ ,

Pooled

]]

(Summary stats input)

Computes a two-sample t test. A summary of results is stored in the stat.results

variable. (See page 119.)

Test H

: m 1 = m 2, against one of the following:

For H a

: m 1< m 2, set Hypoth <0

For H a

: m 1 ƒ m 2 (default), set Hypoth =0

For H a

: m 1> m 2, set Hypoth >0

Pooled = 1 pools variances

Pooled = 0 does not pool variances

For information on the effect of empty elements in a list, see “Empty

(void) elements” on page 159.

Output variable stat.t

Description

Standard normal value computed for the difference of means

130 TI-Nspire™ CAS Reference Guide

Catalog >

Output variable stat.PVal

stat.df

stat.

x 1, stat.

x 2 stat.sx1, stat.sx2

stat.n1, stat.n2

stat.sp

Description

Smallest level of significance at which the null hypothesis can be rejected

Degrees of freedom for the t-statistic

Sample means of the data sequences in List 1 and List 2

Sample standard deviations of the data sequences in List 1 and List 2

Size of the samples

The pooled standard deviation. Calculated when

Pooled

=1.

tvmFV() tvmFV(

Pmt

, [

PpY

] , [

CpY

] , [

PmtAt

] )

⇒ value

Financial function that calculates the future value of money.

Note: Arguments used in the TVM functions are described in the table of TVM arguments, page 131. See also amortTbl() , page 7.

tvmI() tvmI(

Pmt

, [

PpY

] , [

CpY

] , [

PmtAt

] )

⇒ value

Financial function that calculates the interest rate per year.

Note: Arguments used in the TVM functions are described in the table of TVM arguments, page 131. See also amortTbl() , page 7.

tvmN() tvmN( I , PV , Pmt , FV , [ PpY ] , [ CpY ] , [ PmtAt ] )

⇒ value

Financial function that calculates the number of payment periods.

Note: Arguments used in the TVM functions are described in the table of TVM arguments, page 131. See also amortTbl() , page 7.

tvmPmt() tvmPmt(

, [

PpY

] , [

CpY

] , [

PmtAt

] )

⇒ value

Financial function that calculates the amount of each payment.

Note: Arguments used in the TVM functions are described in the table of TVM arguments, page 131. See also amortTbl() , page 7.

tvmPV() tvmPV(

Pmt

, [

PpY

] , [

CpY

] , [

PmtAt

] )

⇒ value

Financial function that calculates the present value.

Note: Arguments used in the TVM functions are described in the table of TVM arguments, page 131. See also amortTbl() , page 7.

TVM argument*

Description

Number of payment periods

Annual interest rate

Catalog >

Data type real number real number

TI-Nspire™ CAS Reference Guide 131

TVM argument*

Pmt

PpY

CpY

PmtAt

Description

Present value

Payment amount

Future value

Payments per year, default=1

Compounding periods per year, default=1

Payment due at the end or beginning of each period, default=end

Data type real number real number real number integer > 0 integer > 0 integer (0=end,

1=beginning)

* These time-value-of-money argument names are similar to the TVM variable names (such as tvm.pv

and tvm.pmt

) that are used by the Calculator application’s finance solver.

Financial functions, however, do not store their argument values or results to the TVM variables.

TwoVar

[ , [

Freq

] [ ,

Category

Include

]]

Calculates the TwoVar statistics. A summary of results is stored in the stat.results

variable. (See page 119.)

All the lists must have equal dimension except for Include .

and

are lists of independent and dependent variables.

Freq is an optional list of frequency values. Each element in Freq specifies the frequency of occurrence for each corresponding

and

Y data point. The default value is 1. All elements must be integers | 0.

Category is a list of numeric category codes for the corresponding X and

data.

Include is a list of one or more of the category codes. Only those data items whose category code is included in this list are included in the calculation.

An empty (void) element in any of the lists

Freq

, or

Category results in a void for the corresponding element of all those lists. An empty element in any of the lists

through

X20 results in a void for the corresponding element of all those lists. For more information on empty elements, see page 159.

Catalog >

Output variable stat.

v stat.

G x stat.

G x2 stat.sx

stat.

s x stat.n

stat.

w stat.

G y stat.

G y

2 stat.sy

Description

Mean of x values

Sum of x values

Sum of x2 values

Sample standard deviation of x

Population standard deviation of x

Number of data points

Mean of y values

Sum of y values

Sum of y2 values

Sample standard deviation of y

132 TI-Nspire™ CAS Reference Guide

Output variable stat.

s y stat.

G xy stat.r

stat.MinX

stat.Q

X stat.MedianX

stat.Q

X stat.MaxX

stat.MinY

stat.Q

Y stat.MedY

stat.Q

Y stat.MaxY

stat.

G (x v )

2 stat.

G (y w )

Description

Population standard deviation of y

Sum of x · y values

Correlation coefficient

Minimum of x values

1st Quartile of x

Median of x

3rd Quartile of x

Maximum of x values

Minimum of y values

1st Quartile of y

Median of y

3rd Quartile of y

Maximum of y values

Sum of squares of deviations from the mean of x

Sum of squares of deviations from the mean of y

U

unitV() unitV(

Vector1

)

⇒ vector

Returns either a row- or column-unit vector, depending on the form of

Vector1 .

Vector1 must be either a single-row matrix or a single-column matrix.

Catalog >

To see the entire result, press

and then use

and

to move the cursor.

TI-Nspire™ CAS Reference Guide 133

unLock unLock

Var1

[ ,

Var2

] [ ,

Var3

] ...

unLock

Var .

Unlocks the specified variables or variable group. Locked variables cannot be modified or deleted.

See Lock , page 70, and getLockInfo() , page 53.

V

varPop() varPop(

List

[

, freqList

] )

⇒ expression

Returns the population variance of List .

Each freqList element counts the number of consecutive occurrences of the corresponding element in List .

Note:

List must contain at least two elements.

If an element in either list is empty (void), that element is ignored, and the corresponding element in the other list is also ignored. For more information on empty elements, see page 159.

varSamp() varSamp(

List

[

, freqList

] )

⇒ expression

Returns the sample variance of List .

Each freqList

element counts the number of consecutive occurrences of the corresponding element in List .

Note:

List

must contain at least two elements.

If an element in either list is empty (void), that element is ignored, and the corresponding element in the other list is also ignored. For more information on empty elements, see page 159.

varSamp( Matrix1 [

, freqMatrix ] )

⇒ matrix

Returns a row vector containing the sample variance of each column in Matrix1 .

Each freqMatrix

element counts the number of consecutive occurrences of the corresponding element in Matrix1 .

If an element in either matrix is empty (void), that element is ignored, and the corresponding element in the other matrix is also ignored. For more information on empty elements, see page 159.

Note:

Matrix1 must contain at least two rows.

134 TI-Nspire™ CAS Reference Guide

Catalog >

W

warnCodes()

Catalog > warnCodes( Expr1 , StatusVar )

⇒ expression

Evaluates expression Expr1 , returns the result, and stores the codes of any generated warnings in the StatusVar list variable. If no warnings are generated, this function assigns StatusVar an empty list.

Expr1 can be any valid TI-Nspire™ or TI-Nspire™ CAS math expression. You cannot use a command or assignment as Expr1 .

StatusVar must be a valid variable name.

For a list of warning codes and associated messages, see page 171.

To see the entire result, press

and then use

and

to move the cursor.

when() when(

Condition

⇒ expression

, trueResult

[ , falseResult

][ , unknownResult

] )

Returns trueResult , falseResult , or unknownResult , depending on whether Condition is true, false, or unknown. Returns the input if there are too few arguments to specify the appropriate result.

Omit both falseResult and unknownResult to make an expression defined only in the region where Condition is true.

Use an undef falseResult to define an expression that graphs only on an interval.

when() is helpful for defining recursive functions.

Catalog >

While

Condition

Block

EndWhile

Executes the statements in Block as long as Condition is true.

Block

can be either a single statement or a sequence of statements separated with the “:” character.

Note for entering the example: In the Calculator application on the handheld, you can enter multi-line definitions by pressing

@ instead of

at the end of each line. On the computer keyboard, hold down Alt and press Enter .

Catalog >

“With”

See

(“with”), page 157 .

TI-Nspire™ CAS Reference Guide 135

X

xor

Catalog >

BooleanExpr1

xor

BooleanExpr2 ⇒ Boolean expression

Returns true if

BooleanExpr1

is true and

BooleanExpr2

is false, or vice versa.

Returns false if both arguments are true or if both are false. Returns a simplified Boolean expression if either of the arguments cannot be resolved to true or false.

Note: See or , page 86.

Integer1

xor

Integer2

⇒ integer In Hex base mode:

Important: Zero, not the letter O.

Compares two real integers bit-by-bit using an xor operation.

Internally, both integers are converted to signed, 64-bit binary numbers. When corresponding bits are compared, the result is 1 if either bit (but not both) is 1; the result is 0 if both bits are 0 or both bits are 1. The returned value represents the bit results, and is displayed according to the Base mode.

You can enter the integers in any number base. For a binary or hexadecimal entry, you must use the 0b or 0h prefix, respectively.

Without a prefix, integers are treated as decimal (base 10).

In Bin base mode:

Note: A binary entry can have up to 64 digits (not counting the

0b prefix). A hexadecimal entry can have up to 16 digits.

If you enter a decimal integer that is too large for a signed, 64-bit binary form, a symmetric modulo operation is used to bring the value into the appropriate range. For more information, see 4

Base2 , page 14.

Note: See or , page 86.

Z

zeros() zeros(

Expr

Var

)

⇒ list zeros(

Expr

Var=Guess

)

⇒ list

Returns a list of candidate real values of

Var

that make

Expr

=0. zeros() does this by computing exp 4 list(solve( Expr =0, Var ) ,Var ) .

Catalog >

For some purposes, the result form for zeros() is more convenient than that of solve() . However, the result form of zeros() cannot express implicit solutions, solutions that require inequalities, or solutions that do not involve Var .

Note: See also cSolve() , cZeros() , and solve() .

136 TI-Nspire™ CAS Reference Guide

zeros() zeros({

Expr1

Expr2

{

VarOrGuess1

VarOrGuess2

[ , … ] })

⇒ matrix

Returns candidate real zeros of the simultaneous algebraic expressions, where each VarOrGuess specifies an unknown whose value you seek.

Optionally, you can specify an initial guess for a variable. Each

VarOrGuess must have the form: variable

– or – variable = real or non real number

For example, x is valid and so is x=3.

If all of the expressions are polynomials and if you do NOT specify any initial guesses, zeros() uses the lexical Gröbner/Buchberger elimination method to attempt to determine all real zeros.

For example, suppose you have a circle of radius r at the origin and another circle of radius r centered where the first circle crosses the positive x-axis. Use zeros() to find the intersections.

As illustrated by r in the example to the right, simultaneous polynomial expressions can have extra variables that have no values, but represent given numeric values that could be substituted later.

Each row of the resulting matrix represents an alternate zero, with the components ordered the same as the varOrGuess list. To extract a row, index the matrix by [ row ].

Extract row 2:

You can also (or instead) include unknowns that do not appear in the expressions. For example, you can include z as an unknown to extend the previous example to two parallel intersecting cylinders of radius r.

The cylinder zeros illustrate how families of zeros might contain arbitrary constants in the form ck, where k is an integer suffix from 1 through 255.

If you do not include any guesses and if any expression is nonpolynomial in any variable but all expressions are linear in the unknowns, zeros() uses Gaussian elimination to attempt to determine all real zeros.

Catalog >

TI-Nspire™ CAS Reference Guide 137

zeros()

If a system is neither polynomial in all of its variables nor linear in its unknowns, zeros() determines at most one zero using an approximate iterative method. To do so, the number of unknowns must equal the number of expressions, and all other variables in the expressions must simplify to numbers.

Each unknown starts at its guessed value if there is one; otherwise, it starts at 0.0.

Use guesses to seek additional zeros one by one. For convergence, a guess may have to be rather close to a zero.

zInterval zInterval s

List

[ ,

Freq

[ ,

CLevel

]]

(Data list input) zInterval s

, v

, n [ , CLevel ]

(Summary stats input)

Computes a z confidence interval. A summary of results is stored in the stat.results

variable. (See page 119.)

For information on the effect of empty elements in a list, see “Empty

(void) elements” on page 159.

Output variable Description stat.CLower, stat.CUpper

Confidence interval for an unknown population mean stat.

x Sample mean of the data sequence from the normal random distribution stat.ME

stat.sx

stat.n

stat.

Margin of error

Sample standard deviation

Length of the data sequence with sample mean

Known population standard deviation for data sequence List zInterval_1Prop zInterval_1Prop x

, n

[ ,

CLevel

]

Computes a one-proportion z confidence interval. A summary of results is stored in the stat.results

variable. (See page 119.) x is a non-negative integer.

For information on the effect of empty elements in a list, see “Empty

(void) elements” on page 159.

Output variable Description stat.CLower, stat.CUpper

Confidence interval containing confidence level probability of distribution stat.

The calculated proportion of successes stat.ME

Margin of error

138 TI-Nspire™ CAS Reference Guide

Catalog >

Output variable stat.n

Description

Number of samples in data sequence zInterval_2Prop zInterval_2Prop x1

, n1

, x2

, n2

[ ,

CLevel

]

Computes a two-proportion z

confidence interval. A summary of results is stored in the stat.results

variable. (See page 119.) x1

and x2

are non-negative integers.

For information on the effect of empty elements in a list, see “Empty

(void) elements” on page 159.

stat.ME

stat.

1 stat.

2 stat.n1

stat.n2

Output variable Description stat.CLower, stat.CUpper

Confidence interval containing confidence level probability of distribution stat.

Diff The calculated difference between proportions

Margin of error

First sample proportion estimate

Second sample proportion estimate

Sample size in data sequence one

Sample size in data sequence two zInterval_2Samp zInterval_2Samp s

, s

List1

List2

[ ,

Freq1

[ ,

Freq2

, [

CLevel

]]]

(Data list input) zInterval_2Samp s

, s

, v 1

, n1

, v 2

, n2

[ ,

CLevel

]

(Summary stats input)

Computes a two-sample z confidence interval. A summary of results is stored in the stat.results

variable. (See page 119.)

For information on the effect of empty elements in a list, see “Empty

(void) elements” on page 159.

Catalog >

Output variable Description stat.CLower, stat.CUpper

Confidence interval containing confidence level probability of distribution stat.

x 1

x 2 Sample means of the data sequences from the normal random distribution stat.ME

stat.

x 1, stat.

x 2 stat.

s x1, stat.

s x2

Margin of error

Sample means of the data sequences from the normal random distribution

Sample standard deviations for

List 1

and

List 2 stat.n1, stat.n2

stat.r1, stat.r2

Number of samples in data sequences

Known population standard deviations for data sequence List 1 and List 2

TI-Nspire™ CAS Reference Guide 139

zTest zTest m 0

, s

List

, [

Freq

[ ,

Hypoth

]]

(Data list input) zTest m 0

, s

, v

, n

[ ,

Hypoth

]

(Summary stats input)

Performs a z test with frequency freqlist . A summary of results is stored in the stat.results

variable. (See page 119.)

Test H

: m = m 0, against one of the following:

For H a

: m < m 0, set Hypoth <0

For H a

: m ƒ m 0 (default), set Hypoth =0

For H a

: m > m 0, set

Hypoth

For information on the effect of empty elements in a list, see “Empty

(void) elements” on page 159.

Output variable stat.z

stat.P Value stat.

x stat.sx

stat.n

Description

( x N m 0) / ( s / sqrt(n))

Least probability at which the null hypothesis can be rejected

Sample mean of the data sequence in

List

Sample standard deviation of the data sequence. Only returned for Data input.

Size of the sample

Catalog > zTest_1Prop zTest_1Prop p0 , x , n [ , Hypoth ]

Computes a one-proportion z test. A summary of results is stored in the stat.results

variable. (See page 119.) x is a non-negative integer.

Test H

: p = p0 against one of the following:

For H a

: p > p0 , set Hypoth >0

For H a

: p ƒ p0 (default) , set

: p < p0 , set Hypoth <0

Hypoth =0

For information on the effect of empty elements in a list, see “Empty

(void) elements” on page 159.

Output variable stat.p0

stat.z

stat.PVal

stat.

Ç stat.n

Description

Hypothesized population proportion

Standard normal value computed for the proportion

Smallest level of significance at which the null hypothesis can be rejected

Estimated sample proportion

Size of the sample

Catalog >

140 TI-Nspire™ CAS Reference Guide

zTest_2Prop zTest_2Prop x1

, n1

, x2

, n2

[ ,

Hypoth

]

Computes a two-proportion z

test. A summary of results is stored in the stat.results

variable. (See page 119.) x1

and x2

are non-negative integers.

Test H

: p1 = p2 , against one of the following:

For H a

: p1 > p2 , set Hypoth >0

For H a

: p1 ƒ p2 (default), set

: p < p0

, set

Hypoth

Hypoth =0

For information on the effect of empty elements in a list, see “Empty

(void) elements” on page 159.

Output variable stat.z

stat.PVal

stat.

1 stat.

2 stat.

Ç stat.n1, stat.n2

Description

Standard normal value computed for the difference of proportions

Smallest level of significance at which the null hypothesis can be rejected

First sample proportion estimate

Second sample proportion estimate

Pooled sample proportion estimate

Number of samples taken in trials 1 and 2 zTest_2Samp zTest_2Samp s

, s

List1

List2

[ ,

Freq1

[ ,

Freq2

[ ,

Hypoth

]]]

(Data list input) zTest_2Samp s

1 , s

2 , v 1

, n1

, v 2

, n2

[ ,

Hypoth

]

(Summary stats input)

Computes a two-sample z

test. A summary of results is stored in the stat.results

variable. (See page 119.)

Test H

: m 1 = m 2, against one of the following:

For H a

: m 1 < m 2, set Hypoth <0

For H a

: m 1 ƒ m 2 (default), set Hypoth =0 m 1 > m 2, Hypoth >0

For information on the effect of empty elements in a list, see “Empty

(void) elements” on page 159.

Catalog >

Output variable stat.z

stat.PVal

stat.

x 1 , stat.

x 2 stat.sx1, stat.sx2

stat.n1, stat.n2

Description

Standard normal value computed for the difference of means

Smallest level of significance at which the null hypothesis can be rejected

Sample means of the data sequences in

List1

and

List2

Sample standard deviations of the data sequences in List1 and List2

Size of the samples

TI-Nspire™ CAS Reference Guide 141

Symbols

+ (add)

Expr1

Expr2

⇒ expression

Returns the sum of the two arguments.

List1

List2 ⇒ list

Matrix1

Matrix2 ⇒ matrix

Returns a list (or matrix) containing the sums of corresponding elements in List1 and List2 (or Matrix1 and Matrix2 ).

Dimensions of the arguments must be equal.

Expr

List1

Expr

⇒ list

Returns a list containing the sums of

Expr

and each element in

List1

Expr

Matrix1

Expr

⇒ matrix

Returns a matrix with Expr added to each element on the diagonal of

Matrix1 . Matrix1 must be square.

Note: Use .+ (dot plus) to add an expression to each element.

N (subtract)

Expr1 N Expr2

⇒ expression

Returns

Expr1

minus

Expr2

List1 N List2 ⇒ list

Matrix1 N Matrix2

⇒ matrix

Subtracts each element in

List2

(or

Matrix2

) from the corresponding element in List1 (or Matrix1 ), and returns the results.

Dimensions of the arguments must be equal.

Expr N List1

⇒ list

List1 N Expr ⇒ list

Subtracts each List1 element from Expr or subtracts Expr from each

List1

element, and returns a list of the results.

142 TI-Nspire™ CAS Reference Guide

key

N (subtract)

Expr N Matrix1 ⇒ matrix

Matrix1 N Expr ⇒ matrix

Expr N Matrix1

returns a matrix of

Expr minus

Matrix1

must be square.

times the identity matrix

Matrix1 N Expr

returns a matrix of

Expr times the identity matrix subtracted from Matrix1 .

Matrix1 must be square.

Note: Use .

N (dot minus) to subtract an expression from each element.

· (multiply)

Expr1 · Expr2

⇒ expression

Returns the product of the two arguments.

List1 · List2 ⇒ list

Returns a list containing the products of the corresponding elements in List1 and List2 .

Dimensions of the lists must be equal.

Matrix1 · Matrix2

⇒ matrix

Returns the matrix product of

Matrix1

and

Matrix2

The number of columns in Matrix1 must equal the number of rows in

Matrix2

Expr · List1

⇒ list

List1 · Expr

⇒ list

Returns a list containing the products of Expr and each element in

List1 .

Expr · Matrix1 ⇒ matrix

Matrix1 · Expr ⇒ matrix

Returns a matrix containing the products of Expr and each element in

Matrix1 .

Note: Use .

· (dot multiply) to multiply an expression by each element.

à (divide)

Expr1 à Expr2

⇒ expression

Returns the quotient of

Expr1

divided by

Expr2

Note: See also Fraction template , page 1.

key r

key p

key

TI-Nspire™ CAS Reference Guide 143

à (divide)

List1 à List2 ⇒ list

Returns a list containing the quotients of

List1

divided by

List2 .

Dimensions of the lists must be equal.

Expr à List1

⇒ list

List1 à Expr ⇒ list

Returns a list containing the quotients of

Expr

divided by

List1 or

List1

divided by

Expr .

Matrix1 à Expr ⇒ matrix

Returns a matrix containing the quotients of Matrix1 à Expr .

Note: Use . / (dot divide) to divide an expression by each element.

^ (power)

Expr1

Expr2

⇒

List1

List2

⇒ expression list

Returns the first argument raised to the power of the second argument.

Note: See also Exponent template , page 1.

For a list, returns the elements in

List1

raised to the power of the corresponding elements in List2 .

In the real domain, fractional powers that have reduced exponents with odd denominators use the real branch versus the principal branch for complex mode.

Expr

List1 ⇒ list

Returns

Expr

raised to the power of the elements in

List1

Expr ⇒ list

Returns the elements in List1 raised to the power of Expr .

squareMatrix1

^ integer

⇒ matrix

Returns squareMatrix1 raised to the integer power.

squareMatrix1 must be a square matrix.

If integer = L 1, computes the inverse matrix.

If integer < L 1, computes the inverse matrix to an appropriate positive power.

144 TI-Nspire™ CAS Reference Guide p

key l

key

(square)

Expr1 2 ⇒ expression

Returns the square of the argument.

List1 2 ⇒ list

Returns a list containing the squares of the elements in List1 .

squareMatrix1 2 ⇒ matrix

Returns the matrix square of squareMatrix1

. This is not the same as calculating the square of each element. Use .^2 to calculate the square of each element.

.+ (dot add)

Matrix1

Matrix2

⇒ matrix

Expr

Matrix1

⇒ matrix

Matrix1 .+ Matrix2 returns a matrix that is the sum of each pair of corresponding elements in

Matrix1

and

Matrix2

Expr .+ Matrix1 returns a matrix that is the sum of Expr and each element in

Matrix1

(dot subt.)

Matrix1

N Matrix2

⇒ matrix

Expr

N Matrix1 ⇒ matrix

Matrix1 .

N Matrix2 returns a matrix that is the difference between each pair of corresponding elements in Matrix1 and Matrix2 .

Expr

N Matrix1

returns a matrix that is the difference of

Expr

and each element in Matrix1 .

· (dot mult.)

Matrix1

· Matrix2 ⇒ matrix

Expr

· Matrix1 ⇒ matrix

Matrix1 .

· Matrix2 returns a matrix that is the product of each pair of corresponding elements in Matrix1 and Matrix2 .

Expr .

· Matrix1 returns a matrix containing the products of Expr and each element in Matrix1 .

key

keys

TI-Nspire™ CAS Reference Guide 145

. / (dot divide)

Matrix1

. /

Matrix2

⇒ matrix

Expr

. /

Matrix1 ⇒ matrix

Matrix1 ./ Matrix2 returns a matrix that is the quotient of each pair of corresponding elements in

Matrix1

and

Matrix2

Expr ./ Matrix1 returns a matrix that is the quotient of Expr and each element in Matrix1 .

keys

.^ (dot power)

Matrix1 .

Matrix2

⇒ matrix

Expr .

Matrix1 ⇒ matrix

Matrix1 .^ Matrix2 returns a matrix where each element in Matrix2 is the exponent for the corresponding element in

Matrix1

Expr

Matrix1

returns a matrix where each element in

Matrix1

is the exponent for Expr .

L (negate)

L Expr1 ⇒ expression

LL List1 ⇒ list

L Matrix1 ⇒ matrix

Returns the negation of the argument.

For a list or matrix, returns all the elements negated.

If the argument is a binary or hexadecimal integer, the negation gives the two’s complement.

In Bin base mode:

Important: Zero, not the letter O

keys v

key

To see the entire result, press

and then use

and

to move the cursor.

% (percent)

Expr1

⇒ expression

List1

⇒ list

Matrix1

⇒ matrix

Returns

Press Ctrl + Enter evaluate:

keys

/·

(Macintosh®: “ + Enter ) to

For a list or matrix, returns a list or matrix with each element divided by 100.

Press Ctrl + Enter

/·

(Macintosh®: “ + Enter ) to evaluate:

146 TI-Nspire™ CAS Reference Guide

= (equal)

Expr1

Expr2

List1

List2

⇒

⇒ Boolean expression

Boolean list

Matrix1

Matrix2 ⇒ Boolean matrix

Returns true if Expr1 is determined to be equal to Expr2 .

Returns false if

Expr1

is determined to not be equal to

Expr2

Anything else returns a simplified form of the equation.

For lists and matrices, returns comparisons element by element.

Note for entering the example: In the Calculator application on the handheld, you can enter multi-line definitions by pressing

@ instead of

at the end of each line. On the computer keyboard, hold down Alt and press Enter .

key

Example function that uses math test symbols: =, ƒ , <, { , >, |

Result of graphing g(x)

ƒ (not equal)

Expr1 ƒ Expr2 ⇒ Boolean expression

List1 ƒ List2 ⇒ Boolean list

Matrix1 ƒ Matrix2

⇒

Boolean matrix

Returns true if

Expr1

is determined to be not equal to

Expr2

Returns false if Expr1 is determined to be equal to Expr2 .

Anything else returns a simplified form of the equation.

For lists and matrices, returns comparisons element by element.

Note: You can insert this operator from the keyboard by typing /=

See “=” (equal) example.

< (less than)

Expr1

Expr2 ⇒ Boolean expression

List1

List2

⇒

Boolean list

Matrix1

Matrix2

⇒

Boolean matrix

Returns true if Expr1 is determined to be less than Expr2 .

Returns false if Expr1 is determined to be greater than or equal to

Expr2 .

Anything else returns a simplified form of the equation.

For lists and matrices, returns comparisons element by element.

See “=” (equal) example.

keys

TI-Nspire™ CAS Reference Guide 147

{ (less or equal)

Expr1 { Expr2

⇒

Boolean expression

List1 { List2 ⇒ Boolean list

Matrix1 { Matrix2 ⇒ Boolean matrix

Returns true if Expr1 is determined to be less than or equal to Expr2 .

Returns false if Expr1 is determined to be greater than Expr2 .

Anything else returns a simplified form of the equation.

See “=” (equal) example.

For lists and matrices, returns comparisons element by element.

Note: You can insert this operator from the keyboard by typing <=

> (greater than)

Expr1

Expr2

⇒

Boolean expression

List1

List2 ⇒ Boolean list

Matrix1

Matrix2 ⇒ Boolean matrix

Returns true if Expr1 is determined to be greater than Expr2 .

Returns false if Expr1 is determined to be less than or equal to

Expr2 .

Anything else returns a simplified form of the equation.

For lists and matrices, returns comparisons element by element.

See “=” (equal) example.

| (greater or equal)

Expr1 | Expr2 ⇒ Boolean expression

List1 | List2 ⇒ Boolean list

Matrix1 | Matrix2

⇒

Boolean matrix

Returns true if Expr1 is determined to be greater than or equal to

Expr2 .

Returns false if Expr1 is determined to be less than Expr2 .

Anything else returns a simplified form of the equation.

For lists and matrices, returns comparisons element by element.

Note: You can insert this operator from the keyboard by typing >=

See “=” (equal) example.

! (factorial)

Expr1 !

⇒ expression

List1

⇒ list

Matrix1 !

⇒ matrix

Returns the factorial of the argument.

For a list or matrix, returns a list or matrix of factorials of the elements.

& (append)

String1

String2 ⇒ string

Returns a text string that is String2 appended to String1 .

keys

key

keys

148 TI-Nspire™ CAS Reference Guide

d () (derivative) d (

Expr1

Var

[ ,

Order

] )

⇒ expression d (

List1 , Var

[ ,

Order

] )

⇒ list d (

Matrix1 , Var

[ ,

Order

] )

⇒ matrix

Returns the first derivative of the first argument with respect to variable Var .

Order , if included, must be an integer. If the order is less than zero, the result will be an anti-derivative.

Note: You can insert this function from the keyboard by typing derivative( ...

) .

d () does not follow the normal evaluation mechanism of fully simplifying its arguments and then applying the function definition to these fully simplified arguments. Instead, d () performs the following steps:

Simplify the second argument only to the extent that it does not lead to a non-variable.

Simplify the first argument only to the extent that it does recall any stored value for the variable determined by step 1.

Determine the symbolic derivative of the result of step 2 with respect to the variable from step 1.

If the variable from step 1 has a stored value or a value specified by a

“with” (|) operator, substitute that value into the result from step 3.

Note: See also First derivative , page 5;

Second derivative , page 5; or Nth derivative , page 5.

‰ () (integral)

‰

(

Expr1

Var

[ ,

Lower

Upper

] )

⇒ expression

‰

(

Expr1 , Var

[ ,

Constant

] )

⇒ expression

Returns the integral of

Expr1

with respect to the variable

Var

from

Lower to Upper .

Note: See also Definite or Indefinite integral template , page

Note: You can insert this function from the keyboard by typing integral( ...

) .

If Lower and Upper are omitted, returns an anti-derivative. A symbolic constant of integration is omitted unless you provide the

Constant argument.

Catalog >

Equally valid anti-derivatives might differ by a numeric constant. Such a constant might be disguised—particularly when an anti-derivative contains logarithms or inverse trigonometric functions. Moreover, piecewise constant expressions are sometimes added to make an anti-derivative valid over a larger interval than the usual formula.

‰ () returns itself for pieces of

Expr1

that it cannot determine as an explicit finite combination of its built-in functions and operators.

When you provide Lower and Upper , an attempt is made to locate any discontinuities or discontinuous derivatives in the interval Lower

< Var < Upper

and to subdivide the interval at those places.

TI-Nspire™ CAS Reference Guide 149

‰ () (integral)

For the Auto setting of the Auto or Approximate mode, numerical integration is used where applicable when an antiderivative or a limit cannot be determined.

For the Approximate setting, numerical integration is tried first, if applicable. Anti-derivatives are sought only where such numerical integration is inapplicable or fails.

Catalog >

Press Ctrl + Enter

/·

(Macintosh®: “ + Enter ) to evaluate:

‰ () can be nested to do multiple integrals. Integration limits can depend on integration variables outside them.

Note: See also nInt() , page 82.

keys ‡ () (square root)

‡

(

Expr1

)

⇒ expression

‡

(

List1

)

⇒ list

Returns the square root of the argument.

For a list, returns the square roots of all the elements in List1 .

Note: You can insert this function from the keyboard by typing sqrt( ...

)

Note: See also Square root template , page 1.

() (prodSeq)

(

Expr1

Var

Low

High

)

⇒ expression

Note: You can insert this function from the keyboard by typing prodSeq( ...

) .

Evaluates Expr1 for each value of Var from Low to High , and returns the product of the results.

Note: See also Product template (

Π)

, page 4.

Catalog >

150 TI-Nspire™ CAS Reference Guide

() (prodSeq)

(

Expr1

Var

Low

Low N

1 )

⇒

(

Expr1

Var

Low

High

)

⇒

(

Expr1

Var

High+1

Low N 1

) if

High

Low N 1

The product formulas used are derived from the following reference:

Ronald L. Graham, Donald E. Knuth, and Oren Patashnik. Concrete

Mathematics: A Foundation for Computer Science

. Reading,

Massachusetts: Addison-Wesley, 1994.

G () (sumSeq)

(

Expr1

Var

Low

High

)

⇒ expression

Note: You can insert this function from the keyboard by typing sumSeq( ...

) .

Evaluates

Expr1

for each value of

Var

from

Low

High

, and returns the sum of the results.

Note: See also Sum template , page 4.

(

Expr1

Var

Low

Low N 1

)

⇒

(

Expr1

Var

Low

High

)

⇒ MG

(

Expr1

Var

High+1

Low N

1 ) if

High

Low N 1

The summation formulas used are derived from the following reference:

Ronald L. Graham, Donald E. Knuth, and Oren Patashnik. Concrete

Mathematics: A Foundation for Computer Science . Reading,

Massachusetts: Addison-Wesley, 1994.

Catalog >

TI-Nspire™ CAS Reference Guide 151

G Int()

Int(

NPmt1

NPmt2

, [

Pmt

] , [

PpY

] , [

CpY

] ,

[

PmtAt

] , [ roundValue

] )

⇒ value

Int(

NPmt1

NPmt2

, amortTable

)

⇒ value

Amortization function that calculates the sum of the interest during a specified range of payments.

NPmt1

and

NPmt2

define the start and end boundaries of the payment range.

Pmt

PpY

CpY

, and

PmtAt

are described in the table of TVM arguments, page 131.

• If you omit

Pmt

, it defaults to

Pmt = tvmPmt( N , I , PV , FV , PpY , CpY , PmtAt ) .

• If you omit

, it defaults to

=0.

• The defaults for PpY , CpY , and PmtAt are the same as for the

TVM functions.

roundValue specifies the number of decimal places for rounding.

Default=2.

G Int( NPmt1,NPmt2 , amortTable ) calculates the sum of the interest based on amortization table amortTable . The amortTable argument must be a matrix in the form described under amortTbl() , page 7.

Note: See also G Prn() , below, and Bal() , page 13.

G Prn()

Prn(

NPmt1

NPmt2

, [

Pmt

] , [

PpY

] , [

CpY

] ,

[

PmtAt

] , [ roundValue

] )

⇒ value

Prn( NPmt1 , NPmt2 , amortTable )

⇒ value

Amortization function that calculates the sum of the principal during a specified range of payments.

NPmt1 and NPmt2 define the start and end boundaries of the payment range.

N , I , PV , Pmt , FV , PpY , CpY , and PmtAt are described in the table of TVM arguments, page 131.

• If you omit Pmt , it defaults to

Pmt = tvmPmt( N , I , PV , FV , PpY , CpY , PmtAt ) .

• If you omit FV , it defaults to FV =0.

• The defaults for PpY , CpY , and PmtAt are the same as for the

TVM functions.

roundValue specifies the number of decimal places for rounding.

Default=2.

G Prn( NPmt1,NPmt2 , amortTable ) calculates the sum of the principal paid based on amortization table amortTable . The amortTable argument must be a matrix in the form described under amortTbl() , page 7.

Note: See also G Int() , above, and Bal() , page 13.

152 TI-Nspire™ CAS Reference Guide

Catalog >

# (indirection)

# varNameString

Refers to the variable whose name is varNameString . This lets you use strings to create variable names from within a function.

Creates or refers to the variable xyz .

keys

(scientific notation) mantissa

E exponent

Enters a number in scientific notation. The number is interpreted as mantissa × 10 exponent

Hint: If you want to enter a power of 10 without causing a decimal value result, use 10^ integer .

Note: You can insert this operator from the computer keyboard by typing @E . for example, type 2.3@E4 to enter 2.3

E 4.

Returns the value of the variable (r) whose name is stored in variable s1.

key g

(gradian)

Expr1 g

List1 g

⇒ expression

⇒ list

Matrix1 g ⇒ matrix

This function gives you a way to specify a gradian angle while in the

Degree or Radian mode.

In Radian angle mode, multiplies

Expr1

by p /200.

In Degree angle mode, multiplies

Expr1

by g/100.

In Gradian mode, returns Expr1 unchanged.

Note: You can insert this symbol from the computer keyboard by typing @g .

In Degree, Gradian or Radian mode:

(radian)

Expr1 R ⇒ expression

List1 R ⇒ list

Matrix1 R ⇒ matrix

This function gives you a way to specify a radian angle while in

Degree or Gradian mode.

In Degree angle mode, multiplies the argument by 180/ p .

In Radian angle mode, returns the argument unchanged.

In Gradian mode, multiplies the argument by 200/ p .

Hint: Use R if you want to force radians in a function definition regardless of the mode that prevails when the function is used.

Note: You can insert this symbol from the computer keyboard by typing @r .

In Degree, Gradian or Radian angle mode:

key

TI-Nspire™ CAS Reference Guide 153

¡ (degree)

Expr1 ¡ ⇒ expression

List1 ¡ ⇒ list

Matrix1 ¡ ⇒ matrix

This function gives you a way to specify a degree angle while in

Gradian or Radian mode.

In Radian angle mode, multiplies the argument by p /180.

In Degree angle mode, returns the argument unchanged.

In Gradian angle mode, multiplies the argument by 10/9.

Note: You can insert this symbol from the computer keyboard by typing @d .

In Degree, Gradian or Radian angle mode:

In Radian angle mode:

key

Press Ctrl + Enter

/·

(Macintosh®: “ + Enter ) to evaluate:

¡ , ', '' (degree/minute/second) dd ¡ mm

' ss.ss

⇒ expression dd A positive or negative number mm

A non-negative number ss.ss

A non-negative number

Returns dd

+( mm

/60)+( ss.ss

/3600).

This base-60 entry format lets you:

• Enter an angle in degrees/minutes/seconds without regard to the current angle mode.

• Enter time as hours/minutes/seconds.

Note: Follow ss.ss with two apostrophes ( '' ), not a quote symbol (").

In Degree angle mode:

keys

± (angle)

[

Radius

, ±q _Angle

]

⇒ vector

(polar input)

[ Radius , ±q _Angle , Z_Coordinate ]

⇒ vector

(cylindrical input)

[ Radius , ±q _Angle , ±q _Angle ]

⇒ vector

(spherical input)

Returns coordinates as a vector depending on the Vector Format mode setting: rectangular, cylindrical, or spherical.

Note: You can insert this symbol from the computer keyboard by typing @< .

In Radian mode and vector format set to: rectangular cylindrical spherical

keys

154 TI-Nspire™ CAS Reference Guide

± (angle) /k

keys

( Magnitude ± Angle )

⇒ complexValue

(polar input)

Enters a complex value in (r ±q ) polar form. The

Angle

is interpreted according to the current Angle mode setting.

In Radian angle mode and Rectangular complex format:

Press Ctrl + Enter

/·

(Macintosh®: “ + Enter ) to evaluate:

' (prime) variable

' variable

Enters a prime symbol in a differential equation. A single prime symbol denotes a 1st-order differential equation, two prime symbols denote a 2nd-order, and so on.

key

_ (underscore as an empty element) See “Empty (void) elements” , page 159.

_ (underscore as unit designator) /_

keys

Expr

Unit

Designates the units for an

Expr

. All unit names must begin with an underscore.

Note: You can find the conversion symbol, 4 , in the Catalog.

You can use pre-defined units or create your own units. For a list of pre-defined units, open the Catalog and display the Unit Conversions tab. You can select unit names from the Catalog or type the unit names directly.

Variable

Click , and then click

Assuming z is undefined:

Math Operators .

When

Variable

has no value, it is treated as though it represents a complex number. By default, without the _ , the variable is treated as real.

If Variable has a value, the _ is ignored and Variable retains its original data type.

Note: You can store a complex number to a variable without using _ . However, for best results in calculations such as cSolve() and cZeros() , the _ is recommended.

TI-Nspire™ CAS Reference Guide 155

4 (convert)

Expr

Unit1 4

Unit2 ⇒ Expr

Unit2

Converts an expression from one unit to another.

The _ underscore character designates the units. The units must be in the same category, such as Length or Area.

For a list of pre-defined units, open the Catalog and display the Unit

Conversions tab:

• You can select a unit name from the list.

• You can select the conversion operator, 4 , from the top of the list.

You can also type unit names manually. To type “_” when typing unit names on the handheld, press

Note: To convert temperature units, use tmpCnv() and

@ tmpCnv() . The 4 conversion operator does not handle temperature units.

10^()

10^ (

Expr1

)

10^ (

List1

)

⇒ expression

⇒ list

Returns 10 raised to the power of the argument.

For a list, returns 10 raised to the power of the elements in

List1

10^( squareMatrix1

)

⇒ squareMatrix

Returns 10 raised to the power of squareMatrix1 . This is not the same as calculating 10 raised to the power of each element. For information about the calculation method, refer to cos() .

squareMatrix1

must be diagonalizable. The result always contains floating-point numbers.

^ / (reciprocal)

Expr1

/ ⇒ expression

List1

/ ⇒ list

Returns the reciprocal of the argument.

For a list, returns the reciprocals of the elements in List1 .

squareMatrix1

/ ⇒ squareMatrix

Returns the inverse of squareMatrix1 .

squareMatrix1 must be a non-singular square matrix.

keys

Catalog >

156 TI-Nspire™ CAS Reference Guide

| (“with”)

Expr

BooleanExpr1

[ and

BooleanExpr2

]...

The “with” (|) symbol serves as a binary operator. The operand to the left of | is an expression. The operand to the right of | specifies one or more relations that are intended to affect the simplification of the expression. Multiple relations after | must be joined by a logical

“ and ”.

The “with” operator provides three basic types of functionality: substitutions, interval constraints, and exclusions.

Substitutions are in the form of an equality, such as x=3 or y=sin(x).

To be most effective, the left side should be a simple variable.

Expr

Variable = value will substitute value for every occurrence of

Variable in Expr .

Interval constraints take the form of one or more inequalities joined by logical “ and ” operators. Interval constraints also permit simplification that otherwise might be invalid or not computable.

Exclusions use the “not equals” (/= or ƒ ) relational operator to exclude a specific value from consideration. They are used primarily to exclude an exact solution when using cSolve() , cZeros() , fMax() , fMin() , solve() , zeros() , and so on.

& (store)

Expr & Var

List & Var

Matrix & Var

Expr & Function

(

Param1

, ...

)

List & Function

(

Param1

, ...

)

Matrix & Function

(

Param1

, ...

)

If the variable Var does not exist, creates it and initializes it to Expr ,

List

, or

Matrix

If the variable Var already exists and is not locked or protected, replaces its contents with

Expr

List

, or

Matrix

Hint: If you plan to do symbolic computations using undefined variables, avoid storing anything into commonly used, one-letter variables such as a, b, c, x, y, z, and so on.

Note: You can insert this operator from the keyboard by typing =: as a shortcut. For example, type pi/4 =: myvar .

keys

key

TI-Nspire™ CAS Reference Guide 157

:= (assign)

Var

Expr

Var

List

Var

Matrix

Function

(

Param1

, ...

) :=

Expr

Function

(

Param1

, ...

) :=

List

Function

(

Param1

, ...

) :=

Matrix

If variable Var does not exist, creates Var and initializes it to Expr ,

List , or Matrix .

If Var already exists and is not locked or protected, replaces its contents with Expr , List , or Matrix .

Hint: If you plan to do symbolic computations using undefined variables, avoid storing anything into commonly used, one-letter variables such as a, b, c, x, y, z, and so on.

© [ text

]

as a comment line, allowing you to annotate functions and programs that you create.

Note for entering the example: In the Calculator application on the handheld, you can enter multi-line definitions by pressing

@ instead of

at the end of each line. On the computer keyboard, hold down Alt and press Enter .

keys

0b, 0h

0b binaryNumber

0h hexadecimalNumber

In Dec base mode:

Denotes a binary or hexadecimal number, respectively. To enter a binary or hex number, you must enter the 0b or 0h prefix regardless of the Base mode. Without a prefix, a number is treated as decimal

(base 10).

In Bin base mode:

Results are displayed according to the Base mode.

In Hex base mode:

keys,

keys

158 TI-Nspire™ CAS Reference Guide

Empty (void) elements

When analyzing real-world data, you might not always have a complete data set.

TI-Nspire™ CAS Software allows empty, or void, data elements so you can proceed with the nearly complete data rather than having to start over or discard the incomplete cases.

You can find an example of data involving empty elements in the Lists & Spreadsheet chapter, under “ Graphing spreadsheet data .”

The delVoid() function lets you remove empty elements from a list. The isVoid() function lets you test for an empty element. For details, see delVoid() , page 35 , and isVoid() , page 61 .

Note: To enter an empty element manually in a math expression, type “_” or the keyword void . The keyword void is automatically converted to a “_” symbol when the expression is evaluated. To type “_” on the handheld, press

/ _

Calculations involving void elements

The majority of calculations involving a void input will produce a void result. See special cases below.

List arguments containing void elements

The following functions and commands ignore (skip) void elements found in list arguments. count , countIf , cumulativeSum , freqTable 4 list , frequency , max , mean , median , product , stDevPop , stDevSamp , sum , sumIf , varPop , and varSamp , as well as regression calculations,

OneVar , TwoVar , and FiveNumSummary statistics, confidence intervals, and stat tests

SortA and SortD move all void elements within the first argument to the bottom.

TI-Nspire™ CAS Reference Guide 159

List arguments containing void elements(continued)

In regressions, a void in an X or Y list introduces a void for the corresponding element of the residual.

An omitted category in regressions introduces a void for the corresponding element of the residual.

A frequency of 0 in regressions introduces a void for the corresponding element of the residual.

160 TI-Nspire™ CAS Reference Guide

Shortcuts for entering math expressions

Shortcuts let you enter elements of math expressions by typing instead of using the Catalog or

Symbol Palette. For example, to enter the expression ‡ 6, you can type sqrt(6) on the entry line.

When you press

, the expression sqrt(6) is changed to ‡ 6. Some shortrcuts are useful from both the handheld and the computer keyboard. Others are useful primarily from the computer keyboard.

From the handheld or computer keyboard

To enter this: p q

{

& ( store operator)

| | (absolute value)

‡ () d

()

‰ ()

G () (Sum template)

() (Product template) sin / () , cos / () , ...

@ List()

@ tmpCnv()

From the computer keyboard

Type this shortcut: pi theta infinity abs( ...

) sqrt( ...

) derivative( ...

) integral( ...

) sumSeq( ...

) prodSeq( ...

) arcsin( ...

) , arccos( ...

) , ...

deltaList( ...

) deltaTmpCnv( ...

)

To enter this: c1 , c2 , ... (constants)

Type this shortcut:

@c1 , @c2 , ... n1

, n2

, ... (integer constants) @n1 , @n2 , ...

i (imaginary constant) @i e (natural log base e)

E (scientific notation)

TI-Nspire™ CAS Reference Guide 161

To enter this:

T (transpose)

R (radians)

¡ (degrees) g (gradians)

± (angle)

4 (conversion)

4 Decimal , 4 approxFraction() , and so on.

Type this shortcut:

@>Decimal , @>approxFraction() , and so on.

162 TI-Nspire™ CAS Reference Guide

EOS™ (Equation Operating System) hierarchy

This section describes the Equation Operating System (EOS™) that is used by the

TI-Nspire™ CAS math and science learning technology. Numbers, variables, and functions are entered in a simple, straightforward sequence. EOS™ software evaluates expressions and equations using parenthetical grouping and according to the priorities described below.

Order of evaluation

Level

Operator

Parentheses ( ), brackets [ ], braces { }

Indirection (#)

Function calls

(

Post operators: degrees-minutes-seconds ( ¡ ,',"), factorial (!), percentage (%), radian

RS ), subscript ([ ]), transpose ( T )

Exponentiation, power operator (^)

Negation (

)

String concatenation (&)

Multiplication ( † ), division (/)

Addition (+), subtraction (-)

Equality relations: equal (=), not equal ( ƒ or /=), less than (<), less than or equal ( { or <=), greater than (>), greater than or equal

( | or >=)

Logical not

Logical and

Logical or , exclusive logical xor

Constraint “with” operator (|)

Store ( & )

Parentheses, brackets, and braces

All calculations inside a pair of parentheses, brackets, or braces are evaluated first. For example, in the expression 4(1+2), EOS™ software first evaluates the portion of the expression inside the parentheses, 1+2, and then multiplies the result, 3, by 4.

The number of opening and closing parentheses, brackets, and braces must be the same within an expression or equation. If not, an error message is displayed that indicates the missing element. For example, (1+2)/(3+4 will display the error message “Missing ).”

Note: Because the TI-Nspire™ CAS software allows you to define your own functions, a variable name followed by an expression in parentheses is considered a “function call” instead of implied multiplication. For example a (b+c) is the function a evaluated by b+c. To multiply the expression b+c by the variable a , use explicit multiplication: a

∗

(b+c).

TI-Nspire™ CAS Reference Guide 163

Indirection

The indirection operator (#) converts a string to a variable or function name. For example,

#(“x”&”y”&”z”) creates the variable name xyz. Indirection also allows the creation and modification of variables from inside a program. For example, if 10 & r and “r” & s1, then #s1=10.

Post operators

Post operators are operators that come directly after an argument, such as 5!, 25%, or 60 ¡ 15'

45". Arguments followed by a post operator are evaluated at the fourth priority level. For example, in the expression 4^3!, 3! is evaluated first. The result, 6, then becomes the exponent of 4 to yield 4096.

Exponentiation

Exponentiation (^) and element-by-element exponentiation (.^) are evaluated from right to left. For example, the expression 2^3^2 is evaluated the same as 2^(3^2) to produce 512. This is different from (2^3)^2, which is 64.

Negation

To enter a negative number, press v

followed by the number. Post operations and exponentiation are performed before negation. For example, the result of L x

is a negative number, and L 9

= L 81. Use parentheses to square a negative number such as ( L 9)

to produce

81.

Constraint (|)

The argument following the “with” (|) operator provides a set of constraints that affect the evaluation of the argument preceding the “with” operator.

164 TI-Nspire™ CAS Reference Guide

100

130

140

160

165

170

180

Error codes and messages

When an error occurs, its code is assigned to variable errCode . User-defined programs and functions can examine errCode to determine the cause of an error. For an example of using errCode , See Example 2 under the Try command, page 129 .

Note: Some error conditions apply only to TI-Nspire™ CAS products, and some apply only to

TI-Nspire™ products.

Error code

190

200

210

220

Description

A function did not return a value

A test did not resolve to TRUE or FALSE.

Generally, undefined variables cannot be compared. For example, the test If a<b will cause this error if either a or b is undefined when the If statement is executed.

Argument cannot be a folder name.

Argument error

Argument mismatch

Two or more arguments must be of the same type.

Argument must be a Boolean expression or integer

Argument must be a decimal number

Argument must be a list

Argument must be a matrix

Argument must be a string

Argument must be a variable name.

Make sure that the name:

• does not begin with a digit

• does not contain spaces or special characters

• does not use underscore or period in invalid manner

• does not exceed the length limitations

See the Calculator section in the documentation for more details.

Argument must be an expression

Batteries too low for sending or receiving

Install new batteries before sending or receiving.

Bound

The lower bound must be less than the upper bound to define the search interval.

Break

The d

or c

key was pressed during a long calculation or during program execution.

Circular definition

This message is displayed to avoid running out of memory during infinite replacement of variable values during simplification. For example, a+1->a, where a is an undefined variable, will cause this error.

Constraint expression invalid

For example, solve(3x^2-4=0,x) | x<0 or x>5 would produce this error message because the constraint is separated by “or” instead of “and.”

Invalid Data type

An argument is of the wrong data type.

Dependent limit

TI-Nspire™ CAS Reference Guide 165

450

490

510

550

320

345

350

360

380

390

400

410

430

435

440

250

260

295

300

310

270

280

290

Error code

230

235

240

560

565

Description

Dimension

A list or matrix index is not valid. For example, if the list {1,2,3,4} is stored in L1, then L1[5] is a dimension error because L1 only contains four elements.

Dimension Error. Not enough elements in the lists.

Dimension mismatch

Two or more arguments must be of the same dimension. For example, [1,2]+[1,2,3] is a dimension mismatch because the matrices contain a different number of elements.

Divide by zero

Domain error

An argument must be in a specified domain. For example, rand(0) is not valid.

Duplicate variable name

Else and ElseIf invalid outside of If...EndIf block

EndTry is missing the matching Else statement

Excessive iteration

Expected 2 or 3-element list or matrix

The first argument of nSolve must be an equation in a single variable. It cannot contain a non-valued variable other than the variable of interest.

First argument of solve or cSolve must be an equation or inequality

For example, solve(3x^2-4,x) is invalid because the first argument is not an equation.

Inconsistent units

Index out of range

Indirection string is not a valid variable name

Undefined Ans

Either the previous calculation did not create Ans, or no previous calculation was entered.

Invalid assignment

Invalid assignment value

Invalid command

Invalid for the current mode settings

Invalid guess

Invalid implied multiply

For example, x(x+1) is invalid; whereas, x*(x+1) is the correct syntax. This is to avoid confusion between implied multiplication and function calls.

Invalid in a function or current expression

Only certain commands are valid in a user-defined function.

Invalid in Try..EndTry block

Invalid list or matrix

Invalid outside function or program

A number of commands are not valid outside a function or program. For example, Local cannot be used unless it is in a function or program.

Invalid outside Loop..EndLoop, For..EndFor, or While..EndWhile blocks

For example, the Exit command is valid only inside these loop blocks.

Invalid outside program

166 TI-Nspire™ CAS Reference Guide

750

765

780

720

730

740

800

680

690

700

710

830

850

855

860

870

900

Error code

570

575

580

630

640

650

600

605

610

620

665

670

Description

Invalid pathname

For example, \var is invalid.

Invalid polar complex

Invalid program reference

Programs cannot be referenced within functions or expressions such as 1+p(x) where p is a program.

Invalid table

Invalid use of units

Invalid variable name in a Local statement

Invalid variable or function name

Invalid variable reference

Invalid vector syntax

Link transmission

A transmission between two units was not completed. Verify that the connecting cable is connected firmly to both ends.

Matrix not diagonalizable

Low Memory

1. Delete some data in this document

2. Save and close this document

If 1 and 2 fail, pull out and re-insert batteries

Missing (

Missing )

Missing “

Missing ]

Missing }

Missing start or end of block syntax

Missing Then in the If..EndIf block

Name is not a function or program

No functions selected

No solution found

Non-real result

For example, if the software is in the Real setting, ‡ (-1) is invalid.

To allow complex results, change the “Real or Complex” Mode Setting to RECTANGULAR or POLAR.

Overflow

Program not found

A program reference inside another program could not be found in the provided path during execution.

Rand type functions not allowed in graphing

Recursion too deep

Reserved name or system variable

Argument error

Median-median model could not be applied to data set.

TI-Nspire™ CAS Reference Guide 167

1110

1120

1130

1140

1040

1045

1050

1060

1000

1010

1020

1030

1070

1080

1090

965

970

980

990

940

950

955

960

Error code

920

930

1100

Description

Text not found

Too few arguments

The function or command is missing one or more arguments.

Too many arguments

The expression or equation contains an excessive number of arguments and cannot be evaluated.

Too many subscripts

Too many undefined variables

Variable is not defined

No value is assigned to variable. Use one of the following commands:

• sto &

• :=

• Define to assign values to variables.

Unlicensed OS

Variable in use so references or changes are not allowed

Variable is protected

Invalid variable name

Make sure that the name does not exceed the length limitations

Window variables domain

Zoom

Internal error

Protected memory violation

Unsupported function. This function requires Computer Algebra System. Try TI-Nspire™ CAS.

Unsupported operator. This operator requires Computer Algebra System. Try TI-Nspire™ CAS.

Unsupported feature. This operator requires Computer Algebra System. Try TI-Nspire™ CAS.

Input argument must be numeric. Only inputs containing numeric values are allowed.

Trig function argument too big for accurate reduction

Unsupported use of Ans.This application does not support Ans.

Function is not defined. Use one of the following commands:

• Define

• :=

• sto & to define a function.

Non-real calculation

For example, if the software is in the Real setting, ‡ (-1) is invalid.

To allow complex results, change the “Real or Complex” Mode Setting to RECTANGULAR or POLAR.

Invalid bounds

No sign change

Argument cannot be a list or matrix

Argument error

The first argument must be a polynomial expression in the second argument. If the second argument is omitted, the software attempts to select a default.

168 TI-Nspire™ CAS Reference Guide

1220

1230

1250

1270

1280

1290

1300

Error code

1150

1160

1170

1180

1190

1200

1210

1260

Description

Argument error

The first two arguments must be polynomial expressions in the third argument. If the third argument is omitted, the software attempts to select a default.

Invalid library pathname

A pathname must be in the form xxx

\ yyy

, where:

• The xxx part can have 1 to 16 characters.

• The yyy part can have 1 to 15 characters.

See the Library section in the documentation for more details.

Invalid use of library pathname

• A value cannot be assigned to a pathname using Define , := , or sto & .

• A pathname cannot be declared as a Local variable or be used as a parameter in a function or program definition.

Invalid library variable name.

Make sure that the name:

• Does not contain a period

• Does not begin with an underscore

• Does not exceed 15 characters

See the Library section in the documentation for more details.

Library document not found:

• Verify library is in the MyLib folder.

• Refresh Libraries.

See the Library section in the documentation for more details.

Library variable not found:

• Verify library variable exists in the first problem in the library.

• Make sure library variable has been defined as LibPub or LibPriv.

• Refresh Libraries.

See the Library section in the documentation for more details.

Invalid library shortcut name.

Make sure that the name:

• Does not contain a period

• Does not begin with an underscore

• Does not exceed 16 characters

• Is not a reserved name

See the Library section in the documentation for more details.

Domain error:

The tangentLine and normalLine functions support real-valued functions only.

Domain error.

Trigonometric conversion operators are not supported in Degree or Gradian angle modes.

Argument Error

Use a system of linear equations.

Example of a system of two linear equations with variables x and y:

3x+7y=5

2y-5x=-1

Argument Error:

The first argument of nfMin or nfMax must be an expression in a single variable. It cannot contain a non-valued variable other than the variable of interest.

Argument Error

Order of the derivative must be equal to 1 or 2.

Argument Error

Use a polynomial in expanded form in one variable.

Argument Error

Use a polynomial in one variable.

Argument Error

The coefficients of the polynomial must evaluate to numeric values.

TI-Nspire™ CAS Reference Guide 169

Error code

1310

Description

Argument error:

A function could not be evaluated for one or more of its arguments.

170 TI-Nspire™ CAS Reference Guide

Warning codes and messages

You can use the warnCodes() function to store the codes of warnings generated by evaluating an expression. This table lists each numeric warning code and its associated message.

For an example of storing warning codes, see warnCodes() , page

135

10022

10023

10024

10025

10026

10016

10017

10018

10019

10020

10021

10005

10006

10007

10008

10009

10012

Warning code

10000

10001

10002

10003

10004

10013

10014

10015

Message

Operation might introduce false solutions.

Differentiating an equation may produce a false equation.

Questionable solution

Questionable accuracy

Operation might lose solutions.

cSolve might specify more zeros.

Solve may specify more zeros.

Service and Support

Texas Instruments Support and Service

For general information

For more information about TI products and services, contact TI by e-mail or visit the TI Internet address.

E-mail inquiries:

Home Page: [email protected]

education.ti.com

Service and warranty information

For information about the length and terms of the warranty or about product service, refer to the warranty statement enclosed with this product or contact your local Texas Instruments retailer/distributor.

Service and Support 173

174 Service and Support

Index

Symbols

^, power

144

^ / , reciprocal

156

_, unit designation

155

:=, assign

158

!, factorial

148

.^, dot power

146

.*, dot multiplication

145

.+, dot addition

145

N , dot subtraction

145

P , dot division

146

', minute notation

154

', prime

155

", second notation

154

{ , less than or equal

148

©, comment

158

@ list( ), list difference

, degree notation

154

, degrees/minutes/seconds

154

4 , convert units

156

, integral

149

á , square root

150

É , not equal

147

N , subtract

142

, divide

143

, product

150

( ), sum

151

*, multiply

143

&, append

148

& , store

157

#, indirection

153

#, indirection operator

164

%, percent

146

+, add

142

<, less than

147

=, equal

147

>, greater than

148

| , greater than or equal

148

|, with

157

Numerics

0b, binary indicator

158

0h, hexadecimal indicator

158

10^( ), power of ten

156

2-sample F Test

4 approxFraction( )

A abs( ), absolute value

absolute value template for

add, +

142

amortization table, amortTbl( )

amortTbl( ), amortization table

and, Boolean and

angle, angle( )

angle( ), angle

ANOVA, one-way variance analysis

ANOVA2way, two-way variance analysis

Ans, last answer

answer (last), Ans

append, &

148

approx( ), approximate

approximate, approx( )

approxRational( )

arc length, arcLen( )

arccos()

arccosh()

arccosine, cos / ( )

arccot()

arccoth()

arccsc()

arccsch()

arcLen( ), arc length

arcsec()

arcsech()

arcsin()

arcsine, sin / ( )

112

arcsinh()

arctan()

arctangent, tan / ( )

124

arctanh()

arguments in TVM functions

131

augment( ), augment/concatenate

augment/concatenate, augment( )

175

average rate of change, avgRC( )

avgRC( ), average rate of change

4 Base10, display as decimal integer

Base16, display as hexadecimal

Base2, display as binary

binary display, 4 Base2

indicator, 0b

158

binomCdf( )

binomPdf( )

Boolean and, and

exclusive or, xor

136

not, not

or, or

C c c c c

2way

Cdf( )

GOF

Pdf( )

Cdf( )

ceiling, ceiling( )

ceiling( ), ceiling

centralDiff( )

cFactor( ), complex factor

char( ), character string

character string, char( )

characters numeric code, ord( )

string, char( )

charPoly( )

clear error, ClrErr

ClearAZ

ClrErr, clear error

colAugment

colDim( ), matrix column dimension

colNorm( ), matrix column norm

combinations, nCr( )

comDenom( ), common denominator

comment, ©

158

176 common denominator, comDenom( )

completeSquare( ), complete square

complex conjugate, conj( )

factor, cFactor( )

solve, cSolve( )

zeros, cZeros( )

conj( ), complex conjugate

constant in solve( )

115

constants in cSolve( )

in cZeros( )

in deSolve( )

in solve( )

116

in zeros( )

137

shortcuts for

161

construct matrix, constructMat( )

constructMat( ), construct matrix

contact information

173

convert

4 Grad

Rad

units

156

copy variable or function, CopyVar

correlation matrix, corrMat( )

corrMat( ), correlation matrix

4 cos, display in terms of cosine

cos( ), cosine

cos

, arccosine

cosh( ), hyperbolic cosine

cosh / ( ), hyperbolic arccosine

cosine display expression in terms of

cosine, cos( )

cot( ), cotangent

cot / ( ), hyperbolic arccotangent

cotangent, cot( )

coth( ), hyperbolic cotangent

coth / ( ), hyperbolic arccotangent

count days between dates, dbd( )

count items in a list conditionally , countif( )

count items in a list, count( )

count( ), count items in a list

countif( ), conditionally count items in a list

cPolyRoots()

cross product, crossP( )

crossP( ), cross product

csc( ), cosecant

csc / ( ), inverse cosecant

csch( ), hyperbolic cosecant

csch / ( ), inverse hyperbolic cosecant

cSolve( ), complex solve

cubic regression, CubicReg

CubicReg, cubic regression

cumulative sum, cumulativeSum( )

cumulativeSum( ), cumulative sum

customer support and service

173

Cycle, cycle

cycle, Cycle

4 Cylind, display as cylindrical vector

cylindrical vector display, 4 Cylind

cZeros( ), complex zeros

D d ( ), first derivative

149

days between dates, dbd( )

dbd( ), days between dates

DD, display as decimal angle

Decimal, display result as decimal

decimal angle display,

integer display,

Base10

Define

Define LibPriv

Define LibPub

Define, define

define, Define

defining private function or program

public function or program

definite integral template for

degree notation, -

154

degree/minute/second display,

DMS

degree/minute/second notation

154

delete void elements from list

deleting variable, DelVar

deltaList()

deltaTmpCnv()

DelVar, delete variable

delVoid( ), remove void elements

denominator

derivative or nth derivative template for

derivative()

derivatives first derivative, d ( )

149

numeric derivative, nDeriv( )

numeric derivative, nDerivative( )

deSolve( ), solution

det( ), matrix determinant

diag( ), matrix diagonal

dim( ), dimension

dimension, dim( )

Disp, display data

display as binary, 4 Base2

cylindrical vector,

Cylind

decimal angle, 4 DD

decimal integer, 4 Base10

degree/minute/second, 4 DMS

hexadecimal,

Base16

polar vector,

Polar

rectangular vector, 4 Rect

spherical vector, 4 Sphere

118

display data, Disp

distribution functions binomCdf( )

binomPdf( )

c c c c

Inv

2way( )

Cdf( )

GOF( )

Pdf( )

( )

invNorm( )

invt( )

normCdf( )

177

normPdf( )

poissCdf( )

poissPdf( )

tCdf( )

125

tPdf( )

128

divide, P

143

4 DMS, display as degree/minute/ second

dominant term, dominantTerm( )

dominantTerm( ), dominant term

dot addition, .+

145

division, .

146

multiplication, .*

145

power, .^

146

product, dotP( )

subtraction, .

145

dotP( ), dot product

E e exponent template for

e to a power, e^( )

40 ,

e^( ), e to a power

e , display expression in terms of

E , exponent

153

eff ), convert nominal to effective rate

effective rate, eff( )

eigenvalue, eigVl( )

eigenvector, eigVc( )

eigVc( ), eigenvector

eigVl( ), eigenvalue

else if, ElseIf

else, Else

ElseIf, else if

empty (void) elements

159

end for, EndFor

function, EndFunc

if, EndIf

loop, EndLoop

program, EndPrgm

try, EndTry

129

while, EndWhile

135

end function, EndFunc

end if, EndIf

end loop, EndLoop

end while, EndWhile

135

EndTry, end try

129

EndWhile, end while

135

EOS (Equation Operating System)

163

equal, =

147

Equation Operating System (EOS)

163

error codes and messages

165

errors and troubleshooting clear error, ClrErr

pass error, PassErr

euler( ), Euler function

evaluate polynomial, polyEval( )

evaluation, order of

163

exact, exact( )

exact( ), exact

exclusive or (Boolean), xor

136

Exit, exit

exit, Exit

4 exp, display in terms of e

exp( ), e to a power

exp 4 list( ), expression to list

expand, expand( )

expand( ), expand

exponent, E

153

exponential regession, ExpReg

exponents template for

expr( ), string to expression

45 ,

ExpReg, exponential regession

expressions expression to list, exp

4 list( )

string to expression, expr( )

F factor, factor( )

factor( ), factor

factorial, !

148

Fill, matrix fill

financial functions, tvmFV( )

131

financial functions, tvmI( )

131

financial functions, tvmN( )

131

financial functions, tvmPmt( )

131

financial functions, tvmPV( )

131

178

first derivative template for

FiveNumSummary

floor, floor( )

floor( ), floor

fMax( ), function maximum

fMin( ), function minimum

For

For, for

for, For

format string, format( )

format( ), format string

fpart( ), function part

fractions propFrac

template for

freqTable( )

frequency( )

Frobenius norm, norm( )

Func, function

Func, program function

functions maximum, fMax( )

minimum, fMin( )

part, fpart( )

program function, Func

user-defined

functions and variables copying

G g

, gradians

153

gcd( ), greatest common divisor

geomCdf( )

geomPdf( )

get/return denominator, getDenom( )

number, getNum( )

variables injformation, getVarInfo( )

getDenom( ), get/return denominator

getLangInfo( ), get/return language information

getLockInfo( ), tests lock status of variable or variable group

getMode( ), get mode settings

getNum( ), get/return number

getType( ), get type of variable

getVarInfo( ), get/return variables information

go to, Goto

Goto, go to

4 , convert to gradian angle

gradian notation, g

153

greater than or equal,

148

greater than, >

148

greatest common divisor, gcd( )

groups, locking and unlocking

134

groups, testing lock status

H hexadecimal display, 4 Base16

indicator, 0h

158

hyperbolic arccosine, cosh / ( )

arcsine, sinh / ( )

113

arctangent, tanh / ( )

125

cosine, cosh( )

sine, sinh( )

113

tangent, tanh( )

124

I identity matrix, identity( )

identity( ), identity matrix

If, if

if, If

ifFn( )

imag( ), imaginary part

imaginary part, imag( )

ImpDif( ), implicit derivative

implicit derivative, Impdif( )

indefinite integral template for

indirection operator (#)

164

indirection, #

153

Input, input

input, Input

inString( ), within string

int( ), integer

intDiv( ), integer divide

integer divide, intDiv( )

179

integer part, iPart( )

integer, int( )

integral, â

149

interpolate( ), interpolate

Inv c

( )

inverse cumulative normal distribution (invNorm( )

inverse, ^ /

156

invF( )

invNorm( ), inverse cumulative normal distribution)

invt( )

iPart( ), integer part

irr( ), internal rate of return internal rate of return, irr( )

isPrime( ), prime test

isVoid( ), test for void

L label, Lbl

language get language information

Lbl, label

lcm, least common multiple

least common multiple, lcm

left, left( )

left( ), left

length of string

less than or equal, {

148

less than,

147

LibPriv

LibPub

library create shortcuts to objects

libShortcut( ), create shortcuts to library objects

limit lim( )

limit( )

template for

limit( ) or lim( ), limit

linear regression, LinRegAx

linear regression, LinRegBx

LinRegBx, linear regression

LinRegMx, linear regression

LinRegtIntervals, linear regression

180

LinRegtTest

linSolve()

list to matrix, list 4 mat( )

list, conditionally count items in

list, count items in

list 4 mat( ), list to matrix

lists augment/concatenate, augment( )

cross product, crossP( )

cumulative sum, cumulativeSum( )

difference,

@ list( )

differences in a list, @ list( )

dot product, dotP( )

empty elements in

159

expression to list, exp

4 list( )

list to matrix, list 4 mat( )

matrix to list, mat 4 list( )

maximum, max( )

mid-string, mid( )

minimum, min( )

new, newList( )

product, product( )

sort ascending, SortA

117

sort descending, SortD

117

summation, sum( )

122

ln( ), natural logarithm

LnReg, logarithmic regression

local variable, Local

local, Local

Local, local variable

Lock, lock variable or variable group

locking variables and variable

Log groups

template for

logarithmic regression, LnReg

logarithms

logistic regression, Logistic

logistic regression, LogisticD

Logistic, logistic regression

LogisticD, logistic regression

Loop, loop

loop, Loop

LU, matrix lower-upper decomposition

M mat 4 list( ), matrix to list

matrices augment/concatenate, augment( )

column dimension, colDim( )

column norm, colNorm( )

cumulative sum, cumulativeSum( )

determinant, det( )

diagonal, diag( )

dimension, dim( )

dot addition, .+

145

dot division, .

146

dot multiplication, .*

145

dot power, .^

146

dot subtraction, .

145

eigenvalue, eigVl( )

eigenvector, eigVc( )

filling, Fill

identity, identity( )

list to matrix, list 4 mat( )

lower-upper decomposition, LU

matrix to list, mat 4 list( )

maximum, max( )

minimum, min( )

new, newMat( )

product, product( )

QR factorization, QR

random, randMat( )

reduced row echelon form, rref( )

104

row addition, rowAdd( )

104

row dimension, rowDim( )

104

row echelon form, ref( )

row multiplication and addition, mRowAdd( )

row norm, rowNorm( )

104

row operation, mRow( )

row swap, rowSwap( )

104

submatrix, subMat( )

121 ,

122

summation, sum( )

122

transpose, T

123

matrix (1

2) template for

matrix (2 Q 1) template for

matrix (2 Q 2) template for

matrix (m Q n) template for

matrix to list, mat 4 list( )

max( ), maximum

maximum, max( )

mean, mean( )

mean( ), mean

median, median( )

median( ), median

medium-medium line regression,

MedMed

MedMed, medium-medium line regression

mid( ), mid-string

mid-string, mid( )

min( ), minimum

minimum, min( )

minute notation, '

154

mirr( ), modified internal rate of return

mixed fractions, using propFrac(› with

mod( ), modulo

mode settings, getMode( )

modes setting, setMode( )

109

modified internal rate of return, mirr( )

modulo, mod( )

mRow( ), matrix row operation

mRowAdd( ), matrix row multiplication and addition

Multiple linear regression t test

multiply, *

143

MultReg

MultRegIntervals( )

MultRegTests( )

N natural logarithm, ln( )

nCr( ), combinations

nDerivative( ), numeric derivative

negation, entering negative numbers

164

181

net present value, npv( )

new list, newList( )

matrix, newMat( )

newList( ), new list

newMat( ), new matrix

nfMax( ), numeric function maximum

nfMin( ), numeric function minimum

nInt( ), numeric integral

nom ), convert effective to nominal rate

nominal rate, nom( )

norm( ), Frobenius norm

normal distribution probability, normCdf( )

normal line, normalLine( )

normalLine( )

normCdf( )

normPdf( )

not (Boolean), not

not equal, É

147

not, Boolean not

nPr( ), permutations

npv( ), net present value

nSolve( ), numeric solution

nth root template for

numeric derivative, nDeriv( )

derivative, nDerivative( )

integral, nInt( )

solution, nSolve( )

O objects create shortcuts to library

OneVar, one-variable statistics

one-variable statistics, OneVar

operators order of evaluation

163

or (Boolean), or

or, Boolean or

ord( ), numeric character code

P 4 Rx( ), rectangular x coordinate

P 4 Ry( ), rectangular y coordinate

pass error, PassErr

PassErr, pass error

Pdf( )

percent, %

146

permutations, nPr( )

piecewise function (2-piece) template for

piecewise function (N-piece) template for

piecewise( )

poissCdf( )

poissPdf( )

Polar, display as polar vector

polar coordinate, R 4 P q ( )

coordinate, R 4 Pr( )

vector display,

Polar

polyCoef( )

polyDegree( )

polyEval( ), evaluate polynomial

polyGcd( )

polynomials evaluate, polyEval( )

random, randPoly( )

PolyRoots()

power of ten, 10^( )

156

power regression, PowerReg

, 100

101 ,

126

power, ^

144

PowerReg, power regression

Prgm, define program

prime number test, isPrime( )

prime, '

155

probability densiy, normPdf( )

prodSeq()

product (

) template for

product,

( )

150

product, product( )

product( ), product

programming define program, Prgm

display data, Disp

pass error, PassErr

182

programs defining private library

defining public library

programs and programming clear error, ClrErr

display I/O screen, Disp

end program, EndPrgm

end try, EndTry

129

try, Try

129

proper fraction, propFrac

propFrac, proper fraction

QR factorization, QR

QR, QR factorization

quadratic regression, QuadReg

QuadReg, quadratic regression

quartic regression, QuartReg

QuartReg, quartic regression

R , radian

153

R 4 P q ( ), polar coordinate

R 4 Pr( ), polar coordinate

Rad, convert to radian angle

radian, R

153

rand( ), random number

randBin, random number

randInt( ), random integer

randMat( ), random matrix

randNorm( ), random norm

random matrix, randMat( )

norm, randNorm( )

number seed, RandSeed

polynomial, randPoly( )

random sample

randPoly( ), random polynomial

randSamp( )

RandSeed, random number seed

real, real( )

real( ), real

reciprocal, ^ /

156

4 Rect, display as rectangular vector

rectangular x coordinate, P 4 Rx( )

rectangular y coordinate, P 4 Ry( )

rectangular-vector display,

Rect

reduced row echelon form, rref( )

104

ref( ), row echelon form

regressions cubic, CubicReg

exponential, ExpReg

linear regression, LinRegAx

linear regression, LinRegBx

logarithmic, LnReg

Logistic

logistic, Logistic

medium-medium line, MedMed

MultReg

power regression, PowerReg

91 ,

100

101

126

quadratic, QuadReg

quartic, QuartReg

sinusoidal, SinReg

114

remain( ), remainder

remainder, remain( )

remove void elements from list

Request

100

RequestStr

101

result display in terms of cosine

display in terms of e

display in terms of sine

111

result values, statistics

120

results, statistics

119

Return, return

101

return, Return

101

right, right( )

, 42 ,

60 ,

101

, 102 ,

135

right( ), right

101

rk23( ), Runge Kutta function

102

rotate, rotate( )

102

103

rotate( ), rotate

102

103

round, round( )

103

round( ), round

103

row echelon form, ref( )

rowAdd( ), matrix row addition

104

rowDim( ), matrix row dimension

104

rowNorm( ), matrix row norm

104

rowSwap( ), matrix row swap

104

183

rref( ), reduced row echelon form

104

S sec( ), secant

105

sec / ( ), inverse secant

105

sech( ), hyperbolic secant

105

sech

( ), inverse hyperbolic secant

106

second derivative template for

second notation, "

154

seq( ), sequence

106

seqGen( )

107

seqn( )

107

sequence, seq( )

106

, 107

series, series( )

108

series( ), series

108

service and support

173

set mode, setMode( )

109

setMode( ), set mode

109

settings, get current

shift, shift( )

110

shift( ), shift

110

sign, sign( )

110

sign( ), sign

110

simult( ), simultaneous equations

111

simultaneous equations, simult( )

111

4 sin, display in terms of sine

111

sin( ), sine

112

sin / ( ), arcsine

112

sine display expression in terms of

111

sine, sin( )

112

sinh( ), hyperbolic sine

113

sinh

( ), hyperbolic arcsine

113

SinReg, sinusoidal regression

114

Int( )

152

sinusoidal regression, SinReg

114

solution, deSolve( )

solve, solve( )

114

solve( ), solve

114

SortA, sort ascending

117

184

SortD, sort descending

117

sorting ascending, SortA

117

descending, SortD

117

Sphere, display as spherical vector

118

spherical vector display, 4 Sphere

118

Prn( )

152

sqrt( ), square root

118

square root template for

square root, ‡ ( )

118

, 150

standard deviation, stdDev( )

120 ,

134

stat.results

119

stat.values

120

statistics combinations, nCr( )

factorial, !

148

mean, mean( )

median, median( )

one-variable statistics, OneVar

permutations, nPr( )

random norm, randNorm( )

random number seed, RandSeed

standard deviation, stdDev( )

120

134

two-variable results, TwoVar

132

variance, variance( )

134

stdDevPop( ), population standard deviation

120

stdDevSamp( ), sample standard deviation

120

Stop command

121

storing symbol,

157 ,

158

string dimension, dim( )

length

string( ), expression to string

121

strings append, &

148

character code, ord( )

character string, char( )

expression to string, string( )

121

format, format( )

formatting

indirection, #

153

left, left( )

mid-string, mid( )

right, right( )

20 ,

, 60

, 101 ,

102 ,

135

rotate, rotate( )

102 ,

103

shift, shift( )

110

string to expression, expr( )

45 ,

using to create variable names

164

within, InString

studentt distribution probability, tCdf( )

125

studentt

probability density, tPdf( )

128

subMat( ), submatrix

121 ,

122

submatrix, subMat( )

121 ,

122

subtract, N

142

sum (

) template for

sum of interest payments

152

sum of principal payments

152

sum,

( )

151

sum( ), summation

122

sumIf( )

122

summation, sum( )

122

sumSeq()

122

support and service

173

system of equations (2-equation) template for

system of equations (N-equation) template for

T t test, tTest

130

T , transpose

123

tan( ), tangent

123

tan

( ), arctangent

124

tangent line, tangentLine( )

124

tangent, tan( )

123

tangentLine( )

124

tanh( ), hyperbolic tangent

124

tanh / ( ), hyperbolic arctangent

125

Taylor polynomial, taylor( )

125

taylor( ), Taylor polynomial

125

tCdf( ), studentt

distribution probability

125

tCollect( ), trigonometric collection

126

templates absolute value

definite integral

derivative or nth derivative

exponent

first derivative

fraction

indefinite integral

limit

Log

matrix (1 Q 2)

matrix (2

matrix (2 Q 2)

matrix (m Q n)

nth root

piecewise function (2-piece)

piecewise function (N-piece)

product (

)

second derivative

square root

sum ( G )

system of equations (2-equation)

system of equations (Nequation)

test for void, isVoid( )

Test_2S, 2-sample F test

tExpand( ), trigonometric expansion

126

Text command

126

time value of money, Future Value

131

time value of money, Interest

131

time value of money, number of payments

131

time value of money, payment amount

131

time value of money, present value

131

tInterval_2Samp, two-sample t confidence interval

127

tInterval, t confidence interval

127

4 tmpCnv()

128

185

tmpCnv()

128

tPdf( ), studentt probability density

128

trace( )

129

transpose, T

123

trigonometric collection, tCollect( )

126

trigonometric expansion, tExpand( )

126

Try, error handling command

129

tTest_2Samp, two-sample t test

130

tTest, t

test

130

TVM arguments

131

tvmFV( )

131

tvmI( )

131

tvmN( )

131

tvmPmt( )

131

tvmPV( )

131

TwoVar, two-variable results

132

two-variable results, TwoVar

132

U underscore, _

155

unit vector, unitV( )

133

units convert

156

unitV( ), unit vector

133

unLock, unlock variable or variable group

134

unlocking variables and variable groups

134

user-defined functions

user-defined functions and programs

, 35

V variable creating name from a character string

164

variable and functions copying

variables clear all single-letter

delete, DelVar

local, Local

variables, locking and unlocking

, 134

186 variance, variance( )

134

varPop( )

134

varSamp( ), sample variance

134

vectors cross product, crossP( )

cylindrical vector display, 4 Cylind

dot product, dotP( )

unit, unitV( )

133

void elements

159

void elements, remove

void, test for

W warnCodes( ), Warning codes

135

warning codes and messages

171

when, when( )

135

when( ), when

135

While, while

135

while, While

135

with, |

157

within string, inString( )

X x2, square

145

xor, Boolean exclusive or

136

Z zeroes, zeroes( )

136

zeroes( ), zeroes

136

zInterval_1Prop, one-proportion z confidence interval

138

zInterval_2Prop, two-proportion z confidence interval

139

zInterval_2Samp, two-sample z confidence interval

139

zInterval, z confidence interval

138

zTest

140

zTest_1Prop, one-proportion z test

140

zTest_2Prop, two-proportion z test

141

zTest_2Samp, two-sample z

test

141

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Reference Guide

This guidebook applies to TI-Nspire™ software version 3.0. To obtain the latest version of the documentation, go to education.ti.com/guides.

Important Information

License

Please see the complete license installed in

C:\Program Files\TI

Education\TI-Nspire CAS

.

© 2006 - 2011 Texas Instruments Incorporated

Contents

TI-Nspire™ CAS Reference Guide

Expression templates

Alphabetical listing

A

B

C

D

E

F

G

I

L

M

N

O

P

Q

R

S

T

U

V

W

X

Z

Symbols

Empty (void) elements

Shortcuts for entering math expressions

From the handheld or computer keyboard

From the computer keyboard

EOS™ (Equation Operating System) hierarchy

Order of evaluation

Parentheses, brackets, and braces

Indirection

Post operators

Exponentiation

Negation

Constraint (|)

Error codes and messages

Warning codes and messages

Service and Support

Texas Instruments Support and Service

For general information

For more information about TI products and services, contact TI by e-mail or visit the TI Internet address.

E-mail inquiries:

Home Page: [email protected]

education.ti.com

Service and warranty information

For information about the length and terms of the warranty or about product service, refer to the warranty statement enclosed with this product or contact your local Texas Instruments retailer/distributor.

Index

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