Texas Instruments TI-Nspire CAS Reference Guide

CAS

Reference Guide

This guidebook applies to TI-Nspire™ software version 1.4. To obtain the latest version of the documentation, go to education.ti.com/guides.

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License

Please see the complete license installed in C:\Program Files\TI Education\TI-Nspire CAS.

Macintosh®, Windows®, Excel®, Vernier EasyLink®, EasyTemp®, Go!®Link, Go!®Motion, and Go!®Temp are trademarks of their respective owners.

Expression templates

Fraction template ........................................ 1

Exponent template ......................................1

Square root template .................................. 1

Nth root template ........................................1

e exponent template ................................... 2

Log template ................................................ 2

Piecewise template (2-piece) .......................2

Piecewise template (N-piece) ......................2

System of 2 equations template ................. 3

System of N equations template .................3

Absolute value template .............................3

dd°mm’ss.ss’’ template ................................3

Matrix template (2 x 2) ................................3

Matrix template (1 x 2) ................................4

Matrix template (2 x 1) ................................4

Matrix template (m x n) .............................. 4

Sum template (G) ......................................... 4

Product template (Π) ...................................4

First derivative template ............................. 5

Nth derivative template .............................. 5

Definite integral template ..........................5

indefinite integral template ....................... 5

Limit template .............................................. 5

Alphabetical listing A

abs() ..............................................................6

amortTbl() .................................................... 6

and ................................................................6

angle() ..........................................................7

ANOVA .........................................................7

ANOVA2way ................................................ 8

Ans ..............................................................10

approx() ......................................................10

approxRational() ........................................ 10

arcLen() .......................................................10

augment() ...................................................10

avgRC() ....................................................... 11

bal() .............................................................11

4Base2 .........................................................12

4Base10 .......................................................12

4Base16 .......................................................12

binomCdf() ................................................. 13

binomPdf() ................................................. 13

ceiling() .......................................................13

cFactor() ......................................................13

char() ...........................................................14

charPoly() ....................................................14

2way ........................................................14

Cdf() .........................................................15

GOF ......................................................... 15

Pdf() .........................................................15

ClearAZ .......................................................16

ClrErr .......................................................... 16

colAugment() ............................................. 16

colDim() ...................................................... 16

colNorm() ................................................... 16

comDenom() .............................................. 17

conj() .......................................................... 17

constructMat() ........................................... 18

CopyVar ...................................................... 18

corrMat() .................................................... 18

4cos ............................................................. 19

cos() ............................................................ 19

cosê() .......................................................... 20

cosh() .......................................................... 21

coshê() ........................................................ 21

cot() ............................................................ 21

cotê() .......................................................... 22

coth() .......................................................... 22

cothê() ........................................................ 22

count() ........................................................ 22

countif() ..................................................... 23

crossP() ....................................................... 23

csc() ............................................................. 23

cscê() ........................................................... 24

csch() ........................................................... 24

cschê() ......................................................... 24

cSolve() ....................................................... 24

CubicReg .................................................... 26

cumSum() ................................................... 27

Cycle ........................................................... 27

4Cylind ........................................................ 27

cZeros() ....................................................... 27

dbd() ........................................................... 29

4DD ............................................................. 29

4Decimal ..................................................... 30

Define ......................................................... 30

Define LibPriv ............................................ 31

Define LibPub ............................................ 31

DelVar ........................................................ 31

deSolve() .................................................... 32

det() ............................................................ 33

diag() .......................................................... 33

dim() ........................................................... 33

Disp ............................................................. 34

4DMS ........................................................... 34

dominantTerm() ........................................ 35

dotP() .......................................................... 35

e^() ............................................................. 36

eff() ............................................................. 36

eigVc() ........................................................ 36

eigVl() ......................................................... 37

Else ............................................................. 37

ElseIf ........................................................... 37

EndFor ........................................................ 37

EndFunc ...................................................... 37

EndIf ........................................................... 37

EndLoop ..................................................... 37

iii

EndPrgm .....................................................37

EndTry .........................................................37

EndWhile ....................................................38

exact() .........................................................38

Exit ..............................................................38

4exp .............................................................38

exp() ............................................................38

exp4list() ......................................................39

expand() ......................................................39

expr() ...........................................................40

ExpReg ........................................................40

factor() ........................................................41

FCdf() ..........................................................42

Fill ................................................................42

FiveNumSummary ......................................42

floor() ..........................................................43

fMax() .........................................................43

fMin() ..........................................................43

For ...............................................................44

format() ......................................................44

fPart() ..........................................................44

FPdf() ..........................................................44

freqTable4list() ............................................45

frequency() .................................................45

FTest_2Samp ..............................................45

Func .............................................................46

gcd() ............................................................46

geomCdf() ...................................................46

geomPdf() ...................................................47

getDenom() ................................................47

getLangInfo() .............................................47

getMode() ...................................................47

getNum() ....................................................48

getVarInfo() ................................................48

Goto ............................................................49

4Grad ...........................................................49

identity() .....................................................50

If ..................................................................50

ifFn() ............................................................51

imag() ..........................................................51

impDif() .......................................................52

Indirection ..................................................52

inString() .....................................................52

int() .............................................................52

intDiv() ........................................................52

integrate .....................................................52

() .........................................................53

invc

invF() ...........................................................53

invNorm() ....................................................53

invt() ............................................................53

iPart() ..........................................................53

irr() ..............................................................53

isPrime() ......................................................54

Lbl ...............................................................54

lcm() ............................................................54

left() ............................................................ 55

libShortcut() ............................................... 55

limit() or lim() ............................................. 55

LinRegBx ..................................................... 56

LinRegMx ................................................... 57

LinRegtIntervals ......................................... 57

LinRegtTest ................................................ 59

@List() .......................................................... 59

list4mat() ..................................................... 60

4ln ................................................................ 60

ln() .............................................................. 60

LnReg .......................................................... 61

Local ........................................................... 61

log() ............................................................ 62

4logbase ...................................................... 62

Logistic ....................................................... 63

LogisticD ..................................................... 63

Loop ............................................................ 64

LU ................................................................ 65

mat4list() ..................................................... 65

max() ........................................................... 66

mean() ........................................................ 66

median() ..................................................... 66

MedMed ..................................................... 67

mid() ........................................................... 67

min() ........................................................... 68

mirr() ........................................................... 68

mod() .......................................................... 68

mRow() ....................................................... 68

mRowAdd() ................................................ 69

MultReg ...................................................... 69

MultRegIntervals ....................................... 69

MultRegTests ............................................. 70

nCr() ............................................................ 71

nDeriv() ....................................................... 71

newList() ..................................................... 71

newMat() .................................................... 72

nfMax() ....................................................... 72

nfMin() ....................................................... 72

nInt() ........................................................... 72

nom() .......................................................... 73

norm() ......................................................... 73

normalLine() ............................................... 73

normCdf() ................................................... 73

normPdf() ................................................... 73

not .............................................................. 74

nPr() ............................................................ 74

npv() ........................................................... 75

nSolve() ....................................................... 75

OneVar ....................................................... 76

or ................................................................ 77

ord() ............................................................ 77

P4Rx() .......................................................... 77

P4Ry() .......................................................... 78

PassErr ........................................................ 78

piecewise() ..................................................78

poissCdf() .................................................... 78

poissPdf() ....................................................78

4Polar ..........................................................79

polyCoeffs() ................................................ 79

polyDegree() .............................................. 80

polyEval() .................................................... 80

polyGcd() ....................................................80

polyQuotient() ........................................... 81

polyRemainder() ........................................ 81

PowerReg ...................................................82

Prgm ...........................................................83

Product (PI) ................................................. 83

product() ..................................................... 83

propFrac() ................................................... 83

QR ...............................................................84

QuadReg .....................................................85

QuartReg ....................................................86

R4Pq() ..........................................................87

R4Pr() ...........................................................87

4Rad .............................................................87

rand() ..........................................................88

randBin() ..................................................... 88

randInt() ..................................................... 88

randMat() ................................................... 88

randNorm() ................................................. 88

randPoly() ................................................... 88

randSamp() ................................................. 89

RandSeed .................................................... 89

real() ...........................................................89

4Rect ............................................................89

ref() .............................................................90

remain() ......................................................90

Return .........................................................91

right() ..........................................................91

root() ...........................................................91

rotate() .......................................................91

round() ........................................................92

rowAdd() ....................................................92

rowDim() ....................................................92

rowNorm() ..................................................93

rowSwap() ..................................................93

rref() ............................................................93

sec() .............................................................93

sec/() ...........................................................94

sech() ...........................................................94

sechê() ......................................................... 94

seq() ............................................................94

series() .........................................................95

setMode() ................................................... 96

shift() ..........................................................97

sign() ...........................................................97

simult() ........................................................98

4sin ..............................................................98

sin() .............................................................99

sinê() ...........................................................99

sinh() .........................................................100

sinhê() ....................................................... 100

SinReg ...................................................... 101

solve() ....................................................... 101

SortA ........................................................ 103

SortD ........................................................ 104

4Sphere ..................................................... 104

sqrt() ......................................................... 104

stat.results ................................................ 105

stat.values ................................................ 106

stDevPop() ................................................ 106

stDevSamp() ............................................. 106

Stop .......................................................... 107

Store ......................................................... 107

string() ...................................................... 107

subMat() ................................................... 107

Sum (Sigma) ............................................. 107

sum() ......................................................... 108

sumIf() ...................................................... 108

system() .................................................... 108

T (transpose) ............................................ 109

tan() .......................................................... 109

tanê() ........................................................ 110

tangentLine() ........................................... 110

tanh() ........................................................ 110

tanhê() ...................................................... 111

taylor() ...................................................... 111

tCdf() ........................................................ 111

tCollect() ................................................... 112

tExpand() .................................................. 112

Then ......................................................... 112

tInterval .................................................... 112

tInterval_2Samp ....................................... 113

tmpCnv() .................................................. 113

@tmpCnv() ................................................ 114

tPdf() ........................................................ 114

trace() ....................................................... 114

Try ............................................................. 115

tTest .......................................................... 115

tTest_2Samp ............................................. 116

tvmFV() ..................................................... 116

tvmI() ........................................................ 117

tvmN() ...................................................... 117

tvmPmt() .................................................. 117

tvmPV() ..................................................... 117

TwoVar ..................................................... 118

unitV() ...................................................... 119

varPop() .................................................... 119

varSamp() ................................................. 120

when() ...................................................... 120

While ........................................................ 121

“With” ...................................................... 121

xor ............................................................ 121

zeros() .......................................................122

zInterval ....................................................123

zInterval_1Prop ........................................124

zInterval_2Prop ........................................124

zInterval_2Samp .......................................124

zTest ..........................................................125

zTest_1Prop ..............................................125

zTest_2Prop ..............................................126

zTest_2Samp .............................................126

Symbols

+ (add) .......................................................128

N(subtract) ................................................128

·(multiply) ...............................................129

à (divide) ...................................................129

^ (power) ..................................................130

(square) ................................................131

.+ (dot add) ...............................................131

.. (dot subt.) ..............................................131

·(dot mult.) .............................................131

. / (dot divide) ...........................................132

.^ (dot power) ..........................................132

ë(negate) ..................................................132

% (percent) ...............................................133

= (equal) ....................................................133

ƒ (not equal) .............................................133

< (less than) ..............................................134

{ (less or equal) ........................................134

> (greater than) ........................................134

| (greater or equal) ..................................134

! (factorial) ................................................134

& (append) ............................................... 135

d() (derivative) ......................................... 135

‰() (integrate) ............................................ 135

‡() (square root) ...................................... 136

Π() (product) ............................................ 136

G() (sum) ................................................... 137

GInt() ......................................................... 138

GPrn() ........................................................ 138

# (indirection) .......................................... 139

í (scientific notation) .............................. 139

g (gradian) ............................................... 139

ô(radian) ................................................... 139

¡ (degree) ................................................. 140

¡, ', '' (degree/minute/second) ................. 140

 (angle) .................................................. 140

' (prime) .................................................... 141

_ (underscore) .......................................... 141

4 (convert) ................................................. 141

10^() .......................................................... 142

^ê (reciprocal) .......................................... 142

| (“with”) .................................................. 142

& (store) ................................................... 143

:= (assign) ................................................. 143

0b, 0h ........................................................ 144

Error codes and messages Texas Instruments Support and

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TI-Nspire™

This guide lists the templates, functions, commands, and operators available for evaluating math expressions.

CAS Reference Guide

Expression templates

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

value or expression for the element. Press

Fraction template

Note: See also / (divide), page 129.

e to move the cursor to each element’s position, and type a

· or /· to evaluate the expression.

/p keys

Example:

Exponent template

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 130.

Square root template

Note: See also

Nth root template

Note: See also root(), page 91.

‡

() (square root), page 136.

l key

Example:

/q keys

Example:

/l keys

Example:

TI-Nspire™ CAS Reference Guide 1

e exponent template

Natural exponential e raised to a power

Note: See also e^(), page 36.

u keys

Example:

Log template

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

Note: See also log(), page 62.

Piecewise template (2-piece)

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 78.

Piecewise template (N-piece)

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

/s key

Example:

Catalog >

Example:

Catalog >

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

Note: See also piecewise(), page 78.

2 TI-Nspire™ CAS Reference Guide

System of 2 equations template

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 108.

Catalog >

Example:

System of N equations template

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

Note: See also system(), page 108.

Absolute value template

Note: See also abs(), page 6.

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.

Matrix template (2 x 2)

Catalog >

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

Catalog >

Example:

Catalog >

Example:

Catalog >

Example:

Creates a 2 x 2 matrix.

TI-Nspire™ CAS Reference Guide 3

Matrix template (1 x 2)

Catalog >

Example:

Matrix template (2 x 1)

Matrix template (m x n)

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

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)

Catalog >

Example:

Catalog >

Example:

Catalog >

Example:

Product template (Π)

Example:

Note: See also Π() (product), page 136.

Catalog >

4 TI-Nspire™ CAS Reference Guide

First derivative template

Catalog >

Example:

Note: See also

d() (derivative)

, page 135.

Nth derivative template

Note: See also

d() (derivative)

, page 135.

Definite integral template

Note: See also ‰() integrate(), page 135.

indefinite integral template

Note: See also

‰()

integrate()

, page 135.

Limit template

Catalog >

Example:

Catalog >

Example:

Catalog >

Example:

Catalog >

Example:

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

Note: See also limit(), page 55.

TI-Nspire™ CAS Reference Guide 5

Alphabetical listing

Items whose names are not alphabetic (such as +, !, and >) are listed at the end of this section, starting on page 128. Unless otherwise specified, all examples in this section were performed in the default reset mode, and all variables are assumed to be undefined.

abs()

abs(Expr1) ⇒ expression abs(

List1) ⇒ list

abs(Matrix1) ⇒ 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.

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.

N, I, PV, Pmt, FV, PpY, CpY, and PmtAt are described in the table of TVM arguments, page 117.

• 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 GInt() and GPrn(), page 138, and bal(), page 11.

Catalog

and

BooleanExpr1 and BooleanExpr2 ⇒ Boolean expression BooleanList1 and BooleanList2 ⇒ Boolean list BooleanMatrix1 and BooleanMatrix2 ⇒ Boolean matrix

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

Catalog

6 TI-Nspire™ CAS Reference Guide

and

Integer1 and Integer2 ⇒ integer

Compares two real integers bit-by-bit using an 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).

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.

and operation.

Catalog

In Hex base mode:

Important: Zero, not the letter O.

In Bin base mode:

In Dec 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.

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.

angle(List1) ⇒ list angle(Matrix1) ⇒ matrix

Returns a list or matrix of angles of the elements in List1 or Matrix1, interpreting each element as a complex number that represents a two-dimensional rectangular coordinate point.

ANOVA

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 105.) Flag=0 for Data, Flag=1 for Stats

In Degree angle mode:

In Gradian angle mode:

In Radian angle mode:

Catalog

Output variable Description

stat.F Value of the F statistic

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

stat.df Degrees of freedom of the groups

stat.SS Sum of squares of the groups

TI-Nspire™ CAS Reference Guide 7

Output variable Description

stat.MS Mean squares for the groups

stat.dfError Degrees of freedom of the errors

stat.SSError Sum of squares of the errors

stat.MSError Mean square for the errors

stat.sp Pooled standard deviation

stat.xbarlist Mean of the input of the lists

stat.CLowerList 95% confidence intervals for the mean of each input list

stat.CUpperList 95% confidence intervals for the mean of each input list

ANOVA2way

ANOVA2way List1,List2[,List3,…,List20][,levRow]

Computes a two-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 105.) 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 Description

stat.FF statistic of the column factor

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

stat.df Degrees of freedom of the column factor

stat.SS Sum of squares of the column factor

stat.MS Mean squares for column factor

stat.FBlock F statistic for factor

stat.PValBlock Least probability at which the null hypothesis can be rejected

stat.dfBlock Degrees of freedom for factor

stat.SSBlock Sum of squares for factor

stat.MSBlock Mean squares for factor

stat.dfError Degrees of freedom of the errors

stat.SSError Sum of squares of the errors

stat.MSError Mean squares for the errors

stat.s Standard deviation of the error

Catalog

8 TI-Nspire™ CAS Reference Guide

COLUMN FACTOR Outputs

Output variable Description

stat.Fcol F statistic of the column factor

stat.PValCol Probability value of the column factor

stat.dfCol Degrees of freedom of the column factor

stat.SSCol Sum of squares of the column factor

stat.MSCol Mean squares for column factor

ROW FACTOR Outputs

Output variable Description

stat.FRow F statistic of the row factor

stat.PValRow Probability value of the row factor

stat.dfRow Degrees of freedom of the row factor

stat.SSRow Sum of squares of the row factor

stat.MSRow Mean squares for row factor

INTERACTION Outputs

Output variable Description

stat.FInteract F statistic of the interaction

stat.PValInteract Probability value of the interaction

stat.dfInteract Degrees of freedom of the interaction

stat.SSInteract Sum of squares of the interaction

stat.MSInteract Mean squares for interaction

ERROR Outputs

Output variable Description

stat.dfError Degrees of freedom of the errors

stat.SSError Sum of squares of the errors

stat.MSError Mean squares for the errors

s Standard deviation of the error

TI-Nspire™ CAS Reference Guide 9

Ans

Ans ⇒ value

Returns the result of the most recently evaluated expression.

keys

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

This is equivalent to entering the argument and pressing

mode.

·.

approx(List1) ⇒ list approx(Matrix1) ⇒ matrix

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

approxRational()

approxRational(Expr[, tol]) ⇒ expression approxRational(List[, tol]) ⇒ 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.

arcLen()

arcLen(Expr1,Var ,St art,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.

Catalog

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 Va r .

augment()

augment(List1, List2) ⇒ list

Returns a new list that is List2 appended to the end of List1.

Catalog

10 TI-Nspire™ CAS Reference Guide

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, Va r [=Value] [, H]) ⇒ expression avgRC(Expr1, Va r [=Value] [, List1]) ⇒ list avgRC(List1, Va r [=Value] [, H]) ⇒ list avgRC(Matrix1, Var [=Value] [, H]) ⇒ 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 o r

any current “such that” substitution for the variable. H is the step value. If H is omitted, it defaults to 0.001.

Note that the similar function nDeriv() uses the central-difference quotient.

bal()

bal(NPmt,N,I,PV ,[Pmt], [FV], [PpY], [CpY], [PmtAt],

roundValue]) ⇒ value

[

bal(NPmt,amortTable) ⇒ value

Amortization function that calculates schedule balance after a specified payment.

N, I, PV, Pmt, FV, PpY, CpY, and PmtAt are described in the table of TVM arguments, page 117.

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

N, I, PV, Pmt, FV, PpY, CpY, and PmtAt are described in the table of TVM arguments, page 117.

• 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.

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 6.

Note: See also GInt() and GPrn(), page 138.

Catalog

TI-Nspire™ CAS Reference Guide 11

4Base2

4Base2 ⇒ integer

Integer1

Converts Integer1 to a binary 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 binary, 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.

Catalog

4Base10

Integer1 4Base10 ⇒ integer

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.

4Base16

Integer1 4Base16 ⇒ integer

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.

Catalog

12 TI-Nspire™ CAS Reference Guide

binomCdf()

binomCdf(n,p,lowBound,upBound) ⇒ number if lowBound

upBound are numbers, list if lowBound and upBound are

and lists

binomCdf(

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

n,p,upBound) ⇒ number if upBound is a number,

Catalog

binomPdf()

binomPdf(n,p) ⇒ number binomPdf(n,p,XVal) ⇒ number if XVal is a number, list if

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.

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.

cFactor()

cFactor(Expr1[,Var ]) ⇒ expression cFactor(List1[,Va r]) ⇒ 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.

Catalog

TI-Nspire™ CAS Reference Guide 13

cFactor()

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

Var . Expr1 is factored as much as possible toward factors that are linear

in Va r, 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 Va r as the main variable. Similar powers of Va r are collected in each factor. Include Va r 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 Va r . There might be some incidental factoring with respect to other variables.

For the Auto setting of the Auto or Approximate mode, including Va r 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 Va r might yield more complete factorization.

Note: See also factor().

Catalog

To see the entire result, press £ and then use ¡ and ¢ to move the cursor.

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 A, denoted by pA(l), is the polynomial defined by

pA(l) = det(l• I NA)

where I denotes the n×n identity matrix. squareMatrix1 and squareMatrix2 must have the equal dimensions.

2way

2way obsMatrix

chi22way obsMatrix

Computes a c2 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 105.)

Output variable Description

stat.c2 Chi square stat: sum (observed - expected)2/expected

Catalog

14 TI-Nspire™ CAS Reference Guide

Output variable Description

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

stat.df Degrees of freedom for the chi square statistics

stat.ExpMat Matrix of expected elemental count table, assuming null hypothesis

stat.CompMat Matrix of elemental chi square statistic contributions

Cdf()

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 c2 distribution probability between lowBound and upBound for the specified degrees of freedom df.

For P(X  upBound), set lowBound = 0.

GOF

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 105.)

Output variable Description

stat.c2 Chi square stat: sum((observed - expected)2/expected

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

stat.df Degrees of freedom for the chi square statistics

stat.CompList Elemental chi square statistic contributions

Catalog

Pdf()

Pdf(XVal,df) ⇒ number if XVal is a number, list if XVal is a

list

chi2Pdf(

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

a list

Computes the probability density function (pdf) for the c2 distribution at a specified XVal value for the specified degrees of freedom df.

Catalog

TI-Nspire™ CAS Reference Guide 15

ClearAZ

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

Catalog

ClrErr

Clears the error status and sets system variable errCode to zero. The Else claus e 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, us e PassErr to se nd it to the next error handler. If there are no more pendin g Try...Else...EndTry error handlers, the error dialog box will be displayed as normal.

Note: See also PassErr, page 78, and Try , page 115. 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.

colDim()

colDim(Matrix) ⇒ expression

Returns the number of columns contained in Matrix.

Note: See also rowDim() .

Catalog

For an example of ClrErr, See Example 2 under the Try command, page 115.

Catalog

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().

Catalog

16 TI-Nspire™ CAS Reference Guide

comDenom()

comDenom(Expr1[,Va r]) ⇒ expression comDenom(List1[,Var ]) ⇒ list comDenom(Matrix1[,Var ]) ⇒ matrix

comDenom(Expr1) returns a reduced ratio of a fully expanded

numerator over a fully expanded denominator.

comDenom(Expr1,Va r) returns a reduced ratio of numerator and

denominator expanded with respect to Va r . 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 Va r , 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.

If 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, memor y, 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().

Catalog

conj()

conj(Expr1) ⇒ expression conj(List1) ⇒ list conj(Matrix1) ⇒ matrix

Catalog

Returns the complex conjugate of the argument.

Note: All undefined variables are treated as real variables.

TI-Nspire™ CAS Reference Guide 17

constructMat()

constructMat(Expr,Var 1 ,Var 2 ,numRows,numCols)

⇒ matrix

Returns a matrix based on the arguments. Expr is an expression in variables Va r 1 and Va r 2 . Elements in the

resulting matrix are formed by evaluating Expr for each incremented value of Var 1 and Va r 2.

Var 1 is automatically incremented from each row, Va r2 is incremented from 1 through numCols.

1 through numRows. Within

Catalog

CopyVar

CopyVar Var 1 , Va r 2 CopyVar Var 1 ., Va r2 .

CopyVar Var 1 , Var 2 copies the value of variable Va r 1 to variable

Var 2 , creating Va r 2 if necessary. Variable Va r1 must have a value. If Var 1 is the name of an existing user-defined function, copies the

definition of that function to function Va r 2. Function Va r 1 must be defined.

Var 1 must meet the variable-naming requirements or must be an indirection expression that simplifies to a variable name meeting the requirements.

CopyVar Var 1 ., Va r 2. copies all members of the Var 1 . variable

group to the Var 2 . group, creating Var 2 . if necessary. Var 1 . must be the name of an existing variable group, such as the

statistics stat.nn results, or variables created using the

LibShortcut() function. If Var 2 . already exists, this command

replaces all members that are common to both groups and adds the members that do not already exist. If a simple (non-group) variable named Va r2 exists, an error occurs.

corrMat()

corrMat(List1,List2[,…[,List20]])

Computes the correlation matrix for the augmented matrix [List1, List2, ..., List20].

Catalog

18 TI-Nspire™ CAS Reference Guide

cos

4cos

Expr

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

cos reduces all powers of

sin(...) modulo 1Ncos(...)^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.

Catalog

cos()

cos(Expr1) ⇒ expression cos(List1) ⇒ 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 settin g. You can use ó,G, or ôto override the angle mode temporarily.

n key

In Degree angle mode:

In Gradian angle mode:

In Radian angle mode:

TI-Nspire™ CAS Reference Guide 19

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 (li) and eigenvectors (Vi) of A.

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

Form the matrices:

Then A = X B Xêand f(A) = X f(B) Xê. For example, cos(A) = X cos(B) Xê where:

cos(B) =

All computations are performed using floating-point arithmetic.

n key

In Radian angle mode:

cosê()

cosê(Expr1) ⇒ expression cosê(List1) ⇒ list

cosê(Expr1) returns the angle whose cosine is Expr1 as an

expression.

cosê(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.

cosê(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 Degree angle mode:

In Gradian angle mode:

In Radian angle mode:

In Radian angle mode and Rectangular Complex Format:

To see the entire result, press £ and then use ¡ and ¢ to move the cursor.

/n keys

20 TI-Nspire™ CAS Reference Guide

cosh()

cosh(Expr1) ⇒ expression cosh(List1) ⇒ 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 o f

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

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

cos().

In Radian angle mode:

Catalog

coshê()

coshê(Expr1) ⇒ expression coshê(List1) ⇒ list

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.

coshê(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.

cot()

cot(Expr1) ⇒ expression cot(List1) ⇒ 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 settin g. You can use ó,G, orôto override the angle mode temporarily.

Catalog

In Radian angle mode and In Rectangular Complex Format:

To see the entire result, press £ and then use ¡ and ¢ to move the cursor.

Catalog

In Degree angle mode:

In Gradian angle mode:

In Radian angle mode:

TI-Nspire™ CAS Reference Guide 21

cotê()

cotê(Expr1) ⇒ expression cotê(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.

In Degree angle mode:

In Gradian angle mode:

In Radian angle mode:

Catalog

coth()

coth(Expr1) ⇒ expression coth(List1) ⇒ list

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

cothê()

cothê(Expr1) ⇒ expression cothê(List1) ⇒ list

Returns the inverse hyperbolic cotangent of Expr1 or returns a list containing the inverse hyperbolic cotangents of each element of List1.

count()

count(Val u e 1 or L i s t1 [,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.

Catalog

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.

22 TI-Nspire™ CAS Reference Guide

countif()

countif(List,Criteria) ⇒ value

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

Criteria can be:

• 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.

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

Note: See also sumIf(), page 108, and frequency(), page 45.

Catalog

Counts the number of elements equal to 3.

Counts the number of elements equal to “def.”

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.

Counts 1, 3, 7, and 9.

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.

csc()

csc(Expr1) ⇒ expression csc(List1) ⇒ 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:

Catalog

TI-Nspire™ CAS Reference Guide 23

cscê()

cscê(Expr1) ⇒ expression cscê(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.

In Degree angle mode:

In Gradian angle mode:

In Radian angle mode:

Catalog

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.

cschê()

cschê(Expr1) ⇒ expression cschê(List1) ⇒ list

Returns the inverse hyperbolic cosecant of Expr1 or returns a list containing the inverse hyperbolic cosecants of each element of List1.

cSolve()

cSolve(Equation, Va r ) ⇒ Boolean expression cSolve(Equation, Va r =G u e s s) ⇒ Boolean expression cSolve(Inequality, Va r ) ⇒ 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

24 TI-Nspire™ CAS Reference Guide

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TI-Nspire™ CAS Reference Guide 1

Alphabetical listing