Texas Instruments TI-Nspire Reference Guide

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

Except as otherwise expressly stated in the License that accompanies a program, Texas Instruments makes no warranty, either express or implied, including but not limited to any implied warranties of merchantability and fitness for a particular purpose, regarding any programs or book materials and makes such materials available solely on an "as-is" basis. In no event shall Texas Instruments be liable to anyone for special, collateral, incidental, or consequential damages in connection with or arising out of the purchase or use of these materials, and the sole and exclusive liability of Texas Instruments, regardless of the form of action, shall not exceed the amount set forth in the license for the program. Moreover, Texas Instruments shall not be liable for any claim of any kind whatsoever against the use of these materials by any other party.

License

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

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

Second derivative template ........................ 5

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

Alphabetical listing

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

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

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

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

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

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

Ans ................................................................9

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

4approxFraction() ....................................... 10

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

arccos() ........................................................10

arccosh() ..................................................... 10

arccot() ........................................................10

arccoth() ..................................................... 11

arccsc() ........................................................ 11

arccsch() ......................................................11

arcsec() ........................................................ 11

arcsech() ......................................................11

arcsin() ........................................................11

arcsinh() ......................................................11

arctan() .......................................................11

arctanh() ..................................................... 11

augment() ...................................................11

avgRC() ....................................................... 12

bal() .............................................................12

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

4Base10 .......................................................13

4Base16 .......................................................14

binomCdf() ................................................. 14

binomPdf() ................................................. 14

ceiling() ...................................................... 14

centralDiff() ............................................... 15

char() .......................................................... 15

2way ........................................................ 15

Cdf() ........................................................ 16

GOF ......................................................... 16

Pdf() ........................................................ 16

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

ClrErr .......................................................... 17

colAugment() ............................................. 17

colDim() ...................................................... 17

colNorm() ................................................... 17

completeSquare() ...................................... 18

conj() .......................................................... 18

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

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

corrMat() .................................................... 19

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

cos/() .......................................................... 20

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

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

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

cot/() .......................................................... 22

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

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

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

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

cPolyRoots() ............................................... 23

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

csc() ............................................................. 24

csc/() ........................................................... 24

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

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

CubicReg .................................................... 25

cumulativeSum() ........................................ 25

Cycle ........................................................... 26

4Cylind ........................................................ 26

dbd() ........................................................... 26

4DD ............................................................. 27

4Decimal ..................................................... 27

Define ......................................................... 27

Define LibPriv ............................................ 28

Define LibPub ............................................ 28

deltaList() ................................................... 29

DelVar ........................................................ 29

delVoid() .................................................... 29

det() ............................................................ 29

diag() .......................................................... 30

dim() ........................................................... 30

Disp ............................................................. 30

4DMS ........................................................... 31

dotP() .......................................................... 31

e^() ............................................................. 31

eff() ............................................................. 32

iii

eigVc() .........................................................32

eigVl() .........................................................32

Else ..............................................................32

ElseIf ............................................................33

EndFor .........................................................33

EndFunc ......................................................33

EndIf ............................................................33

EndLoop ...................................................... 33

EndPrgm ..................................................... 33

EndTry .........................................................33

EndWhile ....................................................33

euler() .........................................................34

Exit ..............................................................34

exp() ............................................................35

expr() ...........................................................35

ExpReg ........................................................35

factor() ........................................................36

FCdf() ..........................................................36

Fill ................................................................36

FiveNumSummary ...................................... 37

floor() ..........................................................37

For ...............................................................38

format() ......................................................38

fPart() ..........................................................38

FPdf() ..........................................................38

freqTable4list() ............................................39

frequency() .................................................39

FTest_2Samp .............................................. 39

Func .............................................................40

gcd() ............................................................40

geomCdf() ...................................................41

geomPdf() ...................................................41

getDenom() ................................................ 41

getLangInfo() ............................................. 41

getLockInfo() ..............................................42

getMode() ...................................................42

getNum() .................................................... 43

getType() ....................................................43

getVarInfo() ................................................43

Goto ............................................................44

4Grad ...........................................................44

identity() .....................................................45

If ..................................................................45

ifFn() ............................................................46

imag() ..........................................................46

Indirection .................................................. 47

inString() .....................................................47

int() .............................................................47

intDiv() ........................................................47

interpolate() ...............................................48

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

invc

invF() ...........................................................48

invNorm() ....................................................48

invt() ............................................................48

iPart() ..........................................................49

irr() ..............................................................49

isPrime() ......................................................49

isVoid() ....................................................... 49

Lbl ............................................................... 50

lcm() ............................................................ 50

left() ............................................................ 50

libShortcut() ............................................... 51

LinRegBx ..................................................... 51

LinRegMx ................................................... 52

LinRegtIntervals ......................................... 52

LinRegtTest ................................................ 54

linSolve() ..................................................... 55

@List() .......................................................... 55

list4mat() ..................................................... 55

ln() .............................................................. 55

LnReg .......................................................... 56

Local ........................................................... 57

Lock ............................................................ 57

log() ............................................................ 58

Logistic ....................................................... 58

LogisticD ..................................................... 59

Loop ............................................................ 60

LU ................................................................ 60

mat4list() ..................................................... 60

max() ........................................................... 61

mean() ........................................................ 61

median() ..................................................... 61

MedMed ..................................................... 62

mid() ........................................................... 62

min() ........................................................... 63

mirr() ........................................................... 63

mod() .......................................................... 64

mRow() ....................................................... 64

mRowAdd() ................................................ 64

MultReg ...................................................... 64

MultRegIntervals ....................................... 65

MultRegTests ............................................. 65

nCr() ............................................................ 66

nDerivative() .............................................. 67

newList() ..................................................... 67

newMat() .................................................... 67

nfMax() ....................................................... 67

nfMin() ....................................................... 68

nInt() ........................................................... 68

nom() .......................................................... 68

norm() ......................................................... 68

normCdf() ................................................... 69

normPdf() ................................................... 69

not .............................................................. 69

nPr() ............................................................ 69

npv() ........................................................... 70

nSolve() ....................................................... 70

OneVar ....................................................... 71

or ................................................................ 72

ord() ............................................................ 72

P4Rx() ...........................................................72

P4Ry() ...........................................................73

PassErr .........................................................73

piecewise() ..................................................73

poissCdf() .................................................... 73

poissPdf() ....................................................73

4Polar .......................................................... 74

polyEval() .................................................... 74

polyRoots() ................................................. 74

PowerReg ...................................................75

Prgm ...........................................................76

prodSeq() .................................................... 76

Product (PI) ................................................. 76

product() ..................................................... 76

propFrac() ................................................... 77

QR ............................................................... 77

QuadReg .....................................................78

QuartReg ....................................................78

R4Pq() ..........................................................79

R4Pr() ...........................................................79

4Rad .............................................................80

rand() ..........................................................80

randBin() ..................................................... 80

randInt() ..................................................... 80

randMat() ................................................... 80

randNorm() ................................................. 80

randPoly() ................................................... 81

randSamp() ................................................. 81

RandSeed .................................................... 81

real() ........................................................... 81

4Rect ............................................................81

ref() ............................................................. 82

remain() ......................................................83

Request ....................................................... 83

RequestStr .................................................. 84

Return .........................................................84

right() .......................................................... 84

rk23() .......................................................... 85

root() ...........................................................85

rotate() .......................................................85

round() ........................................................86

rowAdd() ....................................................86

rowDim() ....................................................87

rowNorm() ..................................................87

rowSwap() ..................................................87

rref() ............................................................87

sec() ............................................................. 88

sec/() ...........................................................88

sech() ...........................................................88

sech/() ......................................................... 88

seq() ............................................................89

seqGen() .....................................................89

seqn() ..........................................................90

setMode() ................................................... 90

shift() ..........................................................91

sign() ...........................................................92

simult() ........................................................ 92

sin() ............................................................. 93

sin/() ........................................................... 93

sinh() ........................................................... 94

sinh/() ......................................................... 94

SinReg ........................................................ 95

SortA .......................................................... 95

SortD .......................................................... 96

4Sphere ....................................................... 96

sqrt() ........................................................... 96

stat.results .................................................. 97

stat.values .................................................. 98

stDevPop() .................................................. 98

stDevSamp() ............................................... 98

Stop ............................................................ 99

Store ........................................................... 99

string() ........................................................ 99

subMat() ..................................................... 99

Sum (Sigma) ............................................... 99

sum() ........................................................... 99

sumIf() ...................................................... 100

sumSeq() ................................................... 100

system() .................................................... 100

T (transpose) ............................................ 100

tan() .......................................................... 101

tan/() ........................................................ 101

tanh() ........................................................ 102

tanh/() ...................................................... 102

tCdf() ........................................................ 103

Text ........................................................... 103

Then ......................................................... 103

tInterval .................................................... 103

tInterval_2Samp ....................................... 104

tPdf() ........................................................ 104

trace() ....................................................... 104

Try ............................................................. 105

tTest .......................................................... 105

tTest_2Samp ............................................. 106

tvmFV() ..................................................... 106

tvmI() ........................................................ 107

tvmN() ...................................................... 107

tvmPmt() .................................................. 107

tvmPV() ..................................................... 107

TwoVar ..................................................... 108

unitV() ...................................................... 109

unLock ...................................................... 109

varPop() .................................................... 109

varSamp() ................................................. 110

warnCodes() ............................................. 110

when() ...................................................... 110

While ........................................................ 111

“With” ...................................................... 111

xor ............................................................ 111

zInterval ....................................................112

zInterval_1Prop ........................................112

zInterval_2Prop ........................................113

zInterval_2Samp .......................................113

zTest ..........................................................114

zTest_1Prop .............................................. 114

zTest_2Prop .............................................. 115

zTest_2Samp .............................................115

Symbols

+ (add) .......................................................116

N(subtract) ................................................116

·(multiply) ............................................... 117

à (divide) ...................................................117

^ (power) .................................................. 118

(square) ................................................118

.+ (dot add) ...............................................119

.. (dot subt.) ..............................................119

·(dot mult.) .............................................119

. / (dot divide) ...........................................119

.^ (dot power) ..........................................119

L(negate) ...................................................120

% (percent) ...............................................120

= (equal) ....................................................121

ƒ (not equal) .............................................121

< (less than) ..............................................121

{ (less or equal) ........................................122

> (greater than) ........................................122

| (greater or equal) ..................................122

! (factorial) ................................................122

& (append) ................................................122

d() (derivative) ..........................................123

‰() (integral) ..............................................123

‡() (square root) .......................................123

Π() (prodSeq) ............................................124

G() (sumSeq) ..............................................124

GInt() .........................................................125

GPrn() ........................................................ 125

# (indirection) .......................................... 126

E (scientific notation) ............................... 126

g (gradian) ............................................... 126

R(radian) .................................................... 126

¡ (degree) ................................................. 127

¡, ', '' (degree/minute/second) ................. 127

± (angle) .................................................. 127

_ (underscore as an empty element) ...... 127

10^() .......................................................... 128

^/(reciprocal) ........................................... 128

| (“with”) .................................................. 128

& (store) ................................................... 129

:= (assign) ................................................. 129

0b, 0h ........................................................ 130

Empty (void) elements

Calculations involving void

elements ................................................... 131

List arguments containing void

elements ................................................... 131

Shortcuts for entering math expressions

EOS™ (Equation Operating System) hierarchy

Error codes and messages

Warning codes and messages

Texas Instruments Support and Service

TI-Nspire™

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

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

or expression for the element. Press

Fraction template

Note: See also / (divide), page 117.

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 118.

Square root template

Note: See also ‡() (square root), page 123.

Nth root template

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

· or /· to evaluate the expression.

/p keys

Example:

l key

Example:

/q keys

Example:

/l keys

Example:

Note: See also root(), page 85.

TI-Nspire™ Reference Guide 1

e exponent template

Natural exponential e raised to a power

Note: See also e^(), page 31.

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 58.

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 73.

Piecewise template (N-piece)

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

Example:

Catalog >

Example:

Catalog >

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

/s key

Note: See also piecewise(), page 73.

2 TI-Nspire™ Reference Guide

System of 2 equations template

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

Note: See also system(), page 100.

Catalog >

Example:

System of N equations template

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

Note: See also system(), page 100.

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, an d 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™ 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:

Note: See also G() (sumSeq), page 124.

Product template (Π)

Note: See also Π() (prodSeq), page 124.

4 TI-Nspire™ Reference Guide

Catalog >

Example:

First derivative template

The first derivative template can be used to calculate first derivative at a point numerically, using auto differentiation methods.

Note: See also d() (derivative), page 123.

Catalog >

Example:

Second derivative template

The second derivative template can be used to calculate second derivative at a point numerically, using auto differentiation methods.

Note: See also d() (derivative), page 123.

Definite integral template

The definite integral template can be used to calculate the definite integral numerically, using the same method as nInt().

183Note: See also nInt(), page 68.

Catalog >

Example:

Catalog >

Example:

TI-Nspire™ 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

116. 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(Val u e 1 ) ⇒ value 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.

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 107.

• 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 125, and bal(), page 12.

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.

6 TI-Nspire™ Reference Guide

Catalog

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).

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(Val u e 1 ) ⇒ value

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

In Degree angle mode:

In Gradian angle mode:

In Radian angle mode:

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 97.)

Flag=0 for Data, Flag=1 for Stats

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

stat.MS Mean squares for the groups

stat.dfError Degrees of freedom of the errors

Catalog

TI-Nspire™ Reference Guide 7

Output variable Description

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,…,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 97.)

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

COLUMN FACTOR Outputs

Output variable Description

stat.Fcol F statistic of the column factor

8 TI-Nspire™ Reference Guide

Output variable Description

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

Ans

Ans ⇒ value

Returns the result of the most recently evaluated expression.

keys

TI-Nspire™ Reference Guide 9

approx()

approx(Val u e 1 ) ⇒ number

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

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

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

mode.

Catalog

4approxFraction()

Val u e

approxFraction([Tol ]) ⇒ value

List

approxFraction([Tol ]) ⇒ list

Matrix

approxFraction([Tol ]) ⇒ matrix

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

Note: You can insert this function from the computer keyboard by

typing @>approxFraction(...).

approxRational()

approxRational(Val u e [, Tol ]) ⇒ value approxRational(List[, Tol ]) ⇒ list approxRational(Matrix[, Tol ]) ⇒ matrix

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

arccos()

arccosh()

arccot()

Catalog

See cos/(), page 20.

See cosh/(), page 21.

See cot/(), page 22.

10 TI-Nspire™ Reference Guide

arccoth()

See coth/(), page 22.

arccsc()

arccsch()

arcsec()

arcsech()

arcsin()

arcsinh()

arctan()

arctanh()

augment()

augment(List1, List2) ⇒ list

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

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.

See csc/(), page 24.

See csch/(), page 24.

See sec/(), page 88.

See sech/(), page 88.

See sin/(), page 93.

See sinh/(), page 94.

See tan/(), page

See tanh/(), page

Catalog

101

102

TI-Nspire™ Reference Guide 11

avgRC()

avgRC(Expr1, Va r [=Value] [, Step]) ⇒ ex pression avgRC(Expr1, Va r [=Value] [, List1]) ⇒ list avgRC(List1, Va r [=Value] [, Step]) ⇒ list avgRC(Matrix1, Var [=Value] [, Step]) ⇒ matrix

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

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

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

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

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

Catalog

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 107.

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 107.

• 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 125.

Base2

Integer1 4Base2 ⇒ 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.

Catalog

12 TI-Nspire™ Reference Guide

Base2

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,

N1 is displayed as

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

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.

263 becomes N263 and is displayed as 0h8000000000000000 in Hex base mode 0b100...000 (63 zeros) in Binary base mode

264 becomes 0 and is displayed as 0h0 in Hex base mode 0b0 in Binary base mode

N 1 becomes 2

0h7FFFFFFFFFFFFFFF in Hex base mode 0b111...111 (64 1’s) in Binary base mode

N 1 and is displayed as

Catalog

4Base10

Integer1 4Base10 ⇒ 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.

Catalog

TI-Nspire™ Reference Guide 13

4Base16

4Base16 ⇒ integer

Integer1

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 page 12.

4Base2,

Catalog

binomCdf()

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

upBound are numbers, list if lowBound and upBound are

and lists

binomCdf(

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 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.

n,p,upBound) for P(0{X{upBound) ⇒ number if

ceiling()

ceiling(Val u e 1 ) ⇒ value

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

14 TI-Nspire™ Reference Guide

centralDiff()

centralDiff(Expr1,Va r [=Value][,Step]) ⇒ expression centralDiff(Expr1,Va r [,Step ])|Var =Va l u e ⇒ expression centralDiff(Expr1,Va r [=Value][,List]) ⇒ list centralDiff(List1,Va r [=Value][,St ep]) ⇒ list centralDiff(Matrix1,Va r [=Value][,Step]) ⇒ matrix

Returns the numerical derivative using the centra l difference quotient formula.

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

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

When using List1 or Matrix1, the operation gets mapped across the values in the list or across the matrix elements.

Note: See also avgRC().

Catalog

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.

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 97.)

For information on the effect of empty elements in a matrix, see “Empty (void) elements” on page 131.

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

stat.CompMat Matrix of elemental chi square statistic contributions

Catalog

TI-Nspire™ Reference Guide 15

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.

{ upBound), set lowBound = 0.

For P(X

For information on the effect of empty elements in a list, see “Empty (void) elements” on page 131.

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 97.)

For information on the effect of empty elements in a list, see “Empty (void) elements” on page 131.

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.

For information on the effect of empty elements in a list, see “Empty (void) elements” on page 131.

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 109.

16 TI-Nspire™ Reference Guide

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.

Note: See also PassErr, page 73, and Try, page 105.

Note for entering the example: In the Calculator application

on the handheld, you can enter multi-line definiti ons by pressing @ instead of · at the end of each line. On the computer keyboard,

hold down Alt and press Enter.

Catalog

For an example of ClrErr, See Example 2 under the Try command, page 105.

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().

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

TI-Nspire™ Reference Guide 17

completeSquare()

completeSquare(ExprOrEqn, Var ) ⇒ expression or equation

completeSquare(ExprOrEqn, Var ^ Po w e r)

equation

completeSquare(ExprOrEqn, Var1, Var2 [,...]) equation

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

⇒ expression or

⇒ expression

Converts a quadratic polynomial expression of the form a·x2+b·x+c into the form a·(x-h)2+k

- or -

Converts a quadratic equation of the form a·x2+b·x+c=d into the form a·(x-h)2=k

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, y2,orz

The third and fourth syntax attempt to complete the square with respect to variables Var 1 , Va r2 [,… ]).

(1/3)

Catalog

conj()

conj(Val u e 1 ) ⇒ value conj(List1) ⇒ list conj(Matrix1) ⇒ matrix

Returns the complex conjugate of the argument.

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 1 through numRows. Within each row, Va r2 is incremented from 1 through numCols.

CopyVar

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

CopyVar Var 1 , Va r2 copies the value of variable Var 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.

Catalog

18 TI-Nspire™ Reference Guide

CopyVar

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

group to the Var 2

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 replaces all members that are common to both groups and adds the members that do not already exist. If one or more members of Va r 2 . are locked, all members of Va r 2

. group, creating Var 2. if necessary.

. already exists, this command

. are left unchanged.

Catalog

corrMat()

corrMat(List1,List2[,…[,List20]])

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

cos()

cos(Val u e 1 ) ⇒ value cos(List1) ⇒ list

cos(Va lu e 1 ) returns the cosine of the argument as a value.

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 ¡,G, or R to override the angle mode temporarily.

In Degree angle mode:

In Gradian angle mode:

In Radian angle mode:

Catalog

μ key

TI-Nspire™ 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:

μ key

In Radian angle mode:

Then A = X B X X/ where:

cos(B) =

All computations are performed using floating-point arithmetic.

cos/()

cos/(Va lu e 1 ) ⇒ value cos/(List1) ⇒ list

cos/(Va lu e 1 ) returns the angle whose cosine is Va l ue 1 .

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(...).

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.

/and f(A) = X f(B) X/. For example, cos(A) = X cos(B)

μ key

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.

20 TI-Nspire™ Reference Guide

cosh()

cosh(Va lu e 1 ) ⇒ value cosh(List1) ⇒ list

cosh(Va lu e 1 ) returns the hyperbolic cosine of the argument.

cosh(List1) returns a list of the hyperbolic co sines 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/(Va lu e 1 ) ⇒ value cosh/(List1) ⇒ list

cosh/(Va lu e 1 ) returns the inverse hyperbolic cosine of the

argument.

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.

cot()

cot(Val u e 1 ) ⇒ value cot(List1) ⇒ list

Returns the cotangent of Val u e1 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 ¡,G, or R to 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.

μ key

In Degree angle mode:

In Gradian angle mode:

In Radian angle mode:

TI-Nspire™ Reference Guide 21

cot/()

cot/(Va lu e 1 ) ⇒ value cot/(List1) ⇒ list

Returns the angle whose cotangent is Va l ue 1 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(...).

μ key

In Degree angle mode:

In Gradian angle mode:

In Radian angle mode:

coth()

coth(Val u e 1 ) ⇒ value coth(List1) ⇒ list

Returns the hyperbolic cotangent of Va l ue 1 or returns a list of the hyperbolic cotangents of all elements of List1.

coth/()

coth/(Va lu e 1 ) ⇒ value coth/(List1) ⇒ list

Returns the inverse hyperbolic cotangent of Va l u e1 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(...).

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.

Empty (void) elements are ignored. For more information on empty elements, see page 131.

Catalog

22 TI-Nspire™ 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.

Empty (void) elements in the list are ignored. For more information on empty elements, see page 131.

Note: See also sumIf(), page 100, and frequency(), page 39.

Counts the number of elements equal to 3.

Counts the number of elements equal to “def.”

Counts 1 and 3.

Counts 3, 5, and 7.

Counts 1, 3, 7, and 9.

Catalog

cPolyRoots()

cPolyRoots(Poly,Var ) ⇒ list cPolyRoots(ListOfCoeffs) ⇒ list

The first syntax, cPolyRoots(Poly,Va r), returns a list of complex roots of polynomial Poly with respect to variable Var .

Poly must be a polynomial in expanded form in one variable. Do not use unexpanded forms such as y2·y+1 or x·x+2·x+1

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

Note: See also polyRoots(), page 74.

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.

Catalog

TI-Nspire™ Reference Guide 23

csc()

csc(Val u e 1 ) ⇒ value csc(List1) ⇒ list

Returns the cosecant of Va lu e 1 or returns a list containing the cosecants of all elements in List1.

μ key

In Degree angle mode:

In Gradian angle mode:

In Radian angle mode:

csc/()

csc/(Va l ue 1 ) ⇒ value csc/(List1) ⇒ list

Returns the angle whose cosecant is Va l ue 1 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(...).

csch()

csch(Val u e 1 ) ⇒ value csch(List1) ⇒ list

Returns the hyperbolic cosecant of Va lu e 1 or returns a list of the hyperbolic cosecants of all elements of List1.

csch/()

csch/(Val u e ) ⇒ value csch/(List1) ⇒ list

Returns the inverse hyperbolic cosecant of Va l u e1 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(...).

In Degree angle mode:

In Gradian angle mode:

In Radian angle mode:

Catalog

μ key

24 TI-Nspire™ Reference Guide

CubicReg

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

Computes the cubic polynomial regression y = a·x3+b·

+c·x+d on lists X and Y with frequency Freq. A summary of

results is stored in the stat.results variable. (See page 97.)

Catalog

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

Category is a list of numeric or string 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 131.

| 0.

Output variable Description

stat.RegEqn Regression equation: a·x3+b·x2+c·x+d

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

stat.R

Regression coefficients

Coefficient of determination

stat.Resid Residuals from the regression

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

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

Category List, and Include Categories

stat.FreqReg List of frequencies corresponding to stat.XReg and stat.YReg

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 131.

Catalog

TI-Nspire™ Reference Guide 25

Cycle

Transfers control immediately to the next iteration of t he current loop (For, While, or Loop).

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 definiti ons by pressing instead of · at the end of each line. On the computer keyboard,

hold down Alt and press Enter.

Catalog

Function listing that sums the integers from 1 to 100 skipping

50.

4Cylind

Vec t o r 4Cylind

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].

Vec t o r must have exactly three elements. It can be either a row or a column.

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)

Catalog

26 TI-Nspire™ Reference Guide

4DD

4DD ⇒ value

Expr1 List1 4DD ⇒ list Matrix1

4DD ⇒ matrix

Note: You can insert this operator from the computer keyboard by

typing @>DD.

Returns the decimal equivalent of the argument expresse d in degrees. The argument is a number, list, or matrix that is interpreted by the Angle mode setting in gradians, radians or degrees.

In Degree angle mode:

In Gradian angle mode:

In Radian angle mode:

Catalog

4Decimal

Number1

4Decimal

List1

Decimal

Matrix1

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.

Define

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).

⇒ value

Catalog

TI-Nspire™ Reference Guide 27

Define

Define Function(Param1, Param2, ...) = Func

Block

EndFunc

Program(Param1, Param2, ...) = Prgm

Define

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 definiti ons 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 28, and Define LibPub,

page 28.

Catalog

Define LibPriv

Define LibPriv Var = Expression Define LibPriv Function(Param1, Param2, ...) = Expression

Define LibPriv Function(Param1, Param2, ...) = Func

Block

EndFunc

Define LibPriv

EndPrgm

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

Note: See also Define, page 27, and Define LibPub, page 28.

Program(Param1, Param2, ...) = Prgm

Block

Define LibPub

Define LibPub Var = Expression Define LibPub Function(Param1, Param2, ...) = Expression

Define LibPub Function(Param1, Param2, ...) = Func

Block

EndFunc

Define LibPub

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 27, and Define LibPriv, page 28.

Program(Param1, Param2, ...) = Prgm

Block

28 TI-Nspire™ Reference Guide

Catalog

deltaList()

See

@List()

, page 55.

DelVar

DelVar Var 1 [, Va r 2] [, Va r 3 ] ... 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 109.

DelVar Var . deletes all members of the Va r . variable group (such as

the statistics stat.nn 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.

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 131.

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

mode to Approximate, computations are done using floatingpoint arithmetic.

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

calculated as:

5EM14 ·max(dim(squareMatrix))·

rowNorm(squareMatrix)

or set the Auto or Approximate

Catalog

TI-Nspire™ Reference Guide 29

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.

Catalog

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(Strin g) ⇒ integer

Returns the number of characters contained in character string Strin g.

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 definiti ons by pressing @ instead of · at the end of each line. On the computer keyboard,

hold down Alt and press Enter.

Catalog

30 TI-Nspire™ Reference Guide

4DMS

Val u e List 4DMS Matrix 4DMS

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 127 for DMS

(degree, minutes, seconds) format.

Note: 4DMS 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 4DMS only at the end of an entry line.

In Degree angle mode:

Catalog

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.

e^()

e^(Val u e 1 ) ⇒ value

Returns e raised to the Val u e 1 power.

Note: See also e exponent template, page 2.

Note: Pressing u to display e^( is different from pressing the

character E on the keyboard.

You can enter a complex number in re 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.

i q

polar form. However, use this

Catalog

u key

TI-Nspire™ Reference Guide 31

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 68.

Catalog

eigVc()

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 = [x1, x2, … , xn], then:

+ … + x

= 1

squareMatrix is first balanced with similarity transformations until the row and column norms are as close to the same va lue as possible. The squareMatrix is then reduced to upper Hessenberg form and the eigenvectors are computed via a Schur factorization.

In Rectangular Complex Format:

Catalog

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

eigVl()

eigVl(squareMatrix) ⇒ list

In Rectangular complex format mode:

Catalog

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 va lue as possible. The squareMatrix is then reduced to upper Hessenberg form and the eigenvalues are computed from the upper Hessenberg matrix.

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

Else See If, page 45.

32 TI-Nspire™ Reference Guide

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 definiti ons by pressing @ instead of · at the end of each line. On the computer keyboard,

hold down Alt and press Enter.

EndFor See For, page 38.

EndFunc See Func, page 40.

EndIf See If, page 45.

EndLoop See Loop, page 60.

EndPrgm See Prgm, page 76.

Catalog

EndTry See Try, page

EndWhile See While, page

TI-Nspire™ Reference Guide 33

105

111

euler()

depVard

euler(Expr, Var , depVar, {Var 0, Va rM ax }, depVar0, VarS t ep

[, eulerStep])

euler(SystemOfExpr, Var , ListOfDepVars, {Var0 , Va r Ma x },

ListOfDepVars0, Va r St e p [, eulerStep])

euler(ListOfExpr, Var , ListOfDepVars, {Var0 , Va r Ma x },

ListOfDepVars0, Va rS t ep [, eulerStep])

Uses the Euler method to solve the system

-------------------

Vard

with depVar(Va r 0 )=depVar0 on the interval [Var 0 ,Va r Ma x ]. Returns a matrix whose first row defines the Va r output values and whose second row defines the value of the first solution component at the corresponding Va r values, and so on.

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.

{Var 0 , Va rM a x } is a two-element list that tells the function to integrate from Va r0 to Va r M ax .

ListOfDepVars0 is a list of initial values for dependent variables.

Var S te p is a nonzero number such that sign(Va rS t ep ) =

sign(Var M ax -Va r 0) and solutions are returned at Va r0 +i·Va r St e p for all i=0,1,2,… such that Va r0 +i·Va r St e p is in [var 0,VarM a x ] (there may not be a solution value at Va rM a x ).

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 Va rS t ep àeulerStep.

⇒ matrix

Expr(Var , depVar)

⇒ matrix

Catalog

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

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

System of equations:

with y1(0)=2 and y2(0)=5

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 definiti ons by pressing @ instead of · at the end of each line. On the computer keyboard,

hold down Alt and press Enter.

34 TI-Nspire™ Reference Guide

Function listing:

Catalog

exp()

exp(Val u e 1 ) ⇒ value

Returns e raised to the Val u e 1 power.

Note: See also e exponent template, page 2.

You can enter a complex number in re form in Radian angle mode only; it causes a Domain error in Degree or Gradian angle mode.

exp(List1) ⇒ list

e raised to the power of each element in List1.

Returns

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.

i q

polar form. However, use this

u key

expr()

expr(Stri ng) ⇒ expression

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

ExpReg

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

Computes the exponential regression y = a·(b)xon lists X and Y with frequency Freq. A summary of results is stored in the stat.results variable. (See page 97.)

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 numeric or string 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 131.

Output variable Description

stat.RegEqn

Regression equation: a·(b)

stat.a, stat.b Regression coefficients

stat.r

Coefficient of linear determination for transformed data

stat.r Correlation coefficient for transformed data (x, ln(y))

Catalog

TI-Nspire™ Reference Guide 35

Output variable Description

stat.Resid Residuals associated with the exponential model

stat.ResidTrans Residuals associated with linear fit of transformed data

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

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

stat.FreqReg List of frequencies corresponding to stat.XReg and stat.YReg

Category List, and Include Categories

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.

FCdf()

FCdf(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 F distribution probability between lowBound and upBound for the specified dfNumer (degrees of freedom) and dfDenom.

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

Fill

Fill Value, matrixVar ⇒ matrix

Replaces each element in variable matrixVar with Val u e.

matrixVar must already exist.

Catalog

36 TI-Nspire™ Reference Guide

Fill

Fill Value, listVar ⇒ list

Replaces each element in variable listVar with Val u e.

listVar must already exist.

Catalog

FiveNumSummary

Provides an abbreviated version of the 1-variable statistics on list X. A summary of results is stored in the stat.results variable. (See page

97.)

X[,[Freq][,Category,Include]]

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 X, Freq, or Category results in a void for the corresponding element of all those lists. For more information on empty elements, see page 131.

Output variable Description

stat.MinX Minimum of x values.

stat.Q1X 1st Quartile of x.

stat.MedianX Median of x.

stat.Q3X 3rd Quartile of x.

stat.MaxX Maximum of x values.

floor()

floor(Val u e 1 ) ⇒ 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().

Catalog

TI-Nspire™ Reference Guide 37

For

For Var , Low, High [, St ep]

Block

EndFor

Executes the statements in Block iteratively for each value of Va r , from Low to 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 definiti ons by pressing @ instead of · at the end of each line. On the computer keyboard,

hold down Alt and press Enter.

Catalog

format()

format(Val u e [, formatString]) ⇒ string

Returns Val u e as a character string based on the format template.

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) ⇒ expression fPart(List1) ⇒ 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.

FPdf()

FPdf(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.

Catalog

38 TI-Nspire™ Reference Guide

freqTable4list()

freqTable4list(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 131.

Catalog

frequency()

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 131.

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

Note: See also countIf(), page 23.

FTest_2Samp

FTest_2Samp List1,List2[,Freq1[,Freq2[,Hypoth]]]

FTest_2Samp

(Data list input)

List1,List2[,Freq1[,Freq2[,Hypoth]]]

FTest_2Samp sx1,n1,sx2,n2[,Hypoth]

FTest_2Samp

(Summary stats input)

Performs a two-sample F test. A summary of results is stored in the stat.results variable. (See page 97.)

For Ha: s1 > s2, set Hypoth>0 For Ha: s1 ƒ s2 (default), set Hypoth =0 For Ha: s1 < s2, set Hypoth<0

For information on the effect of empty elements in a list, see “Empty (void) elements” on page 131.

sx1,n1,sx2,n2[,Hypoth]

Catalog

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.

Catalog

TI-Nspire™ Reference Guide 39

Output variable Description

stat.F Calculated F statistic for the data sequence

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

stat.dfNumer numerator degrees of freedom = n1-1

stat.dfDenom denominator degrees of freedom = n2-1

stat.sx1, stat.sx2 Sample standard deviations of the data sequences in List 1 and List 2

stat.x1_bar stat.x2_bar

stat.n1, stat.n2 Size of the samples

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

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.

Note for entering the example: In the Calculator application

on the handheld, you can enter multi-line definiti ons by pressing @ instead of · at the end of each line. On the computer keyboard,

hold down Alt and press Enter.

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.

Define a piecewise function:

Result of graphing g(x)

Catalog

40 TI-Nspire™ Reference Guide

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{X{upBound) ⇒ number if

upBound is a number, list if upBound is a list

Computes a cumulative geometric probability from lowBound to upBound with the specified probability of success p.

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

Catalog

geomPdf()

geomPdf(p,XVal) ⇒ number if XVal is a number, list if XVal

is a list

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(Fraction1) ⇒ value

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”

Catalog

TI-Nspire™ Reference Guide 41

getLockInfo()

getLockInfo(Var ) ⇒ value

Returns the current locked/unlocked state of variable Var .

value =0: Va r is unlocked or does not exist. value =1: Va r is locked and cannot be modified or deleted.

See Lock, page 57, and unLock, page 109.

Catalog

getMode()

getMode(ModeNameInteger) ⇒ value getMode(0) ⇒ list

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 90.

Mode Name

Display Digits

Angle

Exponential Format

Real or Complex

Auto or Approx.

Vector Format

Base

Mode Integer Setting Integers

=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

=Radian, 2=Degree, 3=Gradian

=Normal, 2=Scientific, 3=Engineering

=Real, 2=Rectangular, 3=Polar

=Auto, 2=Approximate

=Rectangular, 2=Cylindrical, 3=Spherical

=Decimal, 2=Hex, 3=Binary

Catalog

42 TI-Nspire™ Reference Guide

getNum()

getNum(Fraction1) ⇒ value

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

Catalog

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.

Catalog

TI-Nspire™ Reference Guide 43

getVarInfo()

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

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 definiti ons by pressing @ instead of · at the end of each line. On the computer keyboard,

hold down Alt and press Enter.

4Grad

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:

Catalog

44 TI-Nspire™ Reference Guide

identity()

identity(Integer) ⇒ matrix

Returns the identity matrix with a dimension of Integer.

Integer must be a positive integer.

If 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 definiti ons by pressing @ instead of · at the end of each line. On the computer keyboard,

hold down Alt and press Enter.

If 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.

Catalog

TI-Nspire™ Reference Guide 45

If BooleanExpr1 Then

Block1

ElseIf

BooleanExpr2 Then

Block2

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

ifFn()

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).

imag()

imag(Va l ue 1 ) ⇒ value

Returns the imaginary part of the argument.

imag(List1) ⇒ list

Returns a list of the imaginary parts of the elements.

Catalog

Test va lue o f 1 is less than 2.5, so its corresponding Value_If_True element of 5 is copied to the result list.

Test va lue o f 2 is less than 2.5, so its corresponding Value_If_True element of 6 is copied to the result list.

Test va lue o f 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 cor responds to any selected

position.

Value_If_false is not specified. Undef is used.

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

Catalog

46 TI-Nspire™ Reference Guide

imag()

imag(Matrix1) ⇒ matrix

Returns a matrix of the imaginary parts of the elements.

Catalog

Indirection See

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(Va l ue ) ⇒ integer

int(List1) ⇒ list int(Matrix1) ⇒ matrix

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

Catalog

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) ⇒ integer intDiv(List1, List2) ⇒ list intDiv(Matrix1, Matrix2) ⇒ matrix

Catalog

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.

#()

, page

126

TI-Nspire™ Reference Guide 47

interpolate( )

interpolate(xValue, xList, yList, yPrimeList) ⇒ list

This function does the following:

xList, yList=f(xList), and yPrimeList=f'(xList) for some

Given 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 for an interval [ an interval, it returns an interpolated valu e for f(xValue); otherwise, it returns undef.

xList, yList, and yPrimeList must be of equal dimension | 2 and

contain expressions that simplify to numbers.

xValue can be a number or a list of numbers.

xList[i], xList[i+1]] that contains xValue. If it finds such

xList looking

Catalog

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

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

Use the interpolate() function to calculate the function values for the xvaluelist:

invc2()

invc2(Area,df)

Area,df)

invChi2(

Computes the Inverse cumulative c2 (chi-square) probability function specified by degree of freedom, df for a given Area under the curve.

invF()

invF(Area,dfNumer,dfDenom)

Area,dfNumer,dfDenom)

invF(

computes the Inverse cumulative F 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.

48 TI-Nspire™ Reference Guide

Catalog

iPart()

iPart(Number) ⇒ integer

iPart(List1) ⇒ list iPart

(Matrix1) ⇒ 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.

Catalog

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 63.

isPrime()

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.

Note for entering the example: In the Calculator application

on the handheld, you can enter multi-line definiti ons by pressing @ instead of · at the end of each line. On the computer keyboard,

hold down Alt and press Enter.

isVoid()

isVoid(Var ) ⇒ Boolean constant expression isVoid(Expr) ⇒ Boolean constant expression isVoid(List) ⇒ 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 131.

Catalog

Function to find the next prime after a specified number:

Catalog

TI-Nspire™ Reference Guide 49

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 definiti ons by pressing @ instead of · at the end of each line. On the computer keyboard,

hold down Alt and press Enter.

lcm()

lcm(Number1, Number2) ⇒ expression lcm(List1, List2) ⇒ list lcm(Matrix1, Matrix2) ⇒ 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

50 TI-Nspire™ Reference Guide

libShortcut()

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=

To copy a variable group, see CopyVar on page 18. To delete a variable group, see DelVar on page 29.

1 to include private library objects

Catalog

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

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 97.)

Catalog

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 numeric or string 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 131.

Output variable Description

stat.RegEqn Regression Equation: a+b·x

stat.a, stat.b Regression coefficients

stat.r

Coefficient of determination

stat.r Correlation coefficient

stat.Resid Residuals from the regression

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

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

Category List, and Include Categories

stat.FreqReg List of frequencies corresponding to stat.XReg and stat.YReg

TI-Nspire™ Reference Guide 51

LinRegMx

LinRegMx X,Y[,[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 97.)

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 numeric or string 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 131.

Output variable Description

stat.RegEqn Regression Equation: y = m·x+b

stat.m, stat.b Regression coefficients

stat.r

stat.r Correlation coefficient

stat.Resid Residuals from the regression

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

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

stat.FreqReg List of frequencies corresponding to stat.XReg and stat.YReg

Coefficient of determination

Category List, and Include Categories

Catalog

LinRegtIntervals

LinRegtIntervals X,Y[,F[,0[,CLev]]]

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

LinRegtIntervals X,Y[,F[,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

97.)

All the lists must have equal dimension.

X and Y 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 X and Y 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 131.

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Catalog

Output variable Description

stat.RegEqn Regression Equation: a+b·x

stat.a, stat.b Regression coefficients

stat.df Degrees of freedom

stat.r

stat.r Correlation coefficient

stat.Resid Residuals from the regression

For Slope type only

Output variable Description

[stat.CLower, stat.CUpper]

stat.ME Confidence interval margin of error

stat.SESlope Standard error of slope

stat.s Standard error about the line

For Response type only

Output variable Description

[stat.CLower, stat.CUpper]

stat.ME Confidence interval margin of error

stat.SE Standard error of mean response

[stat.LowerPred , stat.UpperPred]

stat.MEPred Prediction interval margin of error

stat.SEPred Standard error for prediction

stat.y

Coefficient of determination

Confidence interval for the slope

Confidence interval for the mean response

Prediction interval for a single observation

a + b·XVal

TI-Nspire™ Reference Guide 53

LinRegtTest

LinRegtTest X,Y[,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+bx. It tests the null hypothesis H0:b=0 (equivalently, r=0) against one of three alternative hypotheses.

All the lists must have equal dimension.

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.

Hypoth is an optional value specifying one of three alternative hypotheses against which the null hypothesis (H0:b=r=0) will be tested.

For Ha: bƒ0 and rƒ0 (default), set Hypoth=0 For Ha: b<0 and r<0, set Hypoth<0 For Ha: b>0 and r>0, set Hypoth>0

A summary of results is stored in the stat.results variable. (See page

97.)

For information on the effect of empty elements in a list, see “Empty (void) elements” on page 131.

Output variable Description

stat.RegEqn Regression equation: a + b·x

stat.t t-Statistic for significance test

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

stat.df Degrees of freedom

stat.a, stat.b Regression coefficients

stat.s Standard error about the line

stat.SESlope Standard error of slope

stat.r

stat.r Correlation coefficient

stat.Resid Residuals from the regression

Coefficient of determination

Catalog

54 TI-Nspire™ Reference Guide

linSolve()

linSolve( SystemOfLinearEqns, Var 1, Va r 2 , ...) ⇒ list

linSolve(LinearEqn1 and LinearEqn2 and ...,

Var 1 , Va r 2, ...) ⇒ list

LinearEqn1, LinearEqn2, ...}, Var 1, Va r 2 , ...)

linSolve({

⇒ list

SystemOfLinearEqns, {Var 1 , Va r 2, ...})

linSolve(

⇒ list

LinearEqn1 and LinearEqn2 and ...,

linSolve(

{Var 1 , Va r 2 , ...}) ⇒ list

LinearEqn1, LinearEgn2, ...}, {Var 1 , Va r 2, ... })

linSolve({

⇒ list

Returns a list of solutions for the variables Va r 1, Va r 2 , ...

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

list4mat()

list4mat(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).

If List does not fill the resulting matrix, zeros are added.

Note: You can insert this function from the computer keyboard by

typing list@>mat(...).

ln()

ln(Va l u e1 ) ⇒ value

ln(List1) ⇒ list

Returns the natural logarithm of the argument.

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

Catalog

If complex format mode is Real:

If complex format mode is Rectangular:

TI-Nspire™ Reference Guide 55

keys

ln()

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:

keys

To see the entire result, press move the cursor.

LnReg

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

Computes the logarithmic regression y = a+b·ln(x) on lists X and Y with frequency Freq. A summary of results is stored in the stat.results variable. (See page 97.)

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 numeric or string 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 131.

Output variable Description

stat.RegEqn Regression equation: a+b·ln(x)

stat.a, stat.b Regression coefficients

stat.r

stat.r Correlation coefficient for transformed data (ln(x), y)

stat.Resid Residuals associated with the logarithmic model

stat.ResidTrans Residuals associated with linear fit of transformed data

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

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

stat.FreqReg List of frequencies corresponding to stat.XReg and stat.YReg

Coefficient of linear determination for transformed data

Category List, and Include Categories

£ and then use ¡ and ¢ to

Catalog

56 TI-Nspire™ Reference Guide

Local

Local Var 1 [, Va r 2] [, Va r 3 ] ...

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 definiti ons by pressing @ instead of · at the end of each line. On the computer keyboard,

hold down Alt and press Enter.

Catalog

Lock

Lock Var 1 [, Va r 2] [, Va r 3 ] ... 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 109, and getLockInfo(), page 42.

Catalog

TI-Nspire™ Reference Guide 57

log()

log(Val u e 1 [,Val u e 2 ]) ⇒ value log(List1[,Val u e 2] ) ⇒ list

Returns the base-Value2 logarithm of the first argument.

Note: See also Log template, page 2.

For a list, returns the base-Value2 logarithm of the elements.

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

If complex format mode is Real:

If complex format mode is Rectangular:

keys

log(squareMatrix1[,Val u e ]) ⇒ squareMatrix

Returns the matrix base-Val u e logarithm of squareMatrix1. This is not the same as calculating the base-Va lu e logarithm of each element. For information about the calculation method, refer to cos().

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

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

Logistic

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

Computes the logistic regression y = (c/(1+a·e with frequency Freq. A summary of results is stored in the stat.results variable. (See page 97.)

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 numeric or string 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 131.

-bx

)) on lists X and Y

In Radian angle mode and Rectangular complex format:

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

Catalog

58 TI-Nspire™ Reference Guide

Output variable Description

stat.RegEqn

Regression equation: c/(1+a·e

-bx

)

stat.a, stat.b, stat.c Regression coefficients

stat.Resid Residuals from the regression

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

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

Category List, and Include Categories

stat.FreqReg List of frequencies corresponding to stat.XReg and stat.YReg

LogisticD

LogisticD X, Y [ , [Iterations] , [Freq] [, Category, Include] ]

Computes the logistic regression y = (c/(1+a·e Y with frequency Freq, using a specified number of Iterations. A summary of results is stored in the stat.results variable. (See page

97.)

-bx

)+d) on lists X and

Catalog

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 numeric or string 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 131.

Output variable Description

stat.RegEqn

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

Regression equation: c/(1+a·e

Regression coefficients

-bx

)+d)

stat.Resid Residuals from the regression

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

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

Category List, and Include Categories

stat.FreqReg List of frequencies corresponding to stat.XReg and stat.YReg

TI-Nspire™ Reference Guide 59

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 definiti ons by pressing instead of · at the end of each line. On the computer keyboard,

hold down Alt and press Enter.

Catalog

LU 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, To l is ignored.

• If you use mode to Approximate, computations are done using floating-

point arithmetic.

•If Tol is omitted or not used, the default tolerance is calculated as: 5EM14 ·max(dim(Matrix)) ·rowNorm(Matrix)

The LU factorization algorithm uses partial pivoting with row interchanges.

or set the Auto or Approximate

mat4list()

mat4list(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(...).

Catalog

60 TI-Nspire™ Reference Guide

max()

max(Va l ue 1 , Va l ue 2 ) ⇒ expression

max(List1, List2) ⇒ 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 131.

Note: See also min().

Catalog

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 131.

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.

In Rectangular vector format:

Catalog

TI-Nspire™ Reference Guide 61

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 131.

Catalog

MedMed

MedMed X,Y [, 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 97.)

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 numeric or string 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 131.

Output variable Description

stat.RegEqn Median-median line equation: m·x+b

stat.m, stat.b Model coefficients

stat.Resid Residuals from the median-median line

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

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

stat.FreqReg List of frequencies corresponding to stat.XReg and stat.YReg

Category List, and Include Categories

Catalog

mid()

mid(sourceString, Start[, Count]) ⇒ string

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

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.

62 TI-Nspire™ Reference Guide

Catalog

mid()

mid(sourceList, Start [, Count]) ⇒ list

Returns Count elements from sourceList, beginning with element number Start.

If Count is omitted or is greater than the dimension of sourceList, returns all elements from sourceList, beginning with element number

Start.

Count must be

mid(sourceStringList, Start[, Count]) ⇒ list

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

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

min()

min(Val u e 1, Va l u e 2) ⇒ expression min(List1, List2) ⇒ 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) ⇒ ex pression

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 max().

Catalog

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.

rein vestRa te 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 49.

Catalog

TI-Nspire™ Reference Guide 63

mod()

mod(Va lu e 1 , Val u e 2 ) ⇒ expression mod(List1, List2) ⇒ 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

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 83

- y floor(x/y)

Catalog

mRow()

mRow(Va lu e , Matrix1, Index) ⇒ matrix

Returns a copy of Matrix1 with each element in row Index of Matrix1 multiplied by Va lu e .

mRowAdd()

mRowAdd(Val u e , Matrix1, Index1, Index2) ⇒ matrix

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

Val u e · row Index1 + row Index2

MultReg

MultReg Y, X1[,X2[,X3,…[,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

97.)

All the lists must have equal dimension.

For information on the effect of empty elements in a list, see “Empty (void) elements” on page 131.

Output variable Description

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

stat.b0, stat.b1, ... Regression coefficients

stat.R

Coefficient of multiple determination

stat.yList yList = b0+b1·x1+ ...

stat.Resid Residuals from the regression

Catalog

64 TI-Nspire™ Reference Guide

MultRegIntervals

MultRegIntervals Y, X1[,X2[,X3,…[,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

97.)

All the lists must have equal dimension.

For information on the effect of empty elements in a list, see “Empty (void) elements” on page 131.

Output variable Description

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

stat.y 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 Confidence interval margin of error

stat.SE Standard error of mean response

stat.LowerPred, stat.UpperrPred

stat.MEPred Prediction interval margin of error

stat.SEPred Standard error for prediction

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

stat.Resid Residuals from the regression

Prediction interval for a single observation

Catalog

MultRegTests

MultRegTests Y, X1[,X2[,X3,…[,X10]]]

Multiple linear regression test computes a multiple linear regression on the given data and provides the global F test statistic and t test statistics for the coefficients.

A summary of results is stored in the stat.results variable. (See page

97.)

For information on the effect of empty elements in a list, see “Empty (void) elements” on page 131.

Outputs

Output variable Description

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

stat.F Global F test statistic

stat.PVal P-value associated with global F statistic

stat.R

Coefficient of multiple determination

Catalog

TI-Nspire™ Reference Guide 65

Output variable Description

stat.AdjR

stat.s Standard deviation of the error

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

stat.dfReg Regression degrees of freedom

stat.SSReg Regression sum of squares

stat.MSReg Regression mean square

stat.dfError Error degrees of freedom

stat.SSError Error sum of squares

stat.MSError Error mean square

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

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

stat.PList List P-values for each t statistic

stat.SEList List of standard errors for coefficients in bList

stat.yList yList = b0+b1·x1+...

stat.Resid Residuals from the regression

stat.sResid Standardized residuals; obtained by dividing a residual by its standard deviation

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

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

Adjusted coefficient of multiple determination

nCr()

nCr(Va l u e1 , Va l ue 2 ) ⇒ expression

For integer Va l ue 1 and Va l ue 2 with Va lu e 1 | Va lu e 2 | 0, nCr() is the number of combinations of Va lu e 1 things taken Va l ue 2 at a time. (This is also known as a binomial coefficient.)

nCr(Va lu e , 0) ⇒ 1

Va l ue , negInteger) ⇒ 0

nCr(

Va l ue , posInteger ) ⇒ Va l ue ·(Va l u eN1)...

nCr(

Val u e NposInteger+1)/ posInteger!

(

Va l ue , nonInteger ) ⇒ expression!/

nCr(

((

Val u e NnonInteger)!·nonInteger!)

List1, List2) ⇒ list

nCr(

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

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.

66 TI-Nspire™ Reference Guide

Catalog

nDerivative()

nDerivat iv e(Expr1,Var = Va lu e [,Order]) ⇒ value

nDerivat iv e(

Returns the numerical derivative calculated using auto differentiation methods.

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

If the variable Var does not contain a numeric value, you must provide Va lu e .

Order of the derivative must be

Note: The nDerivative() algorithm has a limitiation: it works recursively through the unsimplified expression, computing the numeric value of the first derivative (and second, if applicable) and the evaluation of each subexpression, which may lead to an unexpected result.

Consider the example on the right. The first derivative of x·(x^2+x)^(1/3) at x=0 is equal to 0. However, because the first derivative of the subexpression (x^2+x)^(1/3) is undefined at x=0, and this value is used to calculate the derivative of the total expression, nDerivative() reports the result as undefined and displays a warning message.

If you encounter this limitation, verify the solution graphically. You can also try using centralDiff().

Expr1,Va r [,Order]) | Va r= Va l u e ⇒ value

1 or 2.

Catalog

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, Va r) ⇒ value nfMax(Expr, Va r, lowBound) ⇒ value nfMax(Expr, Va r, lowBound, upBound) ⇒ value nfMax(Expr, Var) | lowBound<Var <upBound ⇒ value

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

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

Catalog

TI-Nspire™ Reference Guide 67

nfMin()

nfMin(Expr, Va r) ⇒ value nfMin(Expr, Va r, lowBound) ⇒ value

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

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

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

Catalog

nInt()

nInt(Expr1, Var, Lower, Upper) ⇒ expression

If the integrand Expr1 contains no variable other than Va r , and if Lower and Upper are constants, positive ˆ, or negative ˆ, then

nInt() returns an approximation of ‰(Expr1, Va r , Lower, Upper). This approximation is a weighted average of some sample values of the integrand in the interval Lower<Va r <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.

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 32.

norm()

norm(Matrix) ⇒ expression norm(Ve c to r ) ⇒ expression

Returns the Frobenius norm.

Catalog

68 TI-Nspire™ Reference Guide

normCdf()

normCdf(lowBound,upBound[,m[,s]]) ⇒ number if lowBound

upBound are numbers, list if lowBound and upBound are

and lists

Computes the normal distribution probability between lowBound and upBound for the specified m (default=0) and s (default=1).

For P(X { upBound), set lowBound = .9E999.

Catalog

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.

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.

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).

nPr()

nPr(Va l ue 1 , Va l ue 2 ) ⇒ expression

For integer Va l ue 1 and Va l ue 2 with Va lu e 1 | Va lu e 2 | 0, nPr() is the number of permutations of Va lu e 1 things taken Va l u e2 at a time.

nPr(Val u e , 0) ⇒ 1

Val u e , negInteger) ⇒ 1/((Va l ue +1)·(Va l u e +2)...

nPr(

(

Val u e NnegInteger))

Val u e , posInteger ) ⇒ Va l ue ·(Va l u eN1)...

nPr(

(

Val u e NposInteger+1)

Val u e , nonInteger) ⇒ Va l ue ! / (Va l ue NnonInteger)!

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.

Catalog

In Hex base mode:

Important: Zero, not the letter O.

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.

Catalog

TI-Nspire™ Reference Guide 69

nPr()

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<Va r <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.

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.”

Catalog

Note: If there are multiple solutions, you can use a guess to

help find a particular solution.

70 TI-Nspire™ Reference Guide

OneVar

OneVar [1,]X[,[Freq][,Category,Include]] OneVar [

n,]X1,X2[X3[,…[,X20]]]

Calculates 1-variable statistics on up to 20 lists. A summary of results is stored in the stat.results variable. (See page 97.)

All the lists must have equal dimension except for Include.

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 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 131.

Output variable Description

stat.v

stat.Gx

stat.sx Sample standard deviation of x

stat.sx Population standard deviation of x

stat.n Number of data points

stat.MinX Minimum of x values

stat.Q1X 1st Quartile of x

stat.MedianX Median of x

stat.Q3X 3rd Quartile of x

stat.MaxX Maximum of x values

stat.SSX Sum of squares of deviations from the mean of x

Mean of x values

Sum of x values

Sum of x2 values

Catalog

TI-Nspire™ Reference Guide 71

BooleanExpr1 or 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 definiti ons by pressing @ instead of · at the end of each line. On the computer keyboard,

hold down Alt and press Enter.

Integer1 or Integer2 ⇒ integer

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.

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).

Note: See xor.

Catalog

In Hex 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.

ord()

ord(Str ing) ⇒ integer ord(List1) ⇒ lis t

Returns the numeric code of the first character in character string Strin g, or a list of the first characters of each list element.

P4Rx()

P4Rx(rExpr, qExpr) ⇒ expression P4Rx(rList, qList) ⇒ list P4Rx(rMatrix, qMatrix) ⇒ 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 ¡,G or R to override the angle mode

setting temporarily.

Note: You can insert this function from the computer keyboard by

typing P@>Rx(...).

72 TI-Nspire™ Reference Guide

In Radian angle mode:

Catalog

P4Ry()

P4Ry(rValue, qVal u e ) ⇒ value P4Ry(rList, qList) ⇒ list P4Ry(rMatrix, qMatrix) ⇒ 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.

Note: You can insert this function from the computer keyboard by

typing P@>Ry(...).

¡R

In Radian angle mode:

Catalog

PassErr

Passes an error to the next level.

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

Note: See also ClrErr, page 17, and Try, page 105.

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.

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{X{upBound) ⇒ number if

upBound is a number, list if upBound is a list

Computes a cumulative probability for the discrete Poisson distribution with specified mean l.

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

Catalog

For an example of PassErr, See Example 2 under the Try command, page 105.

Catalog

poissPdf()

poissPdf(l,XVal) ⇒ number if XVal is a number, list if XVal is

a list

Computes a probability for the discrete Poisson distribution with the specified mean l.

Catalog

TI-Nspire™ Reference Guide 73

4Polar

Vec t o r

Note:

You can insert this operator from the computer keyboard by

typing @>Polar.

Displays vector in polar form [r dimension 2 and can be a row or a column.

Note: 4Polar 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 4Rect, page 81.

complexValue 4Polar

Displays complexVector in polar form.

• Degree angle mode returns (r±q).

• Radian angle mode returns reiq.

complexValue can have any complex form. However, an reiq entry causes an error in Degree angle mode.

Note: You must use the parentheses for an (r±q) polar entry.

±q]. The vector must be of

In Radian angle mode:

In Gradian angle mode:

In Degree angle mode:

Catalog

polyEval()

polyEval(List1, Expr1) ⇒ expression 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.

polyRoots()

polyRoots(Poly,Var ) ⇒ list polyRoots(ListOfCoeffs) ⇒ list

The first syntax, polyRoots(Poly,Va r), 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 expanded form in one variable. Do not use unexpanded forms such as y2·y+1 or x·x+2·x+1

The second syntax, polyRoots(ListOfCoeffs), returns a list of real roots for the coefficients in ListOfCoeffs.

Note: See also cPolyRoots(), page 23.

74 TI-Nspire™ Reference Guide

Catalog

PowerReg

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

Computes the power regression y = (a·(x)b) on lists X and Y with frequency Freq. A summary of results is stored in the stat.results variable. (See page 97.)

Catalog

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 numeric or string 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 131.

Output variable Description

stat.RegEqn

Regression equation: a·(x)

stat.a, stat.b Regression coefficients

stat.r

Coefficient of linear determination for transformed data

stat.r Correlation coefficient for transformed data (ln(x), ln(y))

stat.Resid Residuals associated with the power model

stat.ResidTrans Residuals associated with linear fit of transformed data

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

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

Category List, and Include Categories

stat.FreqReg List of frequencies corresponding to stat.XReg and stat.YReg

TI-Nspire™ Reference Guide 75

Prgm

Block

EndPrgm

Template for creating a user-defined progra m. 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. O n the computer keyboard,

hold down Alt and press Enter.

Calculate GCD and display intermediate results.

Catalog

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 131.

76 TI-Nspire™ Reference Guide

See Π(), page

Catalog

124

propFrac()

propFrac(Va l ue 1 [, Va r ]) ⇒ value

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 Va r . The degree of Va r in the denominator exceeds the degree of Va r in the numerator in each proper ratio. Similar powers of Va r are collected. The terms and their factors are sorted with Var as the main variable.

If 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.

You can use the propFrac() function to represent mixed fractions and demonstrate addition and subtraction of mixed fractions.

Catalog

QR 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.

• If you use mode to Approximate, computations are done using floating-

point arithmetic.

•If Tol is omitted or not used, the default tolerance is calculated as: 5EL14 ·max(dim(Matrix)) ·rowNorm(Matrix)

The QR factorization is computed numerically using Householder transformations. The symbolic solution is computed using GramSchmidt. The columns in qMatName are the orthonormal basis vectors that span the space defined by matrix.

or set the Auto or Approximate

Catalog

The floating-point number (9.) in m1 causes results to be calculated in floating-point form.

TI-Nspire™ Reference Guide 77

QuadReg

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

Computes the quadratic polynomial regression y = a·x2+b·x+c on lists X and Y with frequency Freq. A summary of results is stored in the stat.results variable. (See page 97.)

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 numeric or string 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 131.

Output variable Description

stat.RegEqn

stat.a, stat.b, stat.c Regression coefficients

stat.R

stat.Resid Residuals from the regression

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

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

stat.FreqReg List of frequencies corresponding to stat.XReg and stat.YReg

Regression equation: a·x2+b·x+c

Coefficient of determination

Category List, and Include Categories

Catalog

QuartReg

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

Computes the quartic polynomial regression y = a·x4+b·x3+c· x2+d·x+e on lists X and Y with frequency Freq.

A summary of results is stored in the stat.results variable. (See page

97.)

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 numeric or string 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 131.

78 TI-Nspire™ Reference Guide

Catalog

Output variable Description

stat.RegEqn

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

stat.R

stat.Resid Residuals from the regression

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

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

stat.FreqReg List of frequencies corresponding to stat.XReg and stat.YReg

Regression equation: a·x4+b·x3+c· x2+d·x+e

Regression coefficients

Coefficient of determination

Category List, and Include Categories

R4Pq()

R4Pq (xValue, yValue) ⇒ value R4Pq (xList, yList) ⇒ list R4Pq (xMatrix, yMatrix) ⇒ matrix

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

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(...).

R4Pr()

R4Pr (xValue, yValue) ⇒ value R4Pr (xList, yList) ⇒ list R4Pr (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 Degree angle mode:

In Gradian angle mode:

In Radian angle mode:

Catalog

TI-Nspire™ Reference Guide 79

4Rad

4Rad ⇒ value

Val u e 1

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:

Catalog

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.

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 co ntaining #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.

Sets the random-number seed.

Catalog

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 [mN3·s, m+3·s].

randNorm(m, s, #Trials) returns a list containing #Trials decimal

numbers from the specified normal distribution.

80 TI-Nspire™ Reference Guide

Note: The value s in this matr ix will change each time you press

·.

Catalog

randPoly()

randPoly(Va r , Order) ⇒ expression

Returns a polynomial in Va r of the specified Order. The coefficients are random integers in the range coefficient will not be zero.

L9 through 9. The leading

Order must be 0–99.

Catalog

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.

RandSeed

RandSeed Number

If 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(Va l ue 1 ) ⇒ value

Returns the real part of the argument.

real(List1) ⇒ list

Returns the real parts of all elements.

real(Matrix1) ⇒ matrix

Returns the real parts of all elements.

4Rect

Vec t o r 4Rect

Note:

You can insert this operator from the computer keyboard by

typing @>Rect.

Displays Vec t o r in rectangular form [x, y, z]. The vector must be of dimension 2 or 3 and can be a row or a column.

Note: 4Rect 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 4Polar, page 74.

Catalog

TI-Nspire™ Reference Guide 81

Rect

complexValue 4Rect

Displays complexValue in rectangular form a+bi. The complexValue can have any complex form. However, an reiq entry causes an error in

Degree angle mode.

Note: You must use parentheses for an (r±q) polar entry.

Catalog

In Radian angle mode:

In Gradian angle mode:

In Degree angle mode:

Note: To type ±, select it from the symbol list in the Catalog.

ref()

ref(Matrix1[, To l]) ⇒ matrix

Returns the row echelon form of Matrix1.

• If you use mode to Approximate, computations are done using floating-

point arithmetic.

•If Tol is omitted or not used, the default tolerance is calculated as: 5EL14 ·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 87.

or set the Auto or Approximate

Catalog

82 TI-Nspire™ Reference Guide

remain()

remain(Va lu e 1 , Val u e 2 ) ⇒ value remain(List1, List2) ⇒ 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

 xNy·iPart(x/y)

remain(x,y)

As a consequence, note that remain(Nx,y)  Nremain(x,y). The result is either zero or it has the same sign as the first argument.

Note: See also mod(), page 64.

Catalog

Request

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.

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.

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.

• 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.

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 command within a user-defined program but not within a function.

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 84.

Catalog

Define a program:

Define request_demo()=Prgm

Request “Radius: ”,r Disp “Area = “,pi*r2

EndPrgm

Run the program and type a response:

request_demo()

Result after selecting OK:

Radius: 6/2 Area= 28.2743

Define a program:

Define polynomial()=Prgm

Request "Enter a polynomial in x:",p(x) Disp "Real roots are:",polyRoots(p(x),x)

EndPrgm

Run the program and type a response:

polynomial()

Result after selecting OK:

Enter a polynomial in x: x^3+3x+1 Real roots are: {-0.322185}

TI-Nspire™ Reference Guide 83

RequestStr

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 encl oses it in quotation marks (““).

Note: You can use the defined 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.

RequestStr command within a user-

• Handheld: Hold down the c key and press · repeatedly.

Note: See also Request, page 83.

Catalog

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()

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 definiti ons by pressing @ instead of · at the end of each line. On the computer keyboard,

hold down Alt and press Enter.

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

84 TI-Nspire™ Reference Guide

rk23()

depVard

rk23(Expr, Var , depVar, {Var 0 , Va r Ma x }, depVar0, Var St e p

[, diftol]) ⇒ matrix

rk23(SystemOfExpr, Var , ListOfDepVars, {Var0 , Va r Ma x },

ListOfDepVars0, Va rS t ep [, diftol ]) rk23(ListOfExpr, Var , ListOfDepVars, {Var0 , Va r Ma x }, ListOfDepVars0, Va r St e p [, diftol])

Uses the Runge-Kutta method to solve the system

-------------------

with depVar(Var 0 )=depVar0 on the interval [Var 0,Va r M a x ]. Returns a matrix whose first row defines the Va r output values as defined by

Var S te p . The second row defines the value of the first solution

component at the corresponding Va r values, and so on.

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).

Var is the independent variable.

ListOfDepVars is a list of dependent variables.

{Var 0 , Va rM a x } is a two-element list that tells the function to integrate from Va r0 to Va r M ax .

ListOfDepVars0 is a list of initial values for dependent variables.

If Var S te p evaluates to a nonzero number: sign(Va r St e p ) = sign(Var M a x-Va r 0 ) and solutions are returned at Va r 0 +i*Va r St e p for all i=0,1,2,… such that Va r0 +i* Var St e p is in [var0,Va rM a x ] (may not get a solution value at Va rM a x ).

if Var S te p evaluates to zero, solutions are returned at the "RungeKutta" Var values.

diftol is the error tolerance (defaults to 0.001).

= Expr(Var , depVar)

Vard

⇒ matrix

Catalog

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

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

Same equation with diftol set to 1.E•6

System of equations:

with y1(0)=2 and y2(0)=5

root()

root(Val u e ) ⇒ root root(Val u e 1 , Val u e 2 ) ⇒ root

root(Val u e ) returns the square root of Val u e .

root(Val u e 1 , Val u e 2 ) returns the Val u e 2 root of Va l u e 1. Va l u e 1

can be a real or complex floating point constant or an integer or complex rational constant.

Note: See also Nth root template, page 1.

rotate()

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 4Base2, page 12.

In Bin base mode:

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

TI-Nspire™ Reference Guide 85

Catalog

rotate()

If #ofRotations is positive, the rotation is to the left. If #ofRotations is negative, the rotation is to the right. The default is L1 (rotate right one bit).

For example, in a right rotation:

In Hex base mode:

Catalog

Each bit rotates right.

0b00000000000001111010110000110101

Rightmost bit rotates to leftmost.

produces:

0b10000000000000111101011000011010

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 L1 (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 L1 (rotate right one character).

round()

round(Va l ue 1 [, digits]) ⇒ value

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.

Important: To enter a binary or hexadecimal number, always use the 0b or 0h prefix (zero, not the letter O).

In Dec base mode:

Catalog

rowAdd()

rowAdd(Matrix1, rIndex1, rIndex2) ⇒ matrix

Returns a copy of Matrix1 with row rIndex2 replaced by the sum of rows rIndex1 and rIndex2.

86 TI-Nspire™ Reference Guide

Catalog

rowDim()

rowDim(Matrix) ⇒ expression

Returns the number of rows in Matrix.

Note: See also colDim(), page 17.

Catalog

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 17.

rowSwap()

rowSwap(Matrix1, rIndex1, rIndex2) ⇒ matrix

Returns Matrix1 with rows rIndex1 and rIndex2 exchanged.

rref()

rref(Matrix1[, To l]) ⇒ matrix

Returns the reduced row echelon form of Matrix1.

• If you use

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

Note: See also ref(), page 82.

mode to Approximate, computations are done using floatingpoint arithmetic.

as: 5EL14 ·max(dim(Matrix1)) ·rowNorm(Matrix1)

or set the Auto or Approximate

Catalog

TI-Nspire™ Reference Guide 87

sec()

sec(Val u e 1 ) ⇒ value sec(List1) ⇒ list

Returns the secant of Va lu e 1 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 ¡,G, or R to override the angle mode temporarily.

sec/()

sec/(Val u e 1 ) ⇒ value sec/(List1) ⇒ list

Returns the angle whose secant is Va l u e1 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(...).

sech()

sech(Val u e 1 ) ⇒ value sech(List1) ⇒ list

Returns the hyperbolic secant of Va lu e 1 or returns a list containing the hyperbolic secants of the List1 elements.

sech/()

sech/(Va l ue 1 ) ⇒ value sech/ (List1) ⇒ list

Returns the inverse hyperbolic secant of Va l ue 1 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(...).

In Degree angle mode:

In Gradian angle mode:

In Radian angle mode:

Catalog

In Radian angle and Rectangular complex mode:

μ key

88 TI-Nspire™ Reference Guide

seq()

seq(Expr, Va r, Low, High[, St ep]) ⇒ list

Increments Va r 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 Ste p = 1.

Catalog

Press Ctrl+Enter /· (Macintosh®: “+Enter) to evaluate:

seqGen()

seqGen(Expr, Var , depVar, {Var 0, Va r M ax }[, ListOfInitTerms

[, Var S te p [, CeilingValue]]])

Generates a list of terms for sequence depVar(Var )=Expr as follows: Increments independent variable Va r from Var 0 through Va r Ma x by Var S t ep , evaluates depVar(Var ) for corresponding values of Va r using the Expr formula and ListOfInitTerms, and returns the results as a list.

seqGen(ListOrSystemOfExpr, Var , ListOfDepVars, {Va r 0, Va r M ax }

[, MatrixOfInitTerms [, Va rS t ep [, CeilingValue]]])

Generates a matrix of terms for a system (or list) of sequences ListOfDepVars(Va r )=ListOrSystemOfExpr as follows: Increments independent variable Va r from Var 0 through Va r Ma x by Va r St e p , evaluates ListOfDepVars(Var ) for corresponding values of Var using ListOrSystemOfExpr formula and MatrixOfInitTerms, and returns the results as a matrix.

The original contents of Va r are unchanged after seqGen() is completed.

The default value for Va r St e p = 1.

⇒ list

⇒ matrix

Catalog

Generate the first 5 terms of the sequence u(n) = u(n-1)2/2, with u(1)=2 and Va rS t ep =1.

Example in which Var0=2:

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.

TI-Nspire™ Reference Guide 89

seqn()

seqn(Expr(u, n [, ListOfInitTerms[, nMax

[, CeilingValue]]])

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.

⇒ 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

Catalog

Generate the first 6 terms of the sequence u(n) = u(n-1)/2, with u(1)=2.

setMode()

setMode(modeNameInteger, settingInteger) ⇒ integer setMode(list) ⇒ integer list

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.

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 42.

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

Mode Integer Setting Integers

=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

=Radian, 2=Degree, 3=Gradian

Catalog

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.

90 TI-Nspire™ Reference Guide

Mode Name

Exponential Format

Real or Complex

Auto or Approx.

Vector Format

Base

Mode Integer Setting Integers

=Normal, 2=Scientific, 3=Engineering

=Real, 2=Rectangular, 3=Polar

=Auto, 2=Approximate

=Rectangular, 2=Cylindrical, 3=Spherical

=Decimal, 2=Hex, 3=Binary

shift()

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 4Base2, page 12.

If #ofShifts is positive, the shift is to the left. If #ofShifts is negative, the shift is to the right. The default is L1 (shift right one bit).

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

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. Lea ding zeros are not shown.

shift(List1 [,#ofShifts]) ⇒ list

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 L1 (shift right one element).

Elements introduced at the beginning or end of list by t he 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.

If #ofShifts is positive, the shift is to the left. If #ofShifts is negative, the shift is to the right. The default is L1 (shift right one character).

Characters introduced at the beginning or end of string by the shift are set to a space.

Catalog

In Bin base mode:

In Hex base mode:

Important: To enter a binary or hexadecimal number, always

use the 0b or 0h prefix (zero, not the letter O).

In Dec base mode:

TI-Nspire™ Reference Guide 91

sign()

sign(Va l ue 1 ) ⇒ value sign(List1) ⇒ list sign(Matrix1) ⇒ matrix

For real and complex Val u e1 , returns Va lu e 1 / abs(Val u e1 ) when

ƒ 0.

Val u e 1

Returns 1 if Val u e 1 is positive. Returns L1 if Val u e 1 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

simult()

simult(coeffMatrix, constVector[, Tol ]) ⇒ matrix

Returns a column vector that contains the solutions to a system of linear equations.

Note: See also linSolve(), page 55.

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.

• 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: 5EL14 ·max(dim(coeffMatrix)) ·rowNorm(coeffMatrix)

simult(coeffMatrix, constMatrix[, To l]) ⇒ 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.

Catalog

Solve for x and y: x + 2y = 1 3x + 4y = L1

The solution is x=L3 and y=2.

Solve: ax + by = 1 cx + dy = 2

Solve:

x + 2y = 1

3x + 4y = L1

x + 2y = 2

3x + 4y = L3

For the first system, x=L3 and y=2. For the second system, x=L7 and y=9/2.

92 TI-Nspire™ Reference Guide

sin()

sin(Va l ue 1 ) ⇒ value sin(List1) ⇒ list

sin(Val u e 1 ) returns the sine of the argument.

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 ¡,G, or R to override the angle mode setting temporarily.

μ key

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.

sin/()

sin/(Val u e 1 ) ⇒ value sin/(List1) ⇒ list

sin/(Val u e 1 ) returns the angle whose sine is Va l ue 1 .

sin/(List1) returns a list of the inverse sines 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

arcsin(...).

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:

μ key

In Degree angle mode:

In Gradian angle mode:

In Radian angle mode:

In Radian angle mode and Rectangular complex format mode:

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

TI-Nspire™ Reference Guide 93

sinh()

sinh(Numver1) ⇒ value sinh(List1) ⇒ list

sinh (Val u e 1 ) returns the hyperbolic sine of the argument.

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/(Val u e 1 ) ⇒ value sinh/(List1) ⇒ list

sinh/(Val u e 1 ) returns the inverse hyperbolic sine of the argument.

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

94 TI-Nspire™ Reference Guide

Texas Instruments TI-Nspire Reference Guide

Specifications and Main Features

Frequently Asked Questions

User Manual

Important Information

Contents

Expression templates

TI-Nspire™ Reference Guide 1

Alphabetical listing