TI-Nspire ReferenceGuide

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TI-Nspire/TI-Nspire CXReference Guide

This guidebook applies to TI-Nspire software version 3.2. To obtain thelatest version of the documentation, go to education.ti.com/guides.
http://www.education.ti.com/guideshttp://www.education.ti.com/guides


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Important Information

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party.

License

Please see the complete license installed inC:\Program Files\TI Education\\license.

2006 - 2012 Texas Instruments Incorporated


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Contents

Expression TemplatesFraction template ........................................1Exponent template ......................................1Square root template ..................................1

Nth root template ........................................1e exponent template ...................................2Log template ................................................2Piecewise template (2-piece) .......................2Piecewise template (N-piece) ......................2System of 2 equations template .................3System of N equations template .................3Absolute value template .............................3ddmmss.ss template ................................3Matrix template (2 x 2) ................................3Matrix template (1 x 2) ................................4Matrix template (2 x 1) ................................4Matrix template (m x n) ..............................4Sum template (G) .........................................4Product template () ...................................4First derivative template .............................5Second derivative template ........................5Definite integral template ..........................5

Alphabetical Listing

Aabs() ..............................................................6amortTbl() ....................................................6and ................................................................6angle() ..........................................................7ANOVA .........................................................7ANOVA2way ................................................8Ans ................................................................9approx() ......................................................104approxFraction() .......................................10approxRational() ........................................10arccos() ........................................................10arccosh() .....................................................10arccot() ........................................................10arccoth() .....................................................11arccsc() ........................................................11arccsch() ......................................................11arcsec() ........................................................11arcsech() ......................................................11arcsin() ........................................................11arcsinh() ......................................................11arctan() .......................................................11arctanh() .....................................................11augment() ...................................................11avgRC() .......................................................12

Bbal() .............................................................124Base2 .........................................................124Base10 .......................................................134Base16 .......................................................14binomCdf() .................................................14binomPdf() .................................................14

Cceiling() ...................................................... 14centralDiff() ............................................... 15char() .......................................................... 15

c22way ........................................................ 15c2Cdf() ........................................................ 16c2GOF ......................................................... 16c2Pdf() ........................................................ 16ClearAZ ....................................................... 16ClrErr .......................................................... 17colAugment() ............................................. 17colDim() ...................................................... 17colNorm() ................................................... 17completeSquare() ...................................... 18conj() .......................................................... 18constructMat() ........................................... 18CopyVar ...................................................... 18corrMat() .................................................... 19cos() ............................................................ 19cos/() .......................................................... 20cosh() .......................................................... 21cosh/() ........................................................ 21cot() ............................................................ 21cot/() .......................................................... 22coth() .......................................................... 22coth/() ........................................................ 22count() ........................................................ 22countif() ..................................................... 23cPolyRoots() ............................................... 23crossP() ....................................................... 23csc() ............................................................. 24csc/() ........................................................... 24csch() ........................................................... 24csch/() ......................................................... 24CubicReg .................................................... 25cumulativeSum() ........................................ 25Cycle ........................................................... 264Cylind ........................................................ 26

Ddbd() ........................................................... 264DD ............................................................. 274Decimal ..................................................... 27Define ......................................................... 27Define LibPriv ............................................ 28Define LibPub ............................................ 28deltaList() ................................................... 29DelVar ........................................................ 29delVoid() .................................................... 29det() ............................................................ 29diag() .......................................................... 30

dim() ........................................................... 30Disp ............................................................. 304DMS ........................................................... 31dotP() .......................................................... 31

Ee^() ............................................................. 31eff() ............................................................. 32
http://appx_functions.pdf/http://appx_functions.pdf/


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eigVc() .........................................................32eigVl() .........................................................32Else ..............................................................32ElseIf ............................................................33EndFor .........................................................33EndFunc ......................................................33EndIf ............................................................33

EndLoop ......................................................33EndPrgm .....................................................33EndTry .........................................................33EndWhile ....................................................33euler() .........................................................34Exit ..............................................................34exp() ............................................................35expr() ...........................................................35ExpReg ........................................................35

Ffactor() ........................................................36

FCdf() ..........................................................36Fill ................................................................36FiveNumSummary ......................................37floor() ..........................................................37For ...............................................................38format() ......................................................38fPart() ..........................................................38FPdf() ..........................................................38freqTable4list() ............................................39frequency() .................................................39FTest_2Samp ..............................................39Func .............................................................40

Ggcd() ............................................................40geomCdf() ...................................................41geomPdf() ...................................................41getDenom() ................................................41getLangInfo() .............................................41getLockInfo() ..............................................42getMode() ...................................................42getNum() ....................................................43getType() ....................................................43getVarInfo() ................................................43

Goto ............................................................444Grad ...........................................................44

Iidentity() .....................................................45If ..................................................................45ifFn() ............................................................46imag() ..........................................................46Indirection ..................................................47inString() .....................................................47int() .............................................................47intDiv() ........................................................47

interpolate() ...............................................48invc2() .........................................................48invF() ...........................................................48invNorm() ....................................................48invt() ............................................................48iPart() ..........................................................49irr() ..............................................................49isPrime() ......................................................49

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

LLbl ...............................................................50lcm() ............................................................50left() ............................................................50libShortcut() ...............................................51

LinRegBx ..................................................... 51LinRegMx ...................................................52LinRegtIntervals .........................................52LinRegtTest ................................................ 54linSolve() .....................................................55@List() ..........................................................55list4mat() .....................................................55ln() ..............................................................55LnReg ..........................................................56Local ...........................................................57Lock ............................................................57log() ............................................................58

Logistic .......................................................58LogisticD .....................................................59Loop ............................................................60LU ................................................................60

Mmat4list() .....................................................60max() ...........................................................61mean() ........................................................61median() .....................................................61MedMed .....................................................62mid() ...........................................................62

min() ...........................................................63mirr() ...........................................................63mod() ..........................................................64mRow() ....................................................... 64mRowAdd() ................................................ 64MultReg ......................................................64MultRegIntervals .......................................65MultRegTests .............................................65

Nnand ...........................................................66nCr() ............................................................67

nDerivative() ..............................................67newList() .....................................................67newMat() ....................................................68nfMax() .......................................................68nfMin() .......................................................68nInt() ...........................................................68nom() ..........................................................69nor ..............................................................69norm() .........................................................69normCdf() ...................................................69normPdf() ...................................................69not ..............................................................70

nPr() ............................................................70npv() ...........................................................71nSolve() .......................................................71

OOneVar .......................................................72or ................................................................73ord() ............................................................73


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PP4Rx() ...........................................................73P4Ry() ...........................................................74PassErr .........................................................74piecewise() ..................................................74poissCdf() ....................................................74poissPdf() ....................................................74

4Polar ..........................................................75polyEval() ....................................................75polyRoots() .................................................75PowerReg ...................................................76Prgm ...........................................................77prodSeq() ....................................................77Product (PI) .................................................77product() .....................................................77propFrac() ...................................................78

QQR ...............................................................78QuadReg .....................................................79QuartReg ....................................................79

RR4Pq() ..........................................................80R4Pr() ...........................................................804Rad .............................................................81rand() ..........................................................81randBin() .....................................................81randInt() .....................................................81randMat() ...................................................81randNorm() .................................................81randPoly() ...................................................82randSamp() .................................................82RandSeed ....................................................82real() ...........................................................824Rect ............................................................82ref() .............................................................83remain() ......................................................84Request .......................................................84RequestStr ..................................................85Return .........................................................85right() ..........................................................85rk23() ..........................................................86root() ...........................................................86rotate() .......................................................86round() ........................................................87rowAdd() ....................................................87rowDim() ....................................................88rowNorm() ..................................................88rowSwap() ..................................................88rref() ............................................................88

Ssec() .............................................................89

sec/

() ...........................................................89sech() ...........................................................89sech/() .........................................................89seq() ............................................................90seqGen() .....................................................90seqn() ..........................................................91setMode() ...................................................91shift() ..........................................................92

sign() ........................................................... 93simult() ....................................................... 93sin() ............................................................. 94sin/() ........................................................... 94sinh() ........................................................... 95sinh/() ......................................................... 95SinReg ........................................................ 96

SortA .......................................................... 96SortD .......................................................... 974Sphere ....................................................... 97sqrt() ........................................................... 97stat.results .................................................. 98stat.values .................................................. 99stDevPop() .................................................. 99stDevSamp() ............................................... 99Stop .......................................................... 100Store ......................................................... 100string() ...................................................... 100subMat() ................................................... 100

Sum (Sigma) ............................................. 100sum() ......................................................... 100sumIf() ...................................................... 101sumSeq() ................................................... 101system() .................................................... 101

TT (transpose) ............................................ 101tan() .......................................................... 102tan/() ........................................................ 102tanh() ........................................................ 103tanh/() ...................................................... 103

tCdf() ........................................................ 104Text ........................................................... 104Then ......................................................... 104tInterval .................................................... 104tInterval_2Samp ....................................... 105tPdf() ........................................................ 105trace() ....................................................... 105Try ............................................................. 106tTest .......................................................... 106tTest_2Samp ............................................. 107tvmFV() ..................................................... 107tvmI() ........................................................ 108

tvmN() ...................................................... 108tvmPmt() .................................................. 108tvmPV() ..................................................... 108TwoVar ..................................................... 109

UunitV() ...................................................... 110unLock ...................................................... 110

VvarPop() .................................................... 110varSamp() ................................................. 111

WwarnCodes() ............................................. 111when() ...................................................... 111While ........................................................ 112

Xxor ............................................................ 112


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ZzInterval ....................................................113zInterval_1Prop ........................................113zInterval_2Prop ........................................114zInterval_2Samp .......................................114zTest ..........................................................115zTest_1Prop ..............................................115

zTest_2Prop ..............................................116zTest_2Samp .............................................116

Symbols+ (add) .......................................................117N(subtract) ................................................117(multiply) ...............................................118 (divide) ...................................................118^ (power) ..................................................119x2 (square) ................................................119.+ (dot add) ...............................................120.. (dot subt.) ..............................................120.(dot mult.) .............................................120. / (dot divide) ...........................................120.^ (dot power) ..........................................120L(negate) ...................................................121% (percent) ...............................................121= (equal) ....................................................122 (not equal) .............................................122< (less than) ..............................................122{ (less or equal) ........................................123> (greater than) ........................................123| (greater or equal) ..................................123(logical implication) .............................123 (logical double implication, XNOR) ....124! (factorial) ................................................124& (append) ................................................124d() (derivative) ..........................................124() (integral) ..............................................125() (square root) .......................................125() (prodSeq) ............................................125G() (sumSeq) ..............................................126

GInt() .........................................................126GPrn() ........................................................127# (indirection) .......................................... 127E (scientific notation) ............................... 127g (gradian) ...............................................128R(radian) ....................................................128 (degree) .................................................128

, ', '' (degree/minute/second) ................. 128 (angle) ..................................................129_ (underscore as an empty element) ...... 12910^() ..........................................................129^/(reciprocal) ...........................................129| (constraint operator) ............................. 130& (store) ...................................................130:= (assign) ................................................. 131 (comment) ............................................1310b, 0h ........................................................131

Empty (Void) Elements

Calculations involving void elements ..... 132List arguments containing void elements ....132

Shortcuts for Entering Math

Expressions

EOS (Equation Operating

System) Hierarchy

Error Codes and Messages

Texas Instruments Support and

Service

Service and Warranty Information


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TI-Nspire Reference Guide 1

TI-Nspire Reference Guide

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

Expression Templates

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

Use the arrow keys or presse to move the cursor to each elements position, and type a value

or expression for the element. Press or/ to evaluate the expression.

Fraction template

/p keys

Note: See also / (divide), page 118.

Example:

Exponent template l key

Note: Type the first value, pressl, and then type the exponent.

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

Note: See also ^ (power), page 119.

Example:

Square root template /q keys

Note: See also() (square root), page 125.

Example:

Nth root template /l keys

Note: See also root(), page 86.

Example:


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e exponent template u keys

Natural exponential e raised to a power

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

Example:

Log template /s key

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

Note: See also log(), page 58.

Example:

Piecewise template (2-piece)Catalog >

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

Note: See also piecewise(), page 74.

Example:

Piecewise template (N-piece)Catalog >

Lets you create expressions and conditions for anN-piece piecewisefunction. Prompts forN.

Note: See also piecewise(), page 74.

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


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System of 2 equations templateCatalog >

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

Note: See also system(), page 101.

Example:

System of N equations templateCatalog >

Lets you create a system ofNlinear equations. Prompts forN.

Note: See also system(), page 101.

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

Absolute value templateCatalog >

Note: See also abs(), page 6.

Example:

ddmmss.ss templateCatalog >

Lets you enter angles in ddmmss.ss format, where dd is thenumber of decimal degrees, mm is the number of minutes, and ss.ssis the number of seconds.

Example:

Matrix template (2 x 2)Catalog >

Creates a 2 x 2 matrix.

Example:


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.

Example:


Example:

Matrix template (m x n)Catalog >

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 andcolumns, it may take a few moments to appear.

Example:

Sum template (G)Catalog >

Note: See also G() (sumSeq), page 126.

Example:

Product template ()Catalog >

Note: See also() (prodSeq), page 125.

Example:


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First derivative templateCatalog >

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

Note: See also d() (derivative), page 124.

Example:

Second derivative templateCatalog >

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 124.

Example:

Definite integral templateCatalog >

The definite integral template can be used to calculate the definite

integral numerically, using the same method as nInt().

Note: See also nInt(), page 68.

Example:


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Alphabetical Listing

Items whose names are not alphabetic (such as +, !, and >) are listed at the end of this section,starting on page 117. Unless otherwise specified, all examples in this section were performed inthe default reset mode, and all variables are assumed to be undefined.

A

abs()Catalog >

abs(Value1) 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 numbers modulus.

amortTbl()Catalog >

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

[roundValue]) matrix

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

NPmtis the number of payments to be included in the table. Thetable starts with the first payment.

N,I,PV,Pmt,FV,PpY, CpY, andPmtAtare described in the tableof TVM arguments, page 108.

If you omitPmt, it defaults toPmt=tvmPmt(N,I,PV,FV,PpY,CpY,PmtAt).

If you omitFV, it defaults toFV=0. The defaults forPpY, CpY, andPmtAtare 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 126, and bal(), page 12.

andCatalog >

BooleanExpr1 andBooleanExpr2 Boolean expression

BooleanList1 andBooleanList2 Boolean list

BooleanMatrix1 andBooleanMatrix2 Boolean matrix

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


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Integer1 andInteger2 integer

Compares two real integers bit-by-bit using an and operation.Internally, both integers are converted to signed, 64-bit binarynumbers. When corresponding bits are compared, the result is 1 ifboth bits are 1; otherwise, the result is 0. The returned value

represents the bit results, and is displayed according to the Basemode.

You can enter the integers in any number base. For a binary orhexadecimal entry, you must use the 0b or 0h prefix, respectively.Without a prefix, integers are treated as decimal (base 10).

In Hex base mode:

Important: Zero, not the letter O.

In Bin base mode:

In Dec base mode:

Note: A binary entry can have up to 64 digits (not counting the0b prefix). A hexadecimal entry can have up to 16 digits.

angle()Catalog >

angle(Value1)

valueReturns the angle of the argument, interpreting the argument as acomplex 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 inList1 orMatrix1,interpreting each element as a complex number that represents atwo-dimensional rectangular coordinate point.

ANOVACatalog >

ANOVAList1,List2[,List3,...,List20][,Flag]

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

stat.results variable. (See page 98.)

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

andCatalog >


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Outputs: Block Design

COLUMN FACTOR Outputs

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 l ist

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

ANOVA2wayCatalog >

ANOVA2wayList1,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 thestat.results variable. (See page 98.)

LevRow=0 for Block

LevRow=2,3,...,Len-1, for Two Factor, whereLen=length(List1)=length(List2) = = length(List10) andLen / LevRow {2,3, }


stat.F F statistic of the column factor


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 probabili ty 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.MSError Mean squares for the errors

stat.s Standard deviation of the error


stat.Fcol F statistic of the column factor



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ROW FACTOR Outputs

INTERACTION Outputs

ERROR Outputs

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


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


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




stat.MSError Mean squares for the errors

s Standard deviation of the error

Ans /v keys

Ans

valueReturns the result of the most recently evaluated expression.



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approx()Catalog >

approx(Value1) number

Returns the evaluation of the argument as an expression containingdecimal values, when possible, regardless of the current Auto orApproximate mode.

This is equivalent to entering the argument and pressing/

.

approx(List1) list

approx(Matrix1) matrix

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

4approxFraction() Catalog >

Value 4approxFraction([Tol]) value

List4approxFraction([Tol]) list

Matrix 4approxFraction([Tol]) matrix

Returns the input as a fraction, using a tolerance ofTol. IfTolisomitted, a tolerance of 5.E-14 is used.

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

typing @>approxFraction( ...).

approxRational()Catalog >

approxRational(Value[, Tol]) value

approxRational(List[, Tol]) list

approxRational(Matrix[, Tol]) matrix

Returns the argument as a fraction using a tolerance ofTol. IfTolisomitted, a tolerance of 5.E-14 is used.

arccos() See cos/(), page 20.

arccosh() See cosh/(), page 21.

arccot() See cot/(), page 22.


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arccoth() See coth/(), page 22.

arccsc() See csc/(), page 24.

arccsch() See csch/(), page 24.

arcsec() See sec/(), page 89.

arcsech() See sech/(), page 89.

arcsin() See sin/(), page 94.

arcsinh() See sinh/(), page 95.

arctan() See tan/(), page 102.

arctanh() See tanh/(), page 103.

augment()Catalog >

augment(List1,List2) list

Returns a new list that isList2 appended to the end ofList1.

augment(Matrix1,Matrix2) matrix

Returns a new matrix that isMatrix2 appended toMatrix1. Whenthe , character is used, the matrices must have equal row

dimensions, andMatrix2 is appended toMatrix1 as new columns.Does not alterMatrix1 orMatrix2.


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B

avgRC()Catalog >

avgRC(Expr1, Var[=Value] [, Step]) expression

avgRC(Expr1, Var[=Value] [,List1]) list

avgRC(List1, Var[=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 Value is specified, it overrides any prior variable assignment orany current | substitution for the variable.

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

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

bal()Catalog >

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

[roundValue]) value

bal(NPmt,amortTable) value

Amortization function that calculates schedule balance after aspecified payment.


NPmtspecifies the payment number after which you want the datacalculated.


If you omitPmt, it defaults toPmt=tvmPmt(N,I,PV,FV,PpY,CpY,PmtAt).

If you omitFV, it defaults toFV=0. The defaults forPpY, CpY, andPmtAtare 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 numberNPmt, based on amortization table amortTable. The amortTableargument must be a matrix in the form described under amortTbl(),page 6.

Note: See also GInt() and GPrn(), page 126.

4Base2 Catalog >

Integer14Base2 integer

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

ConvertsInteger1 to a binary number. Binary or hexadecimalnumbers always have a 0b or 0h prefix, respectively.


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Without a prefix,Integer1 is treated as decimal (base 10). The resultis displayed in binary, regardless of the Base mode.

Negative numbers are displayed in two's complement form. Forexample,

N1 is displayed as0hFFFFFFFFFFFFFFFF in Hex base mode0b111...111 (64 1s) in Binary base mode

N263 is displayed as

0h8000000000000000 in Hex base mode0b100...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 thevalue into the appropriate range. Consider the following examples ofvalues outside the range.

263 becomes N263 and is displayed as0h8000000000000000 in Hex base mode0b100...000 (63 zeros) in Binary base mode

264 becomes 0 and is displayed as0h0 in Hex base mode

0b0 in Binary base mode

N263N 1 becomes 263N 1 and is displayed as0h7FFFFFFFFFFFFFFF in Hex base mode0b111...111 (64 1s) in Binary base mode

4Base10 Catalog >



ConvertsInteger1 to a decimal (base 10) number. A binary orhexadecimal entry must always have a 0b or 0h prefix, respectively.

0b binaryNumber0h hexadecimalNumber

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

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

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

4Base2Catalog >


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



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C

4Base16 Catalog >



ConvertsInteger1 to a hexadecimal number. Binary or hexadecimalnumbers always have a 0b or 0h prefix, respectively.



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

Without a prefix,Integer1 is treated as decimal (base 10). The resultis displayed in hexadecimal, regardless of the Base mode.

If you enter a decimal integer that is too large for a signed, 64-bitbinary form, a symmetric modulo operation is used to bring the value

into the appropriate range. For more information, see 4Base2,page 12.

binomCdf()Catalog >

binomCdf(n,p) number

binomCdf(n,p,lowBound,upBound) numberif lowBound

and upBoundare numbers, listif lowBoundand upBoundarelists

binomCdf(n,p,upBound) for P(0{X{upBound) numberifupBoundis a number, listif upBoundis a list

Computes a cumulative probability for the discrete binomial

distribution with n number of trials and probabilityp of success oneach trial.

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

binomPdf()Catalog >

binomPdf(n,p) number

binomPdf(n,p,XVal) numberifXValis a number, listif

XValis a list

Computes a probability for the discrete binomial distribution with nnumber of trials and probabilityp of success on each trial.

ceiling()Catalog >

ceiling(Value1) 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.


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centralDiff()Catalog >

centralDiff(Expr1,Var[=Value [,Step]) expression

centralDiff(Expr1,Var[,Step])|Var=Value expression

centralDiff(Expr1,Var[=Value [,List]) list

centralDiff(List1,Var[=Value][,Step]) list

centralDiff(Matrix1,Var[=Value][,Step]) matrix

Returns the numerical derivative using the central difference quotientformula.

When Value is specified, it overrides any prior variable assignment orany current | substitution for the variable.

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

When usingList1 orMatrix1, the operation gets mapped across thevalues in the list or across the matrix elements.

Note: See also avgRC().

char() Catalog >

char(Integer) character

Returns a character string containing the character numberedIntegerfrom the handheld character set. The valid range forIntegeris 065535.

c22way Catalog >

c22way obsMatrixchi22way obsMatrix

Computes a c2 test for association on the two-way table of counts inthe observed matrix obsMatrix. A summary of results is stored in the


For information on the effect of empty elements in a matrix, seeEmpty (Void) Elements on page 132.


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


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


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c2Cdf() Catalog >

c2Cdf(lowBound,upBound,df) numberif lowBoundandupBoundare numbers, listif lowBoundand upBoundare lists

chi2Cdf(lowBound,upBound,df) numberif lowBoundand

upBoundare numbers, listif lowBoundand upBoundare lists

Computes the c2 distribution probability between lowBoundandupBoundfor the specified degrees of freedom df.

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

For information on the effect of empty elements in a list, see Empty(Void) Elements on page 132.

c2GOF Catalog >

c2GOF obsList,expList,dfchi2GOF obsList,expList,df

Performs a test to confirm that sample data is from a population thatconforms to a specified distribution. obsListis a list of counts andmust contain integers. A summary of results is stored in the




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


stat.df Degrees of freedom for the chi square statistics

stat.CompList Elemental chi square statistic contributions

c2Pdf() Catalog >

c2Pdf(XVal,df) numberifXValis a number, listifXValis alist

chi2Pdf(XVal,df) numberifXValis a number, listifXValisa list

Computes the probability density function (pdf) for the c2 distributionat a specifiedXValvalue for the specified degrees of freedom df.


ClearAZCatalog >

ClearAZ

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

If one or more of the variables are locked, this command displays anerror message and deletes only the unlocked variables. See unLock,page 110.


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ClrErrCatalog >

ClrErr

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

The Else clause of the Try...Else...EndTry block should use ClrError 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 thenext error handler. If there are no more pending Try...Else...EndTryerror handlers, the error dialog box will be displayed as normal.

Note: See also PassErr, page 74, and Try, page 106.

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.

For an example of ClrErr, See Example 2 under the Trycommand, page 106.

colAugment()Catalog >

colAugment(Matrix1,Matrix2) matrix

Returns a new matrix that isMatrix2 appended toMatrix1. Thematrices must have equal column dimensions, andMatrix2 isappended toMatrix1 as new rows. Does not alterMatrix1 or

Matrix2.

colDim()

Catalog >colDim(Matrix) expression

Returns the number of columns contained inMatrix.

Note: See also rowDim().

colNorm()Catalog >

colNorm(Matrix) expression

Returns the maximum of the sums of the absolute values of theelements in the columns inMatrix.

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


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completeSquare()Catalog >

completeSquare(ExprOrEqn, Var) expression or equation

completeSquare(ExprOrEqn, Var^Power) expression or

equation

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

equationcompleteSquare(ExprOrEqn, {Var1 Var2 [ ...]}) expression

or equation

Converts a quadratic polynomial expression of the form ax2+bx+c

into the form a(x-h)2+k

- or -

Converts a quadratic equation of the form ax2+bx+c=d into the

form a(x-h)2=k

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

The Second argument must be a single univariate term or a singleunivariate term raised to a rational power, for example x, y2, o r z(1/3).

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

conj()Catalog >

conj(Value1) value

conj(List1) list

conj(Matrix1) matrix

Returns the complex conjugate of the argument.

constructMat()Catalog >

constructMat(Expr,Var1,Var2,numRows,numCols)

matrix

Returns a matrix based on the arguments.

Expris an expression in variables Var1 and Var2. Elements in theresulting matrix are formed by evaluatingExprfor each incrementedvalue ofVar1 and Var2.

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

CopyVarCatalog >

CopyVar Var1, Var2

CopyVar Var1., Var2.

CopyVarVar1, Var2 copies the value of variable Var1 to variableVar2, creating Var2 if necessary. Variable Var1 must have a value.

IfVar1 is the name of an existing user-defined function, copies thedefinition of that function to function Var2. Function Var1 must be

defined.

Var1 must meet the variable-naming requirements or must be anindirection expression that simplifies to a variable name meeting therequirements.


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CopyVar Var1. , Var2. copies all members of the Var1. variablegroup to the Var2. group, creating Var2. if necessary.

Var1. must be the name of an existing variable group, such as thestatisticsstat.nn results, or variables created using the

LibShortcut() function. IfVar2. already exists, this commandreplaces all members that are common to both groups and adds themembers that do not already exist. If one or more members ofVar2.are locked, all members ofVar2. are left unchanged.

corrMat()Catalog >

corrMat(List1,List2[,[,List20]])

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

cos() key

cos(Value1) value

cos(List1) list

cos(Value1) returns the cosine of the argument as a value.

cos(List1) returns a list of the cosines of all elements inList1.

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.




CopyVarCatalog >


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cos(squareMatrix1) squareMatrix

Returns the matrix cosine ofsquareMatrix1. This is not the same ascalculating the cosine of each element.

When a scalar function f(A) operates onsquareMatrix1 (A), theresult is calculated by the algorithm:

Compute the eigenvalues (li) and eigenvectors (Vi) of A.

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

Form the matrices:

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

cos(B) =

All computations are performed using floating-point arithmetic.


cos/() key

cos/(Value1) value

cos/(List1) list

cos/(Value1) returns the angle whose cosine is Value1.

cos/(List1) returns a list of the inverse cosines of each element ofList1.

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 ofsquareMatrix1. This is not thesame as calculating the inverse cosine of each element. Forinformation about the calculation method, refer to cos().

squareMatrix1 must be diagonalizable. The result always containsfloating-point numbers.

In Radian angle mode and Rectangular Complex Format:

To see the entire result, press and then use and tomove the cursor.

cos() key


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cosh()Catalog >

cosh(Value1) value

cosh(List1) list

cosh(Value1) returns the hyperbolic cosine of the argument.

cosh(List1) returns a list of the hyperbolic cosines of each element ofList1.

cosh(squareMatrix1) squareMatrix

Returns the matrix hyperbolic cosine ofsquareMatrix1. This is notthe same as calculating the hyperbolic cosine of each element. Forinformation about the calculation method, refer to cos().



cosh/() Catalog >

cosh/(Value1) value

cosh/(List1) list

cosh/(Value1) returns the inverse hyperbolic cosine of theargument.

cosh/(List1) returns a list of the inverse hyperbolic cosines of eachelement ofList1.


arccosh(...).cosh/(squareMatrix1) squareMatrix

Returns the matrix inverse hyperbolic cosine ofsquareMatrix1. Thisis not the same as calculating the inverse hyperbolic cosine of eachelement. For information about the calculation method, refer tocos().


In Radian angle mode and In Rectangular Complex Format:

To see the entire result, press and then use and to

move the cursor.

cot() key

cot(Value1)value

cot(List1)list

Returns the cotangent ofValue1 or returns a list of the cotangents ofall elements inList1.

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.





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cot/() key

cot/(Value1) value

cot/(List1) list

Returns the angle whose cotangent is Value1 or returns a listcontaining the inverse cotangents of each element ofList1.


Note: You can insert this function from the keyboard by typingarccot(...).




coth()Catalog >

coth(Value1) value

coth(List1) list

Returns the hyperbolic cotangent ofValue1 or returns a list of thehyperbolic cotangents of all elements ofList1.

coth/()Catalog >

coth/(Value1) value

coth/(List1) list

Returns the inverse hyperbolic cotangent ofValue1 or returns a listcontaining the inverse hyperbolic cotangents of each element of

List1.


arccoth(...).

count()Catalog >

count(Value1orList1 [,Value2orList2 [,...]]) value

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

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

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

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

Empty (void) elements are ignored. For more information on emptyelements, see page 132.


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countif()Catalog >

countif(List,Criteria) value

Returns the accumulated count of all elements inListthat meet thespecified Criteria.

Criteria can be:

A value, expression, or string. For example, 3 counts only thoseelements inListthat simplify to the value 3.

A Boolean expression containing the symbol ? as a placeholderfor each element. For example, ?

cPolyRoots(Poly,Var) list

cPolyRoots(ListOfCoeffs) list

The first syntax, cPolyRoots(Poly,Var), returns a list of complexroots of polynomialPoly with respect to variable Var.

Poly must be a polynomial in expanded form in one variable. Do not

use unexpanded forms such as y2y+1 or xx+2x+1

The second syntax, cPolyRoots(ListOfCoeffs), returns a list ofcomplex roots for the coefficients inListOfCoeffs.

Note: See also polyRoots(), page 75.

crossP() Catalog >

crossP(List1,List2) list

Returns the cross product ofList1 andList2 as a list.

List1 andList2 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 isthe cross product ofVector1 and Vector2.

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


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csc() key

csc(Value1) value

csc(List1) list

Returns the cosecant ofValue1 or returns a list containing thecosecants of all elements inList1.




csc/() key

csc/(Value1)value

csc/(List1)list

Returns the angle whose cosecant is Value1 or returns a listcontaining the inverse cosecants of each element ofList1.


Note: You can insert this function from the keyboard by typingarccsc(...).




csch() Catalog >

csch(Value1)value

csch(List1)list

Returns the hyperbolic cosecant ofValue1 or returns a list of thehyperbolic cosecants of all elements ofList1.

csch/() Catalog >

csch/(Value)value

csch/

(List1)

listReturns the inverse hyperbolic cosecant ofValue1 or returns a listcontaining the inverse hyperbolic cosecants of each element ofList1.

Note: You can insert this function from the keyboard by typingarccsch(...).


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CubicRegCatalog >

CubicRegX, Y[, [Freq][, Category,Include]]

Computes the cubic polynomial regression y = ax3+b

x2+cx+d on listsXand Ywith frequencyFreq. A summary ofresults is stored in thestat.results variable. (See page 98.)

All the lists must have equal dimension except forInclude.

Xand Yare lists of independent and dependent variables.

Freq is an optional list of frequency values. Each element inFreqspecifies the frequency of occurrence for each correspondingXand 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 thecorrespondingXand Ydata.

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



stat.RegEqn Regression equation: ax3+bx2+cx+d

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

Regression coefficients

stat.R2 Coefficient of determination

stat.Resid Residuals from the regression

stat.XReg List of data points in the modifiedX Listactually used in the regression based on restrictions ofFreq,Category List, andInclude Categories

stat.YReg List of data points in the modified Y Listactually used in the regression based on restrictions ofFreq,Category List, andInclude Categories

stat.FreqReg List of frequencies corresponding tostat.XRegandstat.YReg

cumulativeSum() Catalog >

cumulativeSum(List1) list

Returns a list of the cumulative sums of the elements inList1,starting at element 1.

cumulativeSum(Matrix1) matrix

Returns a matrix of the cumulative sums of the elements inMatrix1.Each element is the cumulative sum of the column from top tobottom.

An empty (void) element inList1 orMatrix1 produces a void elementin the resulting list or matrix. For more information on empty

elements, see page 132.


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D

CycleCatalog >

Cycle

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

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

While, or Loop).




Function listing that sums the integers from 1 to 100 skipping50.

4Cylind Catalog >

Vector4Cylind

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

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

Vectormust have exactly three elements. It can be either a row or acolumn.

dbd()Catalog >

dbd(date1,date2) value

Returns the number of days between date1 and date2 using theactual-day-count method.

date1 and date2 can be numbers or lists of numbers within the rangeof 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 decimalplacement differentiates between the date formats.

MM.DDYY (format used commonly in the United States)DDMM.YY (format use commonly in Europe)


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4DD Catalog >

Expr14DD valueList14DD listMatrix14DD matrix

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

typing @>DD.

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




4Decimal Catalog >

Number1 4Decimal value

List1 4Decimal value

Matrix1 4Decimal value

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

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

DefineCatalog >

Define Var=Expression

DefineFunction(Param1,Param2, ...) =Expression

Defines the variable Varor the user-defined functionFunction.

Parameters, such asParam1, provide placeholders for passingarguments to the function. When calling a user-defined function, youmust supply arguments (for example, values or variables) thatcorrespond to the parameters. When called, the function evaluates

Expression using the supplied arguments.

VarandFunction cannot be the name of a system variable or built-infunction or command.

Note: This form ofDefine is equivalent to executing the expression:

expression&Function(Param1,Param2).


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DefineFunction(Param1,Param2, ...) = FuncBlock

EndFunc

DefineProgram(Param1,Param2, ...) = PrgmBlock

EndPrgm

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

Blockcan be either a single statement or a series of statements onseparate lines.Blockalso can include expressions and instructions(such as If, Then, Else, and For).




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

Define LibPrivCatalog >

Define LibPriv Var=Expression

Define LibPrivFunction(Param1,Param2, ...) =ExpressionDefine LibPrivFunction(Param1,Param2, ...) = Func

BlockEndFunc

Define LibPrivProgram(Param1,Param2, ...) = PrgmBlock

EndPrgm

Operates the same as Define, except defines a private libraryvariable, function, or program. Private functions and programs do notappear in the Catalog.

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

Define LibPubCatalog >

Define LibPub Var=Expression

Define LibPubFunction(Param1,Param2, ...) =ExpressionDefine LibPubFunction(Param1,Param2, ...) = Func

BlockEndFunc

Define LibPubProgram(Param1,Param2, ...) = PrgmBlock

EndPrgm

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

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

DefineCatalog >


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deltaList() See @List(), page 55.

DelVarCatalog >

DelVar Var1[, Var2][, Var3] ...

DelVar Var.Deletes the specified variable or variable group from memory.

If one or more of the variables are locked, this command displays anerror message and deletes only the unlocked variables. See unLock,page 110.

DelVar Var. deletes all members of the Var. variable group (such asthe statisticsstat.nn results or variables created using theLibShortcut() function). The dot (.) in this form of the DelVarcommand limits it to deleting a variable group; the simple variable

Varis not affected.

delVoid()Catalog >

delVoid(List1) list

Returns a list that has the contents ofList1 with all empty (void)elements removed.

For more information on empty elements, see page 132.

det()Catalog >

det(squareMatrix[, Tolerance]) expression

Returns the determinant ofsquareMatrix.

Optionally, any matrix element is treated as zero if its absolute valueis less than Tolerance. This tolerance is used only if the matrix hasfloating-point entries and does not contain any symbolic variablesthat have not been assigned a value. Otherwise, Tolerance isignored.

If you use/ or set the Auto or Approximatemode to Approximate, computations are done using floating-point arithmetic.

IfTolerance is omitted or not used, the default tolerance iscalculated as:

5EM14 max(dim(squareMatrix))rowNorm(squareMatrix)


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diag()Catalog >

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 diagonalofsquareMatrix.

squareMatrix must be square.

dim()Catalog >

dim(List) integer

Returns the dimension ofList.

dim(Matrix) list

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

dim(String) integer

Returns the number of characters contained in character stringString.

Disp Catalog >

Disp [exprOrString1][, exprOrString2] ...

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

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



instead of at the end of each line. On the computer keyboard,

hold down Alt and press Enter.


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E

4DMS Catalog >

Value4DMSList4DMSMatrix4DMS

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

typing @>DMS.

Interprets the argument as an angle and displays the equivalent DMS

(DDDDDDMM'SS.ss'') number. See , ', '' on page 128for DMS(degree, minutes, seconds) format.

Note:4DMS will convert from radians to degrees when used inradian mode. If the input is followed by a degree symbol , noconversion will occur. You can use 4DMS only at the end of an entryline.


dotP()Catalog >

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^() u key

e^(Value1) value

Returns e raised to the Value1 power.

Note: See also e exponent template, page 2.

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

characterE on the keyboard.

You can enter a complex number in re i q polar form. However, use thisform in Radian angle mode only; it causes a Domain error in Degreeor Gradian angle mode.

e^(List1) list

Returns e raised to the power of each element inList1.

e^(squareMatrix1) squareMatrix

Returns the matrix exponential ofsquareMatrix1. This is not thesame as calculating e raised to the power of each element. Forinformation about the calculation method, refer to cos().



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eff()Catalog >

eff(nominalRate,CpY) value

Financial function that converts the nominal interest ratenominalRate to an annual effective rate, given CpYas the number ofcompounding periods per year.

nominalRatemust be a real number, and CpYmust be a real number> 0.

Note: See also nom(), page 69.

eigVc()Catalog >

eigVc(squareMatrix) matrix

Returns a matrix containing the eigenvectors for a real or complexsquareMatrix, where each column in the result corresponds to aneigenvalue. Note that an eigenvector is not unique; it may be scaledby any constant factor. The eigenvectors are normalized, meaning

that if V = [x1, x2, , xn], then:

x12 + x2

2 + + xn2 = 1

squareMatrix is first balanced with similarity transformations untilthe row and column norms are as close to the same value as possible.ThesquareMatrix is then reduced to upper Hessenberg form and theeigenvectors are computed via a Schur factorization.

In Rectangular Complex Format:


eigVl()Catalog >

eigVl(squareMatrix) list

Returns a list of the eigenvalues of a real or complexsquareMatrix.

squareMatrix is first balanced with similarity transformations untilthe row and column norms are as close to the same value as possible.ThesquareMatrix is then reduced to upper Hessenberg form and theeigenvalues are computed from the upper Hessenberg matrix.

In Rectangular complex format mode:


Else See If, page 45.


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ElseIfCatalog >

IfBooleanExpr1 ThenBlock1

ElseIfBooleanExpr2 ThenBlock2

ElseIfBooleanExprNThenBlockN

EndIf




EndFor See For, page 38.

EndFunc See Func, page 40.

EndIf See If, page 45.

EndLoop See Loop, page 60.

EndPrgm See Prgm, page 77.

EndTry See Try, page 106.

EndWhile See While, page 112.


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euler()Catalog >

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

[, eulerStep]) matrix

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

ListOfDepVars0, VarStep[, eulerStep]) matrix

euler(ListOfExpr, Var,ListOfDepVars, {Var0, VarMax},ListOfDepVars0, VarStep[, eulerStep]) matrix

Uses the Euler method to solve the system

=Expr(Var, depVar)

with depVar(Var0)=depVar0 on the interval [Var0,VarMax]. Returns amatrix whose first row defines the Varoutput values and whosesecond row defines the value of the first solution component at thecorresponding Varvalues, and so on.

Expris the right-hand side that defines the ordinary differentialequation (ODE).

SystemOfExpris the system of right-hand sides that define the systemof ODEs (corresponds to order of dependent variables inListOfDepVars).

ListOfExpris a list of right-hand sides that define the system of ODEs(corresponds to the order of dependent variables inListOfDepVars).

Varis the independent variable.

ListOfDepVars is a list of dependent variables.

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

ListOfDepVars0 is a list of initial values for dependent variables.

VarStep is a nonzero number such that sign(VarStep) =sign(VarMax-Var0) and solutions are returned at Var0+iVarStep forall i=0,1,2, such that Var0+iVarStep is in [var0,VarMax] (there maynot be a solution value at VarMax).

eulerStep is a positive integer (defaults to 1) that defines the numberof euler steps between output values. The actual step size used by the

euler method is VarStepeulerStep.

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


System of equations:

withy1(0)=2 andy2(0)=5

ExitCatalog >

Exit

Exits the current For, While,or Loop block.

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




Function listing:

depVard

Vard----------------------


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exp() u key

exp(Value1) value

Returns e raised to the Value1 power.

Note: See also e exponent template, page 2.

You can enter a complex number in rei q

polar form. However, use thisform in Radian angle mode only; it causes a Domain error in Degreeor Gradian angle mode.

exp(List1) list

Returns e raised to the power of each element inList1.

exp(squareMatrix1) squareMatrix

Returns the matrix exponential ofsquareMatrix1. This is not thesame as calculating e raised to the power of each element. Forinformation about the calculation method, refer to cos().

squareMatrix1 must be diagonalizable. The result always contains

floating-point numbers.

expr()Catalog >

expr(String) expression

Returns the character string contained in Stringas an expression andimmediately executes it.

ExpRegCatalog >

ExpRegX, Y[, [Freq][, Category, Include]]

Computes the exponential regression y = a(b)x on listsXand Ywith frequencyFreq. A summary of results is stored in the


All the lists must have equal dimension except forInclude.

Xand Yare lists of independent and dependent variables.

Freq is an optional list of frequency values. Each element inFreqspecifies the frequency of occurrence for each correspondingXand 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 thecorrespondingXand Ydata.




stat.RegEqn Regression equation: a(b)x

stat.a, stat.b Regression coefficients

stat.r2 Coefficient of linear determination for transformed data

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


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F

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 modifiedX Listactually used in the regression based on restrictions ofFreq,Category List, andInclude Categories

stat.YReg List of data points in the modified Y Listactually used in the regression based on restrictions ofFreq,Category List, andInclude Categories

stat.FreqReg List of frequencies corresponding tostat.XRegandstat.YReg

factor()Catalog >

factor(rationalNumber) returns the rational number factored intoprimes. For composite numbers, the computing time growsexponentially 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 Enterrepeatedly.

Macintosh: Hold down the F5 key and press Enterrepeatedly.

Handheld: Hold down thec key and pressrepeatedly.

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

FCdf() Catalog >

FCdf(lowBound,upBound,dfNumer,dfDenom) numberif

lowBoundand upBoundare numbers, listif lowBoundand

upBoundare lists

FCdf(lowBound,upBound,dfNumer,dfDenom) numberif

lowBoundand upBoundare numbers, listif lowBoundandupBoundare lists

Computes the F distribution probability between lowBoundandupBoundfor the specified dfNumer(degrees of freedom) anddfDenom.

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

FillCatalog >

Fill Value, matrixVar matrix

Replaces each element in variable matrixVarwith Value.

matrixVarmust already exist.



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Fill Value, listVar list

Replaces each element in variable listVarwith Value.

listVarmust already exist.

FiveNumSummaryCatalog >

FiveNumSummaryX[,[Freq][,Category,Include]]

Provides an abbreviated version of the 1-variable statistics on listX.A summary of results is stored in thestat.results variable. (See page98.)

Xrepresents a list containing the data.

Freq is an optional list of frequency values. Each element inFreqspecifies the frequency of occurrence for each correspondingXand Ydata point. The default value is 1.

Category is a list of numeric category codes for the correspondingXdata.


An empty (void) element in any of the listsX,Freq, or Categoryresults in a void for the corresponding element of all those lists. Formore information on empty elements, see page 132.


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()Catalog >

floor(Value1) integer

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


floor(List1) list

floor(Matrix1) matrix

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

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

FillCatalog >


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ForCatalog >

For Var,Low,High[, Step]

BlockEndFor

Executes the statements inBlockiteratively for each value ofVar,

fromLow

toHigh

, in increments ofStep

.Varmust not be a system variable.

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

Blockcan be either a single statement or a series of statementsseparated with the : character.




format() Catalog >

format(Value[, formatString]) string

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

formatStringis 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 thedecimal point.

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

E[n]: Engineering format. n is the number of digits after the firstsignificant digit. The exponent is adjusted to a multiple of three, andthe 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 ofthe radix into groups of three. c specifies the group separatorcharacter and defaults to a comma. If c is a period, the radix will beshown as a comma.

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

fPart()Catalog >

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.


FPdf()Catalog >

FPdf(XVal,dfNumer,dfDenom) numberifXValis a number,

listifXValis a list

Computes the F distribution probability atXValfor the specifieddfNumer(degrees of freedom) and dfDenom.


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freqTable4list() Catalog >

freqTable4list(List1,freqIntegerList) list

Returns a list containing the elements fromList1 expanded accordingto the frequencies infreqIntegerList. This function can be used forbuilding a frequency table for the Data & Statistics application.

List1 can be any valid list.

freqIntegerListmust have the same dimension asList1 and mustcontain non-negative integer elements only. Each element specifiesthe number of times the correspondingList1 element will berepeated in the result list. A value of zero excludes the corresponding

List1 element.

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

Empty (void) elements are ignored. For more information on emptyelements, see page 132.

frequency() Catalog >

frequency(List1,binsList) list

Returns a list containing counts of the elements inList1. The countsare based on ranges (bins) that you define in binsList.

IfbinsListis {b(1

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