TI-Nspire™CXCAS ReferenceGuide

TI-Nspire™ CX CASReference Guide

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Contents

Expression Templates 1

Alphabetical Listing 8A 8B 17C 20D 44E 57F 67G 76I 86L 95M 111N 119O 128P 130Q 139R 142S 157T 182U 197V 198W 199X 201Z 202

Symbols 210

TI-Nspire™ CX II - Draw Commands 236Graphics Programming 236Graphics Screen 236Default View and Settings 237Graphics Screen Errors Messages 238Invalid Commands While in Graphics Mode 238C 239D 240F 243G 245P 246S 248U 250

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Empty (Void) Elements 251

Shortcuts for Entering Math Expressions 253

EOS™ (Equation Operating System) Hierarchy 255

TI-Nspire CX II - TI-Basic Programming Features 257Auto-indentation in Programming Editor 257Improved Error Messages for TI-Basic 257

Constants and Values 260

Error Codes and Messages 261

Warning Codes and Messages 269

General Information 271Online Help 271Contact TI Support 271Service and Warranty Information 271

Index 272

Expression TemplatesExpression templates give you an easy way to enter math expressions in standardmathematical notation. When you insert a template, it appears on the entry line withsmall blocks at positions where you can enter elements. A cursor shows which elementyou can enter.

Position the cursor on each element, and type a value or expression for the element.

Fraction template /p keys

Note: See also / (divide), page 212.

Example:

Exponent template l key

Note: Type the first value, pressl, andthen type the exponent. To return the cursorto the baseline, press right arrow (¢).

Note: See also ^ (power), page 213.

Example:

Square root template /q keys

Note: See also √() (square root), page223.

Example:

Nth root template /l keys

Note: See also root(), page 154.

Example:


2 Expression Templates

Nth root template /l keys

e exponent template u keys

Natural exponential e raised to a power

Note: See also e^(), page 57.

Example:

Log template /s key

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

Note: See also log(), page 106.

Example:

Piecewise template (2-piece) Catalog >

Lets you create expressions and conditionsfor a two-piece piecewise function. To adda piece, click in the template and repeat thetemplate.

Note: See also piecewise(), page 132.

Example:

Piecewise template (N-piece) Catalog >Lets you create expressions and conditionsfor an N-piece piecewise function. Promptsfor N.

Note: See also piecewise(), page 132.

Example:

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

System of 2 equations template Catalog >

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

Note: See also system(), page 181.

Example:

System of N equations template Catalog >Lets you create a system of N equations.Prompts for N.

Note: See also system(), page 181.

Example:

See the example for Systemof equationstemplate (2-equation).

Absolute value template Catalog >

Note: See also abs(), page 8.Example:



Absolute value template Catalog >

dd°mm’ss.ss’’ template Catalog >

Lets you enter angles in dd°mm’ss.ss’’format, where dd is the number of decimaldegrees, mm is the number of minutes, andss.ss is the number of seconds.

Example:

Matrix template (2 x 2) Catalog >

Creates a 2 x 2 matrix.

Example:

Matrix template (1 x 2) Catalog >

.Example:

Matrix template (2 x 1) Catalog >Example:

Matrix template (m x n) Catalog >The template appears after you areprompted to specify the number of rowsand columns.

Example:

Matrix template (m x n) Catalog >

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

Sum template (Σ) Catalog >

Note: See also Σ() (sumSeq), page 224.

Example:

Product template (Π) Catalog >

Note: See alsoΠ() (prodSeq), page 223.

Example:

First derivative template Catalog >

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

Note: See also d() (derivative), page 221.

Example:



Second derivative template Catalog >

The second derivative template can also beused to calculate second derivative at apoint.


Example:

Nth derivative template Catalog >

The nth derivative template can be used tocalculate the nth derivative.


Example:

Definite integral template Catalog >

Note: See also∫() integral(), page 221.

Example:

Indefinite integral template Catalog >

Note: See also ∫() integral(), page 221.

Example:

Limit template Catalog >Example:

Limit template Catalog >Use − or (−) for left hand limit. Use + forright hand limit.

Note: See also limit(), page 6.


8 Alphabetical Listing

Alphabetical ListingItems whose names are not alphabetic (such as +, !, and >) are listed at the end of thissection, page 210. Unless otherwise specified, all examples in this section wereperformed in the default reset mode, and all variables are assumed to be undefined.

A

abs() Catalog >abs(Expr1) ⇒ expression

abs(List1) ⇒ listabs(Matrix1) ⇒ matrix

Returns the absolute value of theargument.

Note: See also Absolute value template,page 3.

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

Note: All undefined variables are treated asreal variables.

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

Amortization function that returns a matrixas an amortization table for a set of TVMarguments.

NPmt is the number of payments to beincluded in the table. The table starts withthe first payment.

N, I, PV, Pmt, FV, PpY, CpY, and PmtAtare described in the table of TVMarguments, page 195.

• If you omit Pmt, it defaults toPmt=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.

amortTbl() Catalog >roundValue specifies the number ofdecimal places for rounding. Default=2.

The columns in the result matrix are in thisorder: Payment number, amount paid tointerest, amount paid to principal, andbalance.

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

You can use the output matrix as input forthe other amortization functions ΣInt() andΣPrn(), page 225, and bal(), page 17.

and Catalog >BooleanExpr1 and BooleanExpr2 ⇒Boolean expression

BooleanList1 and BooleanList2 ⇒Boolean list

BooleanMatrix1 and BooleanMatrix2 ⇒Boolean matrix

Returns true or false or a simplified form ofthe original entry.

Integer1 andInteger2 ⇒ integer

Compares two real integers bit-by-bit usingan and operation. Internally, both integersare converted to signed, 64-bit binarynumbers. When corresponding bits arecompared, the result is 1 if both bits are 1;otherwise, the result is 0. The returnedvalue represents the bit results, and isdisplayed according to the Base mode.

You can enter the integers in any numberbase. For a binary or hexadecimal entry, youmust use the 0b or 0h prefix, respectively.Without a prefix, integers are treated asdecimal (base 10).

InHex basemode:

Important: Zero, not the letter O.

In Bin basemode:

InDec basemode:

Note: A binary entry canhave up to 64 digits(not counting the 0bprefix). A hexadecimalentry canhave up to 16 digits.

Alphabetical Listing 9


angle() Catalog >angle(Expr1) ⇒ expression

Returns the angle of the argument,interpreting the argument as a complexnumber.


InDegree anglemode:

InGradian anglemode:

In Radian anglemode:

angle(List1) ⇒ listangle(Matrix1) ⇒ matrix

Returns a list or matrix of angles of theelements in List1 orMatrix1, interpretingeach element as a complex number thatrepresents a two-dimensional rectangularcoordinate point.

ANOVA Catalog >ANOVA List1,List2[,List3,...,List20][,Flag]

Performs a one-way analysis of variance forcomparing the means of two to 20populations. A summary of results is storedin the stat.results variable. (page 176)

Flag=0 for Data, Flag=1 for Stats

Output variable Description

stat.F Value of the F statistic

stat.PVal Smallest level of significance atwhich the null hypothesis canbe rejected

stat.df Degrees of freedomof the groups

stat.SS Sumof squares of the groups

stat.MS Mean squares for the groups


stat.dfError Degrees of freedomof the errors

stat.SSError Sumof squares of the errors

stat.MSError Mean square for the errors

stat.sp Pooled standarddeviation

stat.xbarlist Meanof the input of the lists

stat.CLowerList 95%confidence intervals for themeanof each input list

stat.CUpperList 95%confidence intervals for themeanof each input list

ANOVA2way Catalog >ANOVA2way List1,List2[,List3,…,List10][,levRow]

Computes a two-way analysis of variance forcomparing the means of two to 10populations. A summary of results is storedin the stat.results variable. (See page 176.)

LevRow=0 for Block

LevRow=2,3,...,Len-1, for Two Factor,where Len=length(List1)=length(List2) = …= length(List10) and Len / LevRow Î {2,3,…}

Outputs: Block Design


stat.F F statistic of the column factor


stat.df Degrees of freedomof the column factor

stat.SS Sumof squares of the column factor

stat.MS Mean squares for column factor

stat.FBlock F statistic for factor

stat.PValBlock Least probability atwhich the null hypothesis canbe rejected

stat.dfBlock Degrees of freedom for factor

stat.SSBlock Sumof squares for factor




stat.MSBlock Mean squares for factor



stat.MSError Mean squares for the errors

stat.s Standarddeviationof the error

COLUMN FACTOR Outputs


stat.Fcol F statistic of the column factor

stat.PValCol Probability value of the column factor

stat.dfCol Degrees of freedomof the column factor

stat.SSCol Sumof squares of the column factor

stat.MSCol Mean squares for column factor

ROW FACTOR Outputs


stat.FRow F statistic of the row factor

stat.PValRow Probability value of the row factor

stat.dfRow Degrees of freedomof the row factor

stat.SSRow Sumof squares of the row factor

stat.MSRow Mean squares for row factor

INTERACTION Outputs


stat.FInteract F statistic of the interaction

stat.PValInteract Probability value of the interaction

stat.dfInteract Degrees of freedomof the interaction

stat.SSInteract Sumof squares of the interaction

stat.MSInteract Mean squares for interaction

ERROR Outputs




stat.MSError Mean squares for the errors

s Standarddeviationof the error

Ans /v keysAns ⇒ value

Returns the result of the most recentlyevaluated expression.

approx() Catalog >approx(Expr1) ⇒ expression

Returns the evaluation of the argument asan expression containing decimal values,when possible, regardless of the currentAuto or Approximate mode.

This is equivalent to entering the argumentand pressing/·.

approx(List1) ⇒ listapprox(Matrix1) ⇒ matrix

Returns a list or matrix where eachelement has been evaluated to a decimalvalue, when possible.

►approxFraction() Catalog >Expr►approxFraction([Tol]) ⇒expression

List►approxFraction([Tol]) ⇒ list

Matrix►approxFraction([Tol]) ⇒ matrix

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



►approxFraction() Catalog >Note: You can insert this function from thecomputer keyboard by typing@>approxFraction(...).

approxRational() Catalog >approxRational(Expr[, Tol]) ⇒ expression

approxRational(List[, Tol]) ⇒ list

approxRational(Matrix[, Tol]) ⇒ matrix

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

arccos() See cos⁻¹(), page 31.

arccosh() See cosh⁻¹(), page 32.

arccot() See cot⁻¹(), page 33.

arccoth() See coth⁻¹(), page 34.

arccsc() See csc⁻¹(), page 37.

arccsch() See csch⁻¹(), page 37.

arcLen() Catalog >arcLen(Expr1,Var,Start,End) ⇒expression

Returns the arc length of Expr1 fromStart to End with respect to variable Var.

Arc length is calculated as an integralassuming a function mode definition.

arcLen(List1,Var,Start,End) ⇒ list

Returns a list of the arc lengths of eachelement of List1 from Start to End withrespect to Var.

arcsec() See sec⁻¹(), page 157.

arcsech() See sech⁻¹(), page 158.

arcsin() See sin⁻¹(), page 167.

arcsinh() See sinh⁻¹(), page 168.

arctan() See tan⁻¹(), page 183.

arctanh() See tanh⁻¹(), page 184.

augment() Catalog >augment(List1, List2) ⇒ list



augment() Catalog >Returns a new list that is List2 appended tothe end of List1.augment(Matrix1,Matrix2) ⇒ matrix

Returns a new matrix that is Matrix2appended toMatrix1. When the “,”character is used, the matrices must haveequal row dimensions, andMatrix2 isappended toMatrix1 as new columns.Does not alterMatrix1 orMatrix2.

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 anyprior variable assignment or any current “|”substitution for the variable.

Step is the step value. If Step is omitted, itdefaults to 0.001.

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

B

bal() Catalog >bal(NPmt,N,I,PV ,[Pmt], [FV], [PpY],[CpY], [PmtAt], [roundValue]) ⇒ value

bal(NPmt,amortTable) ⇒ value

Amortization function that calculatesschedule balance after a specified payment.


NPmt specifies the payment number afterwhich you want the data calculated.





roundValue specifies the number ofdecimal places for rounding. Default=2.

bal(NPmt,amortTable) calculates thebalance after payment number NPmt,based on amortization table amortTable.The amortTable argument must be amatrix in the form described underamortTbl(), page 8.

Note: See also ΣInt() and ΣPrn(), page 225.

►Base2 Catalog >Integer1►Base2⇒ integer

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



►Base2 Catalog >Converts Integer1 to a binary number.Binary or hexadecimal numbers alwayshave a 0b or 0h prefix, respectively. Use azero, not the letter O, followed by b or h.

0b binaryNumber0h hexadecimalNumberA binary number can have up to 64 digits. Ahexadecimal number can have up to 16.

Without a prefix, Integer1 is treated asdecimal (base 10). The result is displayed inbinary, regardless of the Base mode.

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

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

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

If you enter a decimal integer that isoutside the range of a signed, 64-bit binaryform, a symmetric modulo operation isused to bring the value into the appropriaterange. Consider the following examples ofvalues outside the range.

263 becomes ⁻263 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 mode0b0 in Binary base mode

⁻263− 1 becomes 263 − 1 and is displayedas0h7FFFFFFFFFFFFFFF in Hex base mode0b111...111 (64 1’s) in Binary base mode


►Base10 Catalog >Note: You can insert this operator from thecomputer keyboard by typing @>Base10.

Converts Integer1 to a decimal (base 10)number. A binary or hexadecimal entrymust 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. Ahexadecimal number can have up to 16.

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


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

Converts Integer1 to a hexadecimalnumber. Binary or hexadecimal numbersalways 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. Ahexadecimal number can have up to 16.

Without a prefix, Integer1 is treated asdecimal (base 10). The result is displayed inhexadecimal, regardless of the Base mode.

If you enter a decimal integer that is toolarge for a signed, 64-bit binary form, asymmetric modulo operation is used tobring the value into the appropriate range.For more information, see►Base2, page17.



binomCdf() Catalog >binomCdf(n,p) ⇒ list

binomCdf(n,p,lowBound,upBound) ⇒number if lowBound and upBound arenumbers, list if lowBound and upBound arelists

binomCdf(n,p,upBound)for P(0≤X≤upBound)⇒ number if upBound is a number, list ifupBound is a list

Computes a cumulative probability for thediscrete binomial distribution with n numberof trials and probability p of success on eachtrial.

For P(X ≤ upBound), set lowBound=0

binomPdf() Catalog >binomPdf(n,p) ⇒ list

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

Computes a probability for the discretebinomial distribution with n number of trialsand probability p of success on each trial.

C

Catalog >ceiling(Expr1) ⇒ integer

Returns the nearest integer that is ≥ theargument.

The argument can be a real or a complexnumber.

Note: See also floor().

ceiling(List1) ⇒ listceiling(Matrix1) ⇒ matrix

Returns a list or matrix of the ceiling ofeach element.

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 thecentral difference quotient formula.


Step is the step value. If Step is omitted, itdefaults to 0.001.

When using List1 orMatrix1, the operationgets mapped across the values in the list oracross the matrix elements.

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

cFactor() Catalog >cFactor(Expr1[,Var]) ⇒ expressioncFactor(List1[,Var]) ⇒ listcFactor(Matrix1[,Var]) ⇒ matrix

cFactor(Expr1) returns Expr1 factored withrespect to all of its variables over acommon denominator.

Expr1 is factored as much as possibletoward linear rational factors even if thisintroduces new non-real numbers. Thisalternative is appropriate if you wantfactorization with respect to more than onevariable.



cFactor() Catalog >cFactor(Expr1,Var) returns Expr1 factoredwith respect to variable Var.

Expr1 is factored as much as possibletoward factors that are linear in Var, withperhaps non-real constants, even if itintroduces irrational constants orsubexpressions that are irrational in othervariables.

The factors and their terms are sorted withVar as the main variable. Similar powers ofVar are collected in each factor. IncludeVar if factorization is needed with respectto only that variable and you are willing toaccept irrational expressions in any othervariables to increase factorization withrespect to Var. There might be someincidental factoring with respect to othervariables.

For the Auto setting of the Auto orApproximate mode, including Var alsopermits approximation with floating-pointcoefficients where irrational coefficientscannot be explicitly expressed concisely interms of the built-in functions. Even whenthere is only one variable, including Varmight yield more complete factorization.

Note: See also factor().

To see the entire result,press 5 and thenuse 7 and 8 to move thecursor.

char() Catalog >char(Integer) ⇒ character

Returns a character string containing thecharacter numbered Integer from thehandheld character set. The valid range forInteger is 0–65535.

charPoly() Catalog >charPoly(squareMatrix,Var) ⇒polynomial expression

charPoly(squareMatrix,Expr) ⇒polynomial expression

charPoly(squareMatrix1,Matrix2) ⇒polynomial expression

Returns the characteristic polynomial ofsquareMatrix. The characteristicpolynomial of n×nmatrix A, denoted by pA(λ), is the polynomial defined by

pA(λ) = det(λ•I−A)

where I denotes the n×n identity matrix.

squareMatrix1 and squareMatrix2musthave the equal dimensions.

χ22way Catalog >χ22way obsMatrix

chi22way obsMatrix

Computes a χ2 test for association on thetwo-way table of counts in the observedmatrix obsMatrix. A summary of results isstored in the stat.results variable. (page176)

For information on the effect of emptyelements in a matrix, see “Empty (Void)Elements,” page 251.


stat.χ2 Chi square stat: sum (observed - expected)2/expected


stat.df Degrees of freedom for the chi square statistics

stat.ExpMat Matrix of expectedelemental count table, assuming null hypothesis

stat.CompMat Matrix of elemental chi square statistic contributions



χ2Cdf() Catalog >χ2Cdf(lowBound,upBound,df) ⇒ number iflowBound and upBound are numbers, list iflowBound and upBound are lists

chi2Cdf(lowBound,upBound,df) ⇒ numberif lowBound and upBound are numbers, listif lowBound and upBound are lists

Computes the χ2 distribution probabilitybetween lowBound and upBound for thespecified degrees of freedom df.

For P(X ≤ upBound), set lowBound = 0.

For information on the effect of emptyelements in a list, see “Empty (Void)Elements,” page 251.

χ2GOF Catalog >χ2GOF obsList,expList,df

chi2GOF obsList,expList,df

Performs a test to confirm that sample datais from a population that conforms to aspecified distribution. obsList is a list ofcounts and must contain integers. Asummary of results is stored in thestat.results variable. (See page 176.)



stat.χ2 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

χ2Pdf() Catalog >χ2Pdf(XVal,df) ⇒ number if XVal is anumber, list if XVal is a list

χ2Pdf() Catalog >chi2Pdf(XVal,df) ⇒ number if XVal is anumber, list if XVal is a list

Computes the probability density function(pdf) for the χ2 distribution at a specifiedXVal value for the specified degrees offreedom df.


ClearAZ Catalog >ClearAZ

Clears all single-character variables in thecurrent problem space.

If one or more of the variables are locked,this command displays an error messageand deletes only the unlocked variables. SeeunLock, page 197.

ClrErr Catalog >ClrErr

Clears the error status and sets systemvariable errCode to zero.

The Else clause of the Try...Else...EndTryblock should use ClrErr or PassErr. If theerror is to be processed or ignored, useClrErr. If what to do with the error is notknown, use PassErr to send it to the nexterror handler. If there are no more pendingTry...Else...EndTry error handlers, the errordialog box will be displayed as normal.

Note: See also PassErr, page 131, and Try,page 191.

Note for entering the example: Forinstructions on entering multi-line programand function definitions, refer to theCalculator section of your product guidebook.

For anexample of ClrErr, See Example 2under the Try command, page 191.



colAugment() Catalog >colAugment(Matrix1,Matrix2) ⇒ matrix

Returns a new matrix that is Matrix2appended toMatrix1. The matrices musthave equal column dimensions, andMatrix2 is appended toMatrix1 as newrows. Does not alterMatrix1 orMatrix2.

colDim() Catalog >colDim(Matrix) ⇒ expression

Returns the number of columns containedinMatrix.

Note: See also rowDim().

colNorm() Catalog >colNorm(Matrix) ⇒ expression

Returns the maximum of the sums of theabsolute values of the elements in thecolumns inMatrix.

Note: Undefined matrix elements are notallowed. See also rowNorm().

comDenom() Catalog >comDenom(Expr1[,Var]) ⇒ expressioncomDenom(List1[,Var]) ⇒ listcomDenom(Matrix1[,Var]) ⇒ matrix

comDenom(Expr1) returns a reduced ratioof a fully expanded numerator over a fullyexpanded denominator.

comDenom() Catalog >comDenom(Expr1,Var) returns a reducedratio of numerator and denominatorexpanded with respect to Var. The termsand their factors are sorted with Var as themain variable. Similar powers of Var arecollected. There might be some incidentalfactoring of the collected coefficients.Compared to omitting Var, this often savestime, memory, and screen space, whilemaking the expression morecomprehensible. It also makes subsequentoperations on the result faster and lesslikely to exhaust memory.

If Var does not occur in Expr1, comDenom(Expr1,Var) returns a reduced ratio of anunexpanded numerator over an unexpandeddenominator. Such results usually save evenmore time, memory, and screen space.Such partially factored results also makesubsequent operations on the result muchfaster and much less likely to exhaustmemory.

Even when there is no denominator, thecomden function is often a fast way toachieve partial factorization if factor() istoo slow or if it exhausts memory.

Hint: Enter this comden() function definitionand routinely try it as an alternative tocomDenom() and factor().

completeSquare () Catalog >completeSquare(ExprOrEqn, Var) ⇒expression or equation

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

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

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

Converts a quadratic polynomial expressionof the form a•x2+b•x+c into the form a•(x-h)2+k



completeSquare () Catalog >- or -

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

The first argument must be a quadraticexpression or equation in standard formwith respect to the second argument.

The Second argument must be a singleunivariate term or a single univariate termraised to a rational power, for examplex, y2, or z(1/3).

The third and fourth syntax attempt tocomplete the square with respect tovariables Var1, Var2 [,… ]).

conj() Catalog >conj(Expr1) ⇒ expression

conj(List1) ⇒ list

conj(Matrix1) ⇒ matrix

Returns the complex conjugate of theargument.


constructMat() Catalog >constructMat(Expr,Var1,Var2,numRows,numCols) ⇒matrix

Returns a matrix based on the arguments.

Expr is an expression in variables Var1 andVar2. Elements in the resulting matrix areformed by evaluating Expr for eachincremented value of Var1 and Var2.

Var1 is automatically incremented from 1through numRows. Within each row, Var2is incremented from 1 through numCols.

CopyVar Catalog >CopyVar Var1, Var2

CopyVar Var1., Var2.

CopyVar Var1, Var2 copies the value ofvariable Var1 to variable Var2, creatingVar2 if necessary. Variable Var1must havea value.

If Var1 is the name of an existing user-defined function, copies the definition ofthat function to function Var2. FunctionVar1must be defined.

Var1must meet the variable-namingrequirements or must be an indirectionexpression that simplifies to a variablename meeting the requirements.

CopyVar Var1., Var2. copies all membersof the Var1. variable group to the Var2.group, creating Var2. if necessary.

Var1. must be the name of an existingvariable group, such as the statistics stat.nnresults, or variables created using theLibShortcut() function. If Var2. alreadyexists, this command replaces all membersthat are common to both groups and addsthe members that do not already exist. Ifone or more members of Var2. are locked,all members of Var2. are left unchanged.

corrMat() Catalog >corrMat(List1,List2[,…[,List20]])

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

►cos Catalog >Expr►cos

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

Represents Expr in terms of cosine. This isa display conversion operator. It can beused only at the end of the entry line.



►cos Catalog >►cos reduces all powers of sin(...) modulo 1−cos(...)^2so that any remaining powers of cos(...)have exponents in the range (0, 2). Thus,the result will be free of sin(...) if and onlyif sin(...) occurs in the given expression onlyto even powers.

Note: This conversion operator is notsupported in Degree or Gradian Anglemodes. Before using it, make sure that theAngle mode is set to Radians and that Exprdoes not contain explicit references todegree or gradian angles.

cos() µ keycos(Expr1) ⇒ expression

cos(List1) ⇒ list

cos(Expr1) returns the cosine of theargument as an expression.

cos(List1) returns a list of the cosines of allelements in List1.

Note: The argument is interpreted as adegree, gradian or radian angle, accordingto the current angle mode setting. You canuse °, G, or r to override the angle modetemporarily.

InDegree anglemode:



cos(squareMatrix1) ⇒ squareMatrix

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


cos() µ keyWhen a scalar function f(A) operates onsquareMatrix1 (A), the result is calculatedby the algorithm:

Compute the eigenvalues (λi) and

eigenvectors (Vi) of A.

squareMatrix1must be diagonalizable.Also, it cannot have symbolic variables thathave not been assigned a value.

Form the matrices:

Then A = X B X⁻¹ and f(A) = X f(B) X⁻¹. Forexample, cos(A) = X cos(B) X⁻¹ where:

cos(B) =

All computations are performed usingfloating-point arithmetic.

cos⁻¹() µ keycos⁻¹(Expr1) ⇒ expression

cos⁻¹(List1) ⇒ list

cos⁻¹(Expr1) returns the angle whosecosine is Expr1 as an expression.

cos⁻¹(List1) returns a list of the inversecosines of each element of List1.

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

Note: You can insert this function from thekeyboard by typing arccos(...).

InDegree anglemode:





cos⁻¹() µ keycos⁻¹(squareMatrix1) ⇒ squareMatrix

Returns the matrix inverse cosine ofsquareMatrix1. This is not the same ascalculating the inverse cosine of eachelement. For information about thecalculation method, refer to cos().

squareMatrix1must be diagonalizable. Theresult always contains floating-pointnumbers.

In Radian anglemode andRectangularComplex Format:


cosh() Catalog >cosh(Expr1) ⇒ expression

cosh(List1) ⇒ list

cosh(Expr1) returns the hyperbolic cosineof the argument as an expression.

cosh(List1) returns a list of the hyperboliccosines of each element of List1.

InDegree anglemode:

cosh(squareMatrix1) ⇒ squareMatrix

Returns the matrix hyperbolic cosine ofsquareMatrix1. This is not the same ascalculating the hyperbolic cosine of eachelement. For information about thecalculation method, refer to cos().



cosh⁻¹() Catalog >cosh⁻¹(Expr1) ⇒ expression

cosh⁻¹(List1) ⇒ list

cosh⁻¹(Expr1) returns the inversehyperbolic cosine of the argument as anexpression.

cosh⁻¹() Catalog >cosh⁻¹(List1) returns a list of the inversehyperbolic cosines of each element ofList1.

Note: You can insert this function from thekeyboard by typing arccosh(...).

cosh⁻¹(squareMatrix1) ⇒ squareMatrix

Returns the matrix inverse hyperboliccosine of squareMatrix1. This is not thesame as calculating the inverse hyperboliccosine of each element. For informationabout the calculation method, refer to cos().


In Radian anglemode and InRectangularComplex Format:


cot() µ keycot(Expr1) ⇒ expression

cot(List1) ⇒ list

Returns the cotangent of Expr1 or returns alist of the cotangents of all elements inList1.


InDegree anglemode:



cot⁻¹() µ keycot⁻¹(Expr1) ⇒ expression

cot⁻¹(List1) ⇒ list

Returns the angle whose cotangent isExpr1 or returns a list containing theinverse cotangents of each element ofList1.

InDegree anglemode:




cot⁻¹() µ keyNote: The result is returned as a degree,gradian or radian angle, according to thecurrent angle mode setting.

Note: You can insert this function from thekeyboard by typing arccot(...).


coth() Catalog >coth(Expr1) ⇒ expression

coth(List1) ⇒ list

Returns the hyperbolic cotangent of Expr1or returns a list of the hyperboliccotangents of all elements of List1.

coth⁻¹() Catalog >coth⁻¹(Expr1) ⇒ expression

coth⁻¹(List1) ⇒ list

Returns the inverse hyperbolic cotangent ofExpr1 or returns a list containing theinverse hyperbolic cotangents of eachelement of List1.

Note: You can insert this function from thekeyboard by typing arccoth(...).

count() Catalog >count(Value1orList1 [,Value2orList2[,...]]) ⇒ value

Returns the accumulated count of allelements in the arguments that evaluate tonumeric values.

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

For a list, matrix, or range of cells, eachelement is evaluated to determine if itshould be included in the count.

In the last example, only 1/2 and3+4*i arecounted. The remaining arguments,assuming x is undefined, do not evaluate tonumeric values.

count() Catalog >Within the Lists & Spreadsheet application,you can use a range of cells in place of anyargument.

Empty (void) elements are ignored. Formore information on empty elements, seepage 251.

countif() Catalog >countif(List,Criteria) ⇒ value

Returns the accumulated count of allelements in List that meet the specifiedCriteria.

Criteria can be:

• A value, expression, or string. Forexample, 3 counts only those elements inList that simplify to the value 3.

• A Boolean expression containing thesymbol ? as a placeholder for eachelement. For example, ?<5 counts onlythose elements in List that are less than5.

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

Empty (void) elements in the list areignored. For more information on emptyelements, see page 251.

Note: See also sumIf(), page 180, andfrequency(), page 74.

Counts the number of elements equal to 3.

Counts the number of elements equal to“def.”

Counts the number of elements equal to x;this example assumes the variable x isundefined.

Counts 1 and3.

Counts 3, 5, and7.

Counts 1, 3, 7, and9.



cPolyRoots() Catalog >cPolyRoots(Poly,Var) ⇒ list

cPolyRoots(ListOfCoeffs) ⇒ list

The first syntax, cPolyRoots(Poly,Var),returns a list of complex roots ofpolynomial Poly with respect to variableVar.

Poly must be a polynomial in one variable.

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

Note: See also polyRoots(), page 136.

crossP() Catalog >crossP(List1, List2) ⇒ list

Returns the cross product of List1 andList2 as a list.

List1 and List2must have equaldimension, and the dimension must beeither 2 or 3.

crossP(Vector1, Vector2) ⇒ vector

Returns a row or column vector (dependingon the arguments) that is the cross productof Vector1 and Vector2.

Both Vector1 and Vector2must be rowvectors, or both must be column vectors.Both vectors must have equal dimension,and the dimension must be either 2 or 3.

csc() µ keycsc(Expr1) ⇒ expression

csc(List1) ⇒ list

Returns the cosecant of Expr1 or returns alist containing the cosecants of all elementsin List1.

InDegree anglemode:


csc() µ key


csc⁻¹() µ keycsc⁻¹(Expr1) ⇒expression

csc⁻¹(List1) ⇒ list

Returns the angle whose cosecant is Expr1or returns a list containing the inversecosecants of each element of List1.


Note: You can insert this function from thekeyboard by typing arccsc(...).

InDegree anglemode:



csch() Catalog >csch(Expr1) ⇒ expression

csch(List1) ⇒ list

Returns the hyperbolic cosecant of Expr1 orreturns a list of the hyperbolic cosecants ofall elements of List1.

csch⁻¹() Catalog >csch⁻¹(Expr1) ⇒ expression

csch⁻¹(List1) ⇒ list

Returns the inverse hyperbolic cosecant ofExpr1 or returns a list containing theinverse hyperbolic cosecants of eachelement of List1.

Note: You can insert this function from thekeyboard by typing arccsch(...).



cSolve() Catalog >cSolve(Equation, Var) ⇒ Booleanexpression

cSolve(Equation, Var=Guess) ⇒ Booleanexpression

cSolve(Inequality, Var) ⇒ Booleanexpression

Returns candidate complex solutions of anequation or inequality for Var. The goal isto produce candidates for all real and non-real solutions. Even if Equation is real,cSolve() allows non-real results in Realresult Complex Format.

Although all undefined variables that do notend with an underscore (_) are processedas if they were real, cSolve() can solvepolynomial equations for complex solutions.

cSolve() temporarily sets the domain tocomplex during the solution even if thecurrent domain is real. In the complexdomain, fractional powers having odddenominators use the principal rather thanthe real branch. Consequently, solutionsfrom solve() to equations involving suchfractional powers are not necessarily asubset of those from cSolve().

cSolve() starts with exact symbolicmethods. cSolve() also uses iterativeapproximate complex polynomial factoring,if necessary.

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

InDisplay Digits mode of Fix 2:


cSolve(Eqn1andEqn2 [and…],VarOrGuess1, VarOrGuess2 [, … ]) ⇒Boolean expression

cSolve() Catalog >cSolve(SystemOfEqns, VarOrGuess1,VarOrGuess2 [, …]) ⇒Boolean expression

Returns candidate complex solutions to thesimultaneous algebraic equations, whereeach varOrGuess specifies a variable thatyou want to solve for.

Optionally, you can specify an initial guessfor a variable. Each varOrGuess must havethe form:

variable– or –variable = real or non-real number

For example, x is valid and so is x=3+i.If all of the equations are polynomials andif you do NOT specify any initial guesses,cSolve() uses the lexicalGröbner/Buchberger elimination method toattempt to determine all complex solutions.

Complex solutions can include both real andnon-real solutions, as in the example to theright.


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


You can also include solution variables thatdo not appear in the equations. Thesesolutions show how families of solutionsmight contain arbitrary constants of theform ck, where k is an integer suffix from 1through 255.



cSolve() Catalog >For polynomial systems, computation timeor memory exhaustion may depend stronglyon the order in which you list solutionvariables. If your initial choice exhaustsmemory or your patience, try rearrangingthe variables in the equations and/orvarOrGuess list.


If you do not include any guesses and if anyequation is non-polynomial in any variablebut all equations are linear in all solutionvariables, cSolve() uses Gaussianelimination to attempt to determine allsolutions.

If a system is neither polynomial in all of itsvariables nor linear in its solution variables,cSolve() determines at most one solutionusing an approximate iterative method. Todo so, the number of solution variablesmust equal the number of equations, andall other variables in the equations mustsimplify to numbers.

A non-real guess is often necessary todetermine a non-real solution. Forconvergence, a guess might have to berather close to a solution.


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

Computes the cubic polynomial regressiony=a•x3+b•x2+c•x+d on lists X and Y withfrequency Freq. A summary of results isstored in the stat.results variable. (See page176.)

All the lists must have equal dimensionexcept for Include.

X and Y are lists of independent anddependent variables.

CubicReg Catalog >Freq is an optional list of frequency values.Each element in Freq specifies thefrequency of occurrence for eachcorresponding X and Y data point. Thedefault value is 1. All elements must beintegers ≥ 0.

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

Include is a list of one or more of thecategory codes. Only those data itemswhose category code is included in this listare included in the calculation.


Outputvariable Description

stat.RegEqn Regressionequation: a•x3+b•x2+c•x+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 themodifiedX List actually used in the regressionbasedonrestrictions ofFreq, Category List, and Include Categories

stat.YReg List of data points in themodifiedY List actually used in the regressionbasedonrestrictions ofFreq, Category List, and Include Categories

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

cumulativeSum() Catalog >cumulativeSum(List1) ⇒ list

Returns a list of the cumulative sums of theelements in List1, starting at element 1.



cumulativeSum() Catalog >cumulativeSum(Matrix1) ⇒ matrix

Returns a matrix of the cumulative sums ofthe elements inMatrix1. Each element isthe cumulative sum of the column from topto bottom.

An empty (void) element in List1 orMatrix1 produces a void element in theresulting list or matrix. For moreinformation on empty elements, see page251.

Cycle Catalog >Cycle

Transfers control immediately to the nextiteration of the current loop (For, While, orLoop).

Cycle is not allowed outside the threelooping structures (For, While, or Loop).

Note for entering the example: Forinstructions on entering multi-line programand function definitions, refer to theCalculator section of your productguidebook.

Function listing that sums the integers from1to 100 skipping 50.

►Cylind Catalog >Vector►Cylind

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

Displays the row or column vector incylindrical form [r,∠θ, z].

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

cZeros() Catalog >cZeros(Expr, Var) ⇒ list

Returns a list of candidate real and non-realvalues of Var that make Expr=0. cZeros()does this by computingexp►list(cSolve(Expr=0,Var),Var).Otherwise, cZeros() is similar to zeros().

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

InDisplay Digits mode of Fix 3:


cZeros({Expr1, Expr2[, … ] },{VarOrGuess1,VarOrGuess2[, … ] })⇒matrix

Returns candidate positions where theexpressions are zero simultaneously. EachVarOrGuess specifies an unknown whosevalue you seek.

Optionally, you can specify an initial guessfor a variable. Each VarOrGuess must havethe form:


For example, x is valid and so is x=3+i.If all of the expressions are polynomials andyou do NOT specify any initial guesses,cZeros() uses the lexicalGröbner/Buchberger elimination method toattempt to determine all complex zeros.

Complex zeros can include both real andnon-real zeros, as in the example to theright.

Each row of the resulting matrix representsan alternate zero, with the componentsordered the same as the VarOrGuess list.To extract a row, index the matrix by [row].

Extract row2:



cZeros() Catalog >Simultaneous polynomials can have extravariables that have no values, but representgiven numeric values that could besubstituted later.

You can also include unknown variables thatdo not appear in the expressions. Thesezeros show how families of zeros mightcontain arbitrary constants of the form ck,where k is an integer suffix from 1 through255.

For polynomial systems, computation timeor memory exhaustion may depend stronglyon the order in which you list unknowns. Ifyour initial choice exhausts memory or yourpatience, try rearranging the variables inthe expressions and/or VarOrGuess list.If you do not include any guesses and if anyexpression is non-polynomial in any variablebut all expressions are linear in allunknowns, cZeros() uses Gaussianelimination to attempt to determine allzeros.

If a system is neither polynomial in all of itsvariables nor linear in its unknowns, cZeros() determines at most one zero using anapproximate iterative method. To do so, thenumber of unknowns must equal thenumber of expressions, and all othervariables in the expressions must simplifyto numbers.

A non-real guess is often necessary todetermine a non-real zero. Forconvergence, a guess might have to berather close to a zero.

D

dbd() Catalog >dbd(date1,date2) ⇒ value

Returns the number of days between date1and date2 using the actual-day-countmethod.

dbd() Catalog >date1 and date2 can be numbers or lists ofnumbers within the range of the dates onthe standard calendar. If both date1 anddate2 are lists, they must be the samelength.

date1 and date2must be between theyears 1950 through 2049.

You can enter the dates in either of twoformats. The decimal placementdifferentiates between the date formats.

MM.DDYY (format used commonly in theUnited States)DDMM.YY (format use commonly inEurope)

►DD Catalog >Expr1►DD ⇒ valueList1►DD ⇒ listMatrix1►DD ⇒ matrix

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

Returns the decimal equivalent of theargument expressed in degrees. Theargument is a number, list, or matrix that isinterpreted by the Angle mode setting ingradians, radians or degrees.

InDegree anglemode:



►Decimal Catalog >Expression1►Decimal ⇒ expression

List1►Decimal ⇒ expression

Matrix1►Decimal ⇒ expression

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



►Decimal Catalog >Displays the argument in decimal form.This operator can be used only at the end ofthe entry line.

Define Catalog >Define Var = ExpressionDefine Function(Param1, Param2, ...) =Expression

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

Parameters, such as Param1, provideplaceholders for passing arguments to thefunction. When calling a user-definedfunction, you must supply arguments (forexample, values or variables) thatcorrespond to the parameters. When called,the function evaluates Expression usingthe supplied arguments.

Var and Function cannot be the name of asystem variable or built-in function orcommand.

Note: This form of Define is equivalent toexecuting the expression: expression→Function(Param1,Param2).Define Function(Param1, Param2, ...) =Func BlockEndFunc

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

In this form, the user-defined function orprogram can execute a block of multiplestatements.

Block can be either a single statement or aseries of statements on separate lines.Block also can include expressions andinstructions (such as If, Then, Else, and For).

Define Catalog >Note for entering the example: Forinstructions on entering multi-line programand function definitions, refer to theCalculator section of your productguidebook.

Note: See also Define LibPriv, page 47, andDefine LibPub, page 47.

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

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

Define LibPriv Program(Param1, Param2,...) = Prgm BlockEndPrgm

Operates the same as Define, except definesa private library variable, function, orprogram. Private functions and programs donot appear in the Catalog.

Note: See also Define, page 46, and DefineLibPub, page 47.

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

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



Define LibPub Catalog >Define LibPub Program(Param1, Param2,...) = Prgm BlockEndPrgm

Operates the same as Define, except definesa public library variable, function, orprogram. Public functions and programsappear in the Catalog after the library hasbeen saved and refreshed.

Note: See also Define, page 46, and DefineLibPriv, page 47.

deltaList() See ΔList(), page 103.

deltaTmpCnv() See ΔtmpCnv(), page 189.

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

DelVar Var.

Deletes the specified variable or variablegroup from memory.

If one or more of the variables are locked,this command displays an error messageand deletes only the unlocked variables. SeeunLock, page 197.

DelVar Var. deletes all members of theVar. variable group (such as the statisticsstat.nn results or variables created usingthe LibShortcut() function). The dot (.) inthis form of the DelVar command limits itto deleting a variable group; the simplevariable Var is not affected.

delVoid() Catalog >delVoid(List1) ⇒ list

Returns a list that has the contents of List1with all empty (void) elements removed.

For more information on empty elements,see page 251.

derivative() See d(), page 221.

deSolve() Catalog >deSolve(1stOr2ndOrderODE, Var,depVar) ⇒ a general solution

Returns an equation that explicitly orimplicitly specifies a general solution to the1st- or 2nd-order ordinary differentialequation (ODE). In the ODE:

• Use a prime symbol (pressº) to denotethe 1st derivative of the dependentvariable with respect to the independentvariable.

• Use two prime symbols to denote thecorresponding second derivative.

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

The general solution of a 1st-order equationcontains an arbitrary constant of the formck, where k is an integer suffix from 1through 255. The solution of a 2nd-orderequation contains two such constants.

Apply solve() to an implicit solution if youwant to try to convert it to one or moreequivalent explicit solutions.

When comparing your results with textbookor manual solutions, be aware that differentmethods introduce arbitrary constants atdifferent points in the calculation, whichmay produce different general solutions.



deSolve() Catalog >deSolve(1stOrderODE and initCond, Var,depVar) ⇒ a particular solution

Returns a particular solution that satisfies1stOrderODE and initCond. This is usuallyeasier than determining a general solution,substituting initial values, solving for thearbitrary constant, and then substitutingthat value into the general solution.

initCond is an equation of the form:

depVar (initialIndependentValue) =initialDependentValue

The initialIndependentValue andinitialDependentValue can be variablessuch as x0 and y0 that have no storedvalues. Implicit differentiation can helpverify implicit solutions.

deSolve(2ndOrderODE and initCond1 andinitCond2, Var, depVar)⇒ particular solution

Returns a particular solution that satisfies2nd Order ODE and has a specified valueof the dependent variable and its firstderivative at one point.

For initCond1, use the form:

depVar (initialIndependentValue) =initialDependentValue

For initCond2, use the form:

depVar (initialIndependentValue) =initial1stDerivativeValuedeSolve(2ndOrderODE and bndCond1 andbndCond2, Var, depVar)⇒ a particular solution

Returns a particular solution that satisfies2ndOrderODE and has specified values attwo different points.

deSolve() Catalog >

det() Catalog >det(squareMatrix[, Tolerance]) ⇒expression

Returns the determinant of squareMatrix.

Optionally, any matrix element is treated aszero if its absolute value is less thanTolerance. This tolerance is used only if thematrix has floating-point entries and doesnot contain any symbolic variables thathave not been assigned a value. Otherwise,Tolerance is ignored.

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

• If Tolerance is omitted or not used, thedefault tolerance is calculated as:5E⁻14 •max(dim(squareMatrix))•rowNorm(squareMatrix)

diag() Catalog >diag(List) ⇒ matrixdiag(rowMatrix) ⇒ matrixdiag(columnMatrix) ⇒ matrix

Returns a matrix with the values in theargument list or matrix in its maindiagonal.

diag(squareMatrix) ⇒ rowMatrix

Returns a row matrix containing theelements from the main diagonal ofsquareMatrix.

squareMatrix must be square.



dim() Catalog >dim(List) ⇒ integer

Returns the dimension of List.dim(Matrix) ⇒ list

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

dim(String) ⇒ integer

Returns the number of characters containedin character string String.

Disp Catalog >Disp exprOrString1 [, exprOrString2] ...

Displays the arguments in the Calculatorhistory. The arguments are displayed insuccession, with thin spaces as separators.

Useful mainly in programs and functions toensure the display of intermediatecalculations.


DispAt Catalog >DispAt int,expr1 [,expr2 ...] ...

DispAt allows you to specify the linewhere the specified expression or stringwill be displayed on the screen.

The line number can be specified as anexpression.

Please note that the line number is notfor the entire screen but for the areaimmediately following thecommand/program.

Example

DispAt Catalog >This command allows dashboard-likeoutput from programs where the valueof an expression or from a sensorreading is updated on the same line.

DispAtand Disp can be used within thesame program.

Note: The maximum number is set to 8since that matches a screen-full of lineson the handheld screen - as long as thelines don't have 2D math expressions.The exact number of lines depends onthe content of the displayedinformation. Illustrative examples:

Define z()=PrgmFor n,1,3DispAt 1,"N: ",nDisp "Hello"EndForEndPrgm

Outputz()

Iteration 1:Line 1: N:1

Line 2: Hello


Line 2: HelloLine 3: Hello


Line 2: HelloLine 3: HelloLine 4: Hello

Define z1()=PrgmFor n,1,3DispAt 1,"N: ",nEndFor

For n,1,4Disp "Hello"EndForEndPrgm

z1()Line 1: N:3

Line 2: HelloLine 3: HelloLine 4: HelloLine 5: Hello



DispAt Catalog >

Error conditions:

Error Message DescriptionDispAt line number must be between 1 and 8 Expression evaluates the line number

outside the range 1-8 (inclusive)

Too few arguments The function or command is missing oneor more arguments.

No arguments Same as current 'syntax error' dialog

Too many arguments Limit argument. Same error as Disp.

Invalid data type First argument must be a number.

Void: DispAt void "Hello World" Datatype error is thrownfor the void (if the callback is defined)

Conversion operator: DispAt 2_ft @> _m,"Hello World"

CAS: Datatype Error is thrown (if thecallback is defined)Numeric: Conversion will be evaluatedand if the result is a valid argument,DispAt print the string at the result line.

►DMS Catalog >Expr ►DMS

List ►DMS

Matrix ►DMS

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

Interprets the argument as an angle anddisplays the equivalent DMS(DDDDDD°MM'SS.ss'') number. See °, ', ''on page 228 for DMS (degree, minutes,seconds) format.

Note:►DMS will convert from radians todegrees when used in radian mode. If theinput is followed by a degree symbol ° , noconversion will occur. You can use►DMSonly at the end of an entry line.

InDegree anglemode:

domain() Catalog >domain(Expr1, Var) ⇒expression

Returns the domain of Expr1 with respectto Var.

domain() can be used to examine domainsof functions. It is restricted to real and finitedomain.

This functionality has limitations due toshortcomings of computer algebrasimplification and solver algorithms.

Certain functions cannot be used asarguments for domain(), regardless ofwhether they appear explicitly or withinuser-defined variables and functions. In thefollowing example, the expression cannotbe simplified because ∫() is a disallowedfunction.

dominantTerm() Catalog >dominantTerm(Expr1, Var [, Point]) ⇒expression

dominantTerm(Expr1, Var [, Point]) |Var>Point ⇒ expression

dominantTerm(Expr1, Var [, Point]) |Var<Point ⇒ expression



dominantTerm() Catalog >Returns the dominant term of a powerseries representation of Expr1 expandedabout Point. The dominant term is the onewhose magnitude grows most rapidly nearVar = Point. The resulting power of (Var −Point) can have a negative and/orfractional exponent. The coefficient of thispower can include logarithms of (Var −Point) and other functions of Var that aredominated by all powers of (Var − Point)having the same exponent sign.

Point defaults to 0. Point can be ∞ or −∞,in which cases the dominant term will bethe term having the largest exponent ofVar rather than the smallest exponent ofVar.

dominantTerm(…) returns “dominantTerm(…)” if it is unable to determine such arepresentation, such as for essentialsingularities such as sin(1/z) at z=0, e−1/zat z=0, or ez at z = ∞ or −∞.

If the series or one of its derivatives has ajump discontinuity at Point, the result islikely to contain sub-expressions of theform sign(…) or abs(…) for a real expansionvariable or (-1)floor(…angle(…)…) for a complexexpansion variable, which is one endingwith “_”. If you intend to use the dominantterm only for values on one side of Point,then append to dominantTerm(...) theappropriate one of “| Var > Point”, “| Var< Point”, “| “Var ≥ Point”, or “Var ≤Point” to obtain a simpler result.

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

dominantTerm() is useful when you want toknow the simplest possible expression thatis asymptotic to another expression asVar→Point. dominantTerm() is also usefulwhen it isn’t obvious what the degree ofthe first non-zero term of a series will be,and you don’t want to iteratively guesseither interactively or by a program loop.

dominantTerm() Catalog >Note: See also series(), page 161.

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 becolumn vectors.

See Also: TI-Nspire™ CX II - Draw Commands

E

e^() u keye^(Expr1) ⇒ expression

Returns e raised to the Expr1 power.

Note: See also e exponent template, page2.

Note: Pressingu to display e^( is differentfrom pressing the characterE on thekeyboard.

You can enter a complex number in reiθpolar form. However, use this form inRadian angle mode only; it causes aDomain error in Degree or Gradian anglemode.

e^(List1) ⇒ list

Returns e raised to the power of eachelement in List1.e^(squareMatrix1) ⇒ squareMatrix



e^() u keyReturns the matrix exponential ofsquareMatrix1. This is not the same ascalculating e raised to the power of eachelement. For information about thecalculation method, refer to cos().


eff() Catalog >eff(nominalRate,CpY) ⇒ value

Financial function that converts the nominalinterest rate nominalRate to an annualeffective rate, given CpY as the number ofcompounding periods per year.

nominalRate must be a real number, andCpY must be a real number > 0.

Note: See also nom(), page 123.

eigVc() Catalog >eigVc(squareMatrix) ⇒ matrix

Returns a matrix containing theeigenvectors for a real or complexsquareMatrix, where each column in theresult corresponds to an eigenvalue. Notethat an eigenvector is not unique; it may bescaled by any constant factor. Theeigenvectors are normalized, meaning that:

if V = [x1, x2, … , xn]

then x12 + x2

2 + … + xn2 = 1

squareMatrix is first balanced withsimilarity transformations until the row andcolumn norms are as close to the samevalue as possible. The squareMatrix is thenreduced to upper Hessenberg form and theeigenvectors are computed via a Schurfactorization.

In Rectangular Complex Format:


eigVl() Catalog >eigVl(squareMatrix) ⇒ list

Returns a list of the eigenvalues of a real orcomplex squareMatrix.

squareMatrix is first balanced withsimilarity transformations until the row andcolumn norms are as close to the samevalue as possible. The squareMatrix is thenreduced to upper Hessenberg form and theeigenvalues are computed from the upperHessenberg matrix.

In Rectangular complex formatmode:


Else See If, page 86.

ElseIf Catalog >If BooleanExpr1 Then Block1ElseIf BooleanExpr2 Then Block2⋮ElseIf BooleanExprN Then BlockNEndIf⋮


EndFor See For, page 72.

EndFunc See Func, page 75.



EndIf See If, page 86.

EndLoop See Loop, page 110.

EndPrgm See Prgm, page 137.

EndTry See Try, page 191.

EndWhile See While, page 201.

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

with depVar(Var0)=depVar0 on theinterval [Var0,VarMax]. Returns a matrixwhose first row defines the Var outputvalues and whose second row defines thevalue of the first solution component at thecorresponding Var values, and so on.

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

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


Compare above resultwithCAS exactsolutionobtainedusing deSolve() andseqGen():

euler () Catalog >SystemOfExpr is the system of right-handsides that define the system of ODEs(corresponds to order of dependentvariables in ListOfDepVars).

ListOfExpr is a list of right-hand sides thatdefine the system of ODEs (corresponds tothe order of dependent variables inListOfDepVars).

Var is the independent variable.

ListOfDepVars is a list of dependentvariables.

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

ListOfDepVars0 is a list of initial valuesfor dependent variables.

VarStep is a nonzero number such that sign(VarStep) = sign(VarMax-Var0) andsolutions are returned at Var0+i•VarStepfor all i=0,1,2,… such that Var0+i•VarStepis in [var0,VarMax] (there may not be asolution value at VarMax).

eulerStep is a positive integer (defaults to1) that defines the number of euler stepsbetween output values. The actual step sizeused by the euler method isVarStep ⁄ eulerStep.

Systemof equations:

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

eval () Hub Menueval(Expr) ⇒string

eval() is valid only in the TI-Innovator™ HubCommand argument of programmingcommands Get, GetStr, and Send. Thesoftware evaluates expression Expr andreplaces the eval() statement with theresult as a character string.

The argument Expr must simplify to a realnumber.

Set the blue element of the RGB LED to halfintensity.

Reset the blue element to OFF.

eval() argumentmust simplify to a realnumber.



eval () Hub Menu

Program to fade-in the redelement

Execute the program.

Although eval() does not display its result,you can view the resulting Hub commandstring after executing the command byinspecting any of the following specialvariables.

iostr.SendAnsiostr.GetAnsiostr.GetStrAns

Note: See also Get (page 77), GetStr (page84), and Send (page 158).

exact() Catalog >exact(Expr1 [, Tolerance]) ⇒ expressionexact(List1 [, Tolerance]) ⇒ listexact(Matrix1 [, Tolerance]) ⇒ matrix

Uses Exact mode arithmetic to return,when possible, the rational-numberequivalent of the argument.

Tolerance specifies the tolerance for theconversion; the default is 0 (zero).

Exit Catalog >Exit

Exits the current For, While, or Loop block.

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


Function listing:

►exp Catalog >Expr►exp

Represents Expr in terms of the naturalexponential e. This is a display conversionoperator. It can be used only at the end ofthe entry line.

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

exp() u keyexp(Expr1) ⇒ expression

Returns e raised to the Expr1 power.

Note: See also e exponent template, page2.

You can enter a complex number in reiθpolar form. However, use this form inRadian angle mode only; it causes aDomain error in Degree or Gradian anglemode.

exp(List1) ⇒ list

Returns e raised to the power of eachelement in List1.



exp() u keyexp(squareMatrix1) ⇒ squareMatrix

Returns the matrix exponential ofsquareMatrix1. This is not the same ascalculating e raised to the power of eachelement. For information about thecalculation method, refer to cos().


exp►list() Catalog >exp►list(Expr,Var) ⇒ list

Examines Expr for equations that areseparated by the word “or,” and returns alist containing the right-hand sides of theequations of the form Var=Expr. Thisgives you an easy way to extract somesolution values embedded in the results ofthe solve(), cSolve(), fMin(), and fMax()functions.

Note: exp►list() is not necessary with thezeros() and cZeros() functions because theyreturn a list of solution values directly.

You can insert this function from thekeyboard by typing exp@>list(...).

expand() Catalog >expand(Expr1 [, Var]) ⇒ expressionexpand(List1 [,Var]) ⇒ listexpand(Matrix1 [,Var]) ⇒ matrix

expand(Expr1) returns Expr1 expandedwith respect to all its variables. Theexpansion is polynomial expansion forpolynomials and partial fraction expansionfor rational expressions.

The goal of expand() is to transform Expr1into a sum and/or difference of simpleterms. In contrast, the goal of factor() is totransform Expr1 into a product and/orquotient of simple factors.

expand() Catalog >expand(Expr1,Var) returns Expr1expanded with respect to Var. Similarpowers of Var are collected. The terms andtheir factors are sorted with Var as themain variable. There might be someincidental factoring or expansion of thecollected coefficients. Compared toomitting Var, this often saves time,memory, and screen space, while makingthe expression more comprehensible.

Even when there is only one variable, usingVar might make the denominatorfactorization used for partial fractionexpansion more complete.

Hint: For rational expressions, propFrac() isa faster but less extreme alternative toexpand().

Note: See also comDenom() for anexpanded numerator over an expandeddenominator.

expand(Expr1,[Var]) also distributeslogarithms and fractional powersregardless of Var. For increaseddistribution of logarithms and fractionalpowers, inequality constraints might benecessary to guarantee that some factorsare nonnegative.

expand(Expr1, [Var]) also distributesabsolute values, sign(), and exponentials,regardless of Var.

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

expr() Catalog >expr(String) ⇒ expression

Returns the character string contained inString as an expression and immediatelyexecutes it.



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

Computes the exponential regression y = a•(b)x on lists X and Y with frequency Freq. Asummary of results is stored in thestat.results variable. (See page 176.)



Freq is an optional list of frequency values.Each element in Freq specifies thefrequency of occurrence for eachcorresponding X and Y data point. Thedefault value is 1. All elements must beintegers ≥ 0.





stat.RegEqn Regressionequation: a•(b)x

stat.a, stat.b Regression coefficients

stat.r2 Coefficient of linear determination for transformeddata

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

stat.Resid Residuals associatedwith the exponentialmodel

stat.ResidTrans Residuals associatedwith linear fit of transformeddata





F

factor() Catalog >factor(Expr1[, Var]) ⇒ expressionfactor(List1[,Var]) ⇒ listfactor(Matrix1[,Var]) ⇒ matrix

factor(Expr1) returns Expr1 factored withrespect to all of its variables over acommon denominator.

Expr1 is factored as much as possibletoward linear rational factors withoutintroducing new non-real subexpressions.This alternative is appropriate if you wantfactorization with respect to more than onevariable.

factor(Expr1,Var) returns Expr1 factoredwith respect to variable Var.

Expr1 is factored as much as possibletoward real factors that are linear in Var,even if it introduces irrational constants orsubexpressions that are irrational in othervariables.

The factors and their terms are sorted withVar as the main variable. Similar powers ofVar are collected in each factor. IncludeVar if factorization is needed with respectto only that variable and you are willing toaccept irrational expressions in any othervariables to increase factorization withrespect to Var. There might be someincidental factoring with respect to othervariables.

For the Auto setting of the Auto orApproximate mode, including Var permitsapproximation with floating-pointcoefficients where irrational coefficientscannot be explicitly expressed concisely interms of the built-in functions. Even whenthere is only one variable, including Varmight yield more complete factorization.



factor() Catalog >Note: See also comDenom() for a fast wayto achieve partial factoring when factor() isnot fast enough or if it exhausts memory.

Note: See also cFactor() for factoring all theway to complex coefficients in pursuit oflinear factors.

factor(rationalNumber) returns the rationalnumber factored into primes. Forcomposite numbers, the computing timegrows exponentially with the number ofdigits in the second-largest factor. Forexample, factoring a 30-digit integer couldtake more than a day, and factoring a 100-digit number could take more than acentury.

To stop a calculation manually,

• Handheld: Hold down thec key andpress· repeatedly.

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

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

• iPad®: The app displays a prompt. Youcan continue waiting or cancel.

If you merely want to determine if anumber is prime, use isPrime() instead. It ismuch faster, particularly if rationalNumberis not prime and if the second-largest factorhas more than five digits.

FCdf() Catalog >FCdf(lowBound,upBound,dfNumer,dfDenom) ⇒number if lowBound and upBound arenumbers, list if lowBound and upBound arelists

FCdf(lowBound,upBound,dfNumer,dfDenom) ⇒number if lowBound and upBound arenumbers, list if lowBound and upBound arelists

FCdf() Catalog >Computes the F distribution probabilitybetween lowBound and upBound for thespecified dfNumer (degrees of freedom) anddfDenom.


Fill Catalog >Fill Expr, matrixVar⇒ matrix

Replaces each element in variablematrixVar with Expr.

matrixVar must already exist.

Fill Expr, listVar⇒ list

Replaces each element in variable listVarwith Expr.

listVar must already exist.

FiveNumSummary Catalog >FiveNumSummary X[,[Freq][,Category,Include]]

Provides an abbreviated version of the 1-variable statistics on list X. A summary ofresults is stored in the stat.results variable.(See page 176.)

X represents a list containing the data.

Freq is an optional list of frequency values.Each element in Freq specifies thefrequency of occurrence for eachcorresponding X and Y data point. Thedefault value is 1.

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




FiveNumSummary Catalog >An empty (void) element in any of the listsX, Freq, or Category results in a void forthe corresponding element of all those lists.For more information on empty elements,see page 251.


stat.MinX Minimumof x values.

stat.Q1X 1stQuartile of x.

stat.MedianX Medianof x.

stat.Q3X 3rdQuartile of x.

stat.MaxX Maximumof x values.

floor() Catalog >floor(Expr1) ⇒ integer

Returns the greatest integer that is ≤ theargument. This function is identical to int().


floor(List1) ⇒ listfloor(Matrix1) ⇒ matrix

Returns a list or matrix of the floor of eachelement.

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

fMax() Catalog >fMax(Expr, Var) ⇒ Boolean expressionfMax(Expr, Var,lowBound)

fMax(Expr, Var,lowBound,upBound)

fMax(Expr, Var) |lowBound≤Var≤upBound

Returns a Boolean expression specifyingcandidate values of Var that maximizeExpr or locate its least upper bound.

fMax() Catalog >You can use the constraint (“|”) operator torestrict the solution interval and/or specifyother constraints.

For the Approximate setting of the Auto orApproximate mode, fMax() iterativelysearches for one approximate localmaximum. This is often faster, particularlyif you use the “|” operator to constrain thesearch to a relatively small interval thatcontains exactly one local maximum.

Note: See also fMin() andmax().

fMin() Catalog >fMin(Expr, Var) ⇒ Boolean expression

fMin(Expr, Var,lowBound)

fMin(Expr, Var,lowBound,upBound)

fMin(Expr, Var) |lowBound≤Var≤upBound

Returns a Boolean expression specifyingcandidate values of Var that minimizeExpr or locate its greatest lower bound.

You can use the constraint (“|”) operator torestrict the solution interval and/or specifyother constraints.

For the Approximate setting of the Auto orApproximate mode, fMin() iterativelysearches for one approximate localminimum. This is often faster, particularlyif you use the “|” operator to constrain thesearch to a relatively small interval thatcontains exactly one local minimum.

Note: See also fMax() andmin().



For Catalog >For Var, Low, High [, Step] BlockEndFor

Executes the statements in Blockiteratively for each value of Var, from LowtoHigh, in increments of Step.

Var must not be a system variable.

Step can be positive or negative. Thedefault value is 1.

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


format() Catalog >format(Expr[, formatString]) ⇒ string

Returns Expr as a character string based onthe format template.

Expr must simplify to a number.

formatString is a string and must be in theform: “F[n]”, “S[n]”, “E[n]”, “G[n][c]”,where [ ] indicate optional portions.

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

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

E[n]: Engineering format. n is the numberof digits after the first significant digit. Theexponent is adjusted to a multiple of three,and the decimal point is moved to the rightby zero, one, or two digits.

format() Catalog >G[n][c]: Same as fixed format but alsoseparates digits to the left of the radix intogroups of three. c specifies the groupseparator character and defaults to acomma. If c is a period, the radix will beshown as a comma.

[Rc]: Any of the above specifiers may besuffixed with the Rc radix flag, where c is asingle character that specifies what tosubstitute for the radix point.

fPart() Catalog >fPart(Expr1) ⇒ expressionfPart(List1) ⇒ listfPart(Matrix1) ⇒ matrix

Returns the fractional part of the argument.

For a list or matrix, returns the fractionalparts of the elements.


FPdf() Catalog >FPdf(XVal,dfNumer,dfDenom) ⇒ numberif XVal is a number, list if XVal is a list

Computes the F distribution probability atXVal for the specified dfNumer (degrees offreedom) and dfDenom.

freqTable►list() Catalog >freqTable►list(List1,freqIntegerList) ⇒list

Returns a list containing the elements fromList1 expanded according to thefrequencies in freqIntegerList. Thisfunction can be used for building afrequency table for the Data & Statisticsapplication.

List1 can be any valid list.



freqTable►list() Catalog >freqIntegerList must have the samedimension as List1 and must contain non-negative integer elements only. Eachelement specifies the number of times thecorresponding List1 element will berepeated in the result list. A value of zeroexcludes the corresponding List1 element.

Note: You can insert this function from thecomputer keyboard by typingfreqTable@>list(...).


frequency() Catalog >frequency(List1,binsList) ⇒ list

Returns a list containing counts of theelements in List1. The counts are based onranges (bins) that you define in binsList.

If binsList is {b(1), b(2), …, b(n)}, thespecified ranges are {?≤b(1), b(1)<?≤b(2),…,b(n-1)<?≤b(n), b(n)>?}. The resultinglist is one element longer than binsList.

Each element of the result corresponds tothe number of elements from List1 thatare in the range of that bin. Expressed interms 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 ina bin” are ignored. Empty (void) elementsare also ignored. For more information onempty elements, see page 251.

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

Note: See also countIf(), page 35.

Explanationof result:

2 elements fromDatalist are≤2.5

4 elements fromDatalist are >2.5 and≤4.5

3 elements fromDatalist are >4.5

The element “hello” is a string and cannot beplaced in any of the definedbins.

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

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

(Data list input)

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

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

(Summary stats input)

Performs a two-sample F test. A summaryof results is stored in the stat.resultsvariable. (See page 176.)

For Ha: σ1 > σ2, set Hypoth>0

For Ha: σ1 ≠ σ2 (default), set Hypoth =0

For Ha: σ1 < σ2, set Hypoth<0

For information on the effect of emptyelements in a list, see Empty (Void)Elements, page 251.


stat.F CalculatedF statistic for the data sequence


stat.dfNumer numerator degrees of freedom= n1-1

stat.dfDenom denominator degrees of freedom= n2-1

stat.sx1, stat.sx2 Sample standarddeviations of the data sequences inList 1 andList 2

stat.x1_barstat.x2_bar

Samplemeans of the data sequences inList 1 andList 2

stat.n1, stat.n2 Size of the samples

Func Catalog >Func BlockEndFunc

Template for creating a user-definedfunction.

Define a piecewise function:



Func Catalog >Block can be a single statement, a seriesof statements separated with the “:”character, or a series of statements onseparate lines. The function can use theReturn instruction to return a specific result.


Result of graphing g(x)

G

gcd() Catalog >gcd(Number1, Number2) ⇒ expression

Returns the greatest common divisor of thetwo arguments. The gcd of two fractions isthe gcd of their numerators divided by thelcm of their denominators.

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

gcd(List1, List2) ⇒ list

Returns the greatest common divisors ofthe corresponding elements in List1 andList2.gcd(Matrix1, Matrix2) ⇒ matrix

Returns the greatest common divisors ofthe corresponding elements inMatrix1 andMatrix2.

geomCdf() Catalog >geomCdf(p,lowBound,upBound) ⇒ number

geomCdf() Catalog >if lowBound and upBound are numbers, listif lowBound and upBound are lists

geomCdf(p,upBound)for P(1≤X≤upBound)⇒ number if upBound is a number, list ifupBound is a list

Computes a cumulative geometricprobability from lowBound to upBound withthe specified probability of success p.


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

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

Get Hub MenuGet [promptString,] var[, statusVar]

Get [promptString,] func(arg1, ...argn)[, statusVar]

Programming command: Retrieves a valuefrom a connected TI-Innovator™ Hub andassigns the value to variable var.

The value must be requested:

• In advance, through a Send "READ ..."command.

— or —

• By embedding a "READ ..." request asthe optional promptString argument.This method lets you use a singlecommand to request the value andretrieve it.

Example: Request the current value of thehub's built-in light-level sensor. UseGet toretrieve the value andassign it to variablelightval.

Embed the READ requestwithin theGetcommand.



Get Hub MenuImplicit simplification takes place. Forexample, a received string of "123" isinterpreted as a numeric value. To preservethe string, use GetStr instead of Get.

If you include the optional argumentstatusVar, it is assigned a value based onthe success of the operation. A value ofzero means that no data was received.

In the second syntax, the func() argumentallows a program to store the receivedstring as a function definition. This syntaxoperates as if the program executed thecommand:

Define func(arg1, ...argn) = receivedstring

The program can then use the definedfunction func().

Note: You can use the Get command withina user-defined program but not within afunction.

Note: See also GetStr, page 84 and Send,page 158.

getDenom() Catalog >getDenom(Expr1) ⇒ expression

Transforms the argument into anexpression having a reduced commondenominator, and then returns itsdenominator.

getKey() Catalog >getKey([0|1]) ⇒ returnString

Description:getKey() - allows a TI-Basicprogram to get keyboard input -handheld, desktop and emulator ondesktop.

Example:

Example:

getKey() Catalog >• keypressed := getKey() will return a

key or an empty string if no key hasbeen pressed. This call will returnimmediately.

• keypressed := getKey(1) will wait tilla key is pressed. This call will pauseexecution of the program till a key ispressed.

Handling of key presses:

Handheld Device/EmulatorKey Desktop Return Value

Esc Esc "esc"

Touchpad - Top click n/a "up"

On n/a "home"

Scratchapps n/a "scratchpad"

Touchpad - Left click n/a "left"

Touchpad - Center click n/a "center"

Touchpad - Right click n/a "right"

Doc n/a "doc"

Tab Tab "tab"

Touchpad - Bottom click Down Arrow "down"

Menu n/a "menu"

Ctrl Ctrl no return

Shift Shift no return

Var n/a "var"

Del n/a "del"

= = "="

trig n/a "trig"

0 through 9 0-9 "0" ... "9"




Templates n/a "template"

Catalog n/a "cat"

^ ^ "^"

X^2 n/a "square"

/ (division key) / "/"

* (multiply key) * "*"

e^x n/a "exp"

10^x n/a "10power"

+ + "+"

- - "-"

( ( "("

) ) ")"

. . "."

(-) n/a "-" (negate sign)

Enter Enter "enter"

ee n/a "E" (scientific notation E)

a - z a-z alpha = letter pressed (lowercase)("a" - "z")

shift a-z shift a-z alpha = letter pressed"A" - "Z"

Note: ctrl-shift works to lockcaps

?! n/a "?!"

pi n/a "pi"

Flag n/a no return

, , ","

Return n/a "return"


Space Space " " (space)

Inaccessible Special Character Keys like@,!,^, etc.

The character is returned

n/a Function Keys No returned character

n/a Special desktop control keys No returned character

Inaccessible Other desktop keys that arenot available on thecalculator while getkey() iswaiting for a keystroke. ({,},;, :, ...)

Same character you get inNotes (not in a math box)

Note: It is important to note that the presence of getKey() in a program changes howcertain events are handled by the system. Some of these are described below.Terminate program and Handle event - Exactly as if the user were to break out of programby pressing the ON key"Support" below means - System works as expected - program continues to run.

Event Device Desktop - TI-Nspire™Student Software

Quick Poll Terminate program,handle event

Same as the handheld (TI-Nspire™ Student Software,TI-Nspire™ Navigator™ NCTeacher Software-only)

Remote file mgmt

(Incl. sending 'Exit Press 2Test' file from anotherhandheld or desktop-handheld)

Terminate program,handle event

Same as the handheld.(TI-Nspire™ StudentSoftware, TI-Nspire™Navigator™ NC TeacherSoftware-only)

End Class Terminate program,handle event

Support(TI-Nspire™ StudentSoftware, TI-Nspire™Navigator™ NC TeacherSoftware-only)

Event Device Desktop - TI-Nspire™ AllVersions

TI-Innovator™ Hubconnect/disconnect

Support - Can successfullyissue commands to the TI-Innovator™ Hub. After you

Same as the handheld



exit the program the TI-Innovator™ Hub is stillworking with thehandheld.

getLangInfo() Catalog >getLangInfo() ⇒ string

Returns a string that corresponds to theshort name of the currently activelanguage. You can, for example, use it in aprogram or function to determine thecurrent language.

English = “en”Danish = “da”German = “de”Finnish = “fi”French = “fr”Italian = “it”Dutch = “nl”Belgian Dutch = “nl_BE”Norwegian = “no”Portuguese = “pt”Spanish = “es”Swedish = “sv”

getLockInfo() Catalog >getLockInfo(Var) ⇒ value

Returns the current locked/unlocked stateof variable Var.

value =0: Var is unlocked or does not exist.

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

See Lock, page 106, and unLock, page 197.

getMode() Catalog >getMode(ModeNameInteger) ⇒ value

getMode(0) ⇒ list

getMode(ModeNameInteger) returns avalue representing the current setting oftheModeNameInteger mode.

getMode(0) returns a list containingnumber pairs. Each pair consists of a modeinteger and a setting integer.

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

If you save the settings with getMode(0) →var, you can use setMode(var) in a functionor program to temporarily restore thesettings within the execution of thefunction or program only. See setMode(),page 162.

ModeName

ModeInteger Setting Integers

DisplayDigits

1 1=Float, 2=Float1, 3=Float2, 4=Float3, 5=Float4, 6=Float5,7=Float6, 8=Float7, 9=Float8, 10=Float9, 11=Float10,12=Float11, 13=Float12, 14=Fix0, 15=Fix1, 16=Fix2,17=Fix3, 18=Fix4, 19=Fix5, 20=Fix6, 21=Fix7, 22=Fix8,23=Fix9, 24=Fix10, 25=Fix11, 26=Fix12

Angle 2 1=Radian, 2=Degree, 3=Gradian

ExponentialFormat

3 1=Normal, 2=Scientific, 3=Engineering

Real orComplex

4 1=Real, 2=Rectangular, 3=Polar

Auto orApprox.

5 1=Auto, 2=Approximate, 3=Exact

VectorFormat

6 1=Rectangular, 2=Cylindrical, 3=Spherical

Base 7 1=Decimal, 2=Hex, 3=Binary

Unitsystem

8 1=SI, 2=Eng/US



getNum() Catalog >getNum(Expr1) ⇒ expression

Transforms the argument into anexpression having a reduced commondenominator, and then returns itsnumerator.

GetStr Hub MenuGetStr [promptString,] var[, statusVar]

GetStr [promptString,] func(arg1, ...argn)[, statusVar]

Programming command: Operatesidentically to the Get command, except thatthe retrieved value is always interpreted asa string. By contrast, the Get commandinterprets the response as an expressionunless it is enclosed in quotation marks ("").

Note: See also Get, page 77 and Send, page158.

For examples, seeGet.

getType() Catalog >getType(var) ⇒ string

Returns a string that indicates the data typeof variable var.

If var has not been defined, returns thestring "NONE".

getVarInfo() Catalog >getVarInfo() ⇒ matrix or string

getVarInfo(LibNameString) ⇒ matrix orstring

getVarInfo() returns a matrix of information(variable name, type, library accessibility,and locked/unlocked state) for all variablesand library objects defined in the currentproblem.

If no variables are defined, getVarInfo()returns the string "NONE".

getVarInfo(LibNameString)returns a matrixof information for all library objects definedin library LibNameString. LibNameStringmust be a string (text enclosed in quotationmarks) or a string variable.

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

Note the example, in which the result ofgetVarInfo() is assigned to variable vs.Attempting to display row 2 or row 3 of vsreturns an “Invalid list or matrix” errorbecause at least one of elements in thoserows (variable b, for example) revaluates toa matrix.

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

The system gives the above error becausethe current version of the software does notsupport a generalized matrix structurewhere an element of a matrix can be eithera matrix or a list.



Goto Catalog >Goto labelName

Transfers control to the label labelName.

labelName must be defined in the samefunction using a Lbl instruction.


►Grad Catalog >Expr1►Grad⇒ expression

Converts Expr1 to gradian angle measure.

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

InDegree anglemode:


I

identity() Catalog >identity(Integer) ⇒ matrix

Returns the identity matrix with adimension of Integer.

Integer must be a positive integer.

If Catalog >If BooleanExpr

Statement

If BooleanExpr ThenBlock

EndIf

If Catalog >If BooleanExpr evaluates to true, executesthe single statement Statement or the blockof statements Block before continuingexecution.

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

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


If BooleanExpr Then Block1Else Block2EndIf

If BooleanExpr evaluates to true, executesBlock1 and then skips Block2.

If BooleanExpr evaluates to false, skipsBlock1 but executes Block2.

Block1 and Block2 can be a singlestatement.

If BooleanExpr1 Then Block1ElseIf BooleanExpr2 Then Block2⋮ElseIf BooleanExprN Then BlockNEndIf

Allows for branching. If BooleanExpr1evaluates to true, executes Block1. IfBooleanExpr1 evaluates to false, evaluatesBooleanExpr2, and so on.



ifFn() Catalog >ifFn(BooleanExpr,Value_If_true [,Value_If_false [,Value_If_unknown]]) ⇒expression, list, or matrix

Evaluates the boolean expressionBooleanExpr (or each element fromBooleanExpr ) and produces a result basedon the following rules:

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

• If an element of BooleanExpr evaluatesto true, returns the correspondingelement from Value_If_true.

• If an element of BooleanExpr evaluatesto false, returns the correspondingelement from Value_If_false. If youomit Value_If_false, returns undef.

• If an element of BooleanExpr is neithertrue nor false, returns the correspondingelement Value_If_unknown. If you omitValue_If_unknown, returns undef.

• If the second, third, or fourth argumentof the ifFn() function is a singleexpression, the Boolean test is applied toevery position in BooleanExpr.

Note: If the simplified BooleanExprstatement involves a list or matrix, all otherlist or matrix arguments must have thesame dimension(s), and the result will havethe same dimension(s).

Test value of 1 is less than2.5, so itscorresponding

Value_If_True element of 5 is copied tothe result list.

Test value of 2 is less than2.5, so itscorresponding

Value_If_True element of 6 is copied tothe result list.

Test value of 3 is not less than2.5, so itscorresponding Value_If_False element of10 is copied to the result list.

Value_If_true is a single value andcorresponds to any selectedposition.

Value_If_false is not specified. Undef isused.

One element selected fromValue_If_true.One element selected fromValue_If_unknown.

imag() Catalog >imag(Expr1) ⇒ expression

Returns the imaginary part of theargument.

imag() Catalog >Note: All undefined variables are treated asreal variables. See also real(), page 146

imag(List1) ⇒ list

Returns a list of the imaginary parts of theelements.

imag(Matrix1) ⇒ matrix

Returns a matrix of the imaginary parts ofthe elements.

impDif() Catalog >impDif(Equation, Var, dependVar[,Ord])⇒ expression

where the order Ord defaults to 1.

Computes the implicit derivative forequations in which one variable is definedimplicitly in terms of another.

Indirection See #(), page 226.

inString() Catalog >inString(srcString, subString[, Start]) ⇒integer

Returns the character position in stringsrcString at which the first occurrence ofstring subString begins.

Start, if included, specifies the characterposition within srcString where the searchbegins. Default = 1 (the first character ofsrcString).

If srcString does not contain subString orStart is > the length of srcString, returnszero.



int() Catalog >int(Expr) ⇒ integer

int(List1) ⇒ listint(Matrix1) ⇒ matrix

Returns the greatest integer that is lessthan or equal to the argument. Thisfunction is identical to floor().


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

intDiv() Catalog >intDiv(Number1, Number2) ⇒ integerintDiv(List1, List2) ⇒ listintDiv(Matrix1,Matrix2) ⇒ matrix

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

For lists and matrices, returns the signedinteger part of (argument 1 ÷ argument 2)for each element pair.

integral See ∫(), page 221.

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

This function does the following:

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


interpolate () Catalog >Given xList, yList=f(xList), andyPrimeList=f'(xList) for some unknownfunction f, a cubic interpolant is used toapproximate the function f at xValue. It isassumed that xList is a list ofmonotonically increasing or decreasingnumbers, but this function may return avalue even when it is not. This functionwalks through xList looking for an interval[xList[i], xList[i+1]] that contains xValue.If it finds such an interval, it returns aninterpolated value for f(xValue); otherwise,it returns undef.

xList, yList, and yPrimeList must be ofequal dimension ≥ 2 and containexpressions that simplify to numbers.

xValue can be an undefined variable, anumber, or a list of numbers.

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

invχ2() Catalog >invχ2(Area,df)

invChi2(Area,df)

Computes the Inverse cumulative χ2 (chi-square) probability function specified bydegree of freedom, df for a given Areaunder the curve.

invF() Catalog >invF(Area,dfNumer,dfDenom)

invF(Area,dfNumer,dfDenom)

computes the Inverse cumulative Fdistribution function specified by dfNumerand dfDenom for a given Area under thecurve.



invBinom() Catalog >invBinom(CumulativeProb,NumTrials,Prob,OutputForm)⇒scalar or matrix

Inverse binomial. Given the number of trials(NumTrials) and the probability of successof each trial (Prob), this function returnsthe minimum number of successes, k, suchthat the value, k, is greater than or equal tothe given cumulative probability(CumulativeProb).

OutputForm=0, displays result as a scalar(default).

OutputForm=1, displays result as a matrix.

Example: Mary andKevin are playing a dicegame. Mary has to guess themaximumnumber of times 6 shows up in 30 rolls. If thenumber 6 shows up thatmany times or less,Mary wins. Furthermore, the smaller thenumber that she guesses, the greater herwinnings. What is the smallest number Marycan guess if shewants the probability ofwinning to be greater than77%?

invBinomN() Catalog >invBinomN(CumulativeProb,Prob,NumSuccess,OutputForm)⇒scalar ormatrix

Inverse binomial with respect to N. Giventhe probability of success of each trial(Prob), and the number of successes(NumSuccess), this function returns theminimum number of trials, N, such that thevalue, N, is less than or equal to the givencumulative probability (CumulativeProb).

OutputForm=0, displays result as a scalar(default).

OutputForm=1, displays result as a matrix.

Example: Monique is practicing goal shotsfor netball. She knows fromexperience thather chance ofmaking any one shot is 70%.She plans to practice until she scores 50goals. Howmany shots must she attempt toensure that the probability ofmaking at least50 goals is more than0.99?

invNorm() Catalog >invNorm(Area[,μ[,σ]])

Computes the inverse cumulative normaldistribution function for a given Area underthe normal distribution curve specified by μand σ.

invt() Catalog >invt(Area,df)

invt() Catalog >Computes the inverse cumulative student-tprobability function specified by degree offreedom, df for a given Area under thecurve.

iPart() Catalog >iPart(Number) ⇒ integeriPart(List1) ⇒ listiPart(Matrix1) ⇒ matrix

Returns the integer part of the argument.

For lists and matrices, returns the integerpart of each element.


irr() Catalog >irr(CF0,CFList [,CFFreq]) ⇒ value

Financial function that calculates internalrate of return of an investment.

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

CFList is a list of cash flow amounts afterthe initial cash flow CF0.

CFFreq is an optional list in which eachelement specifies the frequency ofoccurrence for a grouped (consecutive) cashflow amount, which is the correspondingelement of CFList. The default is 1; if youenter values, they must be positive integers< 10,000.

Note: See alsomirr(), page 115.

isPrime() Catalog >isPrime(Number) ⇒ Boolean constantexpression



isPrime() Catalog >Returns true or false to indicate if numberis a whole number ≥ 2 that is evenlydivisible only by itself and 1.

If Number exceeds about 306 digits and hasno factors ≤1021, isPrime(Number) displaysan error message.

If you merely want to determine if Numberis prime, use isPrime() instead of factor(). Itis much faster, particularly if Number is notprime and has a second-largest factor thatexceeds about five digits.


Function to find the next prime after aspecifiednumber:

isVoid() Catalog >isVoid(Var) ⇒ Boolean constantexpressionisVoid(Expr) ⇒ Boolean constantexpressionisVoid(List) ⇒ list of Boolean constantexpressions

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

For more information on void elements, seepage 251.

L

Lbl Catalog >Lbl labelName

Defines a label with the name labelNamewithin a function.

You can use a Goto labelName instructionto transfer control to the instructionimmediately following the label.

labelName must meet the same namingrequirements as a variable name.


lcm() Catalog >lcm(Number1, Number2) ⇒ expressionlcm(List1, List2) ⇒ listlcm(Matrix1,Matrix2) ⇒ matrix

Returns the least common multiple of thetwo arguments. The lcm of two fractions isthe lcm of their numerators divided by thegcd of their denominators. The lcm offractional floating-point numbers is theirproduct.

For two lists or matrices, returns the leastcommon multiples of the correspondingelements.

left() Catalog >left(sourceString[, Num]) ⇒ string

Returns the leftmost Num characterscontained in character string sourceString.

If you omit Num, returns all ofsourceString.left(List1[, Num]) ⇒ list



left() Catalog >Returns the leftmost Num elementscontained in List1.

If you omit Num, returns all of List1.left(Comparison) ⇒ expression

Returns the left-hand side of an equation orinequality.

libShortcut() Catalog >libShortcut(LibNameString,ShortcutNameString[, LibPrivFlag]) ⇒ list of variables

Creates a variable group in the currentproblem that contains references to all theobjects in the specified library documentlibNameString. Also adds the groupmembers to the Variables menu. You canthen refer to each object using itsShortcutNameString.

Set LibPrivFlag=0 to exclude privatelibrary objects (default)Set LibPrivFlag=1 to include privatelibrary objects

To copy a variable group, see CopyVar onpage 29.To delete a variable group, see DelVar onpage 48.

This example assumes a properly stored andrefreshed library document named linalg2that contains objects definedas clearmat,gauss1, andgauss2.

limit() or lim() Catalog >limit(Expr1, Var, Point [,Direction]) ⇒expressionlimit(List1, Var, Point [, Direction]) ⇒listlimit(Matrix1, Var, Point [, Direction]) ⇒matrix

Returns the limit requested.

Note: See also Limit template, page 6.

Direction: negative=from left,positive=from right, otherwise=both. (Ifomitted, Direction defaults to both.)

limit() or lim() Catalog >Limits at positive ∞ and at negative ∞ arealways converted to one-sided limits fromthe finite side.

Depending on the circumstances, limit()returns itself or undef when it cannotdetermine a unique limit. This does notnecessarily mean that a unique limit doesnot exist. undef means that the result iseither an unknown number with finite orinfinite magnitude, or it is the entire set ofsuch numbers.

limit() uses methods such as L’Hopital’srule, so there are unique limits that itcannot determine. If Expr1 containsundefined variables other than Var, youmight have to constrain them to obtain amore concise result.

Limits can be very sensitive to roundingerror. When possible, avoid theApproximate setting of the Auto orApproximate mode and approximatenumbers when computing limits.Otherwise, limits that should be zero orhave infinite magnitude probably will not,and limits that should have finite non-zeromagnitude might not.

LinRegBx Catalog >LinRegBx X,Y[,[Freq][,Category,Include]]

Computes the linear regression y = a+b•x onlists X and Y with frequency Freq. Asummary of results is stored in thestat.results variable. (See page 176.)





LinRegBx Catalog >Freq is an optional list of frequency values.Each element in Freq specifies thefrequency of occurrence for eachcorresponding X and Y data point. Thedefault value is 1. All elements must beintegers ≥ 0.





stat.RegEqn Regression Equation: a+b•x


stat.r2 Coefficient of determination

stat.r Correlation coefficient





LinRegMx Catalog >LinRegMx X,Y[,[Freq][,Category,Include]]

Computes the linear regression y = m•x+b onlists X and Y with frequency Freq. Asummary of results is stored in thestat.results variable. (See page 176.)


LinRegMx Catalog >X and Y are lists of independent anddependent variables.






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

stat.m,stat.b








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

For Slope. Computes a level C confidenceinterval for the slope.

LinRegtIntervals X,Y[,F[,1,Xval[,CLev]]]



LinRegtIntervals Catalog >For Response. Computes a predicted y-value,a level C prediction interval for a singleobservation, and a level C confidenceinterval for the mean response.

A summary of results is stored in thestat.results variable. (See page 176.)

All the lists must have equal dimension.


F is an optional list of frequency values.Each element in F specifies the frequency ofoccurrence for each corresponding X and Ydata point. The default value is 1. Allelements must be integers ≥ 0.



stat.RegEqn Regression Equation: a+b•x


stat.df Degrees of freedom




For Slope type only


[stat.CLower, stat.CUpper] Confidence interval for the slope

stat.ME Confidence intervalmargin of error

stat.SESlope Standard error of slope

stat.s Standard error about the line

For Response type only


[stat.CLower, stat.CUpper] Confidence interval for themean response



stat.SE Standard error ofmean response

[stat.LowerPred,stat.UpperPred]

Prediction interval for a single observation

stat.MEPred Prediction intervalmargin of error

stat.SEPred Standard error for prediction

stat.y a + b•XVal

LinRegtTest Catalog >LinRegtTest X,Y[,Freq[,Hypoth]]

Computes a linear regression on the X and Ylists and a t test on the value of slope β andthe correlation coefficient ρ for the equationy=α+βx. It tests the null hypothesis H

0:β=0

(equivalently, ρ=0) against one of threealternative hypotheses.




Hypoth is an optional value specifying oneof three alternative hypotheses againstwhich the null hypothesis (H

0:β=ρ=0) will be

tested.

For Ha: β≠0 and ρ≠0 (default), set Hypoth=0

For Ha: β<0 and ρ<0, set Hypoth<0

For Ha: β>0 and ρ>0, set Hypoth>0






stat.RegEqn Regressionequation: a + b•x

stat.t t-Statistic for significance test




stat.s Standard error about the line

stat.SESlope Standard error of slope




linSolve() Catalog >linSolve( SystemOfLinearEqns, Var1,Var2, ...) ⇒ list

linSolve(LinearEqn1 and LinearEqn2 and..., Var1, Var2, ...) ⇒ list

linSolve({LinearEqn1, LinearEqn2, ...},Var1, Var2, ...) ⇒ list

linSolve(SystemOfLinearEqns, {Var1,Var2, ...}) ⇒ list

linSolve(LinearEqn1 and LinearEqn2 and..., {Var1, Var2, ...}) ⇒ list

linSolve({LinearEqn1, LinearEgn2, ...},{Var1, Var2, ...}) ⇒ list

Returns a list of solutions for the variablesVar1, Var2, ...

The first argument must evaluate to asystem of linear equations or a single linearequation. Otherwise, an argument erroroccurs.

For example, evaluating linSolve(x=1and x=2,x) produces an “ArgumentError” result.

ΔList() Catalog >ΔList(List1) ⇒ list

Note: You can insert this function from thekeyboard by typing deltaList(...).

Returns a list containing the differencesbetween consecutive elements in List1.Each element of List1 is subtracted fromthe next element of List1. The resulting listis always one element shorter than theoriginal List1.

list►mat() Catalog >list►mat(List [, elementsPerRow]) ⇒matrix

Returns a matrix filled row-by-row with theelements from List.

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

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

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

►ln Catalog >Expr►ln⇒ expression

Causes the input Expr to be converted to anexpression containing only natural logs (ln).

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

ln() /u keysln(Expr1) ⇒ expression

ln(List1) ⇒ listIf complex formatmode is Real:



ln() /u keysReturns the natural logarithm of theargument.

For a list, returns the natural logarithms ofthe elements.

If complex formatmode is Rectangular:

ln(squareMatrix1) ⇒ squareMatrix

Returns the matrix natural logarithm ofsquareMatrix1. This is not the same ascalculating the natural logarithm of eachelement. For information about thecalculation method, refer to cos() on.


In Radian anglemode andRectangularcomplex format:


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

Computes the logarithmic regression y =a+b•ln(x) on lists X and Y with frequencyFreq. A summary of results is stored in thestat.results variable. (See page 176.)





LnReg Catalog >Include is a list of one or more of thecategory codes. Only those data itemswhose category code is included in this listare included in the calculation.



stat.RegEqn Regressionequation: a+b•ln(x)



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

stat.Resid Residuals associatedwith the logarithmicmodel





Local Catalog >Local Var1[, Var2] [, Var3] ...

Declares the specified vars as localvariables. Those variables exist only duringevaluation of a function and are deletedwhen the function finishes execution.

Note: Local variables save memory becausethey only exist temporarily. Also, they donot disturb any existing global variablevalues. Local variables must be used for Forloops and for temporarily saving values in amulti-line function since modifications onglobal variables are not allowed in afunction.



Local Catalog >Note for entering the example: Forinstructions on entering multi-line programand function definitions, refer to theCalculator section of your productguidebook.

Lock Catalog >LockVar1[, Var2] [, Var3] ...LockVar.

Locks the specified variables or variablegroup. Locked variables cannot be modifiedor deleted.

You cannot lock or unlock the systemvariable Ans, and you cannot lock thesystem variable groups stat. or tvm.

Note: The Lock command clears theUndo/Redo history when applied tounlocked variables.

See unLock, page 197, and getLockInfo(),page 82.

log() /s keyslog(Expr1[,Expr2]) ⇒ expression

log(List1[,Expr2]) ⇒ list

Returns the base-Expr2 logarithm of thefirst argument.

Note: See also Log template, page 2.

For a list, returns the base-Expr2 logarithmof the elements.

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

If complex formatmode is Real:

If complex formatmode is Rectangular:

log() /s keyslog(squareMatrix1[,Expr]) ⇒squareMatrix

Returns the matrix base-Expr logarithm ofsquareMatrix1. This is not the same ascalculating the base-Expr logarithm ofeach element. For information about thecalculation method, refer to cos().


If the base argument is omitted, 10 is usedas base.



►logbase Catalog >Expr►logbase(Expr1) ⇒ expression

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

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

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

Computes the logistic regression y = (c/(1+a•e-bx)) on lists X and Y with frequencyFreq. A summary of results is stored in thestat.results variable. (See page 176.)






Logistic Catalog >Category is a list of category codes for thecorresponding X and Y data.




stat.RegEqn Regressionequation: c/(1+a•e-bx)

stat.a,stat.b, stat.c






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

Computes the logistic regression y = (c/(1+a•e-bx)+d) on lists X and Y with frequencyFreq, using a specified number ofIterations. A summary of results is stored inthe stat.results variable. (See page 176.)



LogisticD Catalog >Freq is an optional list of frequency values.Each element in Freq specifies thefrequency of occurrence for eachcorresponding X and Y data point. Thedefault value is 1. All elements must beintegers ≥ 0.





stat.RegEqn Regressionequation: c/(1+a•e-bx)+d)









Loop Catalog >Loop BlockEndLoop

Repeatedly executes the statements inBlock. Note that the loop will be executedendlessly, unless a Goto or Exit instructionis executed within Block.

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


LU 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 inlMatrix, the upper triangular matrix inuMatrix, and the permutation matrix(which describes the row swaps doneduring the calculation) in pMatrix.

lMatrix•uMatrix = pMatrix•matrix

Optionally, any matrix element is treated aszero if its absolute value is less than Tol.This tolerance is used only if the matrix hasfloating-point entries and does not containany symbolic variables that have not beenassigned a value. Otherwise, Tol is ignored.


• If Tol is omitted or not used, the defaulttolerance is calculated as:5E⁻14•max(dim(Matrix))•rowNorm(Matrix)

LU Catalog >The LU factorization algorithm uses partialpivoting with row interchanges.

M

mat►list() Catalog >mat►list(Matrix) ⇒ list

Returns a list filled with the elements inMatrix. The elements are copied fromMatrix row by row.

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

max() Catalog >max(Expr1, Expr2) ⇒ expression

max(List1, List2) ⇒ listmax(Matrix1,Matrix2) ⇒ matrix

Returns the maximum of the twoarguments. If the arguments are two listsor matrices, returns a list or matrixcontaining the maximum value of each pairof corresponding elements.

max(List) ⇒ expression

Returns the maximum element in list.max(Matrix1) ⇒ matrix

Returns a row vector containing themaximum element of each column inMatrix1.



max() Catalog >Empty (void) elements are ignored. Formore information on empty elements, seepage 251.

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

mean() Catalog >mean(List[, freqList]) ⇒ expression

Returns the mean of the elements in List.

Each freqList element counts the numberof consecutive occurrences of thecorresponding element in List.mean(Matrix1[, freqMatrix]) ⇒ matrix

Returns a row vector of the means of allthe columns inMatrix1.

Each freqMatrix element counts thenumber of consecutive occurrences of thecorresponding element inMatrix1.


In Rectangular vector format:

median() Catalog >median(List[, freqList]) ⇒ expression

Returns the median of the elements in List.

Each freqList element counts the numberof consecutive occurrences of thecorresponding element in List.median(Matrix1[, freqMatrix]) ⇒ matrix

Returns a row vector containing themedians of the columns inMatrix1.


median() Catalog >Notes:

• All entries in the list or matrix mustsimplify to numbers.

• Empty (void) elements in the list ormatrix are ignored. For more informationon empty elements, see page 251.

MedMed Catalog >MedMed X,Y [, Freq] [, Category, Include]]

Computes the median-median line y =(m•x+b) on lists X and Y with frequencyFreq. A summary of results is stored in thestat.results variable. (See page 176.)








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

stat.m,stat.b

Model coefficients




stat.Resid Residuals from themedian-median line




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

Returns Count characters from characterstring sourceString, beginning withcharacter number Start.

If Count is omitted or is greater than thedimension of sourceString, returns allcharacters from sourceString, beginningwith character number Start.

Count must be ≥ 0. If Count = 0, returns anempty string.

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

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

If Count is omitted or is greater than thedimension of sourceList, returns allelements from sourceList, beginning withelement number Start.

Count must be ≥ 0. If Count = 0, returns anempty list.

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

Returns Count strings from the list ofstrings sourceStringList, beginning withelement number Start.

min() Catalog >min(Expr1, Expr2) ⇒ expression

min(List1, List2) ⇒ listmin(Matrix1, Matrix2) ⇒ matrix

Returns the minimum of the twoarguments. If the arguments are two listsor matrices, returns a list or matrixcontaining the minimum value of each pairof corresponding elements.

min(List) ⇒ expression

Returns the minimum element of List.min(Matrix1) ⇒ matrix

Returns a row vector containing theminimum element of each column inMatrix1.

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

mirr() Catalog >mirr(financeRate,reinvestRate,CF0,CFList[,CFFreq])

Financial function that returns the modifiedinternal rate of return of an investment.

financeRate is the interest rate that youpay on the cash flow amounts.

reinvestRate is the interest rate at whichthe cash flows are reinvested.



CFFreq is an optional list in which eachelement specifies the frequency ofoccurrence for a grouped (consecutive) cashflow amount, which is the correspondingelement of CFList. The default is 1; if youenter values, they must be positive integers< 10,000.



mirr() Catalog >Note: See also irr(), page 93.

mod() Catalog >mod(Expr1, Expr2) ⇒ expression

mod(List1, List2) ⇒ listmod(Matrix1,Matrix2) ⇒ matrix

Returns the first argument modulo thesecond argument as defined by theidentities:

mod(x,0) = xmod(x,y) = x − y floor(x/y)

When the second argument is non-zero, theresult is periodic in that argument. Theresult is either zero or has the same sign asthe second argument.

If the arguments are two lists or twomatrices, returns a list or matrix containingthe modulo of each pair of correspondingelements.

Note: See also remain(), page 149

mRow() Catalog >mRow(Expr,Matrix1, Index) ⇒ matrix

Returns a copy of Matrix1 with eachelement in row Index of Matrix1multipliedby Expr.

mRowAdd() Catalog >mRowAdd(Expr,Matrix1, Index1, Index2)⇒ matrix

Returns a copy of Matrix1 with eachelement in row Index2 of Matrix1 replacedwith:

Expr • row Index1 + row Index2

MultReg Catalog >MultReg Y, X1[,X2[,X3,…[,X10]]]

Calculates multiple linear regression of list Yon lists X1, X2, …, X10. A summary ofresults is stored in the stat.results variable.(See page 176.)




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

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

stat.R2 Coefficient ofmultiple determination

stat.yList yList = b0+b1•x1+ ...


MultRegIntervals Catalog >MultRegIntervals Y, X1[, X2[, X3,…[,X10]]], XValList[, CLevel]

Computes a predicted y-value, a level Cprediction interval for a single observation,and a level C confidence interval for themean response.






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.SE Standard error ofmean response

stat.LowerPred,stat.UpperrPred

Prediction interval for a single observation

stat.MEPred Prediction intervalmargin of error

stat.SEPred Standard error for prediction

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


MultRegTests Catalog >MultRegTests Y, X1[, X2[, X3,…[, X10]]]

Multiple linear regression test computes amultiple linear regression on the given dataand provides the global F test statistic and ttest statistics for the coefficients.



Outputs



stat.F GlobalF test statistic

stat.PVal P-value associatedwith globalF statistic

stat.R2 Coefficient ofmultiple determination

stat.AdjR2 Adjusted coefficient ofmultiple determination

stat.s Standarddeviationof the error

stat.DW Durbin-Watson statistic; used to determinewhether first-order auto correlation ispresent in themodel


stat.dfReg Regressiondegrees of freedom

stat.SSReg Regression sumof squares

stat.MSReg Regressionmean square

stat.dfError Error degrees of freedom

stat.SSError Error sumof 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.sResid Standardized residuals; obtainedby dividing a residual by its standarddeviation

stat.CookDist Cook’s distance; measure of the influence of anobservationbasedon the residualand leverage

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

N

nand /= keysBooleanExpr1 nand BooleanExpr2 returnsBoolean expressionBooleanList1 nand BooleanList2 returnsBoolean listBooleanMatrix1 nand BooleanMatrix2returns Boolean matrix

Returns the negation of a logical andoperation on the two arguments. Returnstrue, false, or a simplified form of theequation.

For lists and matrices, returns comparisonselement by element.



nand /= keysInteger1 nand Integer2⇒ integer

Compares two real integers bit-by-bit usinga nand operation. Internally, both integersare converted to signed, 64-bit binarynumbers. When corresponding bits arecompared, the result is 0 if both bits are 1;otherwise, the result is 1. The returnedvalue represents the bit results, and isdisplayed according to the Base mode.


nCr() Catalog >nCr(Expr1, Expr2) ⇒ expression

For integer Expr1 and Expr2 with Expr1 ≥Expr2 ≥ 0, nCr() is the number ofcombinations of Expr1 things taken Expr2at a time. (This is also known as a binomialcoefficient.) Both arguments can beintegers or symbolic expressions.

nCr(Expr, 0) ⇒ 1

nCr(Expr, negInteger) ⇒ 0

nCr(Expr, posInteger) ⇒ Expr•(Expr−1) ...(Expr−posInteger+1) / posInteger!

nCr(Expr, nonInteger) ⇒ expression! /((Expr−nonInteger)!•nonInteger!)

nCr(List1, List2) ⇒ list

Returns a list of combinations based on thecorresponding element pairs in the twolists. The arguments must be the same sizelist.

nCr(Matrix1,Matrix2) ⇒ matrix

nCr() Catalog >Returns a matrix of combinations based onthe corresponding element pairs in the twomatrices. The arguments must be the samesize matrix.

nDerivative() Catalog >nDerivative(Expr1,Var=Value[,Order])⇒ value

nDerivative(Expr1,Var[,Order])|Var=Value⇒ value

Returns the numerical derivative calculatedusing auto differentiation methods.


Order of the derivative must be 1 or 2.

newList() Catalog >newList(numElements) ⇒ list

Returns a list with a dimension ofnumElements. Each element is zero.

newMat() Catalog >newMat(numRows, numColumns) ⇒matrix

Returns a matrix of zeros with thedimension numRows by numColumns.

nfMax() Catalog >nfMax(Expr, Var) ⇒ valuenfMax(Expr, Var, lowBound) ⇒ valuenfMax(Expr, Var, lowBound, upBound) ⇒valuenfMax(Expr, Var) |lowBound≤Var≤upBound⇒ value



nfMax() Catalog >Returns a candidate numerical value ofvariable Var where the local maximum ofExpr occurs.

If you supply lowBound and upBound, thefunction looks in the closed interval[lowBound,upBound] for the localmaximum.

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

nfMin() Catalog >nfMin(Expr, Var) ⇒ valuenfMin(Expr, Var, lowBound) ⇒ valuenfMin(Expr, Var, lowBound, upBound) ⇒valuenfMin(Expr, Var) |lowBound≤Var≤upBound⇒ value

Returns a candidate numerical value ofvariable Var where the local minimum ofExpr occurs.

If you supply lowBound and upBound, thefunction looks in the closed interval[lowBound,upBound] for the localminimum.

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

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

If the integrand Expr1 contains no variableother than Var, and if Lower andUpperare constants, positive ∞, or negative ∞,then nInt() returns an approximation of ∫(Expr1, Var, Lower, Upper). Thisapproximation is a weighted average ofsome sample values of the integrand in theinterval Lower<Var<Upper.

nInt() Catalog >The goal is six significant digits. Theadaptive algorithm terminates when itseems likely that the goal has beenachieved, or when it seems unlikely thatadditional samples will yield a worthwhileimprovement.

A warning is displayed (“Questionableaccuracy”) when it seems that the goal hasnot been achieved.

Nest nInt() to do multiple numericintegration. Integration limits can dependon integration variables outside them.

Note: See also ∫(), page 221.

nom() Catalog >nom(effectiveRate,CpY) ⇒ value

Financial function that converts the annualeffective interest rate effectiveRate to anominal rate, given CpY as the number ofcompounding periods per year.

effectiveRate must be a real number, andCpY must be a real number > 0.

Note: See also eff(), page 58.

nor /= keysBooleanExpr1 nor BooleanExpr2 returnsBoolean expressionBooleanList1 nor BooleanList2 returnsBoolean listBooleanMatrix1 nor BooleanMatrix2returns Boolean matrix

Returns the negation of a logical oroperation on the two arguments. Returnstrue, false, or a simplified form of theequation.




nor /= keysInteger1 nor Integer2⇒ integer

Compares two real integers bit-by-bit usinga nor operation. Internally, both integersare converted to signed, 64-bit binarynumbers. When corresponding bits arecompared, the result is 1 if both bits are 1;otherwise, the result is 0. The returnedvalue represents the bit results, and isdisplayed according to the Base mode.


norm() Catalog >norm(Matrix) ⇒ expression

norm(Vector) ⇒ expression

Returns the Frobenius norm.

normalLine() Catalog >normalLine(Expr1,Var,Point) ⇒expression

normalLine(Expr1,Var=Point) ⇒expression

Returns the normal line to the curverepresented by Expr1 at the point specifiedin Var=Point.

Make sure that the independent variable isnot defined. For example, If f1(x):=5 andx:=3, then normalLine(f1(x),x,2) returns“false.”

normCdf() Catalog >normCdf(lowBound,upBound[,μ[,σ]]) ⇒number if lowBound and upBound arenumbers, list if lowBound and upBound arelists

Computes the normal distribution probabilitybetween lowBound and upBound for thespecified μ (default=0) and σ (default=1).

For P(X ≤ upBound), set lowBound = ⁻∞.

normPdf() Catalog >normPdf(XVal[,μ[,σ]]) ⇒ number if XVal isa number, list if XVal is a list

Computes the probability density functionfor the normal distribution at a specifiedXVal value for the specified μ and σ.

not Catalog >not BooleanExpr⇒ Boolean expression

Returns true, false, or a simplified form ofthe argument.

not Integer1⇒ integer

Returns the one’s complement of a realinteger. Internally, Integer1 is converted toa signed, 64-bit binary number. The value ofeach bit is flipped (0 becomes 1, and viceversa) for the one’s complement. Resultsare displayed according to the Base mode.

You can enter the integer in any numberbase. For a binary or hexadecimal entry, youmust use the 0b or 0h prefix, respectively.Without a prefix, the integer is treated asdecimal (base 10).


InHex basemode:


In Bin basemode:





nPr() Catalog >nPr(Expr1, Expr2) ⇒ expression

For integer Expr1 and Expr2 with Expr1 ≥Expr2 ≥ 0, nPr() is the number ofpermutations of Expr1 things taken Expr2at a time. Both arguments can be integersor symbolic expressions.

nPr(Expr, 0⇒ 1

nPr(Expr, negInteger) ⇒ 1 / ((Expr+1)•(Expr+2) ... (expression−negInteger))

nPr(Expr, posInteger) ⇒ Expr•(Expr−1) ...(Expr−posInteger+1)

nPr(Expr, nonInteger) ⇒ Expr! /(Expr−nonInteger)!nPr(List1, List2) ⇒ list

Returns a list of permutations based on thecorresponding element pairs in the twolists. The arguments must be the same sizelist.

nPr(Matrix1,Matrix2) ⇒ matrix

Returns a matrix of permutations based onthe corresponding element pairs in the twomatrices. The arguments must be the samesize matrix.

npv() Catalog >npv(InterestRate,CFO,CFList[,CFFreq])

Financial function that calculates netpresent value; the sum of the presentvalues for the cash inflows and outflows. Apositive result for npv indicates a profitableinvestment.

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



npv() Catalog >CFFreq is a list in which each elementspecifies the frequency of occurrence for agrouped (consecutive) cash flow amount,which is the corresponding element ofCFList. The default is 1; if you entervalues, they must be positive integers <10,000.

nSolve() Catalog >nSolve(Equation,Var[=Guess]) ⇒ numberor error_string

nSolve(Equation,Var[=Guess],lowBound)⇒ number or error_string

nSolve(Equation,Var[=Guess],lowBound,upBound) ⇒ numberor error_string

nSolve(Equation,Var[=Guess]) |lowBound≤Var≤upBound⇒ number orerror_string

Iteratively searches for one approximatereal numeric solution to Equation for itsone variable. Specify the variable as:

variable– or –variable = real number

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

Note: If there aremultiple solutions, you canuse a guess to help find a particular solution.

nSolve() is often much faster than solve() orzeros(), particularly if the “|” operator isused to constrain the search to a smallinterval containing exactly one simplesolution.

nSolve() attempts to determine either onepoint where the residual is zero or tworelatively close points where the residualhas opposite signs and the magnitude ofthe residual is not excessive. If it cannotachieve this using a modest number ofsample points, it returns the string “nosolution found.”



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

O

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

OneVar [n,]X1,X2[X3[,…[,X20]]]

Calculates 1-variable statistics on up to 20lists. A summary of results is stored in thestat.results variable. (See page 176.)



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


An empty (void) element in any of the listsX, Freq, or Category results in a void forthe corresponding element of all those lists.An empty element in any of the lists X1through X20 results in a void for thecorresponding element of all those lists. Formore information on empty elements, seepage 251.


stat.v Meanof x values

stat.Σx Sumof x values

stat.Σx2 Sumof x2 values


stat.sx Sample standarddeviationof x

stat.σx Population standarddeviationof x

stat.n Number of data points

stat.MinX Minimumof x values

stat.Q1X 1stQuartile of x

stat.MedianX Medianof x

stat.Q3X 3rdQuartile of x

stat.MaxX Maximumof x values

stat.SSX Sumof squares of deviations from themeanof x

or Catalog >BooleanExpr1 or BooleanExpr2 returnsBoolean expressionBooleanList1 or BooleanList2 returnsBoolean listBooleanMatrix1 or BooleanMatrix2returns Boolean matrix

Returns true or false or a simplified form ofthe original entry.

Returns true if either or both expressionssimplify to true. Returns false only if bothexpressions evaluate to false.

Note: See xor.


Integer1 or Integer2⇒ integer InHex basemode:


In Bin basemode:



or Catalog >Compares two real integers bit-by-bit usingan or operation. Internally, both integersare converted to signed, 64-bit binarynumbers. When corresponding bits arecompared, the result is 1 if either bit is 1;the result is 0 only if both bits are 0. Thereturned value represents the bit results,and is displayed according to the Basemode.



Note: See xor.


ord() Catalog >ord(String) ⇒ integerord(List1) ⇒ list

Returns the numeric code of the firstcharacter in character string String, or a listof the first characters of each list element.

P

P►Rx() Catalog >P►Rx(rExpr, θExpr) ⇒ expressionP►Rx(rList, θList) ⇒ listP►Rx(rMatrix, θMatrix) ⇒ matrix

Returns the equivalent x-coordinate of the(r, θ) pair.


P►Rx() Catalog >Note: The θ argument is interpreted aseither a degree, gradian or radian angle,according to the current angle mode. If theargument is an expression, you can use °, G,or r to override the angle mode settingtemporarily.

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

P►Ry() Catalog >P►Ry(rExpr, θExpr) ⇒ expression

P►Ry(rList, θList) ⇒ listP►Ry(rMatrix, θMatrix) ⇒ matrix

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

Note: The θ argument is interpreted aseither a degree, radian or gradian angle,according to the current angle mode. If theargument is an expression, you can use °, G,or r to override the angle mode settingtemporarily.

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


PassErr Catalog >PassErr

Passes an error to the next level.

If system variable errCode is zero, PassErrdoes not do anything.

The Else clause of the Try...Else...EndTryblock should use ClrErr or PassErr. If theerror is to be processed or ignored, useClrErr. If what to do with the error is notknown, use PassErr to send it to the nexterror handler. If there are no more pendingTry...Else...EndTry error handlers, the errordialog box will be displayed as normal.

For anexample of PassErr, See Example 2under the Try command, page 191.



PassErr Catalog >Note: See also ClrErr, page 25, and Try, page191.

Note for entering the example: Forinstructions on entering multi-line programand function definitions, refer to theCalculator section of your product guidebook.

piecewise() Catalog >piecewise(Expr1[, Cond1[, Expr2 [, Cond2[, … ]]]])

Returns definitions for a piecewise functionin the form of a list. You can also createpiecewise definitions by using a template.

Note: See also Piecewise template, page 3.

poissCdf() Catalog >poissCdf(λ,lowBound,upBound) ⇒ numberif lowBound and upBound are numbers, listif lowBound and upBound are lists

poissCdf(λ,upBound)for P(0≤X≤upBound) ⇒number if upBound is a number, list ifupBound is a list

Computes a cumulative probability for thediscrete Poisson distribution with specifiedmean λ.

For P(X ≤ upBound), set lowBound=0

poissPdf() Catalog >poissPdf(λ,XVal) ⇒ number if XVal is anumber, list if XVal is a list

Computes a probability for the discretePoisson distribution with the specified meanλ.

►Polar Catalog >Vector►Polar

Note: You can insertthis operator from thecomputer keyboard bytyping @>Polar.

Displays vector in polarform [r∠θ]. The vectormust be of dimension 2and can be a row or acolumn.

Note:►Polar is adisplay-formatinstruction, not aconversion function.You can use it only atthe end of an entryline, and it does notupdate ans.

Note: See also►Rect,page 146.

complexValue►Polar

DisplayscomplexVector inpolar form.

• Degree angle modereturns (r∠θ).

• Radian angle modereturns reiθ.

complexValue canhave any complexform. However, an reiθentry causes an error inDegree angle mode.

Note: You must use theparentheses for an(r∠θ) polar entry.



InDegree anglemode:

polyCoeffs() Catalog >polyCoeffs(Poly [,Var]) ⇒ list



polyCoeffs() Catalog >Returns a list of the coefficients ofpolynomial Poly with respect to variableVar.

Poly must be a polynomial expression inVar. We recommend that you do not omitVar unless Poly is an expression in a singlevariable.

Expands the polynomial and selects x for theomittedVar.

polyDegree() Catalog >polyDegree(Poly [,Var]) ⇒ value

Returns the degree of polynomialexpression Poly with respect to variableVar. If you omit Var, the polyDegree()function selects a default from thevariables contained in the polynomial Poly.

Poly must be a polynomial expression inVar. We recommend that you do not omitVar unless Poly is an expression in a singlevariable.

Constant polynomials

The degree canbe extractedeven thoughthe coefficients cannot. This is because thedegree canbe extractedwithout expandingthe polynomial.

polyEval() Catalog >polyEval(List1, Expr1) ⇒ expressionpolyEval(List1, List2) ⇒ expression

Interprets the first argument as thecoefficient of a descending-degreepolynomial, and returns the polynomialevaluated for the value of the secondargument.

polyGcd() Catalog >polyGcd(Expr1,Expr2) ⇒ expression

Returns greatest common divisor of thetwo arguments.

Expr1 and Expr2must be polynomialexpressions.

List, matrix, and Boolean arguments are notallowed.

polyQuotient() Catalog >polyQuotient(Poly1,Poly2 [,Var]) ⇒expression

Returns the quotient of polynomial Poly1divided by polynomial Poly2 with respect tothe specified variable Var.

Poly1 and Poly2must be polynomialexpressions in Var. We recommend thatyou do not omit Var unless Poly1 andPoly2 are expressions in the same singlevariable.



polyRemainder() Catalog >polyRemainder(Poly1,Poly2 [,Var]) ⇒expression

Returns the remainder of polynomial Poly1divided by polynomial Poly2 with respect tothe specified variable Var.

Poly1 and Poly2must be polynomialexpressions in Var. We recommend thatyou do not omit Var unless Poly1 andPoly2 are expressions in the same singlevariable.

polyRoots() Catalog >polyRoots(Poly,Var) ⇒ list

polyRoots(ListOfCoeffs) ⇒ list

The first syntax, polyRoots(Poly,Var),returns a list of real roots of polynomialPoly with respect to variable Var. If no realroots exist, returns an empty list: { }.

Poly must be a polynomial in one variable.

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

Note: See also cPolyRoots(), page 36.

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

Computes the power regressiony = (a•(x)b)on lists X and Y with frequency Freq. Asummary of results is stored in thestat.results variable. (See page 176.)



PowerReg Catalog >Freq is an optional list of frequency values.Each element in Freq specifies thefrequency of occurrence for eachcorresponding X and Y data point. Thedefault value is 1. All elements must beintegers ≥ 0.





stat.RegEqn Regressionequation: a•(x)b



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

stat.Resid Residuals associatedwith the power model





Prgm Catalog >Prgm BlockEndPrgm

Template for creating a user-definedprogram. Must be used with the Define,Define LibPub, or Define LibPriv command.

Calculate GCDanddisplay intermediateresults.



Prgm Catalog >Block can be a single statement, a seriesof statements separated with the “:”character, or a series of statements onseparate lines.


prodSeq() See Π (), page 223.

Product (PI) See Π (), page 223.

product() Catalog >product(List[, Start[, End]]) ⇒ expression

Returns the product of the elementscontained in List. Start and End areoptional. They specify a range of elements.

product(Matrix1[, Start[, End]]) ⇒ matrix

Returns a row vector containing theproducts of the elements in the columns ofMatrix1. Start and end are optional. Theyspecify a range of rows.


propFrac() Catalog >propFrac(Expr1[, Var]) ⇒ expression

propFrac(rational_number) returnsrational_number as the sum of an integerand a fraction having the same sign and agreater denominator magnitude thannumerator magnitude.

propFrac(rational_expression,Var) returnsthe sum of proper ratios and a polynomialwith respect to Var. The degree of Var inthe denominator exceeds the degree of Varin the numerator in each proper ratio.Similar powers of Var are collected. Theterms and their factors are sorted with Varas the main variable.

If Var is omitted, a proper fractionexpansion is done with respect to the mostmain variable. The coefficients of thepolynomial part are then made proper withrespect to their most main variable firstand so on.

For rational expressions, propFrac() is afaster but less extreme alternative toexpand().

You can use the propFrac() function torepresent mixed fractions and demonstrateaddition and subtraction of mixed fractions.

Q

QR Catalog >QR Matrix, qMatrix, rMatrix[, Tol]

Calculates the Householder QR factorizationof a real or complex matrix. The resulting Qand R matrices are stored to the specifiedMatrix. The Q matrix is unitary. The Rmatrix is upper triangular.

The floating-point number (9.) inm1 causesresults to be calculated in floating-pointform.



QR Catalog >Optionally, any matrix element is treated aszero if its absolute value is less than Tol.This tolerance is used only if the matrix hasfloating-point entries and does not containany symbolic variables that have not beenassigned a value. Otherwise, Tol is ignored.


• If Tol is omitted or not used, the defaulttolerance is calculated as:5E−14 •max(dim(Matrix)) •rowNorm(Matrix)

The QR factorization is computednumerically using Householdertransformations. The symbolic solution iscomputed using Gram-Schmidt. Thecolumns in qMatName are the orthonormalbasis vectors that span the space defined bymatrix.

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

Computes the quadratic polynomialregression y=a•x2+b•x+c on lists X and Ywith frequency Freq. A summary of resultsis stored in the stat.results variable. (Seepage 176.)



QuadReg Catalog >Freq is an optional list of frequency values.Each element in Freq specifies thefrequency of occurrence for eachcorresponding X and Y data point. Thedefault value is 1. All elements must beintegers ≥ 0.




Outputvariable

Description

stat.RegEqn Regressionequation: a•x2+b•x+c

stat.a,stat.b, stat.c







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

Computes the quartic polynomial regressiony = a•x4+b•x3+c• x2+d•x+e on lists X and Ywith frequency Freq. A summary of resultsis stored in the stat.results variable. (Seepage 176.)




QuartReg Catalog >X and Y are lists of independent anddependent variables.






stat.RegEqn Regressionequation: a•x4+b•x3+c• x2+d•x+e

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







R

R►Pθ() Catalog >R►Pθ (xExpr, yExpr) ⇒ expression

R►Pθ (xList, yList) ⇒ listR►Pθ (xMatrix, yMatrix) ⇒ matrix

InDegree anglemode:

R►Pθ() Catalog >Returns the equivalent θ-coordinate of the(x,y) pair arguments.


Note: You can insert this function from thecomputer keyboard by typing R@>Ptheta(...).



R►Pr() Catalog >R►Pr (xExpr, yExpr) ⇒ expression

R►Pr (xList, yList) ⇒ listR►Pr (xMatrix, yMatrix) ⇒ matrix

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

Note: You can insert this function from thecomputer keyboard by typing R@>Pr(...).


►Rad Catalog >Expr1►Rad⇒ expressionConverts the argument to radian anglemeasure.

Note: You can insert this operator from thecomputer keyboard by typing @>Rad.

InDegree anglemode:


rand() Catalog >rand() ⇒ expressionrand(#Trials) ⇒ list

Set the random-number seed.



rand() Catalog >rand() returns a random value between 0and 1.

rand(#Trials) returns a list containing#Trials random values between 0 and 1.

randBin() Catalog >randBin(n, p) ⇒ expressionrandBin(n, p, #Trials) ⇒ list

randBin(n, p) returns a random real numberfrom a specified Binomial distribution.

randBin(n, p, #Trials) returns a listcontaining #Trials random real numbersfrom a specified Binomial distribution.

randInt() Catalog >randInt(lowBound,upBound)⇒ expressionrandInt(lowBound,upBound,#Trials) ⇒ list

randInt(lowBound,upBound)returns a randominteger within therange specified bylowBound andupBound integerbounds.

randInt(lowBound,upBound,#Trials) returns alist containing#Trials randomintegers within thespecified range.

randMat() Catalog >randMat(numRows, numColumns) ⇒matrix

Returns a matrix of integers between -9and 9 of the specified dimension.

Both arguments must simplify to integers. Note: The values in this matrix will changeeach time youpress·.

randNorm() Catalog >randNorm(μ, σ) ⇒ expressionrandNorm(μ, σ, #Trials) ⇒ list

randNorm(μ, σ) returns a decimal numberfrom the specified normal distribution. Itcould be any real number but will be heavilyconcentrated in the interval [μ−3•σ, μ+3•σ].

randNorm(μ, σ, #Trials) returns a listcontaining #Trials decimal numbers fromthe specified normal distribution.

randPoly() Catalog >randPoly(Var, Order) ⇒ expression

Returns a polynomial in Var of thespecifiedOrder. The coefficients arerandom integers in the range −9 through 9.The leading coefficient will not be zero.

Order must be 0–99.

randSamp() Catalog >randSamp(List,#Trials[,noRepl]) ⇒ list

Returns a list containing a random sampleof #Trials trials from List with an optionfor sample replacement (noRepl=0), or nosample replacement (noRepl=1). Thedefault is with sample replacement.



RandSeed Catalog >RandSeed Number

If Number = 0, sets the seeds to the factorydefaults for the random-number generator.If Number ≠ 0, it is used to generate twoseeds, which are stored in system variablesseed1 and seed2.

real() Catalog >real(Expr1) ⇒ expression

Returns the real part of the argument.

Note: All undefined variables are treated asreal variables. See also imag(), page 88.

real(List1) ⇒ list

Returns the real parts of all elements.

real(Matrix1) ⇒ matrix

Returns the real parts of all elements.

►Rect Catalog >Vector►Rect

Note: You can insert this operator from thecomputer keyboard by typing @>Rect.

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

Note:►Rect is a display-format instruction,not a conversion function. You can use itonly at the end of an entry line, and it doesnot update ans.

Note: See also►Polar, page 133.

complexValue►Rect

Displays complexValue in rectangular forma+bi. The complexValue can have anycomplex form. However, an reiθ entrycauses an error in Degree angle mode.

Note: You must use parentheses for an(r∠θ) polar entry.


►Rect Catalog >


InDegree anglemode:

Note: To type∠ , select it from the symbollist in the Catalog.

ref() Catalog >ref(Matrix1[, Tol]) ⇒ matrix

Returns the row echelon form of Matrix1.



• If Tol is omitted or not used, the defaulttolerance is calculated as:5E−14 •max(dim(Matrix1)) •rowNorm(Matrix1)

Avoid undefined elements inMatrix1. Theycan lead to unexpected results.

For example, if a is undefined in thefollowing expression, a warning messageappears and the result is shown as:



ref() Catalog >The warning appears because thegeneralized element 1/a would not be validfor a=0.

You can avoid this by storing a value to abeforehand or by using the constraint (“|”)operator to substitute a value, as shown inthe following example.

Note: See also rref(), page 156.

RefreshProbeVars Catalog >RefreshProbeVars

Allows you to access sensor data from allconnected sensor probes in your TI-Basicprogram.

StatusVarValue Status

statusVar=0

Normal (continue with theprogram)

statusVar=1

The Vernier DataQuest™application is in data collectionmode.Note: The Vernier DataQuest™application must be in metermode for this command to work.

statusVar=2

The Vernier DataQuest™application is not launched.

statusVar=3

The Vernier DataQuest™application is launched, but youhave not connected any probes.

Example

Define temp()=

Prgm

© Check if system is ready

RefreshProbeVars status

If status=0 Then

Disp "ready"

For n,1,50

RefreshProbeVars status

temperature:=meter.temperature

Disp "Temperature:",temperature

If temperature>30 Then

Disp "Too hot"

EndIf

© Wait for 1 second betweensamples

Wait 1

EndFor

RefreshProbeVars Catalog >Else

Disp "Not ready. Try againlater"

EndIf

EndPrgm

Note: This can also be used with TI-Innovator™ Hub.

remain() Catalog >remain(Expr1, Expr2) ⇒ expression

remain(List1, List2) ⇒ listremain(Matrix1,Matrix2) ⇒ matrix

Returns the remainder of the firstargument with respect to the secondargument as defined by the identities:

remain(x,0) xremain(x,y) x−y•iPart(x/y)As a consequence, note that remain(−x,y) −remain(x,y). The result is either zero or ithas the same sign as the first argument.

Note: See alsomod(), page 116.

Request Catalog >Request promptString, var[, DispFlag[, statusVar]]

Request promptString, func(arg1, ...argn)[, DispFlag [, statusVar]]

Programming command: Pauses theprogram and displays a dialog boxcontaining the message promptString andan input box for the user’s response.

When the user types a response and clicksOK, the contents of the input box areassigned to variable var.

Define a program:

Define request_demo()=Prgm Request “Radius: ”,r Disp “Area = “,pi*r2EndPrgm

Run the programand type a response:

request_demo()



Request Catalog >If the user clicks Cancel, the programproceeds without accepting any input. Theprogram uses the previous value of var ifvar was already defined.

The optional DispFlag argument can beany expression.

• IfDispFlag is omitted or evaluates to 1,the prompt message and user’s responseare displayed in the Calculator history.

• IfDispFlag evaluates to 0, the promptand response are not displayed in thehistory.

Result after selecting OK:

Radius: 6/2Area= 28.2743

The optional statusVar argument gives theprogram a way to determine how the userdismissed the dialog box. Note thatstatusVar requires the DispFlag argument.

• If the user clicked OK or pressed Enter orCtrl+Enter, variable statusVar is set to avalue of 1.

• Otherwise, variable statusVar is set to avalue of 0.

The func() argument allows a program tostore the user’s response as a functiondefinition. This syntax operates as if theuser executed the command:

Define func(arg1, ...argn) = user’sresponse

The program can then use the definedfunction func(). The promptString shouldguide the user to enter an appropriateuser’s response that completes thefunction definition.

Note: You can use the Request commandwithin a user-defined program but notwithin a function.

To stop a program that contains a Requestcommand inside an infinite loop:


Define a program:

Define polynomial()=Prgm Request "Enter a polynomial inx:",p(x) Disp "Real roots are:",polyRoots(p(x),x)EndPrgm


polynomial()

Result after entering x^3+3x+1 and selectingOK:

Real roots are: {-0.322185}

Request Catalog >• Windows®: Hold down the F12 key and

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

press Enter repeatedly.• iPad®: The app displays a prompt. You

can continue waiting or cancel.

Note: See also RequestStr, page 151.

RequestStr Catalog >RequestStr promptString, var[, DispFlag]

Programming command: Operatesidentically to the first syntax of the Requestcommand, except that the user’s responseis always interpreted as a string. Bycontrast, the Request command interpretsthe response as an expression unless theuser encloses it in quotation marks (““).

Note: You can use the RequestStr commandwithin a user-defined program but notwithin a function.

To stop a program that contains aRequestStr command inside an infinite loop:




• iPad®: The app displays a prompt. Youcan continue waiting or cancel.

Note: See also Request, page 149.

Define a program:

Define requestStr_demo()=Prgm RequestStr “Your name:”,name,0 Disp “Response has “,dim(name),”characters.”EndPrgm


requestStr_demo()

Result after selecting OK (Note that theDispFlag argumentof 0 omits the promptand response from the history):

requestStr_demo()

Response has 5 characters.



Return Catalog >Return [Expr]

Returns Expr as the result of the function.Use within a Func...EndFunc block.

Note: Use Return without an argumentwithin a Prgm...EndPrgm block to exit aprogram.


right() Catalog >right(List1[, Num]) ⇒ list

Returns the rightmost Num elementscontained in List1.

If you omit Num, returns all of List1.right(sourceString[, Num]) ⇒ string

Returns the rightmost Num characterscontained in character string sourceString.

If you omit Num, returns all ofsourceString.right(Comparison) ⇒ expression

Returns the right side of an equation orinequality.

rk23 () Catalog >rk23(Expr, Var, depVar, {Var0, VarMax},depVar0, VarStep [, diftol]) ⇒ matrix

rk23(SystemOfExpr, Var, ListOfDepVars,{Var0, VarMax}, ListOfDepVars0,VarStep[, diftol]) ⇒ matrix

rk23(ListOfExpr, Var, ListOfDepVars,{Var0, VarMax}, ListOfDepVars0,VarStep[, diftol]) ⇒ matrix

Differential equation:

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


rk23 () Catalog >Uses the Runge-Kutta method to solve thesystem

with depVar(Var0)=depVar0 on theinterval [Var0,VarMax]. Returns a matrixwhose first row defines the Var outputvalues as defined by VarStep. The secondrow defines the value of the first solutioncomponent at the corresponding Varvalues, and so on.

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

SystemOfExpr is a system of right-handsides that define the system of ODEs(corresponds to order of dependentvariables in ListOfDepVars).

ListOfExpr is a list of right-hand sides thatdefine the system of ODEs (corresponds toorder of dependent variables inListOfDepVars).

Var is the independent variable.

ListOfDepVars is a list of dependentvariables.

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

ListOfDepVars0 is a list of initial valuesfor dependent variables.

If VarStep evaluates to a nonzero number:sign(VarStep) = sign(VarMax-Var0) andsolutions are returned at Var0+i*VarStepfor all i=0,1,2,… such that Var0+i*VarStepis in [var0,VarMax] (may not get a solutionvalue at VarMax).

if VarStep evaluates to zero, solutions arereturned at the "Runge-Kutta" Var values.

diftol is the error tolerance (defaults to0.001).

Same equationwithdiftol set to 1.E−6

Compare above resultwithCAS exactsolutionobtainedusing deSolve() andseqGen():

System of equations:

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



root() Catalog >root(Expr) ⇒ rootroot(Expr1, Expr2) ⇒ root

root(Expr) returns the square root of Expr.

root(Expr1, Expr2) returns the Expr2 rootof Expr1. Expr1 can be a real or complexfloating point constant, an integer orcomplex rational constant, or a generalsymbolic expression.

Note: See also Nth root template, page 1.

rotate() Catalog >rotate(Integer1[,#ofRotations]) ⇒ integer

Rotates the bits in a binary integer. You canenter Integer1 in any number base; it isconverted automatically to a signed, 64-bitbinary form. If the magnitude of Integer1 istoo large for this form, a symmetric modulooperation brings it within the range. Formore information, see►Base2, page 17.

In Bin basemode:


If #ofRotations is positive, the rotation is tothe left. If #ofRotations is negative, therotation is to the right. The default is −1(rotate right one bit).

For example, in a right rotation:

InHex basemode:

Each bit rotates right.

0b00000000000001111010110000110101

Rightmost bit rotates to leftmost.

produces:

0b10000000000000111101011000011010

The result is displayed according to theBase mode.

Important: To enter a binary orhexadecimal number, always use the 0bor0hprefix (zero, not the letter O).

rotate(List1[,#ofRotations]) ⇒ list

Returns a copy of List1 rotated right or leftby #of Rotations elements. Does not alterList1.

InDec basemode:

rotate() Catalog >If #ofRotations is positive, the rotation is tothe left. If #of Rotations is negative, therotation is to the right. The default is −1(rotate right one element).

rotate(String1[,#ofRotations]) ⇒ string

Returns a copy of String1 rotated right orleft by #ofRotations characters. Does notalter String1.

If #ofRotations is positive, the rotation is tothe left. If #ofRotations is negative, therotation is to the right. The default is −1(rotate right one character).

round() Catalog >round(Expr1[, digits]) ⇒ expression

Returns the argument rounded to thespecified number of digits after the decimalpoint.

digits must be an integer in the range 0–12. If digits is not included, returns theargument rounded to 12 significant digits.

Note: Display digits mode may affect howthis is displayed.

round(List1[, digits]) ⇒ list

Returns a list of the elements rounded tothe specified number of digits.

round(Matrix1[, digits]) ⇒ matrix

Returns a matrix of the elements roundedto the specified number of digits.

rowAdd() Catalog >rowAdd(Matrix1, rIndex1, rIndex2) ⇒matrix

Returns a copy of Matrix1 with rowrIndex2 replaced by the sum of rowsrIndex1 and rIndex2.



rowDim() Catalog >rowDim(Matrix) ⇒ expression

Returns the number of rows inMatrix.

Note: See also colDim(), page 26.

rowNorm() Catalog >rowNorm(Matrix) ⇒ expression

Returns the maximum of the sums of theabsolute values of the elements in the rowsinMatrix.

Note: All matrix elements must simplify tonumbers. See also colNorm(), page 26.

rowSwap() Catalog >rowSwap(Matrix1, rIndex1, rIndex2) ⇒matrix

Returns Matrix1 with rows rIndex1 andrIndex2 exchanged.

rref() Catalog >rref(Matrix1[, Tol]) ⇒ matrix

Returns the reduced row echelon form ofMatrix1.



rref() Catalog >• If Tol is omitted or not used, the default

tolerance is calculated as:5E−14 •max(dim(Matrix1)) •rowNorm(Matrix1)

Note: See also ref(), page 147.

S

sec() µ keysec(Expr1) ⇒ expression

sec(List1) ⇒ list

Returns the secant of Expr1 or returns alist containing the secants of all elementsin List1.


InDegree anglemode:

sec⁻¹() µ keysec⁻¹(Expr1) ⇒ expression

sec⁻¹(List1) ⇒ list

Returns the angle whose secant is Expr1 orreturns a list containing the inverse secantsof each element of List1.

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

Note: You can insert this function from thekeyboard by typing arcsec(...).

InDegree anglemode:





sech() Catalog >sech(Expr1) ⇒ expression

sech(List1) ⇒ list

Returns the hyperbolic secant of Expr1 orreturns a list containing the hyperbolicsecants of the List1 elements.

sech⁻¹() Catalog >sech⁻¹(Expr1) ⇒ expression

sech⁻¹(List1) ⇒ list

Returns the inverse hyperbolic secant ofExpr1 or returns a list containing theinverse hyperbolic secants of each elementof List1.

Note: You can insert this function from thekeyboard by typing arcsech(...).

In Radian angle andRectangular complexmode:

Send Hub MenuSend exprOrString1 [, exprOrString2] ...

Programming command: Sends one ormore TI-Innovator™ Hub commands to aconnected hub.

exprOrStringmust be a validTI-Innovator™ Hub Command. Typically,exprOrString contains a "SET ..." commandto control a device or a "READ ..." commandto request data.

The arguments are sent to the hub insuccession.

Note: You can use the Send commandwithin a user-defined program but notwithin a function.

Note: See also Get (page 77), GetStr (page84), and eval() (page 61).

Example: Turnon the blue element of thebuilt-in RGB LED for 0.5 seconds.

Example: Request the current value of thehub's built-in light-level sensor. A Getcommand retrieves the value andassigns itto variable lightval.

Example: Senda calculated frequency to thehub's built-in speaker. Use special variableiostr.SendAns to show the hub commandwith the expressionevaluated.

Send Hub Menu

seq() Catalog >seq(Expr, Var, Low, High[, Step]) ⇒ list

Increments Var from Low throughHigh byan increment of Step, evaluates Expr, andreturns the results as a list. The originalcontents of Var are still there after seq() iscompleted.

The default value for Step = 1. Note: To force anapproximate result,

Handheld: Press/·.Windows®: Press Ctrl+Enter.Macintosh®: Press “+Enter.iPad®: Holdenter, and select .

seqGen() Catalog >seqGen(Expr, Var, depVar, {Var0,VarMax}[, ListOfInitTerms

[, VarStep[, CeilingValue]]]) ⇒ list

Generates a list of terms for sequencedepVar(Var)=Expr as follows: Incrementsindependent variable Var from Var0through VarMax by VarStep, evaluatesdepVar(Var) for corresponding values ofVar using the Expr formula andListOfInitTerms, and returns the results asa list.

seqGen(ListOrSystemOfExpr, Var,ListOfDepVars, {Var0, VarMax} [,MatrixOfInitTerms[, VarStep[,CeilingValue]]]) ⇒ matrix

Generate the first 5 terms of the sequence u(n) = u(n-1)2/2, withu(1)=2 andVarStep=1.

Example inwhichVar0=2:



seqGen() Catalog >Generates a matrix of terms for a system(or list) of sequences ListOfDepVars(Var)=ListOrSystemOfExpr as follows:Increments independent variable Var fromVar0 through VarMax by VarStep,evaluates ListOfDepVars(Var) forcorresponding values of Var usingListOrSystemOfExpr formula andMatrixOfInitTerms, and returns the resultsas a matrix.

The original contents of Var are unchangedafter seqGen() is completed.

The default value for VarStep = 1.

Example inwhich initial term is symbolic:

Systemof two sequences:

Note: The Void (_) in the initial termmatrixabove is used to indicate that the initial termfor u1(n) is calculatedusing the explicitsequence formula u1(n)=1/n.

seqn() Catalog >seqn(Expr(u, n[, ListOfInitTerms[, nMax[,CeilingValue]]]) ⇒ list

Generates a list of terms for a sequence u(n)=Expr(u, n) as follows: Increments nfrom 1 through nMax by 1, evaluates u(n)for corresponding values of n using theExpr(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) asfollows: Increments n from 1 through nMaxby 1, evaluates u(n) for correspondingvalues of n using the Expr(n) formula, andreturns the results as a list.

If nMax is missing, nMax is set to 2500

If nMax=0, nMax is set to 2500

Note: seqn() calls seqGen( ) with n0=1 andnstep =1

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

series() Catalog >series(Expr1, Var, Order[, Point]) ⇒expression

series(Expr1, Var, Order[, Point]) |Var>Point⇒ expression

series(Expr1, Var, Order[, Point]) |Var<Point⇒ expression

Returns a generalized truncated powerseries representation of Expr1 expandedabout Point through degree Order. Ordercan be any rational number. The resultingpowers of (Var − Point) can includenegative and/or fractional exponents. Thecoefficients of these powers can includelogarithms of (Var − Point) and otherfunctions of Var that are dominated by allpowers of (Var − Point) having the sameexponent sign.

Point defaults to 0. Point can be ∞ or −∞,in which cases the expansion is throughdegree Order in 1/(Var − Point).

series(...) returns “series(...)” if it is unableto determine such a representation, such asfor essential singularities such as sin(1/z)at z=0, e−1/z at z=0, or ez at z = ∞ or −∞.

If the series or one of its derivatives has ajump discontinuity at Point, the result islikely to contain sub-expressions of theform sign(…) or abs(…) for a real expansionvariable or (-1)floor(…angle(…)…) for a complexexpansion variable, which is one endingwith “_”. If you intend to use the series onlyfor values on one side of Point, thenappend the appropriate one of “| Var >Point”, “| Var < Point”, “| “Var ≥ Point”,or “Var ≤ Point” to obtain a simpler result.

series() can provide symbolicapproximations to indefinite integrals anddefinite integrals for which symbolicsolutions otherwise can't be obtained.



series() Catalog >series() distributes over 1st-argument listsand matrices.

series() is a generalized version of taylor().

As illustrated by the last example to theright, the display routines downstream ofthe result produced by series(...) mightrearrange terms so that the dominant termis not the leftmost one.

Note: See also dominantTerm(), page 55.

setMode() Catalog >setMode(modeNameInteger,settingInteger) ⇒ integersetMode(list) ⇒ integer list

Valid only within a function or program.

setMode(modeNameInteger,settingInteger) temporarily sets modemodeNameInteger to the new settingsettingInteger, and returns an integercorresponding to the original setting of thatmode. The change is limited to the durationof the program/function’s execution.

modeNameInteger specifies which modeyou want to set. It must be one of the modeintegers from the table below.

settingInteger specifies the new setting forthe mode. It must be one of the settingintegers listed below for the specific modeyou are setting.

setMode(list) lets you change multiplesettings. list contains pairs of modeintegers and setting integers. setMode(list)returns a similar list whose integer pairsrepresent the original modes and settings.

If you have saved all mode settings withgetMode(0)→var, you can use setMode(var) to restore those settings until thefunction or program exits. See getMode(),page 83.

Display approximate value of π using thedefault setting for Display Digits, and thendisplay π with a setting of Fix2. Check to seethat the default is restored after theprogramexecutes.

setMode() Catalog >Note: The current mode settings are passedto called subroutines. If any subroutinechanges a mode setting, the mode changewill be lost when control returns to thecalling routine.


ModeName

ModeInteger Setting Integers

DisplayDigits

1 1=Float, 2=Float1, 3=Float2, 4=Float3, 5=Float4, 6=Float5,7=Float6, 8=Float7, 9=Float8, 10=Float9, 11=Float10,12=Float11, 13=Float12, 14=Fix0, 15=Fix1, 16=Fix2,17=Fix3, 18=Fix4, 19=Fix5, 20=Fix6, 21=Fix7, 22=Fix8,23=Fix9, 24=Fix10, 25=Fix11, 26=Fix12

Angle 2 1=Radian, 2=Degree, 3=Gradian

ExponentialFormat

3 1=Normal, 2=Scientific, 3=Engineering

Real orComplex

4 1=Real, 2=Rectangular, 3=Polar

Auto orApprox.

5 1=Auto, 2=Approximate, 3=Exact

VectorFormat

6 1=Rectangular, 2=Cylindrical, 3=Spherical

Base 7 1=Decimal, 2=Hex, 3=Binary

Unitsystem

8 1=SI, 2=Eng/US

shift() Catalog >shift(Integer1[,#ofShifts]) ⇒ integer

Shifts the bits in a binary integer. You canenter Integer1 in any number base; it isconverted automatically to a signed, 64-bitbinary form. If the magnitude of Integer1 istoo large for this form, a symmetric modulooperation brings it within the range. Formore information, see►Base2, page 17.

In Bin basemode:

InHex basemode:



shift() Catalog >If #ofShifts is positive, the shift is to theleft. If #ofShifts is negative, the shift is tothe right. The default is −1 (shift right onebit).

In a right shift, the rightmost bit is droppedand 0 or 1 is inserted to match the leftmostbit. In a left shift, the leftmost bit isdropped and 0 is inserted as the rightmostbit.

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 theBase mode. Leading zeros are not shown.

Important: To enter a binary orhexadecimal number, always use the 0bor0hprefix (zero, not the letter O).

shift(List1[,#ofShifts]) ⇒ list

Returns a copy of List1 shifted right or leftby #ofShifts elements. Does not alter List1.

If #ofShifts is positive, the shift is to theleft. If #ofShifts is negative, the shift is tothe right. The default is −1 (shift right oneelement).

Elements introduced at the beginning orend of list by the shift are set to the symbol“undef”.

InDec basemode:

shift(String1[,#ofShifts]) ⇒ string

Returns a copy of String1 shifted right orleft by #ofShifts characters. Does not alterString1.

If #ofShifts is positive, the shift is to theleft. If #ofShifts is negative, the shift is tothe right. The default is −1 (shift right onecharacter).

shift() Catalog >Characters introduced at the beginning orend of string by the shift are set to a space.

sign() Catalog >sign(Expr1) ⇒ expression

sign(List1) ⇒ listsign(Matrix1) ⇒ matrix

For real and complex Expr1, returnsExpr1/abs(Expr1) when Expr1≠ 0.

Returns 1 if Expr1 is positive. Returns −1 ifExpr1is negative.

sign(0) represents the unit circle in thecomplex domain.

For a list or matrix, returns the signs of allthe elements.

If complex formatmode is Real:

simult() Catalog >simult(coeffMatrix, constVector[, Tol]) ⇒matrix

Returns a column vector that contains thesolutions to a system of linear equations.

Note: See also linSolve(), page 102.

coeffMatrix must be a square matrix thatcontains the coefficients of the equations.

constVector must have the same numberof rows (same dimension) as coeffMatrixand contain the constants.


• If you set the Auto or Approximate modeto Approximate, computations are doneusing floating-point arithmetic.

Solve for x and y:x + 2y = 13x + 4y =−1

The solution is x=−3 and y=2.

Solve:ax + by = 1cx + dy = 2



simult() Catalog >• If Tol is omitted or not used, the default

tolerance is calculated as:5E−14 •max(dim(coeffMatrix))•rowNorm(coeffMatrix)

simult(coeffMatrix, constMatrix[, Tol]) ⇒matrix

Solves multiple systems of linear equations,where each system has the same equationcoefficients but different constants.

Each column in constMatrix must containthe constants for a system of equations.Each column in the resulting matrixcontains the solution for the correspondingsystem.

Solve: x + 2y = 13x + 4y =−1

x + 2y = 23x + 4y =−3

For the first system, x=−3 and y=2. For thesecond system, x=−7 and y=9/2.

►sin Catalog >Expr►sin

Note: You can insert this operator from thecomputer keyboard by typing @>sin.

Represents Expr in terms of sine. This is adisplay conversion operator. It can be usedonly at the end of the entry line.

►sin reduces all powers of cos(...) modulo 1−sin(...)^2so that any remaining powers of sin(...)have exponents in the range (0, 2). Thus,the result will be free of cos(...) if and onlyif cos(...) occurs in the given expression onlyto even powers.

Note: This conversion operator is notsupported in Degree or Gradian Anglemodes. Before using it, make sure that theAngle mode is set to Radians and that Exprdoes not contain explicit references todegree or gradian angles.

sin() µ keysin(Expr1) ⇒ expression InDegree anglemode:

sin() µ keysin(List1) ⇒ list

sin(Expr1) returns the sine of the argumentas an expression.

sin(List1) returns a list of the sines of allelements in List1.

Note: The argument is interpreted as adegree, gradian or radian angle, accordingto the current angle mode. You can use °, g,or r to override the angle mode settingtemporarily.



sin(squareMatrix1) ⇒ squareMatrix

Returns the matrix sine of squareMatrix1.This is not the same as calculating the sineof each element. For information about thecalculation method, refer to cos().



sin⁻¹() µ keysin⁻¹(Expr1) ⇒ expression

sin⁻¹(List1) ⇒ list

sin⁻¹(Expr1) returns the angle whose sineis Expr1 as an expression.

sin⁻¹(List1) returns a list of the inversesines of each element of List1.


InDegree anglemode:





sin⁻¹() µ keyNote: You can insert this function from thekeyboard by typing arcsin(...).

sin⁻¹(squareMatrix1) ⇒ squareMatrix

Returns the matrix inverse sine ofsquareMatrix1. This is not the same ascalculating the inverse sine of eachelement. For information about thecalculation method, refer to cos().


In Radian anglemode andRectangularcomplex formatmode:

sinh() Catalog >sinh(Expr1) ⇒ expression

sinh(List1) ⇒ list

sinh (Expr1) returns the hyperbolic sine ofthe argument as an expression.

sinh (List1) returns a list of the hyperbolicsines of each element of List1.sinh(squareMatrix1) ⇒ squareMatrix

Returns the matrix hyperbolic sine ofsquareMatrix1. This is not the same ascalculating the hyperbolic sine of eachelement. For information about thecalculation method, refer to cos().



sinh⁻¹() Catalog >sinh⁻¹(Expr1) ⇒ expression

sinh⁻¹(List1) ⇒ list

sinh⁻¹(Expr1) returns the inverse hyperbolicsine of the argument as an expression.

sinh⁻¹(List1) returns a list of the inversehyperbolic sines of each element of List1.

sinh⁻¹() Catalog >Note: You can insert this function from thekeyboard by typing arcsinh(...).

sinh⁻¹(squareMatrix1) ⇒ squareMatrix

Returns the matrix inverse hyperbolic sineof squareMatrix1. This is not the same ascalculating the inverse hyperbolic sine ofeach element. For information about thecalculation method, refer to cos().



SinReg Catalog >SinReg X, Y[, [Iterations],[Period][,Category, Include]]

Computes the sinusoidal regression on listsX and Y. A summary of results is stored inthe stat.results variable. (See page 176.)



Iterations is a value that specifies themaximum number of times (1 through 16) asolution will be attempted. If omitted, 8 isused. Typically, larger values result in betteraccuracy but longer execution times, andvice versa.

Period specifies an estimated period. Ifomitted, the difference between values in Xshould be equal and in sequential order. Ifyou specify Period, the differences betweenx values can be unequal.





SinReg Catalog >The output of SinReg is always in radians,regardless of the angle mode setting.



stat.RegEqn Regression Equation: a•sin(bx+c)+d







solve() Catalog >solve(Equation, Var) ⇒ Booleanexpressionsolve(Equation, Var=Guess) ⇒ Booleanexpressionsolve(Inequality, Var) ⇒ Booleanexpression

Returns candidate real solutions of anequation or an inequality for Var. The goalis to return candidates for all solutions.However, there might be equations orinequalities for which the number ofsolutions is infinite.

Solution candidates might not be real finitesolutions for some combinations of valuesfor undefined variables.

solve() Catalog >For the Auto setting of the Auto orApproximate mode, the goal is to produceexact solutions when they are concise, andsupplemented by iterative searches withapproximate arithmetic when exactsolutions are impractical.

Due to default cancellation of the greatestcommon divisor from the numerator anddenominator of ratios, solutions might besolutions only in the limit from one or bothsides.

For inequalities of types ≥, ≤, <, or >,explicit solutions are unlikely unless theinequality is linear and contains only Var.For the Exact mode, portions that cannot besolved are returned as an implicit equationor inequality.

Use the constraint (“|”) operator to restrictthe solution interval and/or other variablesthat occur in the equation or inequality.When you find a solution in one interval,you can use the inequality operators toexclude that interval from subsequentsearches.


false is returned when no real solutions arefound. true is returned if solve() candetermine that any finite real value of Varsatisfies the equation or inequality.

Since solve() always returns a Booleanresult, you can use “and,” “or,” and “not” tocombine results from solve() with eachother or with other Boolean expressions.

Solutions might contain a unique newundefined constant of the form nj with jbeing an integer in the interval 1–255. Suchvariables designate an arbitrary integer.




solve() Catalog >In Real mode, fractional powers having odddenominators denote only the real branch.Otherwise, multiple branched expressionssuch as fractional powers, logarithms, andinverse trigonometric functions denote onlythe principal branch. Consequently, solve()produces only solutions corresponding tothat one real or principal branch.

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

solve(Eqn1 and Eqn2[and …],VarOrGuess1, VarOrGuess2[, …])⇒ Boolean expression

solve(SystemOfEqns, VarOrGuess1,VarOrGuess2[, …])⇒ Boolean expression

solve({Eqn1, Eqn2 [,...]}{VarOrGuess1,VarOrGuess2 [, … ]})⇒ Boolean expression

Returns candidate real solutions to thesimultaneous algebraic equations, whereeach VarOrGuess specifies a variable thatyou want to solve for.

You can separate the equations with theand operator, or you can enter aSystemOfEqns using a template from theCatalog. The number of VarOrGuessarguments must match the number ofequations. Optionally, you can specify aninitial guess for a variable. EachVarOrGuess must have the form:



solve() Catalog >If all of the equations are polynomials andif you do NOT specify any initial guesses,solve() uses the lexical Gröbner/Buchbergerelimination method to attempt todetermine all real solutions.

For example, suppose you have a circle ofradius r at the origin and another circle ofradius r centered where the first circlecrosses the positive x-axis. Use solve() tofind the intersections.

As illustrated by r in the example to theright, simultaneous polynomial equationscan have extra variables that have novalues, but represent given numeric valuesthat could be substituted later.

You can also (or instead) include solutionvariables that do not appear in theequations. For example, you can include zas a solution variable to extend the previousexample to two parallel intersectingcylinders of radius r.

The cylinder solutions illustrate howfamilies of solutions might contain arbitraryconstants of the form ck, where k is aninteger suffix from 1 through 255.

For polynomial systems, computation timeor memory exhaustion may depend stronglyon the order in which you list solutionvariables. If your initial choice exhaustsmemory or your patience, try rearrangingthe variables in the equations and/orvarOrGuess list.


If you do not include any guesses and if anyequation is non-polynomial in any variablebut all equations are linear in the solutionvariables, solve() uses Gaussian eliminationto attempt to determine all real solutions.



solve() Catalog >If a system is neither polynomial in all of itsvariables nor linear in its solution variables,solve() determines at most one solutionusing an approximate iterative method. Todo so, the number of solution variablesmust equal the number of equations, andall other variables in the equations mustsimplify to numbers.


Each solution variable starts at its guessedvalue if there is one; otherwise, it starts at0.0.

Use guesses to seek additional solutionsone by one. For convergence, a guess mayhave to be rather close to a solution.

SortA Catalog >SortA List1[, List2] [, List3]...SortA Vector1[, Vector2] [, Vector3]...

Sorts the elements of the first argument inascending order.

If you include additional arguments, sortsthe elements of each so that their newpositions match the new positions of theelements in the first argument.

All arguments must be names of lists orvectors. All arguments must have equaldimensions.

Empty (void) elements within the firstargument move to the bottom. For moreinformation on empty elements, see page251.

SortD Catalog >SortD List1[, List2][, List3]...SortD Vector1[,Vector2][,Vector3]...

Identical to SortA, except SortD sorts theelements in descending order.

Empty (void) elements within the firstargument move to the bottom. For moreinformation on empty elements, see page251.

►Sphere Catalog >Vector►Sphere

Note: You can insert this operator from thecomputer keyboard by typing @>Sphere.

Displays the row or column vector inspherical form [ρ∠θ∠φ].

Vector must be of dimension 3 and can beeither a row or a column vector.

Note:►Sphere is a display-formatinstruction, not a conversion function. Youcan use it only at the end of an entry line.

Note: To force anapproximate result,


Press ·



►Sphere Catalog >

sqrt() Catalog >sqrt(Expr1) ⇒ expression

sqrt(List1) ⇒ list

Returns the square root of the argument.

For a list, returns the square roots of all theelements in List1.

Note: See also Square root template, page1.

stat.results Catalog >stat.results

Displays results from a statisticscalculation.

The results are displayed as a set of name-value pairs. The specific names shown aredependent on the most recently evaluatedstatistics function or command.

You can copy a name or value and paste itinto other locations.

Note: Avoid defining variables that use thesame names as those used for statisticalanalysis. In some cases, an error conditioncould occur. Variable names used forstatistical analysis are listed in the tablebelow.

stat.astat.AdjR²stat.bstat.b0stat.b1stat.b2stat.b3stat.b4stat.b5stat.b6stat.b7stat.b8stat.b9stat.b10stat.bListstat.χ²stat.cstat.CLowerstat.CLowerListstat.CompListstat.CompMatrixstat.CookDiststat.CUpperstat.CUpperListstat.d

stat.dfDenomstat.dfBlockstat.dfColstat.dfErrorstat.dfInteractstat.dfRegstat.dfNumerstat.dfRowstat.DWstat.estat.ExpMatrixstat.Fstat.FBlockstat.Fcolstat.FInteractstat.FreqRegstat.Frowstat.Leveragestat.LowerPredstat.LowerValstat.mstat.MaxXstat.MaxYstat.MEstat.MedianX

stat.MedianYstat.MEPredstat.MinXstat.MinYstat.MSstat.MSBlockstat.MSColstat.MSErrorstat.MSInteractstat.MSRegstat.MSRowstat.nStat.Çstat.Ç1stat.Ç2stat.ÇDiffstat.PListstat.PValstat.PValBlockstat.PValColstat.PValInteractstat.PValRowstat.Q1Xstat.Q1Y

stat.Q3Xstat.Q3Ystat.rstat.r²stat.RegEqnstat.Residstat.ResidTransstat.σxstat.σystat.σx1stat.σx2stat.Σxstat.Σx²stat.Σxystat.Σystat.Σy²stat.sstat.SEstat.SEListstat.SEPredstat.sResidstat.SEslopestat.spstat.SS

stat.SSBlockstat.SSColstat.SSXstat.SSYstat.SSErrorstat.SSInteractstat.SSRegstat.SSRowstat.tListstat.UpperPredstat.UpperValstat.vstat.v1stat.v2stat.vDiffstat.vListstat.XRegstat.XValstat.XValListstat.w

stat.y

stat.yListstat.YReg

Note: Each time the Lists & Spreadsheet application calculates statistical results, itcopies the “stat.” group variables to a “stat#.” group, where # is a number that isincremented automatically. This lets you maintain previous results whileperforming multiple calculations.

stat.values Catalog >stat.values

Displays a matrix of the values calculated forthe most recently evaluated statisticsfunction or command.

Unlike stat.results, stat.values omits thenames associated with the values.

You can copy a value and paste it into otherlocations.

See the stat.results example.



stDevPop() Catalog >stDevPop(List [, freqList]) ⇒ expression

Returns the population standard deviationof the elements in List.

Each freqList element counts the numberof consecutive occurrences of thecorresponding element in List.

Note:List must have at least two elements.Empty (void) elements are ignored. Formore information on empty elements, seepage 251.

In Radian angle andauto modes:

stDevPop(Matrix1[, freqMatrix]) ⇒matrix

Returns a row vector of the populationstandard deviations of the columns inMatrix1.


Note:Matrix1must have at least two rows.Empty (void) elements are ignored. Formore information on empty elements, seepage 251.

stDevSamp() Catalog >stDevSamp(List[, freqList]) ⇒ expression

Returns the sample standard deviation ofthe elements in List.


Note:List must have at least two elements.Empty (void) elements are ignored. Formore information on empty elements, seepage 251.

stDevSamp() Catalog >stDevSamp(Matrix1[, freqMatrix]) ⇒matrix

Returns a row vector of the samplestandard deviations of the columns inMatrix1.


Note:Matrix1must have at least two rows.Empty (void) elements are ignored. Formore information on empty elements, seepage 251.

Stop Catalog >Stop

Programming command: Terminates theprogram.

Stop is not allowed in functions.


Store See→(store), page 233.

string() Catalog >string(Expr) ⇒ string

Simplifies Expr and returns the result as acharacter string.



subMat() Catalog >subMat(Matrix1[, startRow][, startCol][,endRow][, endCol]) ⇒ matrix

Returns the specified submatrix of Matrix1.

Defaults: startRow=1, startCol=1,endRow=last row, endCol=last column.

Sum (Sigma) See Σ(), page 224.

sum() Catalog >sum(List[, Start[, End]]) ⇒ expression

Returns the sum of all elements in List.

Start and End are optional. They specify arange of elements.

Any void argument produces a void result.Empty (void) elements in List are ignored.For more information on empty elements,see page 251.

sum(Matrix1[, Start[, End]]) ⇒ matrix

Returns a row vector containing the sumsof all elements in the columns inMatrix1.

Start and End are optional. They specify arange of rows.

Any void argument produces a void result.Empty (void) elements inMatrix1 areignored. For more information on emptyelements, see page 251.

sumIf() Catalog >sumIf(List,Criteria[, SumList]) ⇒ value

Returns the accumulated sum of allelements in List that meet the specifiedCriteria. Optionally, you can specify analternate list, sumList, to supply theelements to accumulate.

sumIf() Catalog >List can be an expression, list, or matrix.SumList, if specified, must have the samedimension(s) as List.

Criteria can be:

• A value, expression, or string. Forexample, 34 accumulates only thoseelements in List that simplify to thevalue 34.

• A Boolean expression containing thesymbol ? as a placeholder for eachelement. For example, ?<10 accumulatesonly those elements in List that are lessthan 10.

When a List element meets the Criteria,the element is added to the accumulatingsum. If you include sumList, thecorresponding element from sumList isadded to the sum instead.

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


Note: See also countIf(), page 35.

sumSeq() See Σ(), page 224.

system() Catalog >system(Eqn1[, Eqn2[, Eqn3[, ...]]])

system(Expr1[, Expr2[, Expr3[, ...]]])

Returns a system of equations, formattedas a list. You can also create a system byusing a template.

Note: See also System of equations, page 3.



T

T (transpose) Catalog >Matrix1T ⇒ matrix

Returns the complex conjugate transpose ofMatrix1.

Note: You can insert this operator from thecomputer keyboard by typing @t.

tan() µ keytan(Expr1) ⇒ expression

tan(List1) ⇒ list

tan(Expr1) returns the tangent of theargument as an expression.

tan(List1) returns a list of the tangents ofall elements in List1.

Note: The argument is interpreted as adegree, gradian or radian angle, accordingto the current angle mode. You can use °, gor r to override the angle mode settingtemporarily.

InDegree anglemode:



tan(squareMatrix1) ⇒ squareMatrix

Returns the matrix tangent ofsquareMatrix1. This is not the same ascalculating the tangent of each element.For information about the calculationmethod, refer to cos().


tan() µ keysquareMatrix1must be diagonalizable. Theresult always contains floating-pointnumbers.

tan⁻¹() µ keytan⁻¹(Expr1) ⇒ expression

tan⁻¹(List1) ⇒ list

tan⁻¹(Expr1) returns the angle whosetangent is Expr1 as an expression.

tan⁻¹(List1) returns a list of the inversetangents of each element of List1.


Note: You can insert this function from thekeyboard by typing arctan(...).

InDegree anglemode:



tan⁻¹(squareMatrix1) ⇒ squareMatrix

Returns the matrix inverse tangent ofsquareMatrix1. This is not the same ascalculating the inverse tangent of eachelement. For information about thecalculation method, refer to cos().



tangentLine() Catalog >tangentLine(Expr1,Var,Point) ⇒expression

tangentLine(Expr1,Var=Point) ⇒expression

Returns the tangent line to the curverepresented by Expr1 at the point specifiedin Var=Point.



tangentLine() Catalog >Make sure that the independent variable isnot defined. For example, If f1(x):=5 andx:=3, then tangentLine(f1(x),x,2) returns“false.”

tanh() Catalog >tanh(Expr1) ⇒ expression

tanh(List1) ⇒ list

tanh(Expr1) returns the hyperbolic tangentof the argument as an expression.

tanh(List1) returns a list of the hyperbolictangents of each element of List1.tanh(squareMatrix1) ⇒ squareMatrix

Returns the matrix hyperbolic tangent ofsquareMatrix1. This is not the same ascalculating the hyperbolic tangent of eachelement. For information about thecalculation method, refer to cos().



tanh⁻¹() Catalog >tanh⁻¹(Expr1) ⇒ expression

tanh⁻¹(List1) ⇒ list

tanh⁻¹(Expr1) returns the inversehyperbolic tangent of the argument as anexpression.

tanh⁻¹(List1) returns a list of the inversehyperbolic tangents of each element ofList1.

Note: You can insert this function from thekeyboard by typing arctanh(...).

In Rectangular complex format:

tanh⁻¹(squareMatrix1) ⇒ squareMatrix In Radian anglemode andRectangularcomplex format:

tanh⁻¹() Catalog >Returns the matrix inverse hyperbolictangent of squareMatrix1. This is not thesame as calculating the inverse hyperbolictangent of each element. For informationabout the calculation method, refer to cos().



taylor() Catalog >taylor(Expr1, Var, Order[, Point]) ⇒expression

Returns the requested Taylor polynomial.The polynomial includes non-zero terms ofinteger degrees from zero throughOrder in(Var minus Point). taylor() returns itself ifthere is no truncated power series of thisorder, or if it would require negative orfractional exponents. Use substitutionand/or temporary multiplication by a powerof (Var minus Point) to determine moregeneral power series.

Point defaults to zero and is the expansionpoint.

tCdf() Catalog >tCdf(lowBound,upBound,df) ⇒ number iflowBound and upBound are numbers, list iflowBound and upBound are lists

Computes the Student-t distributionprobability between lowBound and upBoundfor the specified degrees of freedom df.

For P(X ≤ upBound), set lowBound = ⁻∞.



tCollect() Catalog >tCollect(Expr1) ⇒ expression

Returns an expression in which productsand integer powers of sines and cosines areconverted to a linear combination of sinesand cosines of multiple angles, angle sums,and angle differences. The transformationconverts trigonometric polynomials into alinear combination of their harmonics.

Sometimes tCollect() will accomplish yourgoals when the default trigonometricsimplification does not. tCollect() tends toreverse transformations done by tExpand().Sometimes applying tExpand() to a resultfrom tCollect(), or vice versa, in twoseparate steps simplifies an expression.

tExpand() Catalog >tExpand(Expr1) ⇒ expression

Returns an expression in which sines andcosines of integer-multiple angles, anglesums, and angle differences are expanded.Because of the identity (sin(x))2+(cos(x))2=1, there are many possible equivalentresults. Consequently, a result might differfrom a result shown in other publications.

Sometimes tExpand() will accomplish yourgoals when the default trigonometricsimplification does not. tExpand() tends toreverse transformations done by tCollect().Sometimes applying tCollect() to a resultfrom tExpand(), or vice versa, in twoseparate steps simplifies an expression.

Note: Degree-mode scaling by π/180interferes with the ability of tExpand() torecognize expandable forms. For bestresults, tExpand() should be used in Radianmode.

Text Catalog >TextpromptString[, DispFlag]

Programming command: Pauses theprogram and displays the character stringpromptString in a dialog box.

When the user selects OK, programexecution continues.

The optional flag argument can be anyexpression.

• IfDispFlag is omitted or evaluates to 1,the text message is added to theCalculator history.

• IfDispFlag evaluates to 0, the textmessage is not added to the history.

If the program needs a typed response fromthe user, refer to Request, page 149, orRequestStr, page 151.

Note: You can use this command within auser-defined program but not within afunction.

Define a program that pauses to displayeachof five randomnumbers in a dialogbox.

Within the Prgm...EndPrgm template,complete each line by pressing@ insteadof·. On the computer keyboard, holddownAlt andpress Enter.

Define text_demo()=Prgm For i,1,5 strinfo:=”Random number “ &string(rand(i)) Text strinfo EndForEndPrgm

Run the program:

text_demo()

Sample of one dialog box:

Then See If, page 86.

tInterval Catalog >tInterval List[, Freq[, CLevel]]

(Data list input)

tInterval v, sx, n[, CLevel]


Computes a t confidence interval. Asummary of results is stored in thestat.results variable. (See page 176.)



tInterval Catalog >For information on the effect of emptyelements in a list, see “Empty (Void)Elements,” page 251.


stat.CLower, stat.CUpper Confidence interval for anunknownpopulationmean

stat.v Samplemeanof the data sequence from the normal randomdistribution

stat.ME Margin of error


stat.σx Sample standarddeviation

stat.n Lengthof the data sequencewith samplemean

tInterval_2Samp Catalog >tInterval_2Samp List1,List2[,Freq1[,Freq2[,CLevel[,Pooled]]]]

(Data list input)

tInterval_2Samp v1,sx1,n1,v2,sx2,n2[,CLevel[,Pooled]]


Computes a two-sample t confidenceinterval. A summary of results is stored inthe stat.results variable. (See page 176.)

Pooled=1 pools variances; Pooled=0 doesnot pool variances.



stat.CLower,stat.CUpper

Confidence interval containing confidence level probability of distribution

stat.v1-v2 Samplemeans of the data sequences from the normal randomdistribution




stat.v1, stat.v2 Samplemeans of the data sequences from the normal randomdistribution

stat.σx1, stat.σx2 Sample standarddeviations for List 1 and List 2

stat.n1, stat.n2 Number of samples in data sequences

stat.sp The pooled standarddeviation. CalculatedwhenPooled = YES

tmpCnv() Catalog >tmpCnv(Expr_°tempUnit, _°tempUnit2)⇒ expression _°tempUnit2

Converts a temperature value specified byExpr from one unit to another. Validtemperature units are:

_°C Celsius_°F Fahrenheit_°K Kelvin_°R Rankine

To type °, select it from the Catalogsymbols.

to type _ , press/_.

For example, 100_°C converts to 212_°F.

To convert a temperature range, useΔtmpCnv() instead.

Note: You canuse the Catalog to selecttemperature units.

ΔtmpCnv() Catalog >ΔtmpCnv(Expr_°tempUnit, _°tempUnit2)⇒ expression _°tempUnit2

Note: You can insert this function from thekeyboard by typing deltaTmpCnv(...).

Converts a temperature range (thedifference between two temperaturevalues) specified by Expr from one unit toanother. Valid temperature units are:

_°C Celsius_°F Fahrenheit_°K Kelvin_°R Rankine

Note: You canuse the Catalog to selecttemperature units.



ΔtmpCnv() Catalog >To enter °, select it from the SymbolPalette or type @d.

To type _ , press/_.

1_°C and 1_°K have the same magnitude,as do 1_°F and 1_°R. However, 1_°C is 9/5as large as 1_°F.

For example, a 100_°C range (from 0_°C to100_°C) is equivalent to a 180_°F range.

To convert a particular temperature valueinstead of a range, use tmpCnv().

tPdf() Catalog >tPdf(XVal,df) ⇒ number if XVal is anumber, list if XVal is a list

Computes the probability density function(pdf) for the Student-t distribution at aspecified x value with specified degrees offreedom df.

trace() Catalog >trace(squareMatrix) ⇒ expression

Returns the trace (sum of all the elementson the main diagonal) of squareMatrix.

Try Catalog >Try block1Else block2EndTry

Executes block1 unless an error occurs.Program execution transfers to block2 if anerror occurs in block1. System variableerrCode contains the error code to allowthe program to perform error recovery. Fora list of error codes, see “Error codes andmessages,” page 261.

block1 and block2 can be either a singlestatement or a series of statementsseparated with the “:” character.


To see the commands Try, ClrErr, andPassErr in operation, enter the eigenvals()program shown at the right. Run theprogram by executing each of the followingexpressions.

Note: See also ClrErr, page 25, and PassErr,page 131.

Define eigenvals(a,b)=Prgm© Programeigenvals(A,B) displayseigenvalues of A•B

Try Disp "A= ",a Disp "B= ",b Disp " "

Disp "Eigenvalues of A•B are:",eigVl(a*b)

Else If errCode=230 Then Disp "Error: Product of A•B must be asquarematrix" ClrErr Else PassErr EndIfEndTry

EndPrgm



tTest Catalog >tTest μ0,List[,Freq[,Hypoth]]

(Data list input)

tTest μ0,v,sx,n,[Hypoth]


Performs a hypothesis test for a singleunknown population mean μ when thepopulation standard deviation σ is unknown.A summary of results is stored in thestat.results variable. (See page 176.)

Test H0: μ = μ0, against one of the

following:

For Ha: μ < μ0, set Hypoth<0

For Ha: μ ≠ μ0 (default), set Hypoth=0

For Ha: μ > μ0, set Hypoth>0



stat.t (v −μ0) / (stdev / sqrt(n))



stat.v Samplemeanof the data sequence inList

stat.sx Sample standarddeviationof the data sequence

stat.n Size of the sample

tTest_2Samp Catalog >tTest_2Samp List1,List2[,Freq1[,Freq2[,Hypoth[,Pooled]]]]

(Data list input)

tTest_2Samp v1,sx1,n1,v2,sx2,n2[,Hypoth[,Pooled]]


tTest_2Samp Catalog >Computes a two-sample t test. A summaryof results is stored in the stat.resultsvariable. (See page 176.)

Test H0: μ1 = μ2, against one of the

following:

For Ha: μ1< μ2, set Hypoth<0

For Ha: μ1≠ μ2 (default), set Hypoth=0

For Ha: μ1> μ2, set Hypoth>0

Pooled=1 pools variancesPooled=0 does not pool variances



stat.t Standardnormal value computed for the difference ofmeans


stat.df Degrees of freedom for the t-statistic

stat.v1, stat.v2 Samplemeans of the data sequences inList 1 andList 2

stat.sx1, stat.sx2 Sample standarddeviations of the data sequences inList 1 andList 2


stat.sp The pooled standarddeviation. CalculatedwhenPooled=1.

tvmFV() Catalog >tvmFV(N,I,PV,Pmt,[PpY],[CpY],[PmtAt])⇒ value

Financial function that calculates the futurevalue of money.

Note: Arguments used in the TVM functionsare described in the table of TVMarguments, page 195. See also amortTbl(),page 8.

tvmI() Catalog >tvmI(N,PV,Pmt,FV,[PpY],[CpY],[PmtAt])⇒ value



tvmI() Catalog >Financial function that calculates theinterest rate per year.


tvmN() Catalog >tvmN(I,PV,Pmt,FV,[PpY],[CpY],[PmtAt])⇒ value

Financial function that calculates thenumber of payment periods.


tvmPmt() Catalog >tvmPmt(N,I,PV,FV,[PpY],[CpY],[PmtAt])⇒ value

Financial function that calculates theamount of each payment.


tvmPV() Catalog >tvmPV(N,I,Pmt,FV,[PpY],[CpY],[PmtAt])⇒ value

Financial function that calculates thepresent value.


TVMargument*

Description Data type

N Number of payment periods real number

I Annual interest rate real number

PV Present value real number

Pmt Payment amount real number

FV Future value real number

PpY Payments per year, default=1 integer > 0

CpY Compounding periods per year, default=1 integer > 0

PmtAt Payment due at the endor beginning of eachperiod,default=end

integer (0=end,1=beginning)

* These time-value-of-money argument names are similar to the TVM variable names(such as tvm.pv and tvm.pmt) that are used by the Calculator application’s financesolver. Financial functions, however, do not store their argument values or results tothe TVM variables.

TwoVar Catalog >TwoVar X, Y[, [Freq][, Category, Include]]

Calculates the TwoVar statistics. A summaryof results is stored in the stat.resultsvariable. (See page 176.)




Category is a list of numeric category codesfor the corresponding X and Y data.




TwoVar Catalog >An empty (void) element in any of the listsX, Freq, or Category results in a void forthe corresponding element of all those lists.An empty element in any of the lists X1through X20 results in a void for thecorresponding element of all those lists. Formore information on empty elements, seepage 251.


stat.v Meanof x values

stat.Σx Sumof x values

stat.Σx2 Sumof x2 values

stat.sx Sample standarddeviationof x

stat.σx Population standarddeviationof x

stat.n Number of data points

stat.w Meanof y values

stat.Σy Sumof y values

stat.Σy2 Sumof y2 values

stat.sy Sample standarddeviationof y

stat.σy Population standarddeviationof y

stat.Σxy Sumof x•y values


stat.MinX Minimumof x values

stat.Q1X 1stQuartile of x

stat.MedianX Medianof x

stat.Q3X 3rdQuartile of x

stat.MaxX Maximumof x values

stat.MinY Minimumof y values

stat.Q1Y 1stQuartile of y

stat.MedY Medianof y

stat.Q3Y 3rdQuartile of y


stat.MaxY Maximumof y values

stat.Σ(x-v)2 Sumof squares of deviations from themeanof x

stat.Σ(y-w)2 Sumof squares of deviations from themeanof y

U

unitV() Catalog >unitV(Vector1) ⇒ vector

Returns either a row- or column-unit vector,depending on the form of Vector1.

Vector1must be either a single-row matrixor a single-column matrix.


unLock Catalog >unLock Var1[, Var2] [, Var3] ...unLock Var.

Unlocks the specified variables or variablegroup. Locked variables cannot be modifiedor deleted.

See Lock, page 106, and getLockInfo(), page82.



V

varPop() Catalog >varPop(List[, freqList]) ⇒ expression

Returns the population variance of List.


Note: List must contain at least twoelements.

If an element in either list is empty (void),that element is ignored, and thecorresponding element in the other list isalso ignored. For more information onempty elements, see page 251.

varSamp() Catalog >varSamp(List[, freqList]) ⇒ expression

Returns the sample variance of List.


Note: List must contain at least twoelements.

If an element in either list is empty (void),that element is ignored, and thecorresponding element in the other list isalso ignored. For more information onempty elements, see page 251.

varSamp(Matrix1[, freqMatrix]) ⇒matrix

Returns a row vector containing the samplevariance of each column inMatrix1.


varSamp() Catalog >If an element in either matrix is empty(void), that element is ignored, and thecorresponding element in the other matrixis also ignored. For more information onempty elements, see page 251.

Note:Matrix1must contain at least tworows.

W

Wait Catalog >Wait timeInSeconds

Suspends execution for a period oftimeInSeconds seconds.

Wait is particularly useful in a program thatneeds a brief delay to allow requested datato become available.

The argument timeInSeconds must be anexpression that simplifies to a decimal valuein the range 0 through 100. The commandrounds this value up to the nearest 0.1seconds.

To cancel a Wait that is in progress,




• iPad®: The app displays a prompt. You cancontinue waiting or cancel.

Note: You can use the Wait command withina user-defined program but not within afunction.

To wait 4 seconds:

Wait 4

To wait 1/2 second:

Wait 0.5

To wait 1.3 seconds using the variableseccount:seccount:=1.3Wait seccount

This example switches a green LEDon for0.5 seconds and then switches it off.

Send "SET GREEN 1 ON"Wait 0.5Send "SET GREEN 1 OFF"



warnCodes () Catalog >warnCodes(Expr1, StatusVar) ⇒expression

Evaluates expression Expr1, returns theresult, and stores the codes of anygenerated warnings in the StatusVar listvariable. If no warnings are generated, thisfunction assigns StatusVar an empty list.

Expr1 can be any valid TI-Nspire™ orTI-Nspire™ CAS math expression. Youcannot use a command or assignment asExpr1.

StatusVar must be a valid variable name.

For a list of warning codes and associatedmessages, see page 269.


when() Catalog >when(Condition, trueResult [, falseResult][, unknownResult]) ⇒ expression

Returns trueResult, falseResult, orunknownResult, depending on whetherCondition is true, false, or unknown.Returns the input if there are too fewarguments to specify the appropriate result.

Omit both falseResult and unknownResultto make an expression defined only in theregion where Condition is true.Use an undef falseResult to define anexpression that graphs only on an interval.

when() is helpful for defining recursivefunctions.

While Catalog >While Condition BlockEndWhile

Executes the statements in Block as longas Condition is true.

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


X

xor Catalog >BooleanExpr1 xor BooleanExpr2 returnsBoolean expressionBooleanList1xor BooleanList2 returns BooleanlistBooleanMatrix1xor BooleanMatrix2 returns Booleanmatrix

Returns true if BooleanExpr1 is true andBooleanExpr2 is false, or vice versa.

Returns false if both arguments are true orif both are false. Returns a simplifiedBoolean expression if either of thearguments cannot be resolved to true orfalse.

Note: See or, page 129.

Integer1 xor Integer2⇒ integer

Compares two real integers bit-by-bit usingan xor operation. Internally, both integersare converted to signed, 64-bit binarynumbers. When corresponding bits arecompared, the result is 1 if either bit (butnot both) is 1; the result is 0 if both bits are0 or both bits are 1. The returned valuerepresents the bit results, and is displayedaccording to the Base mode.

InHex basemode:


In Bin basemode:



xor Catalog >You can enter the integers in any numberbase. For a binary or hexadecimal entry, youmust use the 0b or 0h prefix, respectively.Without a prefix, integers are treated asdecimal (base 10).


Note: See or, page 129.


Z

zeros() Catalog >zeros(Expr, Var) ⇒ list

zeros(Expr, Var=Guess) ⇒ list

Returns a list of candidate real values ofVar that make Expr=0. zeros() does this bycomputing exp►list(solve(Expr=0,Var),Var).For some purposes, the result form forzeros() is more convenient than that ofsolve(). However, the result form of zeros()cannot express implicit solutions, solutionsthat require inequalities, or solutions thatdo not involve Var.

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

zeros({Expr1, Expr2},{VarOrGuess1, VarOrGuess2 [, … ]}) ⇒matrix

Returns candidate real zeros of thesimultaneous algebraic expressions, whereeach VarOrGuess specifies an unknownwhose value you seek.

Optionally, you can specify an initial guessfor a variable. Each VarOrGuess must havethe form:

zeros() Catalog >variable– or –variable = real or non-real number


If all of the expressions are polynomials andif you do NOT specify any initial guesses,zeros() uses the lexical Gröbner/Buchbergerelimination method to attempt todetermine all real zeros.

For example, suppose you have a circle ofradius r at the origin and another circle ofradius r centered where the first circlecrosses the positive x-axis. Use zeros() tofind the intersections.

As illustrated by r in the example to theright, simultaneous polynomial expressionscan have extra variables that have novalues, but represent given numeric valuesthat could be substituted later.

Each row of the resulting matrix representsan alternate zero, with the componentsordered the same as the varOrGuess list.To extract a row, index the matrix by [row].

Extract row2:

You can also (or instead) include unknownsthat do not appear in the expressions. Forexample, you can include z as an unknownto extend the previous example to twoparallel intersecting cylinders of radius r.The cylinder zeros illustrate how families ofzeros might contain arbitrary constants inthe form ck, where k is an integer suffixfrom 1 through 255.

For polynomial systems, computation timeor memory exhaustion may depend stronglyon the order in which you list unknowns. Ifyour initial choice exhausts memory or yourpatience, try rearranging the variables inthe expressions and/or varOrGuess list.



zeros() Catalog >If you do not include any guesses and if anyexpression is non-polynomial in any variablebut all expressions are linear in theunknowns, zeros() uses Gaussianelimination to attempt to determine all realzeros.

If a system is neither polynomial in all of itsvariables nor linear in its unknowns, zeros()determines at most one zero using anapproximate iterative method. To do so, thenumber of unknowns must equal thenumber of expressions, and all othervariables in the expressions must simplifyto numbers.

Each unknown starts at its guessed value ifthere is one; otherwise, it starts at 0.0.

Use guesses to seek additional zeros one byone. For convergence, a guess may have tobe rather close to a zero.

zInterval Catalog >zInterval σ,List[,Freq[,CLevel]]

(Data list input)

zInterval σ,v,n [,CLevel]


Computes a z confidence interval. Asummary of results is stored in thestat.results variable. (See page 176.)



stat.CLower, stat.CUpper Confidence interval for anunknownpopulationmean

stat.x Samplemeanof the data sequence from the normal randomdistribution


stat.sx Sample standarddeviation


stat.n Lengthof the data sequencewith samplemean

stat.σ Knownpopulation standarddeviation for data sequenceList

zInterval_1Prop Catalog >zInterval_1Prop x,n [,CLevel]

Computes a one-proportion z confidenceinterval. A summary of results is stored inthe stat.results variable. (See page 176.)

x is a non-negative integer.



stat.CLower, stat.CUpper Confidence interval containing confidence level probability of distribution

stat.Ç The calculatedproportionof successes


stat.n Number of samples in data sequence

zInterval_2Prop Catalog >zInterval_2Prop x1,n1,x2,n2[,CLevel]

Computes a two-proportion z confidenceinterval. A summary of results is stored inthe stat.results variable. (See page 176.)

x1 and x2 are non-negative integers.



stat.CLower, stat.CUpper Confidence interval containing confidence level probability of distribution

stat.Ç Diff The calculateddifference betweenproportions





stat.Ç1 First sample proportion estimate

stat.Ç2 Second sample proportion estimate

stat.n1 Sample size in data sequence one

stat.n2 Sample size in data sequence two

zInterval_2Samp Catalog >zInterval_2Samp σ1,σ2 ,List1,List2[,Freq1[,Freq2,[CLevel]]]

(Data list input)

zInterval_2Samp σ1,σ2,v1,n1,v2,n2[,CLevel]


Computes a two-sample z confidenceinterval. A summary of results is stored inthe stat.results variable. (See page 176.)



stat.CLower,stat.CUpper

Confidence interval containing confidence level probability of distribution

stat.x1-x2 Samplemeans of the data sequences from the normal randomdistribution


stat.x1, stat.x2 Samplemeans of the data sequences from the normal randomdistribution

stat.σx1, stat.σx2 Sample standarddeviations for List 1 andList 2

stat.n1, stat.n2 Number of samples in data sequences

stat.r1, stat.r2 Knownpopulation standarddeviations for data sequenceList 1 andList2

zTest Catalog >zTest μ0,σ,List,[Freq[,Hypoth]]

zTest Catalog >(Data list input)

zTest μ0,σ,v,n[,Hypoth]


Performs a z test with frequency freqlist. Asummary of results is stored in thestat.results variable. (See page 176.)

Test H0: μ = μ0, against one of the

following:

For Ha: μ < μ0, set Hypoth<0

For Ha: μ ≠ μ0 (default), set Hypoth=0

For Ha: μ > μ0, set Hypoth>0



stat.z (x −μ0) / (σ / sqrt(n))

stat.P Value Least probability atwhich the null hypothesis canbe rejected

stat.x Samplemeanof the data sequence inList

stat.sx Sample standarddeviationof the data sequence. Only returned forData input.


zTest_1Prop Catalog >


stat.p0 Hypothesizedpopulationproportion

stat.z Standardnormal value computed for the proportion


stat.Ç Estimated sample proportion


zTest_2Prop Catalog >zTest_2Prop x1,n1,x2,n2[,Hypoth]



zTest_2Prop Catalog >Computes a two-proportion z test. Asummary of results is stored in thestat.results variable. (See page 176.)

x1 and x2 are non-negative integers.

Test H0: p1 = p2, against one of the

following:

For Ha: p1 > p2, set Hypoth>0

For Ha: p1 ≠ p2 (default), set Hypoth=0

For Ha: p < p0, set Hypoth<0



stat.z Standardnormal value computed for the difference of proportions


stat.Ç1 First sample proportion estimate

stat.Ç2 Second sample proportion estimate

stat.Ç Pooled sample proportion estimate

stat.n1, stat.n2 Number of samples taken in trials 1 and2

zTest_2Samp Catalog >zTest_2Samp σ1,σ2 ,List1,List2[,Freq1[,Freq2[,Hypoth]]]

(Data list input)

zTest_2Samp σ1,σ2,v1,n1,v2,n2[,Hypoth]


Computes a two-sample z test. A summaryof results is stored in the stat.resultsvariable. (See page 176.)

Test H0: μ1 = μ2, against one of the

following:

For Ha: μ1 < μ2, set Hypoth<0

For Ha: μ1 ≠ μ2 (default), set Hypoth=0

For Ha: μ1 > μ2, Hypoth>0

zTest_2Samp Catalog >For information on the effect of emptyelements in a list, see “Empty (Void)Elements,” page 251.


stat.z Standardnormal value computed for the difference ofmeans


stat.x1, stat.x2 Samplemeans of the data sequences inList1 andList2

stat.sx1, stat.sx2 Sample standarddeviations of the data sequences inList1 andList2



210 Symbols

Symbols

+ (add) + keyExpr1 + Expr2⇒ expression

Returns the sum of the two arguments.

List1 + List2⇒ list

Matrix1 +Matrix2⇒ matrix

Returns a list (or matrix) containing thesums of corresponding elements in List1and List2 (orMatrix1 andMatrix2).

Dimensions of the arguments must beequal.

Expr + List1⇒ list

List1 + Expr⇒ list

Returns a list containing the sums of Exprand each element in List1.Expr +Matrix1⇒ matrix

Matrix1 + Expr⇒ matrix

Returns a matrix with Expr added to eachelement on the diagonal of Matrix1.Matrix1must be square.

Note: Use .+ (dot plus) to add an expressionto each element.

− (subtract) - keyExpr1 − Expr2⇒ expression

Returns Expr1minus Expr2.

List1 −List2⇒ list

Matrix1 −Matrix2 ⇒ matrix

− (subtract) - keySubtracts each element in List2 (orMatrix2) from the corresponding elementin List1 (orMatrix1), and returns theresults.

Dimensions of the arguments must beequal.

Expr − List1⇒ list

List1 − Expr⇒ list

Subtracts each List1 element from Expr orsubtracts Expr from each List1 element,and returns a list of the results.

Expr −Matrix1⇒ matrix

Matrix1 − Expr⇒ matrix

Expr −Matrix1 returns a matrix of Exprtimes the identity matrix minusMatrix1. Matrix1must be square.

Matrix1 − Expr returns a matrix of Exprtimes the identity matrix subtracted fromMatrix1. Matrix1must be square.

Note: Use .− (dot minus) to subtract anexpression from each element.

• (multiply) r keyExpr1•Expr2⇒ expression

Returns the product of the two arguments.

List1•List2⇒ list

Returns a list containing the products of thecorresponding elements in List1 and List2.

Dimensions of the lists must be equal.

Matrix1•Matrix2⇒ matrix

Returns the matrix product of Matrix1 andMatrix2.

The number of columns inMatrix1mustequal the number of rows inMatrix2.

Symbols 211

212 Symbols

• (multiply) r keyExpr •List1⇒ list

List1•Expr⇒ list

Returns a list containing the products ofExpr and each element in List1.

Expr •Matrix1⇒ matrix

Matrix1•Expr⇒ matrix

Returns a matrix containing the products ofExpr and each element inMatrix1.

Note: Use .•(dot multiply) to multiply anexpression by each element.

⁄ (divide) p keyExpr1 ⁄ Expr2⇒ expression

Returns the quotient of Expr1 divided byExpr2.

Note: See also Fraction template, page 1.

List1 ⁄ List2⇒ list

Returns a list containing the quotients ofList1 divided by List2.

Dimensions of the lists must be equal.

Expr ⁄ List1⇒ list

List1 ⁄ Expr⇒ list

Returns a list containing the quotients ofExpr divided by List1 orList1 divided byExpr.Matrix1 ⁄ Expr⇒ matrix

Returns a matrix containing the quotientsof Matrix1 ⁄ Expr.

Matrix1 ⁄ Value⇒ matrix

⁄ (divide) p keyNote: Use . ⁄ (dot divide) to divide anexpression by each element.

^ (power) l keyExpr1 ^ Expr2⇒ expression

List1 ^ List2⇒ list

Returns the first argument raised to thepower of the second argument.

Note: See also Exponent template, page 1.

For a list, returns the elements in List1raised to the power of the correspondingelements in List2.

In the real domain, fractional powers thathave reduced exponents with odddenominators use the real branch versusthe principal branch for complex mode.

Expr ^ List1⇒ list

Returns Expr raised to the power of theelements in List1.List1 ^ Expr⇒ list

Returns the elements in List1 raised to thepower of Expr.squareMatrix1 ^ integer⇒ matrix

Returns squareMatrix1 raised to theinteger power.

squareMatrix1must be a square matrix.

If integer = −1, computes the inversematrix.If integer < −1, computes the inversematrix to an appropriate positive power.

Symbols 213

214 Symbols

x2 (square) q keyExpr12⇒ expression

Returns the square of the argument.

List12 ⇒ list

Returns a list containing the squares of theelements in List1.

squareMatrix12 ⇒ matrix

Returns the matrix square ofsquareMatrix1. This is not the same ascalculating the square of each element. Use.^2 to calculate the square of each element.

.+ (dot add) ^+ keysMatrix1 .+Matrix2⇒ matrix

Expr .+Matrix1⇒ matrix

Matrix1.+Matrix2 returns a matrix that isthe sum of each pair of correspondingelements inMatrix1 andMatrix2.

Expr .+ Matrix1 returns a matrix that isthe sum of Expr and each element inMatrix1.

.⁻(dot subt.) ^- keysMatrix1 .−Matrix2⇒ matrix

Expr .−Matrix1⇒matrix

Matrix1.− Matrix2 returns a matrix that isthe difference between each pair ofcorresponding elements inMatrix1 andMatrix2.

Expr .− Matrix1 returns a matrix that isthe difference of Expr and each element inMatrix1.

.

.•(dot mult.) ^r keysMatrix1 .• Matrix2⇒ matrix

Expr .• Matrix1⇒ matrix

Matrix1.• Matrix2 returns a matrix that isthe product of each pair of correspondingelements inMatrix1 andMatrix2.

Expr .• Matrix1 returns a matrixcontaining the products of Expr and eachelement inMatrix1.

. ⁄ (dot divide) ^p keysMatrix1. ⁄Matrix2⇒ matrix

Expr . ⁄Matrix1⇒ matrix

Matrix1 . ⁄Matrix2 returns a matrix that isthe quotient of each pair of correspondingelements inMatrix1 andMatrix2.

Expr . ⁄ Matrix1 returns a matrix that isthe quotient of Expr and each element inMatrix1.

.^ (dot power) ^l keysMatrix1 .^Matrix2⇒ matrix

Expr . ^Matrix1⇒ matrix

Matrix1.^ Matrix2 returns a matrix whereeach element inMatrix2 is the exponentfor the corresponding element inMatrix1.

Expr .^ Matrix1 returns a matrix whereeach element inMatrix1 is the exponentfor Expr.

− (negate) v key−Expr1 ⇒ expression

−List1⇒ list

−Matrix1⇒ matrix

Symbols 215

216 Symbols

− (negate) v keyReturns the negation of the argument.

For a list or matrix, returns all the elementsnegated.

If the argument is a binary or hexadecimalinteger, the negation gives the two’scomplement.

In Bin base mode:



% (percent) /k keysExpr1% ⇒ expression

List1% ⇒ list

Matrix1% ⇒ matrix

Returns

For a list or matrix, returns a list or matrixwith each element divided by 100.



= (equal) = keyExpr1=Expr2⇒ Boolean expression

List1=List2⇒ Boolean list

Matrix1=Matrix2⇒ Boolean matrix

Returns true if Expr1 is determined to beequal to Expr2.

Returns false if Expr1 is determined to notbe equal to Expr2.

Anything else returns a simplified form ofthe equation.


Example function that uses math testsymbols: =, ≠, <, ≤, >, ≥

= (equal) = keyNote for entering the example: Forinstructions on entering multi-line programand function definitions, refer to theCalculator section of your productguidebook.

Result of graphing g(x)

≠ (not equal) /= keysExpr1≠Expr2⇒ Boolean expression

List1≠List2⇒ Boolean list

Matrix1≠Matrix2⇒ Boolean matrix

Returns true if Expr1 is determined to benot equal to Expr2.

Returns false if Expr1 is determined to beequal to Expr2.



Note: You can insert this operator from thekeyboard by typing /=

See “=” (equal) example.

< (less than) /= keysExpr1<Expr2⇒ Boolean expression

List1<List2⇒ Boolean list

Matrix1<Matrix2⇒ Boolean matrix

Returns true if Expr1 is determined to beless than Expr2.


Symbols 217

218 Symbols

< (less than) /= keysReturns false if Expr1 is determined to begreater than or equal to Expr2.



≤ (less or equal) /= keysExpr1≤Expr2⇒ Boolean expression

List1≤List2⇒ Boolean list

Matrix1 ≤Matrix2⇒ Boolean matrix

Returns true if Expr1 is determined to beless than or equal to Expr2.

Returns false if Expr1 is determined to begreater than Expr2.



Note: You can insert this operator from thekeyboard by typing <=


> (greater than) /= keysExpr1>Expr2⇒ Boolean expression

List1>List2⇒ Boolean list

Matrix1>Matrix2⇒ Boolean matrix

Returns true if Expr1 is determined to begreater than Expr2.

Returns false if Expr1 is determined to beless than or equal to Expr2.



> (greater than) /= keysFor lists and matrices, returns comparisonselement by element.

≥ (greater or equal) /= keysExpr1≥Expr2⇒ Boolean expression

List1≥List2⇒ Boolean list

Matrix1 ≥Matrix2⇒ Boolean matrix

Returns true if Expr1 is determined to begreater than or equal to Expr2.

Returns false if Expr1 is determined to beless than Expr2.



Note: You can insert this operator from thekeyboard by typing >=


⇒ (logical implication) /= keysBooleanExpr1⇒ BooleanExpr2 returnsBoolean expression

BooleanList1⇒ BooleanList2 returnsBoolean list

BooleanMatrix1⇒ BooleanMatrix2returns Boolean matrix

Integer1⇒ Integer2 returns Integer

Evaluates the expression not <argument1>or <argument2> and returns true, false, or asimplified form of the equation.


Note: You can insert this operator from thekeyboard by typing =>

Symbols 219

220 Symbols

⇔ (logical double implication, XNOR) /= keysBooleanExpr1⇔ BooleanExpr2 returnsBoolean expression

BooleanList1⇔ BooleanList2 returnsBoolean list

BooleanMatrix1⇔ BooleanMatrix2returns Boolean matrix

Integer1⇔ Integer2 returns Integer

Returns the negation of an XOR Booleanoperation on the two arguments. Returnstrue, false, or a simplified form of theequation.


Note: You can insert this operator from thekeyboard by typing <=>

! (factorial) º keyExpr1! ⇒ expression

List1! ⇒ list

Matrix1! ⇒ matrix

Returns the factorial of the argument.

For a list or matrix, returns a list or matrixof factorials of the elements.

& (append) /k keysString1 & String2⇒ string

Returns a text string that is String2appended to String1.

d() (derivative) Catalog >d(Expr1, Var[, Order]) ⇒ expression

d(List1, Var[, Order]) ⇒ list

d(Matrix1,Var[, Order]) ⇒ matrix

Returns the first derivative of the firstargument with respect to variable Var.

Order, if included, must be an integer. Ifthe order is less than zero, the result will bean anti-derivative.

Note: You can insert this function from thekeyboard by typing derivative(...).

d() does not follow the normal evaluationmechanism of fully simplifying itsarguments and then applying the functiondefinition to these fully simplifiedarguments. Instead, d() performs thefollowing steps:

1. Simplify the second argument only tothe extent that it does not lead to anon-variable.

2. Simplify the first argument only to theextent that it does recall any storedvalue for the variable determined bystep 1.

3. Determine the symbolic derivative ofthe result of step 2 with respect to thevariable from step 1.

If the variable from step 1 has a storedvalue or a value specified by the constraint(“|”) operator, substitute that value intothe result from step 3.

Note: See also First derivative, page 5;Second derivative, page 6; orNth derivative, page 6.

∫() (integral) Catalog >∫(Expr1, Var[,Lower,Upper]) ⇒expression

∫(Expr1,Var[,Constant]) ⇒ expression

Symbols 221

222 Symbols

∫() (integral) Catalog >Returns the integral of Expr1 with respectto the variable Var from Lower toUpper.

Note: See also Definite or Indefinite integraltemplate, page 6.

Note: You can insert this function from thekeyboard by typing integral(...).

If Lower andUpper are omitted, returns ananti-derivative. A symbolic constant ofintegration is omitted unless you providethe Constant argument.

Equally valid anti-derivatives might differ bya numeric constant. Such a constant mightbe disguised—particularly when an anti-derivative contains logarithms or inversetrigonometric functions. Moreover,piecewise constant expressions aresometimes added to make an anti-derivative valid over a larger interval thanthe usual formula.

∫() returns itself for pieces of Expr1 that itcannot determine as an explicit finitecombination of its built-in functions andoperators.

When you provide Lower andUpper, anattempt is made to locate anydiscontinuities or discontinuous derivativesin the interval Lower < Var < Upper and tosubdivide the interval at those places.

For the Auto setting of the Auto orApproximate mode, numerical integration isused where applicable when an anti-derivative or a limit cannot be determined.

For the Approximate setting, numericalintegration is tried first, if applicable. Anti-derivatives are sought only where suchnumerical integration is inapplicable orfails.



∫() (integral) Catalog >

∫() can be nested to do multiple integrals.Integration limits can depend on integrationvariables outside them.

Note: See also nInt(), page 122.

√() (square root) /q keys√(Expr1) ⇒ expression

√(List1) ⇒ list

Returns the square root of the argument.

For a list, returns the square roots of all theelements in List1.

Note: You can insert this function from thekeyboard by typing sqrt(...)

Note: See also Square root template, page1.

Π() (prodSeq) Catalog >Π(Expr1, Var, Low, High) ⇒ expression

Note: You can insert this function from thekeyboard by typing prodSeq(...).

Evaluates Expr1 for each value of Var fromLow toHigh, and returns the product of theresults.

Note: See also Product template (Π), page5.

Symbols 223

224 Symbols

Π() (prodSeq) Catalog >Π(Expr1, Var, Low, Low−1) ⇒ 1

Π(Expr1, Var, Low, High) ⇒ 1/Π(Expr1,Var, High+1, Low−1) if High < Low−1

The product formulas used are derived fromthe following reference:

Ronald L. Graham, Donald E. Knuth, andOren Patashnik. Concrete Mathematics: AFoundation for Computer Science.Reading, Massachusetts: Addison-Wesley,1994.

Σ() (sumSeq) Catalog >Σ(Expr1, Var, Low, High) ⇒ expression

Note: You can insert this function from thekeyboard by typing sumSeq(...).

Evaluates Expr1 for each value of Var fromLow toHigh, and returns the sum of theresults.

Note: See also Sum template, page 5.

Σ(Expr1, Var, Low, Low−1) ⇒ 0

Σ(Expr1, Var, Low, High) ⇒ μ

Σ(Expr1, Var, High+1, Low−1) if High <Low−1

The summation formulas used are derivedfrom the following reference:

Ronald L. Graham, Donald E. Knuth, andOren Patashnik. Concrete Mathematics: AFoundation for Computer Science.Reading, Massachusetts: Addison-Wesley,1994.

ΣInt() Catalog >ΣInt(NPmt1, NPmt2, N, I, PV ,[Pmt], [FV],[PpY], [CpY], [PmtAt], [roundValue])⇒ value

ΣInt(NPmt1,NPmt2,amortTable) ⇒ value

Amortization function that calculates thesum of the interest during a specified rangeof payments.

NPmt1 and NPmt2 define the start and endboundaries of the payment range.






ΣInt(NPmt1,NPmt2,amortTable) calculatesthe sum of the interest based onamortization table amortTable. TheamortTable argument must be a matrix inthe form described under amortTbl(), page8.

Note: See also ΣPrn(), below, and Bal(),page 17.

ΣPrn() Catalog >ΣPrn(NPmt1, NPmt2, N, I, PV, [Pmt],[FV], [PpY], [CpY], [PmtAt],[roundValue]) ⇒ value

ΣPrn(NPmt1, NPmt2, amortTable) ⇒value

Amortization function that calculates thesum of the principal during a specifiedrange of payments.

Symbols 225

226 Symbols

ΣPrn() Catalog >NPmt1 and NPmt2 define the start and endboundaries of the payment range.






ΣPrn(NPmt1,NPmt2,amortTable)calculates the sum of the principal paidbased on amortization table amortTable.The amortTable argument must be amatrix in the form described underamortTbl(), page 8.

Note: See also ΣInt(), above, and Bal(),page 17.

# (indirection) /k keys# varNameString

Refers to the variable whose name isvarNameString. This lets you use strings tocreate variable names from within afunction.

Creates or refers to the variable xyz .

Returns the value of the variable (r) whosename is stored in variable s1.

E (scientific notation) i keymantissaEexponent

Enters a number in scientific notation. Thenumber is interpreted asmantissa × 10exponent.

Hint: If you want to enter a power of 10without causing a decimal value result, use10^integer.

Note: You can insert this operator from thecomputer keyboard by typing @E. forexample, type 2.3@E4 to enter 2.3E4.

g (gradian) ¹ keyExpr1g ⇒ expression

List1g ⇒ list

Matrix1g ⇒ matrix

This function gives you a way to specify agradian angle while in the Degree or Radianmode.

In Radian angle mode, multiplies Expr1 byπ/200.

In Degree angle mode, multiplies Expr1 byg/100.

In Gradian mode, returns Expr1 unchanged.

Note: You can insert this symbol from thecomputer keyboard by typing @g.

InDegree, Gradianor Radianmode:

r(radian) ¹ keyExpr1r ⇒expression

List1r ⇒ list

Matrix1r ⇒ matrix

InDegree, Gradianor Radian anglemode:

Symbols 227

228 Symbols

r(radian) ¹ keyThis function gives you a way to specify aradian angle while in Degree or Gradianmode.

In Degree angle mode, multiplies theargument by 180/π.

In Radian angle mode, returns theargument unchanged.

In Gradian mode, multiplies the argumentby 200/π.

Hint: Use r if you want to force radians in afunction definition regardless of the modethat prevails when the function is used.

Note: You can insert this symbol from thecomputer keyboard by typing @r.

° (degree) ¹ keyExpr1°⇒expression

List1°⇒ list

Matrix1°⇒ matrix

This function gives you a way to specify adegree angle while in Gradian or Radianmode.

In Radian angle mode, multiplies theargument by π/180.

In Degree angle mode, returns theargument unchanged.

In Gradian angle mode, multiplies theargument by 10/9.

Note: You can insert this symbol from thecomputer keyboard by typing @d.

InDegree, Gradianor Radian anglemode:




°, ', '' (degree/minute/second) /k keysdd°mm'ss.ss'' ⇒ expression InDegree anglemode:

°, ', '' (degree/minute/second) /k keysdd A positive or negative numbermm A non-negative numberss.ss A non-negative number

Returns dd+(mm/60)+(ss.ss/3600).

This base-60 entry format lets you:

• Enter an angle indegrees/minutes/seconds without regardto the current angle mode.

• Enter time as hours/minutes/seconds.

Note: Follow ss.ss with two apostrophes(''), not a quote symbol (").

∠ (angle) /k keys[Radius,∠θ_Angle] ⇒ vector(polar input)

[Radius,∠θ_Angle,Z_Coordinate] ⇒vector(cylindrical input)

[Radius,∠θ_Angle,∠θ_Angle] ⇒ vector(spherical input)

Returns coordinates as a vector dependingon the Vector Format mode setting:rectangular, cylindrical, or spherical.

Note: You can insert this symbol from thecomputer keyboard by typing @<.

In Radianmode andvector format set to:rectangular

cylindrical

spherical

(Magnitude∠Angle) ⇒ complexValue(polar input)

Enters a complex value in (r∠θ) polarform. The Angle is interpreted according tothe current Angle mode setting.




Symbols 229

230 Symbols

∠ (angle) /k keys

' (prime) º keyvariable 'variable ' '

Enters a prime symbol in a differentialequation. A single prime symbol denotes a1st-order differential equation, two primesymbols denote a 2nd-order, and so on.

_ (underscore as an empty element)See “Empty (Void) Elements,”

page 251.

_ (underscore as unit designator) /_ keysExpr_Unit

Designates the units for an Expr. All unitnames must begin with an underscore.

You can use pre-defined units or create yourown units. For a list of pre-defined units,open the Catalog and display the UnitConversions tab. You can select unit namesfrom the Catalog or type the unit namesdirectly.

Note: You can find the conversion symbol,

►, in the Catalog. Click , and then clickMathOperators.

Variable_

When Variable has no value, it is treatedas though it represents a complex number.By default, without the _ , the variable istreated as real.

If Variable has a value, the _ is ignored andVariable retains its original data type.

Note: You can store a complex number to avariable withoutusing _ . However, for best results incalculations such as cSolve() and cZeros(),the _ is recommended.

Assuming z is undefined:

► (convert) /k keys

Expr_Unit1►_Unit2⇒ Expr_Unit2

Converts an expression from one unit toanother.

The _ underscore character designates theunits. The units must be in the samecategory, such as Length or Area.

For a list of pre-defined units, open theCatalog and display the Unit Conversionstab:

• You can select a unit name from the list.• You can select the conversion operator,

►, from the top of the list.

You can also type unit names manually. Totype “_” when typing unit names on thehandheld, press/_.

Note: To convert temperature units, usetmpCnv() and ΔtmpCnv(). The► conversionoperator does not handle temperatureunits.

10^() Catalog >10^ (Expr1) ⇒ expression

10^ (List1) ⇒ list

Returns 10 raised to the power of theargument.

For a list, returns 10 raised to the power ofthe elements in List1.10^(squareMatrix1) ⇒ squareMatrix

Returns 10 raised to the power ofsquareMatrix1. This is not the same ascalculating 10 raised to the power of eachelement. For information about thecalculation method, refer to cos().


Symbols 231

232 Symbols

^⁻¹ (reciprocal) Catalog >Expr1 ^⁻¹⇒ expression

List1 ^⁻¹⇒ list

Returns the reciprocal of the argument.

For a list, returns the reciprocals of theelements in List1.squareMatrix1 ^⁻¹⇒ squareMatrix

Returns the inverse of squareMatrix1.

squareMatrix1must be a non-singularsquare matrix.

| (constraint operator) /k keysExpr | BooleanExpr1[andBooleanExpr2]...

Expr | BooleanExpr1[ orBooleanExpr2]...

The constraint (“|”) symbol serves as abinary operator. The operand to the left of |is an expression. The operand to the right of| specifies one or more relations that areintended to affect the simplification of theexpression. Multiple relations after | mustbe joined by logical “and” or “or” operators.

The constraint operator provides three basictypes of functionality:

• Substitutions• Interval constraints• Exclusions

Substitutions are in the form of an equality,such as x=3 or y=sin(x). To be mosteffective, the left side should be a simplevariable. Expr | Variable = value willsubstitute value for every occurrence ofVariable in Expr.

| (constraint operator) /k keysInterval constraints take the form of one ormore inequalities joined by logical “and” or“or” operators. Interval constraints alsopermit simplification that otherwise mightbe invalid or not computable.

Exclusions use the “not equals” (/= or ≠)relational operator to exclude a specificvalue from consideration. They are usedprimarily to exclude an exact solution whenusing cSolve(), cZeros(), fMax(), fMin(),solve(), zeros(), and so on.

→ (store) /h keyExpr → Var

List→ Var

Matrix→ Var

Expr→ Function(Param1,...)

List→ Function(Param1,...)

Matrix→ Function(Param1,...)

If the variable Var does not exist, creates itand initializes it to Expr, List, orMatrix.

If the variable Var already exists and is notlocked or protected, replaces its contentswith Expr, List, orMatrix.

Symbols 233

234 Symbols

→ (store) /h keyHint: If you plan to do symboliccomputations using undefined variables,avoid storing anything into commonly used,one-letter variables such as a, b, c, x, y, z,and so on.

Note: You can insert this operator from thekeyboard by typing =: as a shortcut. Forexample, type pi/4 =: myvar.

:= (assign) /t keysVar := Expr

Var := List

Var :=Matrix

Function(Param1,...) := Expr

Function(Param1,...) := List

Function(Param1,...) :=Matrix

If variable Var does not exist, creates Varand initializes it to Expr, List, orMatrix.

If Var already exists and is not locked orprotected, replaces its contents with Expr,List, orMatrix.

Hint: If you plan to do symboliccomputations using undefined variables,avoid storing anything into commonly used,one-letter variables such as a, b, c, x, y, z,and so on.

© (comment) /k keys© [text]

© processes text as a comment line,allowing you to annotate functions andprograms that you create.

© can be at the beginning or anywhere inthe line. Everything to the right of ©, to theend of the line, is the comment.


0b, 0h 0B keys,0H keys0b binaryNumber0h hexadecimalNumber

Denotes a binary or hexadecimal number,respectively. To enter a binary or hexnumber, you must enter the 0b or 0h prefixregardless of the Base mode. Without aprefix, a number is treated as decimal(base 10).

Results are displayed according to the Basemode.

InDec basemode:

In Bin basemode:

InHex basemode:

Symbols 235

236 TI-Nspire™ CX II - Draw Commands

TI-Nspire™ CX II - Draw CommandsThis is a supplemental document for the TI-Nspire™ Reference Guide and the TI-Nspire™ CAS Reference Guide. All TI-Nspire™ CX II commands will be incorporated andpublished in version 5.1 of the TI-Nspire™ Reference Guide and the TI-Nspire™ CASReference Guide.

Graphics ProgrammingNew commands have been added on TI-Nspire™ CX II Handhelds and TI-Nspire™desktop applications for graphics programming.

The TI-Nspire™ CX II Handhelds will switch into this graphics mode while executinggraphics commands and switch back to the context in which the program was executedafter completion of the program.

The screen will display “Running…” in the top bar while the program is being executed.It will show “Finished” when the program completes. Any key-press will transition thesystem out of the graphics mode.

• The transition to graphics mode is triggered automatically when one of the Draw(graphics) commands is encountered during execution of the TI Basic program.

• This transition will only happen when executing a program from calculator; in adocument or calculator in scratchpad.

• The transition out of graphics mode happens upon termination of the program.

• The graphics mode is only available on the TI-Nspire™ CX II Handhelds and thedesktop TI-Nspire™ CX II Handhelds view. This means it is not available in thecomputer document view or PublishView (.tnsp) on the desktop nor on iOS.

- If a graphics command is encountered while executing a TI Basic program fromthe incorrect context, an error message is displayed and the TI Basic program isterminated.

Graphics ScreenThe graphics screen will contain a header at the top of the screen that cannot bewritten to by graphics commands.

The graphics screen drawing area will be cleared (color = 255,255,255) when thegraphics screen is initialized.

GraphicsScreen

Default

Height 212Width 318Color white: 255,255,255

Default View and Settings• The status icons in the top bar (battery status, press-to-test status, network

indicator etc.) will not be visible while a graphics program is running.

• Default drawing color: Black (0,0,0)

• Default pen style - normal, smooth

- Thickness: 1 (thin), 2 (normal), 3 (thickest)- Style: 1 (smooth), 2 (dotted), 3 (dashed)

• All drawing commands will use the current color and pen settings; either defaultvalues or those which were set via TI-Basic commands.

• Text font is fixed and cannot be changed.

• Any output to the graphics screen will be drawn within a clipping window which isthe size of the graphics screen drawing area. Any drawn output that extendsoutside of this clipped graphics screen drawing area will not be drawn. No errormessage will be displayed.

• All x,y coordinates specified for drawing commands are defined such that 0,0 is atthe top left corner of the graphics screen drawing area.

- Exceptions:

- DrawText uses the coordinates as the bottom left corner of the boundingbox for the text.

- SetWindow uses the bottom left corner of the screen

• All parameters for the commands can be provided as expressions that evaluate toa number which is then rounded to the nearest integer.

TI-Nspire™ CX II - Draw Commands 237


Graphics Screen Errors MessagesIf the validation fails, an error message will display.

Error Message Description View

ErrorSyntax

If the syntax checker finds any syntaxerrors, it displays an error messageand tries to position the cursor nearthe first error so you can correct it.

ErrorToo few arguments

The function or command is missingone or more arguments

ErrorToo manyarguments

The function or command containsand excessive number of argumentsand cannot be evaluated.

ErrorInvalid data type

An argument is of the wrong datatype.

Invalid Commands While in Graphics ModeSome commands are not allowed once the program switches to graphics mode. Ifthese commands are encountered while in graphics mode and error will be displayedand the program will be terminated.

DisallowedCommand

Error Message

Request Request cannot be executed in graphics mode

RequestStr RequestStr cannot be executed in graphics mode

Text Text cannot be executed in graphics mode

The commands that print text to the calculator - disp and dispAt - will be supportedcommands in the graphics context. The text from these commands will be sent to theCalculator screen (not on Graphics) and will be visible after the program exits and thesystem switches back to the Calculator app

C

Clear Catalog >CXII

Clear x, y, width, height

Clears entire screen if no parameters arespecified.

If x, y, width and height are specified, therectangle defined by the parameters will becleared.

Clear

Clears entire screen

Clear 10,10,100,50

Clears a rectangle area with topleft corner on (10, 10) and withwidth 100, height 50



D

DrawArc Catalog >CXII

DrawArc x, y, width, height, startAngle,arcAngle

Draw an arc within the defined boundingrectangle with the provided start and arcangles.

x, y: upper left coordinate of boundingrectangle

width, height: dimensions of boundingrectangle

The "arc angle" defines the sweep of thearc.

These parameters can be provided asexpressions that evaluate to a number whichis then rounded to the nearest integer.

DrawArc 20,20,100,100,0,90

DrawArc 50,50,100,100,0,180

See Also: FillArc

DrawCircle Catalog >CXII

DrawCircle x, y, radius

x, y: coordinate of center

radius: radius of the circle

DrawCircle 150,150,40

See Also: FillCircle

DrawLine Catalog >CXII

DrawLine x1, y1, x2, y2

Draw a line from x1, y1, x2, y2.

Expressions that evaluate to a number whichis then rounded to the nearest integer.

Screen bounds: If the specified coordinatescauses any part of the line to be drawnoutside of the graphics screen, that part ofthe line will be clipped and no errormessage will be displayed.

DrawLine 10,10,150,200

DrawPoly Catalog >CXII

The commands have two variants:

DrawPoly xlist, ylist

or

DrawPoly x1, y1, x2, y2, x3, y3...xn, yn

Note: DrawPoly xlist, ylistShape will connect x1, y1 to x2, y2, x2, y2 tox3, y3 and so on.

Note: DrawPoly x1, y1, x2, y2, x3, y3...xn,ynxn, yn will NOT be automatically connectedto x1, y1.

Expressions that evaluate to a list of realfloatsxlist, ylist

Expressions that evaluate to a single realfloatx1, y1...xn, yn = coordinates for vertices ofpolygon

xlist:={0,200,150,0}

ylist:={10,20,150,10}

DrawPoly xlist,ylist

DrawPoly 0,10,200,20,150,150,0,10



DrawPoly Catalog >CXII

Note: DrawPoly: Input size dimensions(width/height) relative to drawn lines.The lines are drawn in a bounding boxaround the specified coordinate anddimensions such that the actual size of thedrawn polygon will be larger than the widthand height.

See Also: FillPoly

DrawRect Catalog >CXII

DrawRect x, y, width, height

x, y: upper left coordinate of rectangle

width, height: width and height of rectangle(rectangle drawn down and right fromstarting coordinate).

Note: The lines are drawn in a bounding boxaround the specified coordinate anddimensions such that the actual size of thedrawn rectangle will be larger than thewidth and height indicate.

DrawRect 25,25,100,50

See Also: FillRect

DrawText Catalog >CXII

DrawText x, y, exprOrString1[,exprOrString2]...

x, y: coordinate of text output

Draws the text in exprOrString at thespecified x, y coordinate location.

The rules for exprOrString are the same asfor Disp – DrawText can take multiplearguments.

DrawText 50,50,"Hello World"

F

FillArc Catalog >CXII

FillArc x, y, width, height startAngle,arcAngle

x, y: upper left coordinate of boundingrectangle

Draw and fill an arc within the definedbounding rectangle with the provided startand arc angles.

Default fill color is black. The fill color can beset by the SetColor command

The "arc angle" defines the sweep of the arc

FillArc 50,50,100,100,0,180

FillCircle Catalog >CXII

FillCircle x, y, radius

x, y: coordinate of center

Draw and fill a circle at the specified centerwith the specified radius.

Default fill color is black. The fill color can beset by the SetColor command.

FillCircle 150,150,40

Here!

FillPoly Catalog >CXII

FillPoly xlist, ylistor

FillPoly x1, y1, x2, y2, x3, y3...xn, yn

Note: The line and color are specified bySetColor and SetPen

xlist:={0,200,150,0}

ylist:={10,20,150,10}

FillPoly xlist,ylist



FillPoly Catalog >CXII

FillPoly 0,10,200,20,150,150,0,10

FillRect Catalog >CXII

FillRect x, y, width, height

x, y: upper left coordinate of rectangle

width, height: width and height of rectangle

Draw and fill a rectangle with the top leftcorner at the coordinate specified by (x,y)

Default fill color is black. The fill color can beset by the SetColor command

Note: The line and color are specified bySetColor and SetPen

FillRect 25,25,100,50

G

getPlatform() Catalog >CXII

getPlatform()

Returns:“dt” on desktop software applications“hh” on TI-Nspire™ CX handhelds“ios” on TI-Nspire™ CX iPad® app



P

PaintBuffer Catalog >CXII

PaintBuffer

Paint graphics buffer to screen

This command is used in conjunction withUseBuffer to increase the speed of displayon the screen when the program generatesmultiple graphical objects.

UseBuffer

For n,1,10

x:=randInt(0,300)

y:=randInt(0,200)

radius:=randInt(10,50)

Wait 0.5

DrawCircle x,y,radius

EndFor

PaintBuffer

This program will display all the10 circles at once.

If the “UseBuffer” command isremoved, each circle will bedisplayed as it is drawn.

See Also: UseBuffer

PlotXY Catalog >CXII

PlotXY x, y, shape

x, y: coordinate to plot shape

shape : a number between 1 and 13specifying the shape

1 - Filled circle

2 - Empty circle

3 - Filled square

4 - Empty square

5 - Cross

6 - Plus

7 - Thin

8 - medium point, solid

9 - medium point, empty

10 - larger point, solid

11 - larger point, empty

12 - largest point, solid

13 - largest point, empty

PlotXY 100,100,1

For n,1,13

DrawText 1+22*n,40,n

PlotXY 5+22*n,50,n

EndFor



S

SetColor Catalog >CXII

SetColor

Red-value, Green-value, Blue-value

Valid values for red, green and blue arebetween 0 and 255

Sets the color for subsequent Drawcommands

SetColor 255,0,0


SetPen Catalog >CXII

SetPen

thickness, style

thickness: 1 <= thickness <= 3|1 is thinnest,3 is thickest

style: 1 = Smooth, 2 = Dotted, 3 = Dashed

Sets the pen style for subsequent Drawcommands

SetPen 3,3


SetWindow Catalog >CXII

SetWindow

xMin, xMax, yMin, yMax

Establishes a logical window that maps tothe graphics drawing area. All parametersare required.

If the part of drawn object is outside thewindow, the output will be clipped (notshown) and no error message is displayed.

SetWindow 0,160,0,120

will set the output window to have0,0 in the bottom left corner witha width of 160 and a height of 120

DrawLine 0,0,100,100

SetWindow 0,160,0,120

SetPen 3,3

DrawLine 0,0,100,100

SetWindow Catalog >CXII

If xmin is greater than or equal to xmax orymin is greater than or equal to ymax, anerror message is shown.

Any objects drawn before a SetWindowcommand will not be re-drawn in the newconfiguration.

To reset the window parameters to thedefault, use:

SetWindow 0,0,0,0



U

UseBuffer Catalog >CXII

UseBuffer

Draw to an off screen graphics bufferinstead of screen (to increase performance)

This command is used in conjunction withPaintBuffer to increase the speed of displayon the screen when the program generatesmultiple graphical objects.

With UseBuffer, all the graphics aredisplayed only after the next PaintBuffercommand is executed.

UseBuffer only needs to be called once inthe program i.e. every use of PaintBufferdoes not need a corresponding UseBuffer

UseBuffer

For n,1,10

x:=randInt(0,300)

y:=randInt(0,200)

radius:=randInt(10,50)

Wait 0.5

DrawCircle x,y,radius

EndFor

PaintBuffer

This programwill display all the 10 circles atonce.

If the “UseBuffer” command is removed,each circle will be displayedas it is drawn.

See Also: PaintBuffer

Empty (Void) ElementsWhen analyzing real-world data, you might not always have a complete data set.TI-Nspire™ CAS Software allows empty, or void, data elements so you can proceedwith the nearly complete data rather than having to start over or discard theincomplete cases.

You can find an example of data involving empty elements in the Lists & Spreadsheetchapter, under “Graphing spreadsheet data.”

The delVoid() function lets you remove empty elements from a list. The isVoid()function lets you test for an empty element. For details, see delVoid(), page 49, andisVoid(), page 94.

Note: To enter an empty element manually in a math expression, type “_” or thekeyword void. The keyword void is automatically converted to a “_” symbol whenthe expression is evaluated. To type “_” on the handheld, press/_.

Calculations involving void elementsThe majority of calculations involving a voidinput will produce a void result. See specialcases below.

List arguments containing void elementsThe following functions and commandsignore (skip) void elements found in listarguments.

count, countIf, cumulativeSum,freqTable►list, frequency, max, mean,median, product, stDevPop, stDevSamp,sum, sumIf, varPop, and varSamp, as well asregression calculations, OneVar, TwoVar,and FiveNumSummary statistics, confidenceintervals, and stat tests

SortA and SortDmove all void elementswithin the first argument to the bottom.

Empty (Void) Elements 251

252 Empty (Void) Elements

List arguments containing void elements

In regressions, a void in an X or Y listintroduces a void for the correspondingelement of the residual.

An omitted category in regressionsintroduces a void for the correspondingelement of the residual.

A frequency of 0 in regressions introduces avoid for the corresponding element of theresidual.

Shortcuts for Entering Math ExpressionsShortcuts let you enter elements of math expressions by typing instead of using theCatalog or Symbol Palette. For example, to enter the expression √6, you can type sqrt(6) on the entry line. When you press·, the expression sqrt(6) is changed to√6. Some shortcuts are useful from both the handheld and the computer keyboard.Others are useful primarily from the computer keyboard.

From the Handheld or Computer Keyboard

To enter this: Type this shortcut:

π pi

θ theta

∞ infinity

≤ <=

≥ >=

≠ /=

⇒ (logical implication) =>

⇔ (logical double implication, XNOR) <=>

→ (store operator) =:

| | (absolute value) abs(...)

√() sqrt(...)

d() derivative(...)

∫() integral(...)

Σ() (Sum template) sumSeq(...)

Π() (Product template) prodSeq(...)

sin⁻¹(), cos⁻¹(), ... arcsin(...), arccos(...), ...

ΔList() deltaList(...)

ΔtmpCnv() deltaTmpCnv(...)

From the Computer Keyboard


c1, c2, ... (constants) @c1, @c2, ...

Shortcuts for Entering Math Expressions 253

254 Shortcuts for Entering Math Expressions


n1, n2, ... (integer constants) @n1, @n2, ...

i (imaginary constant) @i

e (natural log base e) @e

E (scientific notation) @ET (transpose) @tr (radians) @r

° (degrees) @dg (gradians) @g

∠ (angle) @<

► (conversion) @>

►Decimal,►approxFraction(), andso on.

@>Decimal, @>approxFraction(), andso on.

EOS™ (Equation Operating System) HierarchyThis section describes the Equation Operating System (EOS™) that is used by theTI-Nspire™ CAS math and science learning technology. Numbers, variables, andfunctions are entered in a simple, straightforward sequence. EOS™ software evaluatesexpressions and equations using parenthetical grouping and according to the prioritiesdescribed below.

Order of Evaluation

Level Operator

1 Parentheses ( ), brackets [ ], braces { }

2 Indirection (#)

3 Function calls

4 Post operators: degrees-minutes-seconds (°,',"), factorial (!), percentage(%), radian (r), subscript ([ ]), transpose (T)

5 Exponentiation, power operator (^)

6 Negation (⁻)

7 String concatenation (&)

8 Multiplication (•), division (/)

9 Addition (+), subtraction (-)

10 Equality relations: equal (=), not equal (≠ or /=),less than (<), less than or equal (≤ or <=), greater than (>), greater than orequal (≥ or >=)

11 Logical not

12 Logical and

13 Logical or

14 xor, nor, nand

15 Logical implication (⇒ )

16 Logical double implication, XNOR (⇔ )

17 Constraint operator (“|”)

18 Store (→)

Parentheses, Brackets, and Braces

All calculations inside a pair of parentheses, brackets, or braces are evaluated first. Forexample, in the expression 4(1+2), EOS™ software first evaluates the portion of theexpression inside the parentheses, 1+2, and then multiplies the result, 3, by 4.

EOS™ (Equation Operating System) Hierarchy 255

256 EOS™ (Equation Operating System) Hierarchy

The number of opening and closing parentheses, brackets, and braces must be thesame within an expression or equation. If not, an error message is displayed thatindicates the missing element. For example, (1+2)/(3+4 will display the error message“Missing ).”

Note: Because the TI-Nspire™ CAS software allows you to define your own functions, avariable name followed by an expression in parentheses is considered a “function call”instead of implied multiplication. For example a(b+c) is the function a evaluated byb+c. To multiply the expression b+c by the variable a, use explicit multiplication: a•(b+c).

Indirection

The indirection operator (#) converts a string to a variable or function name. Forexample, #(“x”&”y”&”z”) creates the variable name xyz. Indirection also allows thecreation and modification of variables from inside a program. For example, if 10→rand “r”→s1, then #s1=10.

Post Operators

Post operators are operators that come directly after an argument, such as 5!, 25%, or60°15' 45". Arguments followed by a post operator are evaluated at the fourth prioritylevel. For example, in the expression 4^3!, 3! is evaluated first. The result, 6, thenbecomes the exponent of 4 to yield 4096.

Exponentiation

Exponentiation (^) and element-by-element exponentiation (.^) are evaluated fromright to left. For example, the expression 2^3^2 is evaluated the same as 2^(3^2) toproduce 512. This is different from (2^3)^2, which is 64.

Negation

To enter a negative number, pressv followed by the number. Post operations andexponentiation are performed before negation. For example, the result of −x2 is anegative number, and −92 = −81. Use parentheses to square a negative number suchas (−9)2 to produce 81.

Constraint (“|”)

The argument following the constraint (“|”) operator provides a set of constraints thataffect the evaluation of the argument preceding the operator.

TI-Nspire CX II - TI-Basic Programming FeaturesAuto-indentation in Programming EditorThe TI-Nspire™ program editor now auto-indents statements inside a block command.

Block commands are If/EndIf, For/EndFor, While/EndWhile, Loop/EndLoop, Try/EndTry

The editor will automatically prepend spaces to program commands inside a blockcommand. The closing command of the block will be aligned with the openingcommand.

The example below shows auto-indentation in nested block commands.

Code fragments that are copied and pasted will retain the original indentation.

Opening a program created in an earlier version of the software will retain the originalindentation.

Improved Error Messages for TI-BasicErrors

Error Condition New message

Error in condition statement (If/While) A conditional statement did not resolve to TRUEor FALSENOTE:With the change to place the cursor onthe linewith the error, we no longer need tospecify if the error is in an "If" statement or a"While" statement.

Missing EndIf Expected EndIf but founda different endstatement

Missing EndFor Expected EndFor but founda different endstatement

Missing EndWhile Expected EndWhile but founda different endstatement

Missing EndLoop Expected EndLoopbut founda different endstatement

TI-Nspire CX II - TI-Basic Programming Features 257

258 TI-Nspire CX II - TI-Basic Programming Features

Error Condition New message

Missing EndTry Expected EndTry but founda different endstatement

“Then” omitted after If <condition> Missing If..Then

“Then” omitted after ElseIf <condition> Thenmissing in block: ElseIf.

When “Then”, “Else” and “ElseIf”wereencounteredoutside of control blocks

Else invalid outside of blocks: If..Then..EndIf orTry..EndTry

“ElseIf” appears outside of “If..Then..EndIf”block

ElseIf invalid outside of block: If..Then..EndIf

"Then” appears outside of “If....EndIf” block Then invalid outside of block: If..EndIf

Syntax Errors

In case commands that expect one or more arguments are called with an incompletelist of arguments, a “Too few argument error” will be issued instead of “syntax” error

Current behavior New CX II behavior

Current behavior New CX II behavior

Note: When an incomplete list of arguments is not followed by a comma, the errormessage is: “too few arguments”. This is the same as previous releases.

TI-Nspire CX II - TI-Basic Programming Features 259

260 Constants and Values

Constants and ValuesThe following table lists the constants and their values that are available whenperforming unit conversions. They can be typed in manually or selected from theConstants list in Utilities > Unit Conversions (Handheld: Pressk 3).

Constant Name Value

_c Speedof light 299792458 _m/_s

_Cc Coulombconstant 8987551787.3682 _m/_F

_Fc Faraday constant 96485.33289 _coul/_mol

_g Accelerationof gravity 9.80665 _m/_s2

_Gc Gravitational constant 6.67408E-11 _m3/_kg/_s2

_h Planck's constant 6.626070040E-34 _J _s

_k Boltzmann's constant 1.38064852E-23 _J/_¡K

_m0 Permeability of a vacuum 1.2566370614359E-6 _N/_A2

_mb Bohr magneton 9.274009994E-24 _J _m2/_Wb

_Me Electron restmass 9.10938356E-31 _kg

_Mm Muonmass 1.883531594E-28 _kg

_Mn Neutron restmass 1.674927471E-27 _kg

_Mp Proton restmass 1.672621898E-27 _kg

_Na Avogadro's number 6.022140857E23 /_mol

_q Electron charge 1.6021766208E-19 _coul

_Rb Bohr radius 5.2917721067E-11 _m

_Rc Molar gas constant 8.3144598 _J/_mol/_¡K

_Rdb Rydberg constant 10973731.568508/_m

_Re Electron radius 2.8179403227E-15 _m

_u Atomicmass 1.660539040E-27 _kg

_Vm Molar volume 2.2413962E-2 _m3/_mol

_H0 Permittivity of a vacuum 8.8541878176204E-12 _F/_m

_s Stefan-Boltzmann constant 5.670367E-8 _W/_m2/_¡K4

_f0 Magnetic flux quantum 2.067833831E-15 _Wb

Error Codes and MessagesWhen an error occurs, its code is assigned to variable errCode. User-defined programsand functions can examine errCode to determine the cause of an error. For anexample of using errCode, See Example 2 under the Try command, page 191.

Note: Some error conditions apply only to TI-Nspire™ CAS products, and some applyonly to TI-Nspire™ products.

Errorcode Description

10 A functiondid not return a value

20 A test did not resolve to TRUE or FALSE.

Generally, undefined variables cannot be compared. For example, the test If a<bwill causethis error if either a or b is undefinedwhen the If statement is executed.

30 Argument cannot be a folder name.

40 Argument error

50 Argumentmismatch

Two or more arguments must be of the same type.

60 Argumentmust be a Booleanexpressionor integer

70 Argumentmust be a decimal number

90 Argumentmust be a list

100 Argumentmust be amatrix

130 Argumentmust be a string

140 Argumentmust be a variable name.

Make sure that the name:• does not begin with a digit• does not contain spaces or special characters• does not use underscore or period in invalid manner• does not exceed the length limitations

See the Calculator section in the documentation for more details.

160 Argumentmust be anexpression

165 Batteries too low for sending or receiving

Install newbatteries before sending or receiving.

170 Bound

The lower boundmust be less than the upper bound to define the search interval.


262 Error Codes and Messages


180 Break

Thed orc key was pressedduring a long calculationor during programexecution.

190 Circular definition

This message is displayed to avoid running out ofmemory during infinite replacement ofvariable values during simplification. For example, a+1->a, where a is anundefined variable,will cause this error.

200 Constraint expression invalid

For example, solve(3x^2-4=0,x) | x<0 or x>5wouldproduce this error message because theconstraint is separatedby “or” insteadof “and.”

210 InvalidData type

Anargument is of thewrong data type.

220 Dependent limit

230 Dimension

A list or matrix index is not valid. For example, if the list {1,2,3,4} is stored in L1, then L1[5] is adimensionerror because L1 only contains four elements.

235 Dimension Error. Not enoughelements in the lists.

240 Dimensionmismatch

Two or more arguments must be of the same dimension. For example, [1,2]+[1,2,3] is adimensionmismatchbecause thematrices contain a different number of elements.

250 Divide by zero

260 Domain error

Anargumentmust be in a specifieddomain. For example, rand(0) is not valid.

270 Duplicate variable name

280 Else andElseIf invalid outside of If...EndIf block

290 EndTry is missing thematching Else statement

295 Excessive iteration

300 Expected2 or 3-element list or matrix

310 The first argumentof nSolvemust be anequation in a single variable. It cannot contain a non-valued variable other than the variable of interest.

320 First argumentof solve or cSolvemust be anequationor inequality

For example, solve(3x^2-4,x) is invalid because the first argument is not anequation.


345 Inconsistent units

350 Index out of range

360 Indirection string is not a valid variable name

380 UndefinedAns

Either the previous calculationdid not create Ans, or no previous calculationwas entered.

390 Invalid assignment

400 Invalid assignment value

410 Invalid command

430 Invalid for the currentmode settings

435 Invalid guess

440 Invalid impliedmultiply

For example, x(x+1) is invalid; whereas, x*(x+1) is the correct syntax. This is to avoidconfusionbetween impliedmultiplication and function calls.

450 Invalid in a functionor current expression

Only certain commands are valid in a user-defined function.

490 Invalid in Try..EndTry block

510 Invalid list or matrix

550 Invalid outside functionor program

A number of commands are not valid outside a functionor program. For example, Localcannot be usedunless it is in a functionor program.

560 Invalid outside Loop..EndLoop, For..EndFor, or While..EndWhile blocks

For example, the Exit command is valid only inside these loopblocks.

565 Invalid outside program

570 Invalid pathname

For example, \var is invalid.

575 Invalid polar complex

580 Invalid program reference

Programs cannot be referencedwithin functions or expressions such as 1+p(x) where p is aprogram.




600 Invalid table

605 Invalid use of units

610 Invalid variable name in a Local statement

620 Invalid variable or functionname

630 Invalid variable reference

640 Invalid vector syntax

650 Link transmission

A transmissionbetween two units was not completed. Verify that the connecting cable isconnected firmly to bothends.

665 Matrix not diagonalizable

670 LowMemory

1. Delete some data in this document

2. Save and close this document

If 1 and2 fail, pull out and re-insert batteries

672 Resource exhaustion

673 Resource exhaustion

680 Missing (

690 Missing )

700 Missing “

710 Missing ]

720 Missing }

730 Missing start or endof block syntax

740 Missing Then in the If..EndIf block

750 Name is not a functionor program

765 No functions selected

780 No solution found

800 Non-real result

For example, if the software is in the Real setting, √(-1) is invalid.


To allow complex results, change the “Real or Complex”Mode Setting to RECTANGULAR orPOLAR.

830 Overflow

850 Programnot found

A program reference inside another program couldnot be found in the providedpathduringexecution.

855 Rand type functions not allowed in graphing

860 Recursion too deep

870 Reservedname or systemvariable

900 Argument error

Median-medianmodel could not be applied to data set.

910 Syntax error

920 Text not found

930 Too fewarguments

The functionor command is missing one or more arguments.

940 Too many arguments

The expressionor equation contains anexcessive number of arguments and cannot beevaluated.

950 Too many subscripts

955 Too many undefined variables

960 Variable is not defined

No value is assigned to variable. Use one of the following commands:• sto→• :=• Define

to assign values to variables.

965 UnlicensedOS

970 Variable in use so references or changes are not allowed

980 Variable is protected

990 Invalid variable name

Make sure that the name does not exceed the length limitations




1000 Windowvariables domain

1010 Zoom

1020 Internal error

1030 Protectedmemory violation

1040 Unsupported function. This function requires Computer Algebra System. Try TI-Nspire™CAS.

1045 Unsupportedoperator. This operator requires Computer Algebra System. Try TI-Nspire™CAS.

1050 Unsupported feature. This operator requires Computer Algebra System. Try TI-Nspire™CAS.

1060 Input argumentmust be numeric. Only inputs containing numeric values are allowed.

1070 Trig function argument too big for accurate reduction

1080 Unsupporteduse of Ans.This applicationdoes not support Ans.

1090 Function is not defined. Use one of the following commands:• Define• :=• sto→

to define a function.

1100 Non-real calculation

For example, if the software is in the Real setting, √(-1) is invalid.

To allow complex results, change the “Real or Complex”Mode Setting to RECTANGULAR orPOLAR.

1110 Invalid bounds

1120 No sign change

1130 Argument cannot be a list or matrix

1140 Argument error

The first argumentmust be a polynomial expression in the secondargument. If the secondargument is omitted, the software attempts to select a default.

1150 Argument error

The first two arguments must be polynomial expressions in the third argument. If the thirdargument is omitted, the software attempts to select a default.

1160 Invalid library pathname


A pathnamemust be in the form xxx\yyy, where:• The xxx part can have 1 to 16 characters.• The yyy part can have 1 to 15 characters.

See the Library section in the documentation for more details.

1170 Invalid use of library pathname• A value cannot be assigned to a pathname using Define, :=, or sto→.• A pathname cannot be declared as a Local variable or be used as a

parameter in a function or program definition.

1180 Invalid library variable name.

Make sure that the name:• Does not contain a period• Does not begin with an underscore• Does not exceed 15 characters


1190 Library document not found:• Verify library is in the MyLib folder.• Refresh Libraries.


1200 Library variable not found:• Verify library variable exists in the first problem in the library.• Make sure library variable has been defined as LibPub or LibPriv.• Refresh Libraries.


1210 Invalid library shortcut name.

Make sure that the name:• Does not contain a period• Does not begin with an underscore• Does not exceed 16 characters• Is not a reserved name


1220 Domain error:

The tangentLine andnormalLine functions support real-valued functions only.

1230 Domain error.




Trigonometric conversionoperators are not supported inDegree or Gradian anglemodes.

1250 Argument Error

Use a systemof linear equations.

Example of a systemof two linear equations with variables x and y:

3x+7y=5

2y-5x=-1

1260 Argument Error:

The first argumentof nfMinor nfMaxmust be anexpression in a single variable. It cannotcontain a non-valued variable other than the variable of interest.

1270 Argument Error

Order of the derivativemust be equal to 1 or 2.

1280 Argument Error

Use a polynomial in expanded form inone variable.

1290 Argument Error

Use a polynomial in one variable.

1300 Argument Error

The coefficients of the polynomialmust evaluate to numeric values.

1310 Argument error:

A function couldnot be evaluated for one or more of its arguments.

1380 Argument error:

Nested calls to domain() function are not allowed.

Warning Codes and MessagesYou can use the warnCodes() function to store the codes of warnings generated byevaluating an expression. This table lists each numeric warning code and its associatedmessage. For an example of storing warning codes, see warnCodes(), page 200.

Warningcode Message

10000 Operationmight introduce false solutions.

10001 Differentiating anequationmay produce a false equation.

10002 Questionable solution

10003 Questionable accuracy

10004 Operationmight lose solutions.

10005 cSolvemight specify more zeros.

10006 Solvemay specify more zeros.

10007 More solutionsmay exist. Try specifying appropriate lower andupper bounds and/or aguess.

Examples using solve():• solve(Equation, Var=Guess)|lowBound<Var<upBound• solve(Equation, Var)|lowBound<Var<upBound• solve(Equation, Var=Guess)

10008 Domainof the resultmight be smaller than the domainof the input.

10009 Domainof the resultmight be larger than the domainof the input.

10012 Non-real calculation

10013 ∞^0 or undef^0 replacedby 1

10014 undef^0 replacedby 1

10015 1^∞ or 1^undef replacedby 1

10016 1^undef replacedby 1

10017 Overflow replacedby∞ or −∞

10018 Operation requires and returns 64 bit value.

10019 Resource exhaustion, simplificationmight be incomplete.

10020 Trig function argument too big for accurate reduction.

10021 Input contains anundefinedparameter.

Resultmight not be valid for all possible parameter values.

Warning Codes and Messages 269

270 Warning Codes and Messages

Warningcode Message

10022 Specifying appropriate lower andupper boundsmight produce a solution.

10023 Scalar has beenmultipliedby the identity matrix.

10024 Result obtainedusing approximate arithmetic.

10025 Equivalence cannot be verified in EXACTmode.

10026 Constraintmight be ignored. Specify constraint in the form "\" 'VariableMathTestSymbolConstant' or a conjunct of these forms, for example 'x<3 and x>-12'

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Service and Warranty Informationeducation.ti.com/warranty

Select your country for information about the length and terms of the warranty orabout product service.

Limited Warranty. This warranty does not affect your statutory rights.

General Information 271

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Index

-

-, subtract 210

!

!, factorial 220

"

", second notation 228

#

#, indirection 226#, indirection operator 256

%

%, percent 216

&

&, append 220

*

*, multiply 211

.

.-, dot subtraction 214

.*, dot multiplication 215

./, dot division 215

.^, dot power 215

.+, dot addition 214

/

/, divide 212

:

:=, assign 234

^

^⁻¹, reciprocal 232

^, power 213

_

_, unit designation 230

|

|, constraint operator 232

′

′minute notation 228′, prime 230

+

+, add 210

=

≠, not equal 217≤, less than or equal 218≥, greater than or equal 219>, greater than 218=, equal 216

∏

∏, product 223

∑

∑( ), sum 224∑Int( ) 225∑Prn( ) 225

√

√, square root 223

∠

∠ (angle) 229

∫

∫, integral 221

Index 272

►

►, convert units 231►approxFraction( ) 13►Base10, display as decimal integer 18►Base16, display as hexadecimal 19►Base2, display as binary 17►cos, display in terms of cosine 29►Cylind, display as cylindrical vector 42►DD, display as decimal angle 45►Decimal, display result as decimal 45►DMS, display as

degree/minute/second 54►exp, display in terms of e 63►Grad, convert to gradian angle 86►Polar, display as polar vector 133►Rad, convert to radian angle 143►Rect, display as rectangular vector 146►sin, display in terms of sine 166►Sphere, display as spherical vector 175

⇒

⇒ , logical implication 219, 253

→

→, store variable 233

⇔

⇔ , logical double implication 220, 253

©

©, comment 235

°

°, degree notation 228°, degrees/minutes/seconds 228

0

0b, binary indicator 2350h, hexadecimal indicator 235

1

10^( ), power of ten 231

2

2-sample F Test 75

A

abs( ), absolute value 8absolute value

template for 3-4add, + 210amortization table, amortTbl( ) 8, 17amortTbl( ), amortization table 8, 17and, Boolean operator 9angle( ), angle 10angle, angle( ) 10ANOVA, one-way variance analysis 10ANOVA2way, two-way variance

analysis 11Ans, last answer 13answer (last), Ans 13append, & 220approx( ), approximate 13-14approximate, approx( ) 13-14approxRational( ) 14arc length, arcLen( ) 15arccos(), cos⁻¹() 14arccosh(), cosh⁻¹() 14arccot(), cot⁻¹() 14arccoth(), coth⁻¹() 14arccsc(), csc⁻¹() 14arccsch(), csch⁻¹() 14arcLen( ), arc length 15arcsec(), sec⁻¹() 15arcsech(), csech⁻¹() 15arcsin(), sin⁻¹() 15arcsinh(), sinh⁻¹() 15arctan(), tan⁻¹() 15arctanh(), tanh⁻¹() 15arguments in TVM functions 195augment( ), augment/concatenate 15augment/concatenate, augment( ) 15

273 Index

average rate of change, avgRC( ) 16avgRC( ), average rate of change 16

B

binarydisplay, ►Base2 17indicator, 0b 235

binomCdf( ) 20, 92binomPdf( ) 20Boolean operators

⇒ 219, 253⇔ 220and 9nand 119nor 123not 125or 129xor 201

C

Cdf( ) 68ceiling( ), ceiling 20ceiling, ceiling( ) 20-21, 36centralDiff( ) 21cFactor( ), complex factor 21char( ), character string 22character string, char( ) 22characters

numeric code, ord( ) 130string, char( ) 22

charPoly( ) 23χ²2way 23clear

error, ClrErr 25Clear 239ClearAZ 25ClrErr, clear error 25colAugment 26colDim( ), matrix column dimension 26colNorm( ), matrix column norm 26combinations, nCr( ) 120comDenom( ), common

denominator 26

comment, © 235common denominator, comDenom

( ) 26completeSquare( ), complete square 27complex

conjugate, conj( ) 28factor, cFactor( ) 21solve, cSolve( ) 38zeros, cZeros( ) 43

conj( ), complex conjugate 28constant

in solve( ) 171constants

in cSolve( ) 39in cZeros( ) 44in deSolve( ) 49in solve( ) 173in zeros( ) 203shortcuts for 253

constraint operator "|" 232constraint operator, order of

evaluation 255construct matrix, constructMat( ) 28constructMat( ), construct matrix 28convert

►Grad 86►Rad 143units 231

copy variable or function, CopyVar 29correlation matrix, corrMat( ) 29corrMat( ), correlation matrix 29cos⁻¹, arccosine 31cos( ), cosine 30cosh⁻¹( ), hyperbolic arccosine 32cosh( ), hyperbolic cosine 32cosine

display expression in terms of 29cosine, cos( ) 30cot⁻¹( ), arccotangent 33cot( ), cotangent 33cotangent, cot( ) 33coth⁻¹( ), hyperbolic arccotangent 34coth( ), hyperbolic cotangent 34count days between dates, dbd( ) 44

Index 274

count items in a list conditionally ,countif( ) 35

count items in a list, count( ) 34count( ), count items in a list 34countif( ), conditionally count items

in a list 35cPolyRoots() 36cross product, crossP( ) 36crossP( ), cross product 36csc⁻¹( ), inverse cosecant 37csc( ), cosecant 36csch⁻¹( ), inverse hyperbolic cosecant 37csch( ), hyperbolic cosecant 37cSolve( ), complex solve 38cubic regression, CubicReg 40CubicReg, cubic regression 40cumulative sum, cumulativeSum( ) 41cumulativeSum( ), cumulative sum 41cycle, Cycle 42Cycle, cycle 42cylindrical vector display, ►Cylind 42cZeros( ), complex zeros 43

D

d( ), first derivative 221days between dates, dbd( ) 44dbd( ), days between dates 44decimal

angle display, ►DD 45integer display, ►Base10 18

Define 46Define LibPriv 47Define LibPub 47define, Define 46Define, define 46defining

private function or program 47public function or program 47

definite integraltemplate for 6

degree notation, ° 228degree/minute/second display,

►DMS 54degree/minute/second notation 228

deletevoid elements from list 49

deletingvariable, DelVar 48

deltaList() 48deltaTmpCnv() 48DelVar, delete variable 48delVoid( ), remove void elements 49denominator 26derivative or nth derivative

template for 6derivative() 49derivatives

first derivative, d( ) 221numeric derivative, nDeriv( ) 121-122numeric derivative, nDerivative(

) 121deSolve( ), solution 49det( ), matrix determinant 51diag( ), matrix diagonal 51dim( ), dimension 52dimension, dim( ) 52Disp, display data 52, 158DispAt 52display as

binary, ►Base2 17cylindrical vector, ►Cylind 42decimal angle, ►DD 45decimal integer, ►Base10 18degree/minute/second, ►DMS 54hexadecimal, ►Base16 19polar vector, ►Polar 133rectangular vector, ►Rect 146spherical vector, ►Sphere 175

display data, Disp 52, 158distribution functions

binomCdf( ) 20, 92binomPdf( ) 20invNorm( ) 92invt( ) 92Invχ²( ) 91normCdf( ) 125normPdf( ) 125poissCdf( ) 132

275 Index

poissPdf( ) 132tCdf( ) 185tPdf( ) 190χ²2way( ) 23χ²Cdf( ) 24χ²GOF( ) 24χ²Pdf( ) 24

divide, / 212domain function, domain( ) 55domain( ), domain function 55dominant term, dominantTerm( ) 55dominantTerm( ), dominant term 55dot

addition, .+ 214division, ./ 215multiplication, .* 215power, .^ 215product, dotP( ) 57subtraction, .- 214

dotP( ), dot product 57draw 240-242

E

e exponenttemplate for 2

e to a power, e^( ) 57, 63e, display expression in terms of 63E, exponent 227e^( ), e to a power 57eff( ), convert nominal to effective

rate 58effective rate, eff( ) 58eigenvalue, eigVl( ) 59eigenvector, eigVc( ) 58eigVc( ), eigenvector 58eigVl( ), eigenvalue 59else if, ElseIf 59else, Else 86ElseIf, else if 59empty (void) elements 251end

for, EndFor 72function, EndFunc 75

if, EndIf 86loop, EndLoop 110program, EndPrgm 137try, EndTry 191while, EndWhile 201

end function, EndFunc 75end if, EndIf 86end loop, EndLoop 110end while, EndWhile 201EndTry, end try 191EndWhile, end while 201EOS (Equation Operating System) 255equal, = 216Equation Operating System (EOS) 255error codes and messages 261, 269errors and troubleshooting

clear error, ClrErr 25pass error, PassErr 131

euler( ), Euler function 60evaluate polynomial, polyEval( ) 135evaluation, order of 255exact( ), exact 62exact, exact( ) 62exclusion with "|" operator 232exit, Exit 63Exit, exit 63exp( ), e to a power 63exp►list( ), expression to list 64expand( ), expand 64expand, expand( ) 64exponent, E 227exponential regession, ExpReg 66exponents

template for 1expr( ), string to expression 65, 107ExpReg, exponential regession 66expressions

expression to list, exp►list( ) 64string to expression, expr( ) 65, 107

F

factor( ), factor 67factor, factor( ) 67

Index 276

factorial, ! 220fill 243-244Fill, matrix fill 69financial functions, tvmFV( ) 193financial functions, tvmI( ) 193financial functions, tvmN( ) 194financial functions, tvmPmt( ) 194financial functions, tvmPV( ) 194first derivative

template for 5FiveNumSummary 69floor( ), floor 70floor, floor( ) 70fMax( ), function maximum 70fMin( ), function minimum 71For 72for, For 72For, for 72format string, format( ) 72format( ), format string 72fpart( ), function part 73fractions

propFrac 139template for 1

freqTable( ) 73frequency( ) 74Frobenius norm, norm( ) 124Func, function 75Func, program function 75functions

maximum, fMax( ) 70minimum, fMin( ) 71part, fpart( ) 73program function, Func 75user-defined 46

functions and variablescopying 29

G

g, gradians 227gcd( ), greatest common divisor 76geomCdf( ) 76geomPdf( ) 77Get 77, 245

get/returndenominator, getDenom( ) 78number, getNum( ) 84variables injformation,

getVarInfo( ) 82, 85getDenom( ), get/return

denominator 78getKey() 78getLangInfo( ), get/return language

information 82getLockInfo( ), tests lock status of

variable or variable group 82getMode( ), get mode settings 83getNum( ), get/return number 84GetStr 84getType( ), get typeof variable 84getVarInfo( ), get/return variables

information 85go to, Goto 86Goto, go to 86gradian notation, g 227greater than or equal, ≥ 219greater than, > 218greatest common divisor, gcd( ) 76groups, locking and unlocking 106, 197groups, testing lock status 82

H

hexadecimaldisplay, ►Base16 19indicator, 0h 235

hyperbolicarccosine, cosh⁻¹( ) 32arcsine, sinh⁻¹( ) 168arctangent, tanh⁻¹( ) 184cosine, cosh( ) 32sine, sinh( ) 168tangent, tanh( ) 184

I

identity matrix, identity( ) 86identity( ), identity matrix 86if, If 86If, if 86

277 Index

ifFn( ) 88imag( ), imaginary part 88imaginary part, imag( ) 88ImpDif( ), implicit derivative 89implicit derivative, Impdif( ) 89indefinite integral

template for 6indirection operator (#) 256indirection, # 226input, Input 89Input, input 89inString( ), within string 89int( ), integer 90intDiv( ), integer divide 90integer divide, intDiv( ) 90integer part, iPart( ) 93integer, int( ) 90integral, ∫ 221interpolate( ), interpolate 90inverse cumulative normal

distribution (invNorm( ) 92inverse, ^⁻¹ 232invF( ) 91invNorm( ), inverse cumulative

normal distribution) 92invt( ) 92Invχ²( ) 91iPart( ), integer part 93irr( ), internal rate of return

internal rate of return, irr( ) 93isPrime( ), prime test 93isVoid( ), test for void 94

L

label, Lbl 95language

get language information 82Lbl, label 95lcm, least common multiple 95least common multiple, lcm 95left( ), left 95left, left( ) 95length of string 52

less than or equal, ≤ 218LibPriv 47LibPub 47library

create shortcuts to objects 96libShortcut( ), create shortcuts to

library objects 96limit

lim( ) 96limit( ) 96template for 6

limit( ) or lim( ), limit 96linear regression, LinRegAx 98linear regression, LinRegBx 97, 99LinRegBx, linear regression 97LinRegMx, linear regression 98LinRegtIntervals, linear regression 99LinRegtTest 101linSolve() 102Δlist( ), list difference 103list to matrix, list►mat( ) 103list, conditionally count items in 35list, count items in 34list►mat( ), list to matrix 103lists

augment/concatenate,augment( ) 15

cross product, crossP( ) 36cumulative sum,

cumulativeSum( ) 41differences in a list, Δlist( ) 103dot product, dotP( ) 57empty elements in 251expression to list, exp►list( ) 64list to matrix, list►mat( ) 103matrix to list, mat►list( ) 111maximum, max( ) 111mid-string, mid( ) 114minimum, min( ) 115new, newList( ) 121product, product( ) 138sort ascending, SortA 174sort descending, SortD 175summation, sum( ) 180

Index 278

ln( ), natural logarithm 103LnReg, logarithmic regression 104local variable, Local 105local, Local 105Local, local variable 105Lock, lock variable or variable group 106locking variables and variable groups 106Log

template for 2logarithmic regression, LnReg 104logarithms 103logical double implication,⇔ 220logical implication,⇒ 219, 253logistic regression, Logistic 107logistic regression, LogisticD 108Logistic, logistic regression 107LogisticD, logistic regression 108loop, Loop 110Loop, loop 110LU, matrix lower-upper

decomposition 110

M

mat►list( ), matrix to list 111matrices

augment/concatenate,augment( ) 15

column dimension, colDim( ) 26column norm, colNorm( ) 26cumulative sum,

cumulativeSum( ) 41determinant, det( ) 51diagonal, diag( ) 51dimension, dim( ) 52dot addition, .+ 214dot division, ./ 215dot multiplication, .* 215dot power, .^ 215dot subtraction, .- 214eigenvalue, eigVl( ) 59eigenvector, eigVc( ) 58filling, Fill 69identity, identity( ) 86list to matrix, list►mat( ) 103

lower-upper decomposition, LU 110matrix to list, mat►list( ) 111maximum, max( ) 111minimum, min( ) 115new, newMat( ) 121product, product( ) 138QR factorization, QR 139random, randMat( ) 145reduced row echelon form, rref(

) 156row addition, rowAdd( ) 155row dimension, rowDim( ) 156row echelon form, ref( ) 147row multiplication and addition,

mRowAdd( ) 116row norm, rowNorm( ) 156row operation, mRow( ) 116row swap, rowSwap( ) 156submatrix, subMat( ) 180-181summation, sum( ) 180transpose, T 182

matrix (1 × 2)template for 4



matrix (m ×n)template for 4

matrix to list, mat►list( ) 111max( ), maximum 111maximum, max( ) 111mean( ), mean 112mean, mean( ) 112median( ), median 112median, median( ) 112medium-medium line regression,

MedMed 113MedMed, medium-medium line

regression 113mid-string, mid( ) 114mid( ), mid-string 114min( ), minimum 115minimum, min( ) 115minute notation, ′ 228

279 Index

mirr( ), modified internal rate ofreturn 115

mixed fractions, using propFrac(›with 139

mod( ), modulo 116mode settings, getMode( ) 83modes

setting, setMode( ) 162modified internal rate of return, mirr

( ) 115modulo, mod( ) 116mRow( ), matrix row operation 116mRowAdd( ), matrix row

multiplication and addition 116Multiple linear regression t test 118multiply, * 211MultReg 117MultRegIntervals( ) 117MultRegTests( ) 118

N

nand, Boolean operator 119natural logarithm, ln( ) 103nCr( ), combinations 120nDerivative( ), numeric derivative 121negation, entering negative numbers 256net present value, npv( ) 126new

list, newList( ) 121matrix, newMat( ) 121

newList( ), new list 121newMat( ), new matrix 121nfMax( ), numeric function

maximum 121nfMin( ), numeric function minimum 122nInt( ), numeric integral 122nom ), convert effective to nominal

rate 123nominal rate, nom( ) 123nor, Boolean operator 123norm( ), Frobenius norm 124normal distribution probability,

normCdf( ) 125normal line, normalLine( ) 124

normalLine( ) 124normCdf( ) 125normPdf( ) 125not equal, ≠ 217not, Boolean operator 125nPr( ), permutations 126npv( ), net present value 126nSolve( ), numeric solution 127nth root

template for 1numeric

derivative, nDeriv( ) 121-122derivative, nDerivative( ) 121integral, nInt( ) 122solution, nSolve( ) 127

O

objectscreate shortcuts to library 96

one-variable statistics, OneVar 128OneVar, one-variable statistics 128operators

order of evaluation 255or (Boolean), or 129or, Boolean operator 129ord( ), numeric character code 130

P

P►Rx( ), rectangular x coordinate 130P►Ry( ), rectangular y coordinate 131pass error, PassErr 131PassErr, pass error 131Pdf( ) 73percent, % 216permutations, nPr( ) 126piecewise function (2-piece)

template for 2piecewise function (N-piece)

template for 3piecewise( ) 132poissCdf( ) 132poissPdf( ) 132

Index 280

polarcoordinate, R►Pr( ) 143coordinate, R►Pθ( ) 142vector display, ►Polar 133

polyCoef( ) 133polyDegree( ) 134polyEval( ), evaluate polynomial 135polyGcd( ) 135-136polynomials

evaluate, polyEval( ) 135random, randPoly( ) 145

PolyRoots() 136power of ten, 10^( ) 231power regression,

PowerReg 136, 149, 151, 187power, ^ 213PowerReg, power regression 136Prgm, define program 137primenumber test, isPrime( ) 93prime, ′ 230probability densiy, normPdf( ) 125prodSeq() 138product( ), product 138product, ∏( ) 223

template for 5product, product( ) 138programming

define program, Prgm 137display data, Disp 52, 158pass error, PassErr 131

programsdefining private library 47defining public library 47

programs and programmingclear error, ClrErr 25display I/O screen, Disp 52, 158end program, EndPrgm 137end try, EndTry 191try, Try 191

proper fraction, propFrac 139propFrac, proper fraction 139

Q

QR factorization, QR 139

QR, QR factorization 139quadratic regression, QuadReg 140QuadReg, quadratic regression 140quartic regression, QuartReg 141QuartReg, quartic regression 141

R

R, radian 227R►Pr( ), polar coordinate 143R►Pθ( ), polar coordinate 142radian, R 227rand( ), random number 143randBin, random number 144randInt( ), random integer 144randMat( ), random matrix 145randNorm( ), random norm 145random

matrix, randMat( ) 145norm, randNorm( ) 145number seed, RandSeed 146polynomial, randPoly( ) 145

random sample 145randPoly( ), random polynomial 145randSamp( ) 145RandSeed, random number seed 146real( ), real 146real, real( ) 146reciprocal, ^⁻¹ 232rectangular-vector display, ►Rect 146rectangular x coordinate, P►Rx( ) 130rectangular y coordinate, P►Ry( ) 131reduced row echelon form, rref( ) 156ref( ), row echelon form 147RefreshProbeVars 148regressions

cubic, CubicReg 40exponential, ExpReg 66linear regression, LinRegAx 98linear regression, LinRegBx 97, 99logarithmic, LnReg 104Logistic 107logistic, Logistic 108medium-medium line, MedMed 113

281 Index

MultReg 117power regression,

PowerReg 136, 149, 151, 187quadratic, QuadReg 140quartic, QuartReg 141sinusoidal, SinReg 169

remain( ), remainder 149remainder, remain( ) 149remove

void elements from list 49Request 149RequestStr 151result

display in terms of cosine 29display in terms of e 63display in terms of sine 166

result values, statistics 177results, statistics 176return, Return 152Return, return 152right( ), right 152right, right( ) 27, 60, 90, 152rk23( ), RungeKutta function 152rotate( ), rotate 154rotate, rotate( ) 154round( ), round 155round, round( ) 155row echelon form, ref( ) 147rowAdd( ), matrix row addition 155rowDim( ), matrix row dimension 156rowNorm( ), matrix row norm 156rowSwap( ), matrix row swap 156rref( ), reduced row echelon form 156

S

sec⁻¹( ), inverse secant 157sec( ), secant 157sech⁻¹( ), inverse hyperbolic secant 158sech( ), hyperbolic secant 158second derivative

template for 6second notation, " 228seq( ), sequence 159

seqGen( ) 159seqn( ) 160sequence, seq( ) 159-160series( ), series 161series, series( ) 161set

mode, setMode( ) 162setMode( ), set mode 162settings, get current 83shift( ), shift 163shift, shift( ) 163sign( ), sign 165sign, sign( ) 165simult( ), simultaneous equations 165simultaneous equations, simult( ) 165sin⁻¹( ), arcsine 167sin( ), sine 166sine

display expression in terms of 166sine, sin( ) 166sinh⁻¹( ), hyperbolic arcsine 168sinh( ), hyperbolic sine 168SinReg, sinusoidal regression 169sinusoidal regression, SinReg 169solution, deSolve( ) 49solve( ), solve 170solve, solve( ) 170SortA, sort ascending 174SortD, sort descending 175sorting

ascending, SortA 174descending, SortD 175

spherical vector display, ►Sphere 175sqrt( ), square root 176square root

template for 1square root, √( ) 176, 223standard deviation, stdDev( ) 178, 198stat.results 176stat.values 177statistics

combinations, nCr( ) 120factorial, ! 220mean, mean( ) 112

Index 282

median, median( ) 112one-variable statistics, OneVar 128permutations, nPr( ) 126random norm, randNorm( ) 145random number seed,

RandSeed 146standard deviation, stdDev( ) 178, 198two-variable results, TwoVar 195variance, variance( ) 198

stdDevPop( ), population standarddeviation 178

stdDevSamp( ), sample standarddeviation 178

Stop command 179store variable (→) 233storing

symbol, & 234string

dimension, dim( ) 52length 52

string( ), expression to string 179strings

append, & 220character code, ord( ) 130character string, char( ) 22expression to string, string( ) 179format, format( ) 72formatting 72indirection, # 226left, left( ) 95mid-string, mid( ) 114right, right( ) 27, 60, 90, 152rotate, rotate( ) 154shift, shift( ) 163string to expression, expr( ) 65, 107using to create variable names 256within, InString 89

student-t distribution probability,tCdf( ) 185

student-t probability density, tPdf( ) 190subMat( ), submatrix 180-181submatrix, subMat( ) 180-181substitution with "|" operator 232subtract, - 210sum of interest payments 225

sum of principal payments 225sum( ), summation 180sum, ∑( ) 224

template for 5sumIf( ) 180summation, sum( ) 180sumSeq() 181system of equations (2-equation)

template for 3system of equations (N-equation)

template for 3

T

t test, tTest 192T, transpose 182tan⁻¹( ), arctangent 183tan( ), tangent 182tangent line, tangentLine( ) 183tangent, tan( ) 182tangentLine( ) 183tanh⁻¹( ), hyperbolic arctangent 184tanh( ), hyperbolic tangent 184Taylor polynomial, taylor( ) 185taylor( ), Taylor polynomial 185tCdf( ), studentt distribution

probability 185tCollect( ), trigonometric collection 186templates

absolute value 3-4definite integral 6derivative or nth derivative 6e exponent 2exponent 1first derivative 5fraction 1indefinite integral 6limit 6Log 2matrix (1 × 2) 4matrix (2 × 1) 4matrix (2 × 2) 4matrix (m ×n) 4nth root 1piecewise function (2-piece) 2

283 Index

piecewise function (N-piece) 3product, ∏( ) 5second derivative 6square root 1sum, ∑( ) 5system of equations (2-

equation) 3system of equations (N-

equation) 3test for void, isVoid( ) 94Test_2S, 2-sample F test 75tExpand( ), trigonometric expansion 186Text command 187time value ofmoney, FutureValue 193time value ofmoney, Interest 193time value ofmoney, number of

payments 194time value ofmoney, payment

amount 194time value ofmoney, present value 194tInterval, t confidence interval 187tInterval_2Samp, twosample t

confidence interval 188ΔtmpCnv() 189tmpCnv() 189tPdf( ), student probability density 190trace( ) 190transpose, T 182trigonometric collection, tCollect( ) 186trigonometric expansion, tExpand( ) 186Try, error handling command 191tTest, t test 192tTest_2Samp, two-sample t test 192TVMarguments 195tvmFV( ) 193tvmI( ) 193tvmN( ) 194tvmPmt( ) 194tvmPV( ) 194two-variable results, TwoVar 195TwoVar, two-variable results 195

U

underscore, _ 230

unit vector, unitV( ) 197units

convert 231unitV( ), unit vector 197unLock, unlock variable or variable

group 197unlocking variables and variable

groups 197user-defined functions 46user-defined functions and

programs 47

V

variablecreating name from a character

string 256variable and functions

copying 29variables

clear all single-letter 25delete, DelVar 48local, Local 105

variables, locking and unlocking 82, 106, 197variance, variance( ) 198varPop( ) 198varSamp( ), sample variance 198vectors

cross product, crossP( ) 36cylindrical vector display,

►Cylind 42dot product, dotP( ) 57unit, unitV( ) 197

void elements 251void elements, remove 49void, test for 94

W

Wait command 199warnCodes( ), Warning codes 200warning codes and messages 269when( ), when 200when, when( ) 200while, While 201While, while 201

Index 284

with, | 232within string, inString( ) 89

X

x², square 214XNOR 220xor, Boolean exclusive or 201

Z

zeroes( ), zeroes 202zeroes, zeroes( ) 202zInterval, z confidence interval 204zInterval_1Prop, one-proportion z

confidence interval 205zInterval_2Prop, two-proportion z

confidence interval 205zInterval_2Samp, two-sample z

confidence interval 206zTest 206zTest_1Prop, one-proportion z test 207zTest_2Prop, two-proportion z test 207zTest_2Samp, two-sample z test 208

Χ

χ²Cdf( ) 24χ²GOF 24χ²Pdf( ) 24

285 Index

TI-Nspire™CXCAS ReferenceGuide

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