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TI-Nspire™Reference Guide

This guidebook applies to TI-Nspire™ software version 4.5. To obtain the latest versionof the documentation, go to education.ti.com/go/download.

https://education.ti.com/go/download

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

License

Please see the complete license installed in C:\Program Files\TI Education\<TI-Nspire™Product Name>\license.

© 2006 - 2017 Texas Instruments Incorporated

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Contents

Important Information ii

Expression Templates 1

Alphabetical Listing 7A 7B 15C 19D 34E 43F 50G 57I 66L 74M 88N 97O 105P 107Q 113R 116S 130T 148U 160V 161W 162X 164Z 165

iii

iv

Symbols 171

Empty (Void) Elements 194

Shortcuts for Entering Maths Expressions 196

EOS™ (Equation Operating System) Hierarchy 198

Constants and Values 200

Error Codes and Messages 201

Warning Codes and Messages 209

Texas Instruments Support and Service 211Service and Warranty Information 211

Index 212

Expression TemplatesExpression templates give you an easy way to enter maths 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.

Use the arrow keys or presse to move the cursor to each element’s position, andtype a value or expression for the element. Press· or/· to evaluate theexpression.

Fraction template /p keys

Note: See also / (divide), page 173.

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 174.

Example:

Square root template /q keys

Note: See also √() (square root), page183.

Example:


2 Expression Templates

Nth root template /l keys

Note: See also root(), page 127.

Example:

e exponent template u keys

Natural exponential e raised to a power

Note: See also e^(), page 43.

Example:

Log template /s key

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

Note: See also log(), page 85.

Example:

Piecewise template (2-piece) Catalogue >

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 108.

Example:

Piecewise template (N-piece) Catalogue >Lets you create expressions and conditions for an Example:

Piecewise template (N-piece) Catalogue >N-piece piecewise function. Prompts for N.

Note: See also piecewise(), page 108.

See the example for Piecewisetemplate (2-piece).

System of 2 equations template Catalogue >

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

Note: See also system(), page 148.

Example:

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

Note: See also system(), page 148.

Example:

See the example for Systemofequations template (2-equation).

Absolute value template Catalogue >

Note: See also abs(), page 7.Example:



dd°mm’ss.ss’’ template Catalogue >

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) Catalogue >

Creates a 2 x 2 matrix.

Example:

Matrix template (1 x 2) Catalogue >

.Example:

Matrix template (2 x 1) Catalogue >Example:

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

Example:

Matrix template (m x n) Catalogue >Note: If you create a matrix with a largenumber of rows and columns, it may take afew moments to appear.

Sum template (Σ) Catalogue >

Note: See also Σ() (sumSeq), page 184.

Example:

Product template (Π) Catalogue >

Note: See alsoΠ() (prodSeq), page 183.

Example:

First derivative template Catalogue >

The first derivative template can be used tocalculate first derivative at a pointnumerically, using auto differentiationmethods.

Note: See also d() (derivative), page 182.

Example:

Second derivative template Catalogue >

The second derivative template can be used

Example:



Second derivative template Catalogue >to calculate second derivative at a pointnumerically, using auto differentiationmethods.

Note: See also d() (derivative), page 182.

Definite integral template Catalogue >

The definite integral template can be usedto calculate the definite integralnumerically, using the same method as nInt().

Note: See also nInt(), page 100.

Example:

Alphabetical ListingItems whose names are not alphabetic (such as +, ! and >) are listed at the end of thissection, starting page 171. Unless otherwise specified, all examples in this sectionwere performed in the default reset mode, and all variables are assumed to beundefined.

A

abs() Catalogue >abs(Value1)⇒value

abs(List1)⇒list

abs(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.

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

Amortisation function that returns a matrixas an amortisation 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 158.

• 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.

Alphabetical Listing 7

8 Alphabetical Listing

amortTbl() Catalogue >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 amortisation functions ΣInt() andΣPrn(), page 185, and bal(), page 15.

and Catalogue >BooleanExpr1 andBooleanExpr2⇒Boolean expression

BooleanList1 and BooleanList2⇒Booleanlist

BooleanMatrix1 andBooleanMatrix2⇒Boolean matrix

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

Integer1andInteger2⇒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.

angle() Catalogue >angle(Value1)⇒value

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

InDegree anglemode:

InGradian anglemode:

In Radian anglemode:

angle(List1)⇒list

angle(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 Catalogue >ANOVA List1,List2[,List3,...,List20][,Flag]

Performs a one-way analysis of variance forcomparing the means of two to 20 populations. Asummary of results is stored in the stat.resultsvariable (page 143).

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

Computes a two-way analysis of variance forcomparing the means of two to 10 populations. Asummary of results is stored in the stat.resultsvariable (page 143).

LevRow=0 for Block

LevRow=2,3,...,Len-1, for Two Factor, whereLen=length(List1)=length(List2) = … = length(List10) and Len / LevRow ∈ {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 keys

Ans⇒value

Returns the result of the most recentlyevaluated expression.

approx() Catalogue >approx(Value1)⇒number

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)⇒list

approx(Matrix1)⇒matrix

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

4approxFraction() Catalogue >

Value 4approxFraction([Tol])⇒value

List 4approxFraction([Tol])⇒list

Matrix 4approxFraction([Tol])⇒matrix

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

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

approxRational() Catalogue >approxRational(Value[, Tol])⇒value

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/(), page 26.

arccosh() See cosh/(), page 27.

arccot() See cot/(), page 28.

arccoth() See coth/(), page 29.

arccsc() See csc/(), page 31.



arccsch() See csch/(), page 32.

arcsec() See sec/(), page 130.

arcsech() See sech/(), page 131.

arcsin() See sin/(), page 139.

arcsinh() See sinh/(), page 140.

arctan() See tan/(), page 149.

arctanh() See tanh/(), page 150.

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

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

bal(NPmt,amortTable)⇒value

Amortisation function that calculatesschedule balance after a specified payment.


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


• If you omit Pmt, it defaults to



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

• If you omit FV, it defaults to FV=0.• The defaults for PpY, CpY and PmtAt


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

bal(NPmt,amortTable) calculates thebalance after payment number NPmt,based on amortisation table amortTable.The amortTable argument must be amatrix in the form described underamortTbl(), page 7.

Note: See also GInt() and GPrn(), page 185.

4Base2 Catalogue >Integer1 4Base2⇒integer

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

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 binaryNumber

0h 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,

N1 is displayed as 0hFFFFFFFFFFFFFFFF inHex base mode 0b111...111 (64 1’s) inBinary base mode

N263 is displayed as0h8000000000000000 in Hex base mode0b100...000 (63 zeroes) in Binary base

4Base2 Catalogue >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 N263 and is displayed as0h8000000000000000 in Hex base mode0b100...000 (63 zeroes) in Binary basemode

264 becomes 0 and is displayed as

0h0 in Hex base mode

0b0 in Binary base mode

N263 N1 becomes 263 N 1 and is displayedas

0h7FFFFFFFFFFFFFFF in Hex base mode

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



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

0b binaryNumber

0h hexadecimalNumber

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

A binary number can have up to 64 digits. 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.





Converts Integer1 to a hexadecimalnumber. Binary or hexadecimal numbersalways have a 0b or 0h prefix, respectively.

0b binaryNumber

0h hexadecimalNumber

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

A binary number can have up to 64 digits. 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 4Base2, page 16.

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

binomCdf(n,p,lowBound,upBound)⇒number iflowBound and upBound are numbers, list iflowBound and upBound are lists

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

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

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

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

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

Computes a probability for the discrete binomialdistribution with n number of trials and probability pof success on each trial.

C

ceiling() Catalogue >ceiling(Value1) ⇒ value

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() Catalogue >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.




centralDiff() Catalogue >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().

char() Catalogue >char(Integer) ⇒ character

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

χ22way Catalogue >χ22way obsMatrix

chi22way obsMatrix

Computes a χ2 test for association on the two-waytable of counts in the observed matrix obsMatrix. Asummary of results is stored in the stat.resultsvariable. (page 143)

For information on the effect of empty elements in amatrix, see “Empty (Void) Elements,” page 194.


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

χ2Cdf() Catalogue >chi2Cdf(lowBound,upBound,df) ⇒ number iflowBound and upBound are numbers, list iflowBound and upBound are lists

Computes the χ2 distribution probability betweenlowBound and upBound for the specified degrees offreedom df.

For P(X ≤ upBound), set lowBound = 0.

For information on the effect of empty elements in alist, see “Empty (Void) Elements,” page 194.

χ2GOF Catalogue >χ2GOF obsList,expList,df

chi2GOF obsList,expList,df

Performs a test to confirm that sample data is froma population that conforms to a specifieddistribution. obsList is a list of counts and mustcontain integers. A summary of results is stored inthe stat.results variable. (See page 143.)



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() Catalogue >χ2Pdf(XVal,df) ⇒ number if XVal is a number, listif XVal is a list

chi2Pdf(XVal,df) ⇒ number if XVal is a number,list if XVal is a list

Computes the probability density function (pdf) forthe χ2 distribution at a specified XVal value for thespecified degrees of freedom df.



χ2Pdf() Catalogue >For information on the effect of empty elements in alist, see “Empty (Void) Elements,” page 194.

ClearAZ Catalogue >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 161.

ClrErr Catalogue >ClrErr

Clears the error status and sets system variableerrCode to zero.

The Else clause of the Try...Else...EndTry block shoulduse ClrErr or PassErr. If the error is to be processed orignored, use ClrErr. If what to do with the error is notknown, use PassErr to send it to the next errorhandler. If there are no more pendingTry...Else...EndTry error handlers, the error dialoguebox will be displayed as normal.

Note: See also PassErr, page 108, and Try, page 154.

Note for entering the example: For instructions onentering multi-line programme and functiondefinitions, refer to the Calculator section of yourproduct guidebook.

For anexample of ClrErr, SeeExample 2 under the Trycommand, page 154.

colAugment() Catalogue >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() Catalogue >colDim(Matrix) ⇒ expression

Returns the number of columns containedinMatrix.

Note: See also rowDim().

colNorm() Catalogue >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().

conj() Catalogue >

conj(Value1) ⇒ valueconj(List1) ⇒ listconj(Matrix1) ⇒ matrix

Returns the complex conjugate of theargument.

constructMat() Catalogue >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 Catalogue >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() Catalogue >corrMat(List1,List2[,…[,List20]])

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

cos() µ keycos(Value1) ⇒ value

cos(List1) ⇒ list

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

InDegree anglemode:

cos() µ keycos(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. InGradian anglemode:


cos(squareMatrix1) ⇒ squareMatrix

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

When a scalar function f(A) operates onsquareMatrix1 (A), 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) =




cos() µ key

All computations are performed usingfloating-point arithmetic.

cos⁻¹() µ key

cos⁻¹(Value1) ⇒ valuecos⁻¹(List1) ⇒ list

cos⁻¹(Value1) returns the angle whosecosine is Value1.

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(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:

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

cosh() Catalogue >

cosh(Value1) ⇒ valuecosh(List1) ⇒ list

cosh(Value1) returns the hyperbolic cosine

InDegree anglemode:

cosh() Catalogue >of the argument.

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

cosh⁻¹(Value1) ⇒ valuecosh⁻¹(List1) ⇒ list

cosh⁻¹(Value1) returns the inversehyperbolic cosine of the argument.

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 keyInDegree anglemode:



cot() µ keycot(Value1) ⇒ valuecot(List1) ⇒ list

Returns the cotangent of Value1 or returnsa list of the cotangents of all elements inList1.

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.



cot⁻¹() µ key

cot⁻¹(Value1) ⇒ valuecot⁻¹(List1) ⇒ list

Returns the angle whose cotangent isValue1 or returns a list containing theinverse cotangents of each element ofList1.


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

InDegree anglemode:



coth() Catalogue >

coth(Value1) ⇒ valuecoth(List1) ⇒ list

Returns the hyperbolic cotangent of Value1or returns a list of the hyperboliccotangents of all elements of List1.

coth⁻¹() Catalogue >

coth⁻¹(Value1) ⇒ valuecoth⁻¹(List1) ⇒ list

Returns the inverse hyperbolic cotangent ofValue1 or returns a list containing theinverse hyperbolic cotangents of eachelement of List1.

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

count() Catalogue >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.

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 194.

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

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

Criteria can be:

• A value, expression, or string. For

Counts the number of elements equal to 3.



countif() Catalogue >example, 3 counts only those elements inList that simplify to the value 3.

• A Boolean expression containing thesymbol ? as a place holder 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 194.

Note: See also sumIf(), page 147, andfrequency(), page 55.

Counts the number of elements equal to“def.”

Counts 1 and3.

Counts 3, 5, and7.

Counts 1, 3, 7, and9.

cPolyRoots() Catalogue >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 expandedform in one variable. Do not useunexpanded forms such as y2•y+1 orx•x+2•x+1The second syntax, cPolyRoots(ListOfCoeffs), returns a list of complexroots for the coefficients in ListOfCoeffs.

Note: See also polyRoots(), page 110.

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

Returns the cross product of List1 andList2 as a list.

crossP() Catalogue >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 key

csc(Value1) ⇒ valuecsc(List1) ⇒ list

Returns the cosecant of Value1 or returns alist containing the cosecants of all elementsin List1.

InDegree anglemode:



csc⁻¹() µ key

csc⁻¹(Value1) ⇒valuecsc⁻¹(List1) ⇒ list

Returns the angle whose cosecant isValue1 or returns a list containing theinverse cosecants of each element of List1.


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

InDegree anglemode:





csc⁻¹() µ key

csch() Catalogue >csch(Value1) ⇒ value

csch(List1) ⇒ list

Returns the hyperbolic cosecant of Value1or returns a list of the hyperbolic cosecantsof all elements of List1.

csch⁻¹() Catalogue >

csch⁻¹(Value) ⇒ valuecsch⁻¹(List1) ⇒ list

Returns the inverse hyperbolic cosecant ofValue1 or returns a list containing theinverse hyperbolic cosecants of eachelement of List1.

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

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

Computes the cubic polynomial regressiony=a•x3+b•x2+c•x+d on lists X and Y with frequencyFreq. A summary of results is stored in thestat.results variable. (See page 143.)

All the lists must have equal dimension except forInclude.

X and Y are lists of independent and dependentvariables.

Freq is an optional list of frequency values. Eachelement in Freq specifies the frequency ofoccurrence for each corresponding X and Y datapoint. The default value is 1. All elements must beintegers ≥ 0.

CubicReg Catalogue >Category is a list of numeric or string category codesfor the corresponding X and Y data.

Include is a list of one or more of the category codes.Only those data items whose category code isincluded in this list are 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() Catalogue >cumulativeSum(List1) ⇒ list

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

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 page194.



Cycle Catalogue >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-lineprogramme and function definitions, referto the Calculator section of your productguidebook.

Function listing that sums the integers from1to 100 skipping 50.

►Cylind Catalogue >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.

D

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

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

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 two

dbd() Catalogue >formats. The decimal placementdifferentiates between the date formats.

MM.DDYY (format used commonly in theUnited States)

DDMM.YY (format use commonly inEurope)

4DD Catalogue >Expr1 4DD⇒value

List1 4DD⇒list

Matrix1 4DD⇒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:



4Decimal Catalogue >

Number1 4Decimal⇒value

List1 4Decimal⇒value

Matrix1 4Decimal⇒value

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

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



Define Catalogue >Define Var = Expression

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

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

Parameters, such as Param1, provide placeholders for passing arguments to 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, ...) =FuncBlockEndFunc

Define Program(Param1, Param2, ...) =PrgmBlockEndPrgm

In this form, the user-defined function orprogramme 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 Catalogue >Note: See also Define LibPriv, page 37, andDefine LibPub, page 37.

Define LibPriv Catalogue >Define LibPriv Var = Expression

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

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

Define LibPriv Program(Param1, Param2, ...) =PrgmBlockEndPrgm

Operates the same as Define, except defines aprivate library variable, function, or programme.Private functions and programs do not appear in theCatalogue.

Note: See also Define, page 36, and Define LibPub,page 37.

Define LibPub Catalogue >Define LibPub Var = Expression

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

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

Define LibPub Program(Param1, Param2, ...) = PrgmBlockEndPrgm

Operates the same as Define, except defines a publiclibrary variable, function, or programme. Publicfunctions and programs appear in the Catalogue afterthe library has been saved and refreshed.

Note: See also Define, page 36, and Define LibPriv,page 37.



deltaList() See @List(), page 81.

DelVar Catalogue >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 161.

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() Catalogue >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 194.

det() Catalogue >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:

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

diag() Catalogue >diag(List)⇒matrix

diag(rowMatrix)⇒matrix

diag(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() Catalogue >dim(List)⇒integer

Returns the dimension of List.



dim() Catalogue >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 Catalogue >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 Catalogue >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/programme.

This command allows dashboard-likeoutput from programmes where thevalue of an expression or from a sensorreading is updated on the same line.

Example

DispAt Catalogue >DispAtand Disp can be used within thesame programme.

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 maths 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 Catalogue >

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' dialogue

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)

4DMS Catalogue >Value 4DMS

List 4DMS

Matrix 4DMS

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 ¡, ', ''(page 188) for DMS (degree, minutes,seconds) format.

Note: 4DMS will convert from radians todegrees when used in radian mode. If theinput is followed by a degree symbol ¡ , noconversion will occur. You can use 4DMSonly at the end of an entry line.

InDegree anglemode:

dotP() Catalogue >dotP(List1, List2)⇒expression

Returns the “dot” product of two lists.

dotP(Vector1, Vector2)⇒expression

Returns the “dot” product of two vectors.

dotP() Catalogue >Both must be row vectors, or both must becolumn vectors.

E

e^() u keye^(Value1) ⇒ value

Returns e raised to the Value1 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

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().


eff() Catalogue >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.



eff() Catalogue >nominalRate must be a real number, andCpY must be a real number > 0.

Note: See also nom(), page 101.

eigVc() Catalogue >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() Catalogue >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 67.

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


EndFor See For, page 53.

EndFunc See Func, page 56.

EndIf See If, page 67.

EndLoop See Loop, page 87.

EndPrgm See Prgm, page 111.

EndTry See Try, page 154.

EndWhile See While, page 164.



euler () Catalogue >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).

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•VarStep

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


Systemof equations:

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

euler () Catalogue >is 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.

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.

Programme to fade-in the redelement

Execute the programme.



eval () Hub MenuAlthough 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 58), GetStr (page64), and Send (page 131).

Exit Catalogue >Exit

Exits the current For, While, or Loop block.

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


Function listing:

exp() u keyexp(Value1) ⇒ value

Returns e raised to the Value1 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().


expr() Catalogue >expr(String) ⇒ expression

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

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

Computes the exponential regression y = a•(b)x onlists X and Y with frequency Freq. A summary ofresults is stored in the stat.results variable. (Seepage 143.)



Freq is an optional list of frequency values. Eachelement in Freq specifies the frequency ofoccurrence for each corresponding X and Y datapoint. The default value is 1. All elements must beintegers ≥ 0.

Category is a list of numeric or string category codesfor the corresponding X and Y data.


For information on the effect of empty elements in a



ExpReg Catalogue >list, see “Empty (Void) Elements,” page 194.


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() Catalogue >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.

factor() Catalogue >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() Catalogue >FCdf(lowBound,upBound,dfNumer,dfDenom)⇒number if lowBound and upBound are numbers,list if lowBound and upBound are lists

FCdf(lowBound,upBound,dfNumer,dfDenom)⇒number if lowBound and upBound are numbers,list if lowBound and upBound are lists

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

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

Fill Catalogue >Fill Value, matrixVar⇒matrix

Replaces each element in variablematrixVar with Value.

matrixVar must already exist.

Fill Value, listVar⇒list

Replaces each element in variable listVarwith Value.

listVar must already exist.

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

Provides an abbreviated version of the 1-variablestatistics on list X. A summary of results is stored inthe stat.results variable (page 143).

X represents a list containing the data.



FiveNumSummary Catalogue >Freq is an optional list of frequency values. Eachelement in Freq specifies the frequency ofoccurrence for each corresponding X and Y datapoint. The default value is 1.

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


An empty (void) element in any of the lists X, Freq,or Category results in a void for the correspondingelement of all those lists. For more information onempty elements, see page 194.


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() Catalogue >floor(Value1)⇒integer

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


floor(List1)⇒list

floor(Matrix1)⇒matrix

Returns a list or matrix of the floor of eachelement.

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

For Catalogue >For Var, Low, High [, Step]

Block

EndFor

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() Catalogue >format(Value[, formatString])⇒string

Returns Value as a character string basedon the format template.

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.

G[n][c]: Same as fixed format but alsoseparates digits to the left of the radix intogroups of three. c specifies the group



format() Catalogue >separator 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() Catalogue >fPart(Expr1)⇒expression

fPart(List1)⇒list

fPart(Matrix1)⇒matrix

Returns the fractional part of the argument.

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


FPdf() Catalogue >FPdf(XVal,dfNumer,dfDenom)⇒number if XVal is anumber, list if XVal is a list

Computes the F distribution probability at XVal forthe specified dfNumer (degrees of freedom) anddfDenom.

freqTable4list() Catalogue >freqTable4list(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.

freqIntegerList must have the same

freqTable4list() Catalogue >dimension 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() Catalogue >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 194.

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

Note: See also countIf(), page 29.

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 Catalogue >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 summary of resultsis stored in the stat.results variable (page 143).

For Ha: s1 > s2, set Hypoth>0

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

For Ha: s1 < s2, set Hypoth<0

For information on the effect of empty elements in alist, see “Empty (Void) Elements”, page 194.


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_bar

stat.x2_bar

Samplemeans of the data sequences inList 1 andList 2

stat.n1, stat.n2 Size of the samples

Func Catalogue >FuncBlockEndFunc

Template for creating a user-definedfunction.

Block can be a single statement, a seriesof statements separated with the “:”character, or a series of statements onseparate lines. The function can use the

Define a piecewise function:

Func Catalogue >Return instruction to return a specific result.


Result of graphing g(x)

G

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

Returns the highest common factor 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 highest common factors of thecorresponding elements in List1 and List2.gcd(Matrix1, Matrix2)⇒matrix

Returns the highest common factors of thecorresponding elements inMatrix1 andMatrix2.

geomCdf() Catalogue >geomCdf(p,lowBound,upBound)⇒number iflowBound and upBound are numbers, list iflowBound and upBound are lists

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

Computes a cumulative geometric probability fromlowBound to upBound with the specified probabilityof success p.



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

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

Computes a probability at XVal, the number of thetrial on which the first success occurs, for thediscrete geometric distribution with the specifiedprobability 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.

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

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.

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 programme to store the receivedstring as a function definition. This syntaxoperates as if the programme executed the

Get Hub Menucommand:

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

The programme can then use the definedfunction func().

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

Note: See also GetStr, page 64 and Send,page 131.

getDenom() Catalogue >getDenom(Fraction1)⇒value

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

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

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

Example:

• keypressed := getKey() will return akey 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 programme till a keyis pressed.

Example:



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 - Centre click n/a "centre"

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 to 9 0-9 "0" ... "9"

Templates n/a "template"

Catalogue n/a "cat"

^ ^ "^"

X^2 n/a "square"

/ (division key) / "/"

* (multiply key) * "*"

e^x n/a "exp"

10^x n/a "10power"

+ + "+"

Handheld Device/EmulatorKey Desktop Return Value

- - "-"

( ( "("

) ) ")"

. . "."

(-) 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 maths box)

Note: It is important to note that the presence of getKey() in a programme changes howcertain events are handled by the system. Some of these are described below.



Terminate programme and Handle event - Exactly as if the user were to break out ofprogramme by pressing the ON key"Support" below means - System works as expected - programme continues to run.

Event Device Desktop - TI-Nspire™Student Software

Quick Poll Terminate programme,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 programme,handle event

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

End Class Terminate programme,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 youexit the programme theTI-Innovator™ Hub is stillworking with thehandheld.

Same as the handheld

getLangInfo() Catalogue >getLangInfo()⇒string

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

English = “en”Danish = “da”German = “de”

getLangInfo() Catalogue >Finnish = “fi”French = “fr”Italian = “it”Dutch = “nl”Belgian Dutch = “nl_BE”Norwegian = “no”Portuguese = “pt”Spanish = “es”Swedish = “sv”

getLockInfo() Catalogue >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 84, and unLock, page 161.

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 programme to temporarily restore thesettings within the execution of thefunction or programme only. See setMode(), page 134.



Mode Name 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

VectorFormat

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

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

getNum() Catalogue >getNum(Fraction1)⇒value

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: Operates identically to theGet command, except that the retrieved value isalways interpreted as a string. By contrast, the Getcommand interprets the response as an expressionunless it is enclosed in quotation marks ("").

Note: See also Get, page 58 and Send, page 131.

For examples, seeGet.

getType() Catalogue >getType(var)⇒string

Returns a string that indicates the datatype of variable var.

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

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

getVarInfo(LibNameString)⇒matrix orstring

getVarInfo() returns a matrix of information(variable name, type, library accessibilityand 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 to the left, in which theresult of getVarInfo() is assigned to variablevs. Attempting to display row 2 or row 3 ofvs returns 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 generalised matrix structurewhere an element of a matrix can be eithera matrix or a list.



Goto Catalogue >Goto labelName

Transfers control to the label labelName.

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


4Grad Catalogue >Expr1 4 Grad⇒expression

Converts Expr1 to gradian angle measure.

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

InDegree anglemode:


I

identity() Catalogue >identity(Integer) ⇒ matrix

Returns the identity matrix with adimension of Integer.

Integer must be a positive integer.

If Catalogue >If BooleanExpr

Statement

If BooleanExpr ThenBlock

EndIf

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 Catalogue >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() Catalogue >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 other

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.

ifFn() Catalogue >list or matrix arguments must have thesame dimension(s), and the result will havethe same dimension(s). Value_If_false is not specified. Undef is

used.

One element selected fromValue_If_true.One element selected fromValue_If_unknown.

imag() Catalogue >imag(Value1) ⇒ value

Returns the imaginary part of theargument.

imag(List1) ⇒ list

Returns a list of the imaginary parts of theelements.

imag(Matrix1) ⇒ matrix

Returns a matrix of the imaginary parts ofthe elements.

Indirection See #(), page 186.

inString() Catalogue >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).



inString() Catalogue >If srcString does not contain subString orStart is > the length of srcString, returnszero.

int() Catalogue >

int(Value) ⇒ integerint(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() Catalogue >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.

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

This function does the following:

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 a

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


Use the interpolate() function to calculate the

interpolate () Catalogue >value 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 a number or a list ofnumbers.

function values for the xvaluelist:

invχ2() Catalogue >invχ2(Area,df)

invChi2(Area,df)

Computes the Inverse cumulative χ2 (chi-square)probability function specified by degree of freedom,df for a given Area under the curve.

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

invF(Area,dfNumer,dfDenom)

computes the Inverse cumulative F distributionfunction specified by dfNumer and dfDenom for agiven Area under the curve.

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

Given the number of trials (NumTrials) andthe probability of success of each trial(Prob), this function returns the minimumnumber of successes, k, such that thecumulative probability of k successes isgreater than or equal to the givencumulative probability (CumulativeProb).

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%?



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

OutputForm=1, displays result as a matrix.

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

Given the probability of success of eachtrial (Prob), and the number of successes(NumSuccess), this function returns theminimum number of trials, N, such that thecumulative probability of x successes is lessthan or equal to the given cumulativeprobability (CumulativeProb).

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

OutputForm=1, displays result as a matrix.

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

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

Computes the inverse cumulative normal distributionfunction for a given Area under the normaldistribution curve specified by μ and σ.

invt() Catalogue >invt(Area,df)

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

iPart() Catalogue >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() Catalogue >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 93.

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

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.

Note for entering the example: Forinstructions on entering multi-line

Function to find the next prime after aspecifiednumber:



isPrime() Catalogue >programme and function definitions, referto the Calculator section of your productguidebook.

isVoid() Catalogue >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 194.

L

Lbl Catalogue >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() Catalogue >lcm(Number1, Number2)⇒expression

lcm(List1, List2)⇒list

lcm(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() Catalogue >left(sourceString[, Num])⇒string

Returns the leftmost Num characterscontained in character string sourceString.

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

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() Catalogue >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 its

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



libShortcut() Catalogue >ShortcutNameString.

Set LibPrivFlag=0 to exclude privatelibrary objects (default)

Set LibPrivFlag=1 to include privatelibrary objects

To copy a variable group, see CopyVar, page24.

To delete a variable group, see DelVar,page 38.

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

Computes the linear regressiony = a+b·xon lists Xand Y with frequency Freq. A summary of results isstored in the stat.results variable (page 143).



Freq is an optional list of frequency values. Eachelement in Freq specifies the frequency ofoccurrence for each corresponding X and Y datapoint. The default value is 1. All elements must beintegers | 0.





stat.RegEqn Regression Equation: a+b·x


stat.r2 Coefficient of determination


stat.r Correlation coefficient


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


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

Computes the linear regression y = m·x+b on lists Xand Y with frequency Freq. A summary of results isstored in the stat.results variable (page 143).








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

stat.m,stat.b











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

For Slope. Computes a level C confidence interval forthe slope.

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

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

A summary of results is stored in the stat.resultsvariable (page 143).

All the lists must have equal dimension.


F is an optional list of frequency values. Eachelement in F specifies the frequency of occurrencefor each corresponding X and Y data point. Thedefault value is 1. All elements 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 Catalogue >LinRegtTest X,Y[,Freq[,Hypoth]]

Computes a linear regression on the X and Y lists anda t test on the value of slope b and the correlationcoefficient r for the equation y=a+bx. It tests thenull hypothesis H

0:b=0 (equivalently, r=0) against

one of three alternative hypotheses.



Freq is an optional list of frequency values. Each



LinRegtTest Catalogue >element in Freq specifies the frequency ofoccurrence for each corresponding X and Y datapoint. The default value is 1. All elements must beintegers | 0.

Hypoth is an optional value specifying one of threealternative hypotheses against which the nullhypothesis (H

0:b=r=0) will be tested.

For Ha: bƒ0 and rƒ0 (default), set Hypoth=0

For Ha: b<0 and r<0, set Hypoth<0

For Ha: b>0 and r>0, set Hypoth>0




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() Catalogue >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=1 andx=2,x) produces an “Argument Error” result.

@List() Catalogue >@List(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.



list4mat() Catalogue >list4mat(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,zeroes are added.

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

ln() /u keys

ln(Value1)⇒value

ln(List1)⇒list

Returns the natural logarithm of theargument.

For a list, returns the natural logarithms ofthe elements.

If complex formatmode is Real:

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.

squareMatrix1must be diagonalisable. Theresult always contains floating-pointnumbers.

In Radian anglemode andRectangularcomplex format:


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

Computes the logarithmic regression y = a+b·ln(x) onlists X and Y with frequency Freq. A summary ofresults is stored in the stat.results variable (page143).








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



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

stat.Resid Residuals associatedwith the logarithmicmodel







Local Catalogue >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.


Lock Catalogue >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 161, andgetLockInfo(),page 63.

log() /s keys

log(Value1[,Value2])⇒value

log(List1[,Value2])⇒list

Returns the base-Value2 logarithm of thefirst argument.

Note: See also Log template, page 2.

For a list, returns the base-Value2logarithm of the elements.

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


If complex formatmode is Rectangular:

log(squareMatrix1[,Value])⇒squareMatrix

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


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



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

Computes the logistic regressiony = (c/(1+a·e-bx))onlists X and Y with frequency Freq. A summary ofresults is stored in the stat.results variable (page143).




Logistic Catalogue >X and Y are lists of independent and dependentvariables.






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

stat.a,stat.b, stat.c






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

Computes the logistic regression y = (c/(1+a·e-bx)+d)on lists X and Y with frequency Freq, using aspecified number of Iterations. A summary of resultsis stored in the stat.results variable (page 143).



LogisticD Catalogue >Freq is an optional list of frequency values. Eachelement in Freq specifies the frequency ofoccurrence for each corresponding X and Y datapoint. The default value is 1. All elements must beintegers | 0.





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







Loop Catalogue >Loop

Block

EndLoop

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.




Loop Catalogue >programme and function definitions, referto the Calculator section of your productguidebook.

LU Catalogue >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 (whichdescribes the row swaps done during thecalculation) 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:5EM14 ·max(dim(Matrix)) ·rowNorm(Matrix)

The LU factorization algorithm uses partialpivoting with row interchanges.

M

mat4list() Catalogue >mat4list(Matrix)⇒list

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

mat4list() Catalogue >Note: You can insert this function from thecomputer keyboard by typing mat@>list(...).

max() Catalogue >max(Value1, Value2)⇒expression

max(List1, List2)⇒list

max(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.


Note: See alsomin().

mean() Catalogue >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 the

In Rectangular vector format:



mean() Catalogue >corresponding element inMatrix1.


median() Catalogue >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.

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

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 194.

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

Computes the median-median liney = (m·x+b)onlists X and Y with frequency Freq. A summary ofresults is stored in the stat.results variable (page143).

MedMed Catalogue >All the lists must have equal dimension except forInclude.







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

stat.m,stat.b

Model coefficients

stat.Resid Residuals from themedian-median line




mid() Catalogue >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.



mid() Catalogue >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() Catalogue >min(Value1, Value2)⇒expression

min(List1, List2)⇒list

min(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 alsomax().

mirr() Catalogue >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.

Note: See also irr(), page 73.

mod() Catalogue >mod(Value1, Value2)⇒expression

mod(List1, List2)⇒list

mod(Matrix1,Matrix2)⇒matrix

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

mod(x,0) = x

mod(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 containing



mod() Catalogue >the modulo of each pair of correspondingelements.

Note: See also remain(), page 122

mRow() Catalogue >mRow(Value,Matrix1, Index)⇒matrix

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

mRowAdd() Catalogue >mRowAdd(Value,Matrix1, Index1, Index2)⇒matrix

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

Value · row Index1 + row Index2

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

Calculates multiple linear regression of list Y on listsX1, X2, …, X10. A summary of results is stored in thestat.results variable (page 143).




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

Computes a predicted y-value, a level C predictioninterval for a single observation, and a level Cconfidence interval for the mean 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 Catalogue >MultRegTests Y, X1[,X2[,X3,…[,X10]]]

Multiple linear regression test computes a multiplelinear regression on the given data and provides theglobal F test statistic and t test statistics for thecoefficients.




MultRegTests Catalogue >For information on the effect of empty elements in alist, see “Empty (Void) Elements”, page 194.

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 /= keysBooleanExpr1nandBooleanExpr2 returnsBoolean expression

BooleanList1nandBooleanList2 returnsBoolean list

BooleanMatrix1nandBooleanMatrix2returns 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.

Integer1nandInteger2⇒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 1 if both bits are 1;otherwise, the result is 0. The returnedvalue represents the bit results, and isdisplayed according to the Base mode.


nCr() Catalogue >nCr(Value1, Value2)⇒expression

For integer Value1 and Value2 withValue1 | Value2 | 0, nCr() is the numberof combinations of Value1 things takenValue2 at a time. (This is also known as abinomial coefficient.)

nCr(Value, 0)⇒1



nCr() Catalogue >nCr(Value, negInteger)⇒0

nCr(Value, posInteger)⇒ Value·(ValueN1)... (ValueNposInteger+1)/posInteger!

nCr(Value, nonInteger)⇒expression!/((ValueNnonInteger)!·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

Returns a matrix of combinations based onthe corresponding element pairs in the twomatrices. The arguments must be the samesize matrix.

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

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

Returns the numerical derivative calculatedusing auto differentiation methods.


If the variable Var does not contain anumeric value, you must provide Value.

Order of the derivative must be 1 or 2.

Note: The nDerivative() algorithm has alimitiation: it works recursively through theunsimplified expression, computing thenumeric value of the first derivative (andsecond, if applicable) and the evaluation ofeach subexpression, which may lead to anunexpected result.

nDerivative() Catalogue >Consider the example on the right. The firstderivative of x·(x^2+x)^(1/3) at x=0 is equalto 0. However, because the first derivativeof the subexpression (x^2+x)^(1/3) isundefined at x=0, and this value is used tocalculate the derivative of the totalexpression, nDerivative() reports the resultas undefined and displays a warningmessage.

If you encounter this limitation, verify thesolution graphically. You can also try usingcentralDiff().

newList() Catalogue >newList(numElements)⇒list

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

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

Returns a matrix of zeroes with thedimension numRows by numColumns.

nfMax() Catalogue >nfMax(Expr, Var)⇒value

nfMax(Expr, Var, lowBound)⇒value

nfMax(Expr, Var, lowBound, upBound)⇒value

nfMax(Expr, Var) | lowBound{Var{upBound⇒value

Returns a candidate numerical value 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.



nfMin() Catalogue >nfMin(Expr, Var)⇒value

nfMin(Expr, Var, lowBound)⇒value

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

nfMin(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.

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

If the integrand Expr1 contains no variableother than Var, and if Lower andUpperare constants, positive ˆ, or negative ˆ,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.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.

nom() Catalogue >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 43.

nor /= keysBooleanExpr1norBooleanExpr2 returnsBoolean expression

BooleanList1norBooleanList2 returnsBoolean list

BooleanMatrix1norBooleanMatrix2returns Boolean matrix

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


Integer1norInteger2⇒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() Catalogue >norm(Matrix)⇒expression

norm(Vector)⇒expression

Returns the Frobenius norm.

normCdf() Catalogue >normCdf(lowBound,upBound[,m[,s]])⇒number iflowBound and upBound are numbers, list iflowBound and upBound are lists

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

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

normPdf() Catalogue >normPdf(XVal[,m[,s]])⇒number if XVal is anumber, list if XVal is a list

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

not Catalogue >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.

InHex basemode:


In Bin basemode:

not Catalogue >Without a prefix, the integer is treated asdecimal (base 10).

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 4Base2, page 16. To see the entire result, press£ and then

use ¡ and ¢ to move the cursor.


nPr() Catalogue >nPr(Value1, Value2)⇒expression

For integer Value1 and Value2 withValue1 | Value2 | 0, nPr() is the numberof permutations of Value1 things takenValue2 at a time.

nPr(Value, 0)⇒1

nPr(Value, negInteger)⇒ 1/((Value+1)·(Value+2)... (ValueNnegInteger))

nPr(Value, posInteger)⇒ Value·(ValueN1)... (ValueNposInteger+1)

nPr(Value, nonInteger)⇒Value! /(ValueNnonInteger)!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() Catalogue >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.



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() Catalogue >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 or error_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() Catalogue >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.”

O

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

OneVar [n,]X1,X2[X3[,…[,X20]]]

Calculates 1-variable statistics on up to 20 lists. Asummary of results is stored in the stat.resultsvariable (page 143).



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


An empty (void) element in any of the lists X, Freqor Category results in a void for the correspondingelement of all those lists. An empty element in anyof the lists X1 through X20 results in a void for thecorresponding element of all those lists. For moreinformation on empty elements, see page 194.


stat.v Meanof x values

stat.Gx Sumof x values

stat.Gx2 Sumof x2 values




stat.sx Sample standarddeviationof x

stat.sx 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 Catalogue >BooleanExpr1orBooleanExpr2 returnsBoolean expression

BooleanList1orBooleanList2 returnsBoolean list

BooleanMatrix1orBooleanMatrix2 returnsBoolean 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

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. The

InHex basemode:


In Bin basemode:

or Catalogue >returned value represents the bit resultsand is displayed according to the Basemode.



Note: See xor.


ord() Catalogue >ord(String)⇒integer

ord(List1)⇒list

Returns the numeric code of the firstcharacter in character string String, or a listof the first characters of each list element.

P

P4Rx() Catalogue >P4Rx(rExpr, qExpr)⇒expression

P4Rx(rList, qList)⇒list

P4Rx(rMatrix, qMatrix)⇒matrix

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

Note: The q argument is interpreted aseither a degree, gradian or radian angle,according to the current angle mode. If theargument is an expression, you can use ¡, Gor R to override the angle mode settingtemporarily.

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




P4Ry() Catalogue >P4Ry(rValue, qValue)⇒value

P4Ry(rList, qList)⇒list

P4Ry(rMatrix, qMatrix)⇒matrix

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

Note: The q argument is interpreted aseither a degree, radian or gradian angle,according to the current angle mode.¡R

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


PassErr Catalogue >PassErr

Passes an error to the next level.

If system variable errCode is zero, PassErr does notdo anything.

The Else clause of the Try...Else...EndTry block shoulduse ClrErr or PassErr. If the error is to be processed orignored, use ClrErr. If what to do with the error is notknown, use PassErr to send it to the next errorhandler. If there are no more pendingTry...Else...EndTry error handlers, the error dialoguebox will be displayed as normal.

Note: See also ClrErr, page 22, and Try, page 154.

Note for entering the example: For instructions onentering multi-line programme and functiondefinitions, refer to the Calculator section of yourproduct guidebook.

For anexample of PassErr, SeeExample 2 under the Trycommand, page 155.

piecewise() Catalogue >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 2.

poissCdf() Catalogue >poissCdf(l,lowBound,upBound)⇒number iflowBound and upBound are numbers, list iflowBound and upBound are lists

poissCdf(l,upBound)for P(0{X{upBound)⇒numberif upBound is a number, list if upBound is a list

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

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

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

Computes a probability for the discrete Poissondistribution with the specified mean l.

4Polar Catalogue >Vector 4Polar

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

Displays vector in polar form [r ±q]. Thevector must be of dimension 2 and can be arow or a column.

Note: 4Polar 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 4Rect, page 119.

complexValue 4Polar

Displays complexVector in polar form.

• Degree angle mode returns (r±q).• Radian angle mode returns reiq.

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

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





4Polar Catalogue >

InDegree anglemode:

polyEval() Catalogue >polyEval(List1, Expr1)⇒expression

polyEval(List1, List2)⇒expression

Interprets the first argument as thecoefficient of a descending-degreepolynomial and returns the polynomialevaluated for the value of the secondargument.

polyRoots() Catalogue >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 expandedform in one variable. Do not useunexpanded forms such as y2·y+1 orx·x+2·x+1

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

Note: See also cPolyRoots(), page 30.

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

Computes the power regressiony = (a·(x)b)on lists Xand Y with frequency Freq. A summary of results isstored in the stat.results variable (page 143).

PowerReg Catalogue >All the lists must have equal dimension except forInclude.







stat.RegEqn Regressionequation: a·(x)b



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

stat.Resid Residuals associatedwith the power model





Prgm Catalogue >PrgmBlockEndPrgm

Template for creating a user-definedprogramme. Must be used with the Define,

Calculate GCDanddisplay intermediateresults.



Prgm Catalogue >Define LibPub or Define LibPriv command.

Block can be a single statement, a seriesof statements separated with the “:”character or a series of statements onseparate lines.


prodSeq() See Π(), page 183.

Product (PI) See Π(), page 183.

product() Catalogue >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() Catalogue >propFrac(Value1[, Var])⇒value

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.

You can use the propFrac() function torepresent mixed fractions and demonstrateaddition and subtraction of mixed fractions.

Q

QR Catalogue >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.

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 been

The floating-point number (9.) inm1 causesresults to be calculated in floating-pointform.



QR Catalogue >assigned a value. Otherwise, Tol is ignored.


• If Tol is omitted or not used, the defaulttolerance is calculated as:5EL14 ·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 Catalogue >QuadReg X,Y [, Freq] [, Category, Include]]

Computes the quadratic polynomial regressiony =a·x2+b·x+con lists X and Y with frequency Freq. Asummary of results is stored in the stat.resultsvariable (page 143).







Outputvariable

Description

stat.RegEqn Regressionequation: a·x2+b·x+c

stat.a,stat.b, stat.c







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

Computes the quartic polynomial regressiony =a·x4+b·x3+c· x2+d·x+eon lists X and Y withfrequency Freq. A summary of results is stored in thestat.results variable (page 143).








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() Catalogue >

R►Pθ (xValue, yValue) ⇒ valueR►Pθ (xList, yList) ⇒ listR►Pθ (xMatrix, yMatrix) ⇒ matrix

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


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

InDegree anglemode:



R►Pr() Catalogue >

R►Pr (xValue, yValue) ⇒ valueR►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 the


R►Pr() Catalogue >computer keyboard by typing R@>Pr(...).

►Rad Catalogue >Value1►Rad⇒ valueConverts the argument to radian anglemeasure.

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

InDegree anglemode:


rand() Catalogue >rand() ⇒ expressionrand(#Trials) ⇒ list

rand() returns a random value between 0and 1.

rand(#Trials) returns a list containing#Trials random values between 0 and 1.

Set the random-number seed.

randBin() Catalogue >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() Catalogue >randInt(lowBound,upBound)⇒ expressionrandInt(lowBound,upBound,#Trials) ⇒ list



randInt() Catalogue >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() Catalogue >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() Catalogue >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() Catalogue >randPoly(Var, Order) ⇒ expression

Returns a polynomial in Var of the

randPoly() Catalogue >specifiedOrder. The coefficients arerandom integers in the range −9 through 9.The leading coefficient will not be zero.

Order must be 0–99.

randSamp() Catalogue >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 Catalogue >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() Catalogue >real(Value1) ⇒ value

Returns the real part of the argument.

real(List1) ⇒ list

Returns the real parts of all elements.

real(Matrix1) ⇒ matrix

Returns the real parts of all elements.

►Rect Catalogue >Vector►Rect

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

Displays Vector in rectangular form [x, y,



►Rect Catalogue >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 109.

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.



InDegree anglemode:

Note: To type∠ , select it from the symbollist in the Catalogue.

ref() Catalogue >ref(Matrix1[, Tol]) ⇒ matrix

Returns the row echelon form of Matrix1.



• If Tol is omitted or not used, the default

ref() Catalogue >tolerance 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:

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 130.

RefreshProbeVars Catalogue >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 collection

Example

Define temp()=

Prgm

© Check if system is ready

RefreshProbeVars status

If status=0 Then

Disp "ready"

For n,1,50



RefreshProbeVars Catalogue >

StatusVarValue Status

mode.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.

RefreshProbeVars status

temperature:=meter.temperature

Disp "Temperature:",temperature

If temperature>30 Then

Disp "Too hot"

EndIf

© Wait for 1 second betweensamples

Wait 1

EndFor

Else

Disp "Not ready. Try againlater"

EndIf

EndPrgm

Note: This can also be used with TI-Innovator™ Hub.

remain() Catalogue >

remain(Value1, Value2) ⇒ valueremain(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 93.

Request Catalogue >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.

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.

Define a program:

Define request_demo()=Prgm Request “Radius: ”,r Disp “Area = “,pi*r2

EndPrgm

Run the programand type a response:

request_demo()

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

Define a program:

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


polynomial()

Result after entering x^3+3x+1 and selectingOK:



Request Catalogue >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:





Note: See also RequestStr, page 124.

Real roots are: {-0.322185}

RequestStr Catalogue >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:



• Macintosh®: Hold down the F5 key and

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 the

RequestStr Catalogue >press Enter repeatedly.


Note: See also Request, page 123.

DispFlag argumentof 0 omits the promptand response from the history):

requestStr_demo()

Response has 5 characters.

Return Catalogue >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() Catalogue >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 () Catalogue >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

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:

Differential equation:

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


Same equationwithdiftol set to 1.E−6

Systemof equations:

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

rk23 () Catalogue >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).

root() Catalogue >root(Value) ⇒ rootroot(Value1, Value2) ⇒ root

root(Value) returns the square root ofValue.

root(Value1, Value2) returns the Value2root of Value1. Value1 can be a real orcomplex floating point constant or aninteger or complex rational constant.

Note: See also Nth root template, page 2.

rotate() Catalogue >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 16.

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

Important: To enter a binary orhexadecimal number, always use the 0bor0hprefix (zero, not the letter O).



rotate() Catalogue >Rightmost bit rotates to leftmost.

produces:

0b10000000000000111101011000011010

The result is displayed according to theBase mode.

rotate(List1[,#ofRotations]) ⇒ list

Returns a copy of List1 rotated right or leftby #of Rotations elements. Does not alterList1.

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).

InDec basemode:

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() Catalogue >round(Value1[, digits]) ⇒ value

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() Catalogue >round(Matrix1[, digits]) ⇒ matrix

Returns a matrix of the elements roundedto the specified number of digits.

rowAdd() Catalogue >rowAdd(Matrix1, rIndex1, rIndex2) ⇒matrix

Returns a copy of Matrix1 with rowrIndex2 replaced by the sum of rowsrIndex1 and rIndex2.

rowDim() Catalogue >rowDim(Matrix) ⇒ expression

Returns the number of rows inMatrix.

Note: See also colDim(), page 23.

rowNorm() Catalogue >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 23.

rowSwap() Catalogue >rowSwap(Matrix1, rIndex1, rIndex2) ⇒matrix

Returns Matrix1 with rows rIndex1 andrIndex2 exchanged.



rref() Catalogue >rref(Matrix1[, Tol]) ⇒ matrix

Returns the reduced row echelon form ofMatrix1.



• If Tol is omitted or not used, the defaulttolerance is calculated as:5E−14 •max(dim(Matrix1)) •rowNorm(Matrix1)

Note: See also ref(), page 120.

S

sec() µ key

sec(Value1) ⇒ valuesec(List1) ⇒ list

Returns the secant of Value1 or returns alist containing the secants of all elementsin 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:

sec⁻¹() µ key

sec⁻¹(Value1) ⇒ valueInDegree anglemode:

sec⁻¹() µ keysec⁻¹(List1) ⇒ list

Returns the angle whose secant is Value1or returns a list containing the inversesecants of each element of List1.


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



sech() Catalogue >

sech(Value1) ⇒ valuesech(List1) ⇒ list

Returns the hyperbolic secant of Value1 orreturns a list containing the hyperbolicsecants of the List1 elements.

sech⁻¹() Catalogue >

sech⁻¹(Value1) ⇒ valuesech⁻¹(List1) ⇒ list

Returns the inverse hyperbolic secant ofValue1 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 valid TI-Innovator™

Example: Turnon the blue element of thebuilt-in RGB LED for 0.5 seconds.



Send Hub MenuHub Command. Typically, exprOrStringcontains a "SET ..." command to control adevice or a "READ ..." command to requestdata.

The arguments are sent to the hub insuccession.

Note: You can use the Send commandwithin a user-defined programme but notwithin a function.

Note: See also Get (page 58), GetStr (page64), and eval() (page 47).

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.

seq() Catalogue >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() Catalogue >seqGen(Expr, Var, depVar, {Var0,VarMax}[, ListOfInitTerms

Generate the first 5 terms of the sequence u(n) = u(n-1)2/2, withu(1)=2 andVarStep=1.

seqGen() Catalogue >[, 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

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 inwhichVar0=2:

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() Catalogue >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 nMax

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



seqn() Catalogue >by 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

setMode() Catalogue >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 63.

Note: The current mode settings are passedto called subroutines. If any subroutinechanges a mode setting, the mode change

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() Catalogue >will 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

VectorFormat

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

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

shift() Catalogue >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 16.

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 dropped

In Bin basemode:

InHex basemode:

Important: To enter a binary orhexadecimal number, always use the 0bor



shift() Catalogue >and 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.

0hprefix (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).

Characters introduced at the beginning orend of string by the shift are set to a space.

sign() Catalogue >

sign(Value1) ⇒ valuesign(List1) ⇒ listsign(Matrix1) ⇒ matrix

For real and complex Value1, returnsValue1 / abs(Value1) when Value1 ≠ 0.

Returns 1 if Value1is positive.Returns −1 ifValue1 is negative. sign(0) returns „1 if thecomplex format mode is Real; otherwise, itreturns itself.

sign(0) represents the unit circle in thecomplex domain.

For a list or matrix, returns the signs of allthe elements.


simult() Catalogue >simult(coeffMatrix, constVector[, Tol]) ⇒matrix

Returns a column vector that contains thesolutions to a system of linear equations.

Note: See also linSolve(), page 81.

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.

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

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() Catalogue >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() µ key

sin(Value1) ⇒ valuesin(List1) ⇒ list

sin(Value1) returns the sine of theargument.

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.

InDegree anglemode:



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 key

sin⁻¹(Value1) ⇒ valuesin⁻¹(List1) ⇒ list

sin⁻¹(Value1) returns the angle whose sineis Value1.

sin⁻¹(List1) returns a list of the inversesines of each element of List1.


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

InDegree anglemode:



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() Catalogue >

sinh(Numver1) ⇒ valuesinh(List1) ⇒ list

sinh (Value1) returns the hyperbolic sine ofthe argument.

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() Catalogue >

sinh⁻¹(Value1) ⇒ valuesinh⁻¹(List1) ⇒ list

sinh⁻¹(Value1) returns the inversehyperbolic sine of the argument.

sinh⁻¹(List1) returns a list of the inversehyperbolic sines of each element of List1.

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 Catalogue >SinReg X, Y[, [Iterations],[Period][, Category,Include]]

Computes the sinusoidal regression on lists X and Y.A summary of results is stored in the stat.resultsvariable. (See page 143.)



Iterations is a value that specifies the maximumnumber of times (1 through 16) a solution will beattempted. If omitted, 8 is used. Typically, largervalues result in better accuracy but longer executiontimes, and vice versa.

Period specifies an estimated period. If omitted, thedifference between values in X should be equal andin sequential order. If you specify Period, thedifferences between x values can be unequal.

Category is a list of numeric or string category codes

SinReg Catalogue >for the corresponding X and Y data.


The output of SinReg is always in radians, regardlessof the angle mode setting.



stat.RegEqn Regression Equation: a•sin(bx+c)+d







SortA Catalogue >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 page



SortA Catalogue >194.

SortD Catalogue >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 page194.

►Sphere Catalogue >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.

sqrt() Catalogue >

sqrt(Value1) ⇒ valuesqrt(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 Catalogue >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.b8

stat.dfDenomstat.dfBlockstat.dfColstat.dfErrorstat.dfInteractstat.dfRegstat.dfNumerstat.dfRowstat.DWstat.estat.ExpMatrixstat.F

stat.MedianYstat.MEPredstat.MinXstat.MinYstat.MSstat.MSBlockstat.MSColstat.MSErrorstat.MSInteractstat.MSRegstat.MSRowstat.n

stat.Q3Xstat.Q3Ystat.rstat.r²stat.RegEqnstat.Residstat.ResidTransstat.σxstat.σystat.σx1stat.σx2stat.Σx

stat.SSBlockstat.SSColstat.SSXstat.SSYstat.SSErrorstat.SSInteractstat.SSRegstat.SSRowstat.tListstat.UpperPredstat.UpperValstat.v



stat.b9stat.b10stat.bListstat.χ²stat.cstat.CLowerstat.CLowerListstat.CompListstat.CompMatrixstat.CookDiststat.CUpperstat.CUpperListstat.d

stat.FBlockstat.Fcolstat.FInteractstat.FreqRegstat.Frowstat.Leveragestat.LowerPredstat.LowerValstat.mstat.MaxXstat.MaxYstat.MEstat.MedianX

Stat.Çstat.Ç1stat.Ç2stat.ÇDiffstat.PListstat.PValstat.PValBlockstat.PValColstat.PValInteractstat.PValRowstat.Q1Xstat.Q1Y

stat.Σx²stat.Σxystat.Σystat.Σy²stat.sstat.SEstat.SEListstat.SEPredstat.sResidstat.SEslopestat.spstat.SS

stat.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 Catalogue >stat.values

Displays a matrix of the values calculated for themost recently evaluated statistics function orcommand.

Unlike stat.results, stat.values omits the namesassociated with the values.

You can copy a value and paste it into other locations.

See the stat.results example.

stDevPop() Catalogue >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, see

In Radian angle andauto modes:

stDevPop() Catalogue >page 194.

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 194.

stDevSamp() Catalogue >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 194.

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 194.



Stop Catalogue >Stop

Programming command: Terminates theprogram.

Stop is not allowed in functions.


Store See→(store), page 191.

string() Catalogue >string(Expr) ⇒ string

Simplifies Expr and returns the result as acharacter string.

subMat() Catalogue >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 184.

sum() Catalogue >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 194.

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 194.

sumIf() Catalogue >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.

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 place holder for eachelement. For example, ?<10 accumulatesonly those elements in List that are lessthan 10.



sumIf() Catalogue >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 29.

sumSeq() See Σ(), page 184.

system() Catalogue >system(Value1[, Value2[, Value3[, ...]]])

Returns a system of equations, formatted as a list.You can also create a system by using a template.

T

T (transpose) Catalogue >Matrix1T⇒matrix

Returns the complex conjugate transpose ofMatrix1.

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

tan() µ key

tan(Value1)⇒value

tan(List1)⇒list

tan(Value1) returns the tangent of theargument.

InDegree anglemode:

tan() µ keytan(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.



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 key

tan/(Value1)⇒value

tan/(List1)⇒list

tan/(Value1) returns the angle whosetangent is Value1.

tan/(List1) returns a list of the inversetangents of each element of List1.

InDegree anglemode:




tan/() 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 arctan(...).


tan/(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().



tanh() Catalogue >tanh(Value1)⇒value

tanh(List1)⇒list

tanh(Value1) returns the hyperbolictangent of the argument.

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/() Catalog >tanh/(Value1)⇒value

tanh/(List1)⇒list

In Rectangular complex format:

tanh/() Catalog >tanh/(Value1) returns the inversehyperbolic tangent of the argument.

tanh/(List1) returns a list of the inversehyperbolic tangents of each element ofList1.

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


tanh/(squareMatrix1)⇒squareMatrix

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().




tCdf() Catalogue >tCdf(lowBound,upBound,df)⇒number if lowBoundand upBound are numbers, list if lowBound andupBound are lists

Computes the Student-t distribution probabilitybetween lowBound and upBound for the specifieddegrees of freedom df.

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

Text Catalogue >TextpromptString[, DispFlag]

Programming command: Pauses the programme anddisplays the character string promptString in adialogue box.

When the user selects OK, programme executioncontinues.

The optional flag argument can be any expression.

• IfDispFlag is omitted or evaluates to 1, the text

Define a programme that pausesto display eachof five randomnumbers in a dialogue box.

Within the Prgm...EndPrgmtemplate, complete each line bypressing@ insteadof·. Onthe computer keyboard, holddownAlt andpress Enter.



Text Catalogue >message is added to the Calculator history.

• IfDispFlag evaluates to 0, the text message is notadded to the history.

If the programme needs a typed response from theuser, refer to Request, page 123, or RequestStr, page124.

Note: You can use this command within a user-defined programme but not within a function.

Define text_demo()=Prgm

For i,1,5

strinfo:=”Randomnumber “ &string(rand(i))

Text strinfo

EndFor

EndPrgm

Run the programme:

text_demo()

Sample of one dialogue box:

Then See If, page 67.

tInterval Catalogue >tInterval List[,Freq[,CLevel]]

(Data list input)

tInterval v,sx,n[,CLevel]


Computes a t confidence interval. A summary ofresults is stored in the stat.results variable (page143).



stat.CLower, stat.CUpper Confidence interval for anunknownpopulationmean

stat.x Samplemeanof the data sequence from the normal randomdistribution

stat.ME Margin of error


stat.sx Sample standarddeviation

stat.n Lengthof the data sequencewith samplemean

tInterval_2Samp Catalogue >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 confidence interval. Asummary of results is stored in the stat.resultsvariable (page 143).

Pooled=1 pools variances; Pooled=0 does not poolvariances.



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.sx1, stat.sx2 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

tPdf() Catalogue >tPdf(XVal,df)⇒number if XVal is a number, list ifXVal is a list

Computes the probability density function (pdf) forthe Student-t distribution at a specified x value withspecified degrees of freedom df.

trace() Catalogue >trace(squareMatrix)⇒value

Returns the trace (sum of all the elementson the main diagonal) of squareMatrix.

Try Catalogue >Try

block1

Else

block2

EndTry

Executes block1 unless an error occurs.programme execution transfers to block2 ifan error occurs in block1. System variableerrCode contains the error code to allowthe programme to perform error recovery.For a list of error codes, see “Error codesand messages,” page 201.

block1 and block2 can be either a singlestatement or a series of statementsseparated with the “:” character.


Try Catalogue >programme and function definitions, referto the Calculator section of your productguidebook.

Example 2

To see the commands Try, ClrErr andPassErr in operation, enter the eigenvals()programme shown at the right. Run theprogramme by executing each of thefollowing expressions.

Note: See also ClrErr, page 22, and PassErr,page 108.

Define eigenvals(a,b)=Prgm

© programme eigenvals(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

EndIf

EndTry

EndPrgm

tTest Catalogue >tTest m0,List[,Freq[,Hypoth]]

(Data list input)

tTest m0,x,sx,n,[Hypoth]


Performs a hypothesis test for a single unknownpopulation mean m when the population standarddeviation s is unknown. A summary of results isstored in the stat.results variable (page 143).

Test H0: m = m0, against one of the following:



tTest Catalogue >For H

a: m < m0, set Hypoth<0

For Ha: m ƒ m0 (default), set Hypoth=0

For Ha: m > m0, set Hypoth>0



stat.t (x N m0) / (stdev / sqrt(n))



stat.x Samplemeanof the data sequence inList

stat.sx Sample standarddeviationof the data sequence

stat.n Size of the sample

tTest_2Samp Catalogue >tTest_2Samp List1,List2[,Freq1[,Freq2[,Hypoth[,Pooled]]]]

(Data list input)

tTest_2Samp v1,sx1,n1,v2,sx2,n2[,Hypoth[,Pooled]]


Computes a two-sample t test. A summary of resultsis stored in the stat.results variable (page 143).

Test H0: m1 = m2, against one of the following:

For Ha: m1< m2, set Hypoth<0

For Ha: m1ƒ m2 (default), set Hypoth=0

For Ha: m1> m2, set Hypoth>0

Pooled=1 pools variances

Pooled=0 does not pool variances



stat.t Standardnormal value computed for the difference ofmeans


stat.df Degrees of freedom for the t-statistic

stat.x1, stat.x2 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() Catalogue >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 158. See also amortTbl(),page 7.

tvmI() Catalogue >tvmI(N,PV,Pmt,FV,[PpY],[CpY],[PmtAt])⇒value

Financial function that calculates theinterest rate per year.


tvmN() Catalogue >tvmN(I,PV,Pmt,FV,[PpY],[CpY],[PmtAt])⇒value

Financial function that calculates thenumber of payment periods.

Note: Arguments used in the TVM functions



tvmN() Catalogue >are described in the table of TVMarguments, page 158. See also amortTbl(),page 7.

tvmPmt() Catalogue >tvmPmt(N,I,PV,FV,[PpY],[CpY],[PmtAt])⇒value

Financial function that calculates theamount of each payment.


tvmPV() Catalogue >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 end or beginning of each period,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 Catalogue >TwoVar X, Y[, [Freq] [, Category, Include]]

Calculates the TwoVar statistics. A summary ofresults is stored in the stat.results variable (page143).




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


An empty (void) element in any of the lists X, Freq,or Category results in a void for the correspondingelement of all those lists. An empty element in anyof the lists X1 through X20 results in a void for thecorresponding element of all those lists. For moreinformation on empty elements, see page 194.


stat.v Meanof x values

stat.Gx Sumof x values

stat.Gx2 Sumof x2 values

stat.sx Sample standarddeviationof x

stat.sx Population standarddeviationof x

stat.n Number of data points

stat.w Meanof y values




stat.Gy Sumof y values

stat.Gy2 Sumof y2 values

stat.sy Sample standarddeviationof y

stat.sy Population standarddeviationof y

stat.Gxy 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.G(x-v)2 Sumof squares of deviations from themeanof x

stat.G(y-w)2 Sumof squares of deviations from themeanof y

U

unitV() Catalogue >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 Catalogue >unLock Var1[, Var2] [, Var3] ...

unLock Var.

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

See Lock, page 84, and getLockInfo(), page63.

V

varPop() Catalogue >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 194.

varSamp() Catalogue >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 is



varSamp() Catalogue >also ignored. For more information onempty elements, see page 194.

varSamp(Matrix1[, freqMatrix])⇒matrix

Returns a row vector containing the samplevariance of each column inMatrix1.


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 194.

Note:Matrix1must contain at least tworows.

W

Wait Catalogue >Wait timeInSeconds

Suspends execution for a period oftimeInSeconds seconds.

Wait is particularly useful in a programmethat needs a brief delay to allow requesteddata to 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.

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”

Wait Catalogue >Note: You can use the Wait command withina user-defined programme but not within afunction.

warnCodes () Catalogue >warnCodes(Expr1, StatusVar)⇒expression

Evaluates expression Expr1, returns theresult and stores the codes of any generatedwarnings in the StatusVar list variable. If nowarnings are generated, this functionassigns StatusVar an empty list.

Expr1 can be any valid TI-Nspire™ orTI-Nspire™ CAS maths 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 209.

when() Catalogue >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 Catalogue >While Condition

Block

EndWhile

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 Catalogue >BooleanExpr1xorBooleanExpr2 returnsBoolean expression

BooleanList1xorBooleanList2 returnsBoolean list

BooleanMatrix1xorBooleanMatrix2returns Boolean matrix

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 106.

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 are

InHex basemode:


In Bin basemode:

xor Catalogue >0 or both bits are 1. The returned valuerepresents the bit results and is displayedaccording to the Base mode.



Note: See or, page 106.


Z

zInterval Catalogue >zInterval s,List[,Freq[,CLevel]]

(Data list input)

zInterval s,v,n [,CLevel]


Computes a z confidence interval. A summary ofresults is stored in the stat.results variable (page143).



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.s Knownpopulation standarddeviation for data sequenceList



zInterval_1Prop Catalogue >zInterval_1Prop x,n [,CLevel]

Computes a one-proportion z confidence interval. Asummary of results is stored in the stat.resultsvariable (page 143).

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 Catalogue >zInterval_2Prop x1,n1,x2,n2[,CLevel]

Computes a two-proportion z confidence interval. Asummary of results is stored in the stat.resultsvariable (page 143).

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 Catalogue >zInterval_2Samp s1,s2 ,List1,List2[,Freq1[,Freq2,[CLevel]]]

(Data list input)

zInterval_2Samp s1,s2,v1,n1,v2,n2[,CLevel]


Computes a two-sample z confidence interval. Asummary of results is stored in the stat.resultsvariable (page 143).



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.sx1, stat.sx2 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 Catalogue >zTest m0,s,List,[Freq[,Hypoth]]

(Data list input)

zTest m0,s,v,n[,Hypoth]


Performs a z test with frequency freqlist. A summaryof results is stored in the stat.results variable (page143).

Test H0: m = m0, against one of the following:

For Ha: m < m0, set Hypoth<0



zTest Catalogue >For H

a: m ƒ m0 (default), set Hypoth=0

For Ha: m > m0, set Hypoth>0



stat.z (x N m0) / (s / 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 Catalogue >zTest_1Prop p0,x,n[,Hypoth]

Computes a one-proportion z test. A summary ofresults is stored in the stat.results variable (page143).

x is a non-negative integer.

Test H0: p = p0 against one of the following:

For Ha: p > p0, set Hypoth>0

For Ha: p ƒ p0 (default), set Hypoth=0

For Ha: p < p0, set Hypoth<0



stat.p0 Hypothesizedpopulationproportion

stat.z Standardnormal value computed for the proportion


stat.Ç Estimated sample proportion


zTest_2Prop Catalogue >zTest_2Prop x1,n1,x2,n2[,Hypoth]

Computes a two-proportion z test. A summary ofresults is stored in the stat.results variable (page143).

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 ƒ 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 Catalogue >zTest_2Samp s1,s2 ,List1,List2[,Freq1[,Freq2[,Hypoth]]]

(Data list input)

zTest_2Samp s1,s2,v1,n1,v2,n2[,Hypoth]


Computes a two-sample z test. A summary of resultsis stored in the stat.results variable (page 143).

Test H0: m1 = m2, against one of the following:

For Ha: m1 < m2, set Hypoth<0

For Ha: m1 ƒ m2 (default), set Hypoth=0

For Ha: m1 > m2, Hypoth>0



zTest_2Samp Catalogue >For information on the effect of empty elements in alist, see “Empty (Void) Elements”, page 194.


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


Symbols

+ (add) + keyValue1 + Value2⇒ value

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.

Value + List1⇒ list

List1 + Value⇒ list

Returns a list containing the sums of Valueand each element in List1.Value +Matrix1⇒ matrix

Matrix1 + Value⇒ matrix

Returns a matrix with Value added to eachelement on the diagonal of Matrix1.Matrix1must be square.

Note: Use .+ (dot plus) to add an expressionto each element.

− (subtract) - keyValue1−Value2⇒ value

Returns Value1minus Value2.

Symbols 171

172 Symbols

− (subtract) - keyList1 −List2⇒ list

Matrix1 −Matrix2 ⇒ matrix

Subtracts each element in List2 (orMatrix2) from the corresponding elementin List1 (orMatrix1), and returns theresults.

Dimensions of the arguments must beequal.

Value − List1⇒ list

List1 − Value⇒ list

Subtracts each List1 element from Valueor subtracts Value from each List1element, and returns a list of the results.

Value −Matrix1⇒ matrix

Matrix1 − Value⇒ matrix

Value −Matrix1 returns a matrix of Valuetimes the identity matrix minusMatrix1. Matrix1must be square.

Matrix1 − Value returns a matrix of Valuetimes the identity matrix subtracted fromMatrix1. Matrix1must be square.

Note: Use .− (dot minus) to subtract anexpression from each element.

•(multiply) r keyValue1•Value2⇒ value

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.

•(multiply) r keyThe number of columns inMatrix1mustequal the number of rows inMatrix2.

Value •List1⇒ list

List1•Value⇒ list

Returns a list containing the products ofValue and each element in List1.

Value •Matrix1⇒ matrix

Matrix1•Value⇒ matrix

Returns a matrix containing the products ofValue and each element inMatrix1.

Note: Use .•(dot multiply) to multiply anexpression by each element.

⁄ (divide) p keyValue1 ⁄ Value2⇒ value

Returns the quotient of Value1 divided byValue2.

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.

Value ⁄ List1⇒ list

List1 ⁄ Value⇒ list

Returns a list containing the quotients ofValue divided by List1 or List1 divided byValue.Value ⁄Matrix1⇒ matrix

Matrix1 ⁄ Value⇒ matrix

Returns a matrix containing the quotients

Symbols 173

174 Symbols

⁄ (divide) p keyof Matrix1 ⁄ Value.

Note: Use . ⁄ (dot divide) to divide anexpression by each element.

^ (power) l keyValue1 ^ Value2⇒ value

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.

Value ^ List1⇒ list

Returns Value raised to the power of theelements in List1.List1 ^ Value⇒ list

Returns the elements in List1 raised to thepower of Value.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.

x2 (square) q keyValue12⇒ value

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

Value .+Matrix1⇒ matrix

Matrix1.+Matrix2 returns a matrix that isthe sum of each pair of correspondingelements inMatrix1 andMatrix2.

Value .+ Matrix1 returns a matrix that isthe sum of Value and each element inMatrix1.

.⁻(dot subt.) ^- keysMatrix1 .−Matrix2⇒ matrix

Value .− Matrix1⇒ matrix

Matrix1.− Matrix2 returns a matrix that isthe difference between each pair ofcorresponding elements inMatrix1 andMatrix2.

Value .− Matrix1 returns a matrix that isthe difference of Value and each elementinMatrix1.

Symbols 175

176 Symbols

.•(dot mult.) ^r keysMatrix1 .• Matrix2⇒ matrix

Value .• Matrix1⇒ matrix

Matrix1.• Matrix2 returns a matrix that isthe product of each pair of correspondingelements inMatrix1 andMatrix2.

Value .• Matrix1 returns a matrixcontaining the products of Value and eachelement inMatrix1.

. ⁄ (dot divide) ^p keysMatrix1. ⁄Matrix2⇒ matrix

Value . ⁄Matrix1⇒ matrix

Matrix1 . ⁄Matrix2 returns a matrix that isthe quotient of each pair of correspondingelements inMatrix1 andMatrix2.

Value . ⁄Matrix1 returns a matrix that isthe quotient of Value and each element inMatrix1.

.^ (dot power) ^l keysMatrix1 .^Matrix2⇒ matrix

Value . ^Matrix1⇒ matrix

Matrix1.^ Matrix2 returns a matrix whereeach element inMatrix2 is the exponentfor the corresponding element inMatrix1.

Value .^ Matrix1 returns a matrix whereeach element inMatrix1 is the exponentfor Value.

− (negate) v key−Value1 ⇒ value

−List1⇒ list

−Matrix1⇒ matrix

− (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 basemode:



% (percent) /k keysValue1% ⇒ value

List1% ⇒ list

Matrix1% ⇒ matrix

Returns

For a list or matrix, returns a list or matrixwith each element divided by 100.

Note: To force anapproximate result,


= (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 maths testsymbols: =, ≠, <, ≤, >, ≥

Result of graphing g(x)

Symbols 177

178 Symbols

= (equal) = keyprogramme and function definitions, referto the Calculator section of your productguidebook.

≠ (not equal) /= keysExpr1≠Expr2⇒ Boolean expression

List1≠List2⇒ Boolean list

Matrix1≠Matrix2⇒ Boolean matrix

Returns true if Expr1 is determined to be not equalto Expr2.

Returns false if Expr1 is determined to be equal toExpr2.

Anything else returns a simplified form of theequation.

For lists and matrices, returns comparisons elementby element.

Note: You can insert this operator from the keyboardby 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 be less thanExpr2.

Returns false if Expr1 is determined to be greaterthan or equal to Expr2.


< (less than) /= keysAnything else returns a simplified form of theequation.


≤ (less or equal) /= keysExpr1≤Expr2⇒ Boolean expression

List1≤List2⇒ Boolean list

Matrix1 ≤Matrix2⇒ Boolean matrix

Returns true if Expr1 is determined to be less thanor equal to Expr2.

Returns false if Expr1 is determined to be greaterthan Expr2.



Note: You can insert this operator from the keyboardby typing <=


> (greater than) /= keysExpr1>Expr2⇒ Boolean expression

List1>List2⇒ Boolean list

Matrix1>Matrix2⇒ Boolean matrix

Returns true if Expr1 is determined to be greaterthan Expr2.

Returns false if Expr1 is determined to be less thanor equal to Expr2.




Symbols 179

180 Symbols

≥ (greater or equal) /= keysExpr1≥Expr2⇒ Boolean expression

List1≥List2⇒ Boolean list

Matrix1 ≥Matrix2⇒ Boolean matrix

Returns true if Expr1 is determined to be greaterthan or equal to Expr2.

Returns false if Expr1 is determined to be less thanExpr2.



Note: You can insert this operator from the keyboardby 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 =>

⇔ (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 keyValue1! ⇒ value

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.

Symbols 181

182 Symbols

d() (derivative) Catalogue >d(Expr1, Var[, Order]) | Var=Value⇒value

d(Expr1, Var[, Order]) ⇒ value

d(List1, Var[, Order]) ⇒ list

d(Matrix1, Var[, Order]) ⇒ matrix

Except when using the first syntax, youmust store a numeric value in variable Varbefore evaluating d(). Refer to theexamples.

d() can be used for calculating first andsecond order derivative at a pointnumerically, using auto differentiationmethods.

Order, if included, must be=1 or 2. Thedefault is 1.

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

Note: See also First derivative, page 5 orSecond derivative, page 5.

Note: The d() algorithm has a limitation: itworks recursively through the unsimplifiedexpression, computing the numeric value ofthe first derivative (and second, ifapplicable) and the evaluation of eachsubexpression, which may lead to anunexpected result.

Consider the example on the right. The firstderivative of x•(x^2+x)^(1/3) at x=0 is equalto 0. However, because the first derivativeof the subexpression (x^2+x)^(1/3) isundefined at x=0, and this value is used tocalculate the derivative of the totalexpression, d() reports the result asundefined and displays a warning message.

If you encounter this limitation, verify thesolution graphically. You can also try usingcentralDiff().

∫() (integral) Catalogue >∫(Expr1, Var, Lower,Upper) ⇒ value

Returns the integral of Expr1 with respectto the variable Var from Lower toUpper.Can be used to calculate the definiteintegral numerically, using the samemethod as nInt().

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

Note: See also nInt(), page 100, andDefiniteintegral template, page 6.

√() (square root) /q keys√(Value1) ⇒ value

√(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) Catalogue >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 183

184 Symbols

Π() (prodSeq) Catalogue >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) Catalogue >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() Catalogue >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.

N, I, PV, Pmt, FV, PpY, CpY, and PmtAtare described in the table of TVMarguments, page 158.


• If you omit FV, it defaults to FV=0.• The defaults for PpY, CpY, and PmtAt



ΣInt(NPmt1,NPmt2,amortTable) calculatesthe sum of the interest based onamortization table amortTable. TheamortTable argument must be a matrix inthe form described under amortTbl(), page7.

Note: See also ΣPrn(), below, and Bal(),page 15.

ΣPrn() Catalogue >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 185

186 Symbols

ΣPrn() Catalogue >NPmt1 and NPmt2 define the start and endboundaries of the payment range.

N, I, PV, Pmt, FV, PpY, CpY, and PmtAtare described in the table of TVMarguments, page 158.


• If you omit FV, it defaults to FV=0.• The defaults for PpY, CpY, and PmtAt



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 7.

Note: See also ΣInt(), above, and Bal(),page 15.

# (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 keyValue1r ⇒value

List1r ⇒ list

Matrix1r ⇒ matrix

This function gives you a way to specify aradian angle while in Degree or Gradian

InDegree, Gradianor Radian anglemode:

Symbols 187

188 Symbols

r(radian) ¹ keymode.

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 keyValue1°⇒value

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:


Note: To force anapproximate result,


°, ', '' (degree/minute/second) /k keysdd°mm'ss.ss'' ⇒ expression

dd A positive or negative numbermm A non-negative numberss.ss A non-negative number

InDegree anglemode:

°, ', '' (degree/minute/second) /k keysReturns 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. 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.


_ (underscore as an empty element)See “Empty (Void)

Elements,” page 194.

Symbols 189

190 Symbols

10^() Catalogue >10^ (Value1) ⇒ value

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().


^⁻¹ (reciprocal) Catalogue >Value1 ^⁻¹⇒ value

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 are

| (constraint operator) /k keysintended 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.Interval 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.

→ (store) /h keyValue→ Var

List→ Var

Matrix→ Var

Expr→ Function(Param1,...)

List→ Function(Param1,...)

Matrix→ Function(Param1,...)

Symbols 191

192 Symbols

→ (store) /h keyIf the variable Var does not exist, creates itand initializes it to Value, List, orMatrix.

If the variable Var already exists and is notlocked or protected, replaces its contentswith Value, List, orMatrix.

Note: You can insert this operator from thekeyboard by typing =: as a shortcut. Forexample, type pi/4 =: myvar.

:= (assign) /t keysVar := Value

Var := List

Var :=Matrix

Function(Param1,...) := Expr

Function(Param1,...) := List

Function(Param1,...) :=Matrix

If variable Var does not exist, creates Varand initializes it to Value, List, orMatrix.

If Var already exists and is not locked orprotected, replaces its contents with Value,List, orMatrix.

© (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 193

194 Empty (Void) Elements

Empty (Void) ElementsWhen analyzing real-world data, you might not always have a complete data set.TI-Nspire™ Software allows empty, or void, data elements so you can proceed with thenearly complete data rather than having to start over or discard the incomplete cases.

You can find an example of data involving empty elements in the Lists & 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 38, andisVoid(), page 74.

Note: To enter an empty element manually in a maths 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,freqTable4list, frequency, max, mean,median, product, stDevPop, stDevSamp,sum, sumIf, varPop and varSamp, as well asregression calculations, OneVar, TwoVarand FiveNumSummary statistics, confidenceintervals and stat tests

SortA and SortDmove all void elementswithin the first argument to the bottom.

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.

Empty (Void) Elements 195

196 Shortcuts for Entering Maths Expressions

Shortcuts for Entering Maths ExpressionsShortcuts let you enter elements of maths expressions by typing instead of using theCatalogue or Symbol Palette. For example, to enter the expression ‡6, you can typesqrt(6) on the entry line. When you press·, the expression sqrt(6) is changedto ‡6. Some shortrcuts are useful from both the handheld and the computer keyboard.Others are useful primarily from the computer keyboard.

From the Handheld or Computer Keyboard

To enter this: Type this shortcut:

p pi

q theta

ˆ infinity

{ <=

| >=

ƒ /=

⇒ (logical implication) =>

dd⇔ (logical doubleimplication, XNOR)

<=>

& (store operator) =:

| | (absolute value) abs(...)

‡() sqrt(...)

G() (Sum template) sumSeq(...)

Π() (Product template) prodSeq(...)

sin/(), cos/(), ... arcsin(...), arccos(...), ...

@List() deltaList(...)

From the Computer Keyboard


i (imaginary constant) @i

e (natural log base e) @e

E (scientific notation) @ET (transpose) @t

R (radians) @r

¡ (degrees) @d

g (gradians) @g


± (angle) @<

4 (conversion) @>

4Decimal, 4approxFraction() and so on.

@>Decimal, @>approxFraction() and so on.

Shortcuts for Entering Maths Expressions 197

198 EOS™ (Equation Operating System) Hierarchy

EOS™ (Equation Operating System) HierarchyThis section describes the Equation Operating System (EOS™) that is used by theTI-Nspire™ maths and science learning technology. Numbers, variables and functionsare 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 (QRS), subscript ([ ]), transpose (T)

5 Exponentiation, power operator (^)

6 Negation (L)

7 String concatenation (&)

8 Multiplication (†), division (/)

9 Addition (+), subtraction (-)

10 Equality relations: equal (=), not equal (ƒ or /=), less than (<), less than orequal ({ or <=), greater than (>), greater than or equal (| 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.

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 that

indicates the missing element. For example, (1+2)/(3+4 will display the error message“Missing ).”

Note: Because the TI-Nspire™ 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 programme. 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 Lx2 is anegative number, and L92 = L81. Use parentheses to square a negative number such as(L9)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.

EOS™ (Equation Operating System) Hierarchy 199

200 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 155.

Note: Some error conditions apply only to TI-Nspire™ CAS products, and some applyonly to TI-Nspire™ products.

Error code 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<bwillcause this 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.


202 Error Codes and Messages


180 Break

Thed orc key was pressedduring a long calculationor during programmeexecution.

190 Circular definition

This message is displayed to avoid running out ofmemory during infinitereplacement of variable values during simplification. For example, a+1->a, where a isanundefined variable, will cause this error.

200 Constraint expression invalid

For example, solve(3x^2-4=0,x) | x<0 or x>5wouldproduce this error messagebecause the constraint 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, thenL1[5] is a dimensionerror 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 a dimensionmismatchbecause thematrices contain a different number ofelements.

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 cannotcontain 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 calculationwasentered.

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 programme

A number of commands are not valid outside a functionor programme. Forexample, Local cannot be usedunless it is in a functionor programme.

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 programme

570 Invalid pathname

For example, \var is invalid.

575 Invalid polar complex

580 Invalid programme reference

Programs cannot be referencedwithin functions or expressions such as 1+p(x)where p is a programme.




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 connectingcable is connected firmly to bothends.

665 Matrix not diagonalisable

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 programme

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 toRECTANGULAR or POLAR.


830 Overflow

850 programme not found

A programme reference inside another programme couldnot be found in theprovidedpathduring execution.

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 cannotbe evaluated.

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. TryTI-Nspire™CAS.

1045 Unsupportedoperator. This operator requires Computer Algebra System. TryTI-Nspire™CAS.

1050 Unsupported feature. This operator requires Computer Algebra System. TryTI-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 toRECTANGULAR or POLAR.

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 thesecondargument 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 thethird argument 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 programme 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 nfMax must be anexpression in a single variable. Itcannot contain 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 163.

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 zeroes.

10006 Solvemay specify more zeroes.

10007 More solutionsmay exist. Try specifying appropriate lower andupper boundsand/or a guess.

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 ˆ^0 or undef^0 replacedby 1

10014 undef^0 replacedby 1

10015 1^ˆ or 1^undef replacedby 1

10016 1^undef replacedby 1

10017 Overflow replacedby ˆ or Lˆ

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.

Warning Codes and Messages 209

210 Warning Codes and Messages

Warningcode Message

Resultmight not be valid for all possible parameter values.

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 "\" 'VariableMathTestSymbol Constant' or a conjunct of these forms, for example 'x<3 and x>-12'

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Service and Warranty InformationFor information about the length and terms of the warranty or about product service,refer to the warranty statement enclosed with this product or contact your local TexasInstruments retailer/distributor.

Texas Instruments Support and Service 211

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Index

-

-, subtract 171

!

!, factorial 181

"

", second notation 188

#

#, indirection 186#, indirection operator 199

%

%, percent 177

&

&, append 181

*

*, multiply 172

.

.-, dot subtraction 175

.*, dot multiplication 176

./, dot division 176

.^, dot power 176

.+, dot addition 175

/

/, divide 173

:

:=, assign 192

^

^⁻¹, reciprocal 190

^, power 174

|

|, constraint operator 190

′

′minute notation 188

+

+, add 171

=

≠, not equal 178≤, less than or equal 179≥, greater than or equal 180>, greater than 179=, equal 177

∏

∏, product 183

∑

∑( ), sum 184∑Int( ) 185∑Prn( ) 185

√

√, square root 183

∠

∠ (angle) 189

∫

∫, integral 183

►

►approxFraction( ) 13►Base10, display as decimal integer 17►Base16, display as hexadecimal 18►Base2, display as binary 16

Index 212

►Cylind, display as cylindrical vector 34►DD, display as decimal angle 35►Decimal, display result as decimal 35►DMS, display as

degree/minute/second 42►Grad, convert to gradian angle 66►Polar, display as polar vector 109►Rad, convert to radian angle 117►Rect, display as rectangular vector 119►Sphere, display as spherical vector 142

⇒

⇒ , logical implication 180, 196

→

→, store variable 191

⇔

⇔ , logical double implication 181, 196

©

©, comment 192

°

°, degree notation 188°, degrees/minutes/seconds 188

0

0b, binary indicator 1930h, hexadecimal indicator 193

1

10^( ), power of ten 190

2

2-sample F Test 56

A

abs( ), absolute value 7absolute value

template for 3-4

add, + 171amortisation table, amortTbl( ) 7, 15amortTbl( ), amortisation table 7, 15and, Boolean operator 8angle( ), angle 9angle, angle( ) 9ANOVA, one-way variance analysis 9ANOVA2way, two-way variance

analysis 10Ans, last answer 12answer (last), Ans 12append, & 181approx( ), approximate 12approximate, approx( ) 12approxRational( ) 13arccos(), cos⁻¹() 13arccosh(), cosh⁻¹() 13arccot(), cot⁻¹() 13arccoth(), coth⁻¹() 13arccsc(), csc⁻¹() 13arccsch(), csch⁻¹() 14arcsec(), sec⁻¹() 14arcsech(), sech⁻¹() 14arcsin(), sin⁻¹() 14arcsinh(), sinh⁻¹() 14arctan(), tan⁻¹() 14arctanh(), tanh⁻¹() 14arguments in TVM functions 158augment( ), augment/concatenate 14augment/concatenate, augment( ) 14average rate of change, avgRC( ) 15avgRC( ), average rate of change 15

B

binarydisplay, ►Base2 16indicator, 0b 193

binomCdf( ) 18, 71-72binomPdf( ) 18Boolean operators

⇒ 180, 196⇔ 181and 8nand 97

213 Index

nor 101not 102or 106xor 164

C

Cdf( ) 51ceiling( ), ceiling 19ceiling, ceiling( ) 19, 30centralDiff( ) 19char( ), character string 20character string, char( ) 20characters

numeric code, ord( ) 107string, char( ) 20

χ²2way 20χ²Cdf( ) 20χ²GOF 21χ²Pdf( ) 21clear

error, ClrErr 22ClearAZ 22ClrErr, clear error 22colAugment 22colDim( ), matrix column dimension 23colNorm( ), matrix column norm 23combinations, nCr( ) 97comment, © 192complex

conjugate, conj( ) 23conj( ), complex conjugate 23constraint operator "|" 190constraint operator, order of

evaluation 198construct matrix, constructMat( ) 23constructMat( ), construct matrix 23convert

►Grad 66►Rad 117

copy variable or function, CopyVar 24correlation matrix, corrMat( ) 24corrMat( ), correlation matrix 24cos⁻¹, arccosine 26

cos( ), cosine 24cosh⁻¹( ), hyperbolic arccosine 27cosh( ), hyperbolic cosine 26cosine, cos( ) 24cot⁻¹( ), arccotangent 28cot( ), cotangent 27cotangent, cot( ) 27coth⁻¹( ), hyperbolic arccotangent 29coth( ), hyperbolic cotangent 28count days between dates, dbd( ) 34count items in a list conditionally ,

countif( ) 29count items in a list, count( ) 29count( ), count items in a list 29countif( ), conditionally count items

in a list 29cPolyRoots() 30cross product, crossP( ) 30crossP( ), cross product 30csc⁻¹( ), inverse cosecant 31csc( ), cosecant 31csch⁻¹( ), inverse hyperbolic cosecant 32csch( ), hyperbolic cosecant 32cubic regression, CubicReg 32CubicReg, cubic regression 32cumulative sum, cumulativeSum( ) 33cumulativeSum( ), cumulative sum 33cycle, Cycle 34Cycle, cycle 34cylindrical vector display, ►Cylind 34

D

d( ), first derivative 182days between dates, dbd( ) 34dbd( ), days between dates 34decimal

angle display, ►DD 35integer display, ►Base10 17

Define 36Define LibPriv 37Define LibPub 37define, Define 36Define, define 36

Index 214

definingprivate function or programme 37public function or programme 37

definite integraltemplate for 6

degree notation, ° 188degree/minute/second display,

►DMS 42degree/minute/second notation 188delete

void elements from list 38deleting

variable, DelVar 38deltaList() 38DelVar, delete variable 38delVoid( ), remove void elements 38derivatives

first derivative, d( ) 182numeric derivative, nDeriv( ) 99-100numeric derivative, nDerivative(

) 98det( ), matrix determinant 39diag( ), matrix diagonal 39dim( ), dimension 39dimension, dim( ) 39Disp, display data 40, 131DispAt 40display as

binary, ►Base2 16cylindrical vector, ►Cylind 34decimal angle, ►DD 35decimal integer, ►Base10 17degree/minute/second, ►DMS 42hexadecimal, ►Base16 18polar vector, ►Polar 109rectangular vector, ►Rect 119spherical vector, ►Sphere 142

display data, Disp 40, 131distribution functions

binomCdf( ) 18, 71-72binomPdf( ) 18invNorm( ) 72invt( ) 72Invχ²( ) 71normCdf( ) 102

normPdf( ) 102poissCdf( ) 109poissPdf( ) 109tCdf( ) 151tPdf( ) 154χ²2way( ) 20χ²Cdf( ) 20χ²GOF( ) 21χ²Pdf( ) 21

divide, / 173dot

addition, .+ 175division, ./ 176multiplication, .* 176power, .^ 176product, dotP( ) 42subtraction, .- 175

dotP( ), dot product 42

E

e exponenttemplate for 2

e to a power, e^( ) 43, 48E, exponent 187e^( ), e to a power 43eff( ), convert nominal to effective

rate 43effective rate, eff( ) 43eigenvalue, eigVl( ) 44eigenvector, eigVc( ) 44eigVc( ), eigenvector 44eigVl( ), eigenvalue 44else if, ElseIf 45else, Else 67ElseIf, else if 45empty (void) elements 194end

for, EndFor 53function, EndFunc 56if, EndIf 67loop, EndLoop 87try, EndTry 154while, EndWhile 164

end function, EndFunc 56

215 Index

end if, EndIf 67end loop, EndLoop 87end while, EndWhile 164EndTry, end try 154EndWhile, end while 164EOS (Equation Operating System) 198equal, = 177Equation Operating System (EOS) 198error codes and messages 201errors and troubleshooting

clear error, ClrErr 22pass error, PassErr 108

euler( ), Euler function 46evaluate polynomial, polyEval( ) 110evaluation, order of 198exclusion with "|" operator 190exit, Exit 48Exit, exit 48exp( ), e to a power 48exponent, E 187exponential regession, ExpReg 49exponents

template for 1expr( ), string to expression 49ExpReg, exponential regession 49expressions

string to expression, expr( ) 49

F

factor( ), factor 50factor, factor( ) 50factorial, ! 181Fill, matrix fill 51financial functions, tvmFV( ) 157financial functions, tvmI( ) 157financial functions, tvmN( ) 157financial functions, tvmPmt( ) 158financial functions, tvmPV( ) 158first derivative

template for 5FiveNumSummary 51floor( ), floor 52floor, floor( ) 52

For 53for, For 53For, for 53format string, format( ) 53format( ), format string 53fpart( ), function part 54fractions

propFrac 113template for 1

freqTable( ) 54frequency( ) 55Frobenius norm, norm( ) 102Func, function 56Func, programme function 56functions

part, fpart( ) 54programme function, Func 56user-defined 36

functions and variablescopying 24

G

g, gradians 187gcd( ), greatest common divisor 57geomCdf( ) 57geomPdf( ) 58Get 58get/return

denominator, getDenom( ) 59number, getNum( ) 64variables injformation,

getVarInfo( ) 62, 65getDenom( ), get/return

denominator 59getKey() 59getLangInfo( ), get/return language

information 62getLockInfo( ), tests lock status of

variable or variable group 63getMode( ), get mode settings 63getNum( ), get/return number 64GetStr 64getType( ), get typeof variable 65getVarInfo( ), get/return variables 65

Index 216

informationgo to, Goto 66Goto, go to 66gradian notation, g 187greater than or equal, ≥ 180greater than, > 179greatest common divisor, gcd( ) 57groups, locking and unlocking 84, 161groups, testing lock status 63

H

hexadecimaldisplay, ►Base16 18indicator, 0h 193

hyperbolicarccosine, cosh⁻¹( ) 27arcsine, sinh⁻¹( ) 140arctangent, tanh⁻¹( ) 150cosine, cosh( ) 26sine, sinh( ) 139tangent, tanh( ) 150

I

identity matrix, identity( ) 66identity( ), identity matrix 66if, If 67If, if 67ifFn( ) 68imag( ), imaginary part 69imaginary part, imag( ) 69indirection operator (#) 199indirection, # 186inString( ), within string 69int( ), integer 70intDiv( ), integer divide 70integer divide, intDiv( ) 70integer part, iPart( ) 73integer, int( ) 70integral, ∫ 183interpolate( ), interpolate 70inverse cumulative normal

distribution (invNorm( ) 72inverse, ^⁻¹ 190

invF( ) 71invNorm( ), inverse cumulative

normal distribution) 72invt( ) 72Invχ²( ) 71iPart( ), integer part 73irr( ), internal rate of return

internal rate of return, irr( ) 73isPrime( ), prime test 73isVoid( ), test for void 74

L

label, Lbl 74language

get language information 62Lbl, label 74lcm, least common multiple 75least common multiple, lcm 75left( ), left 75left, left( ) 75length of string 39less than or equal, ≤ 179LibPriv 37LibPub 37library

create shortcuts to objects 75libShortcut( ), create shortcuts to

library objects 75linear regression, LinRegAx 77linear regression, LinRegBx 76, 78LinRegBx, linear regression 76LinRegMx, linear regression 77LinRegtIntervals, linear regression 78LinRegtTest 79linSolve() 81Δlist( ), list difference 81list to matrix, list►mat( ) 82list, conditionally count items in 29list, count items in 29list►mat( ), list to matrix 82lists

augment/concatenate,augment( ) 14

cross product, crossP( ) 30

217 Index

cumulative sum,cumulativeSum( ) 33

differences in a list, Δlist( ) 81dot product, dotP( ) 42empty elements in 194list to matrix, list►mat( ) 82matrix to list, mat►list( ) 88maximum, max( ) 89mid-string, mid( ) 91minimum, min( ) 92new, newList( ) 99product, product( ) 112sort ascending, SortA 141sort descending, SortD 142summation, sum( ) 147

ln( ), natural logarithm 82LnReg, logarithmic regression 83local variable, Local 84local, Local 84Local, local variable 84Lock, lock variable or variable group 84locking variables and variable groups 84Log

template for 2logarithmic regression, LnReg 83logarithms 82logical double implication,⇔ 181logical implication,⇒ 180, 196logistic regression, Logistic 85logistic regression, LogisticD 86Logistic, logistic regression 85LogisticD, logistic regression 86loop, Loop 87Loop, loop 87LU, matrix lower-upper

decomposition 88

M

mat►list( ), matrix to list 88matrices

augment/concatenate,augment( ) 14

column dimension, colDim( ) 23column norm, colNorm( ) 23

cumulative sum,cumulativeSum( ) 33

determinant, det( ) 39diagonal, diag( ) 39dimension, dim( ) 39dot addition, .+ 175dot division, ./ 176dot multiplication, .* 176dot power, .^ 176dot subtraction, .- 175eigenvalue, eigVl( ) 44eigenvector, eigVc( ) 44filling, Fill 51identity, identity( ) 66list to matrix, list►mat( ) 82lower-upper decomposition, LU 88matrix to list, mat►list( ) 88maximum, max( ) 89minimum, min( ) 92new, newMat( ) 99product, product( ) 112QR factorization, QR 113random, randMat( ) 118reduced row echelon form, rref(

) 130row addition, rowAdd( ) 129row dimension, rowDim( ) 129row echelon form, ref( ) 120row multiplication and addition,

mRowAdd( ) 94row norm, rowNorm( ) 129row operation, mRow( ) 94row swap, rowSwap( ) 129submatrix, subMat( ) 146, 148summation, sum( ) 147transpose, T 148

matrix (1 × 2)template for 4



matrix (m ×n)template for 4

Index 218

matrix to list, mat►list( ) 88max( ), maximum 89maximum, max( ) 89mean( ), mean 89mean, mean( ) 89median( ), median 90median, median( ) 90medium-medium line regression,

MedMed 90MedMed, medium-medium line

regression 90mid-string, mid( ) 91mid( ), mid-string 91min( ), minimum 92minimum, min( ) 92minute notation, ′ 188mirr( ), modified internal rate of

return 93mixed fractions, using propFrac()

with 113mod( ), modulo 93mode settings, getMode( ) 63modes

setting, setMode( ) 134modified internal rate of return, mirr

( ) 93modulo, mod( ) 93mRow( ), matrix row operation 94mRowAdd( ), matrix row

multiplication and addition 94Multiple linear regression t test 95multiply, * 172MultReg 94MultRegIntervals( ) 95MultRegTests( ) 95

N

nand, Boolean operator 97natural logarithm, ln( ) 82nCr( ), combinations 97nDerivative( ), numeric derivative 98negation, entering negative numbers 199net present value, npv( ) 104new

list, newList( ) 99

matrix, newMat( ) 99newList( ), new list 99newMat( ), new matrix 99nfMax( ), numeric function

maximum 99nfMin( ), numeric function minimum 100nInt( ), numeric integral 100nom ), convert effective to nominal

rate 101nominal rate, nom( ) 101nor, Boolean operator 101norm( ), Frobenius norm 102normal distribution probability,

normCdf( ) 102normCdf( ) 102normPdf( ) 102not equal, ≠ 178not, Boolean operator 102nPr( ), permutations 103npv( ), net present value 104nSolve( ), numeric solution 104nth root

template for 2numeric

derivative, nDeriv( ) 99-100derivative, nDerivative( ) 98integral, nInt( ) 100solution, nSolve( ) 104

O

objectscreate shortcuts to library 75

one-variable statistics, OneVar 105OneVar, one-variable statistics 105operators

order of evaluation 198or (Boolean), or 106or, Boolean operator 106ord( ), numeric character code 107

P

P►Rx( ), rectangular x coordinate 107P►Ry( ), rectangular y coordinate 108pass error, PassErr 108

219 Index

PassErr, pass error 108Pdf( ) 54percent, % 177permutations, nPr( ) 103piecewise function (2-piece)

template for 2piecewise function (N-piece)

template for 2piecewise( ) 108poissCdf( ) 109poissPdf( ) 109polar

coordinate, R►Pr( ) 116coordinate, R►Pθ( ) 116vector display, ►Polar 109

polyEval( ), evaluate polynomial 110polynomials

evaluate, polyEval( ) 110random, randPoly( ) 118

PolyRoots() 110power of ten, 10^( ) 190power regression,

PowerReg 110, 123-124, 151power, ^ 174PowerReg, power regression 110Prgm, define programme 111primenumber test, isPrime( ) 73probability densiy, normPdf( ) 102prodSeq() 112product( ), product 112product, ∏( ) 183

template for 5product, product( ) 112programmes and programming

display I/O screen, Disp 131programming

define programme, Prgm 111display data, Disp 40, 131pass error, PassErr 108

programsdefining private library 37defining public library 37

programs and programmingclear error, ClrErr 22

display I/O screen, Disp 40end try, EndTry 154try, Try 154

proper fraction, propFrac 113propFrac, proper fraction 113

Q

QR factorization, QR 113QR, QR factorization 113quadratic regression, QuadReg 114QuadReg, quadratic regression 114quartic regression, QuartReg 115QuartReg, quartic regression 115

R

R, radian 187R►Pr( ), polar coordinate 116R►Pθ( ), polar coordinate 116radian, R 187rand( ), random number 117randBin, random number 117randInt( ), random integer 117randMat( ), random matrix 118randNorm( ), random norm 118random

matrix, randMat( ) 118norm, randNorm( ) 118number seed, RandSeed 119polynomial, randPoly( ) 118

random sample 119randPoly( ), random polynomial 118randSamp( ) 119RandSeed, random number seed 119real( ), real 119real, real( ) 119reciprocal, ^⁻¹ 190rectangular-vector display, ►Rect 119rectangular x coordinate, P►Rx( ) 107rectangular y coordinate, P►Ry( ) 108reduced row echelon form, rref( ) 130ref( ), row echelon form 120RefreshProbeVars 121

Index 220

regressionscubic, CubicReg 32exponential, ExpReg 49linear regression, LinRegAx 77linear regression, LinRegBx 76, 78logarithmic, LnReg 83Logistic 85logistic, Logistic 86medium-medium line, MedMed 90MultReg 94power regression,

PowerReg 110, 123-124, 151quadratic, QuadReg 114quartic, QuartReg 115sinusoidal, SinReg 140

remain( ), remainder 122remainder, remain( ) 122remove

void elements from list 38Request 123RequestStr 124result values, statistics 144results, statistics 143return, Return 125Return, return 125right( ), right 125right, right( ) 46, 70, 125-126, 163rk23( ), RungeKutta function 126rotate( ), rotate 127rotate, rotate( ) 127round( ), round 128round, round( ) 128row echelon form, ref( ) 120rowAdd( ), matrix row addition 129rowDim( ), matrix row dimension 129rowNorm( ), matrix row norm 129rowSwap( ), matrix row swap 129rref( ), reduced row echelon form 130

S

sec⁻¹( ), inverse secant 130sec( ), secant 130sech⁻¹( ), inverse hyperbolic secant 131sech( ), hyperbolic secant 131

second derivativetemplate for 5

second notation, " 188seq( ), sequence 132seqGen( ) 132seqn( ) 133sequence, seq( ) 132-133set

mode, setMode( ) 134setMode( ), set mode 134settings, get current 63shift( ), shift 135shift, shift( ) 135sign( ), sign 137sign, sign( ) 137simult( ), simultaneous equations 137simultaneous equations, simult( ) 137sin⁻¹( ), arcsine 139sin( ), sine 138sine, sin( ) 138sinh⁻¹( ), hyperbolic arcsine 140sinh( ), hyperbolic sine 139SinReg, sinusoidal regression 140sinusoidal regression, SinReg 140SortA, sort ascending 141SortD, sort descending 142sorting

ascending, SortA 141descending, SortD 142

spherical vector display, ►Sphere 142sqrt( ), square root 143square root

template for 1square root, √( ) 143, 183standard deviation, stdDev( ) 144-145, 161stat.results 143stat.values 144statistics

combinations, nCr( ) 97factorial, ! 181mean, mean( ) 89median, median( ) 90one-variable statistics, OneVar 105permutations, nPr( ) 103

221 Index

random norm, randNorm( ) 118random number seed,

RandSeed 119standard deviation, stdDev

( ) 144-145, 161two-variable results, TwoVar 159variance, variance( ) 161

stdDevPop( ), population standarddeviation 144

stdDevSamp( ), sample standarddeviation 145

Stop command 146store variable (→) 191storing

symbol, & 192string

dimension, dim( ) 39length 39

string( ), expression to string 146strings

append, & 181character code, ord( ) 107character string, char( ) 20expression to string, string( ) 146format, format( ) 53formatting 53indirection, # 186left, left( ) 75mid-string, mid( ) 91right, right( ) 46, 70, 125-126, 163rotate, rotate( ) 127shift, shift( ) 135string to expression, expr( ) 49using to create variable names 199within, InString 69

student-t distribution probability,tCdf( ) 151

student-t probability density, tPdf( ) 154subMat( ), submatrix 146, 148submatrix, subMat( ) 146, 148substitution with "|" operator 190subtract, - 171sum of interest payments 185sum of principal payments 185

sum( ), summation 147sum, ∑( ) 184

template for 5sumIf( ) 147summation, sum( ) 147sumSeq() 148system of equations (2-equation)

template for 3system of equations (N-equation)

template for 3

T

t test, tTest 155T, transpose 148tan⁻¹( ), arctangent 149tan( ), tangent 148tangent, tan( ) 148tanh⁻¹( ), hyperbolic arctangent 150tanh( ), hyperbolic tangent 150tCdf( ), studentt distribution

probability 151templates

absolute value 3-4definite integral 6e exponent 2exponent 1first derivative 5fraction 1Log 2matrix (1 × 2) 4matrix (2 × 1) 4matrix (2 × 2) 4matrix (m ×n) 4nth root 2piecewise function (2-piece) 2piecewise function (N-piece) 2product, ∏( ) 5second derivative 5square root 1sum, ∑( ) 5system of equations (2-

equation) 3system of equations (N-

equation) 3

Index 222

test for void, isVoid( ) 74Test_2S, 2-sample F test 56Text command 151time value ofmoney, FutureValue 157time value ofmoney, Interest 157time value ofmoney, number of

payments 157time value ofmoney, payment

amount 158time value ofmoney, present value 158tInterval, t confidence interval 152tInterval_2Samp, twosample t

confidence interval 153tPdf( ), studentt probability density 154trace( ) 154transpose, T 148Try, error handling command 154tTest, t test 155tTest_2Samp, two-sample t test 156TVMarguments 158tvmFV( ) 157tvmI( ) 157tvmN( ) 157tvmPmt( ) 158tvmPV( ) 158two-variable results, TwoVar 159TwoVar, two-variable results 159

U

unit vector, unitV( ) 160unitV( ), unit vector 160unLock, unlock variable or variable

group 161unlocking variables and variable

groups 161user-defined functions 36user-defined functions and

programs 37

V

variablecreating name from a character

string 199

variable and functionscopying 24

variablesclear all single-letter 22delete, DelVar 38local, Local 84

variables, locking and unlocking 63, 84, 161variance, variance( ) 161varPop( ) 161varSamp( ), sample variance 161vectors

cross product, crossP( ) 30cylindrical vector display,

►Cylind 34dot product, dotP( ) 42unit, unitV( ) 160

void elements 194void elements, remove 38void, test for 74

W

Wait command 162warnCodes( ), Warning codes 163warning codes and messages 209when( ), when 163when, when( ) 163while, While 164While, while 164with, | 190within string, inString( ) 69

X

x², square 175XNOR 181xor, Boolean exclusive or 164

Z

zInterval, z confidence interval 165zInterval_1Prop, one-proportion z

confidence interval 166zInterval_2Prop, two-proportion z

confidence interval 166zInterval_2Samp, two-sample z

confidence interval 167

223 Index

zTest 167zTest_1Prop, one-proportion z test 168zTest_2Prop, two-proportion z test 169zTest_2Samp, two-sample z test 169

Index 224

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