TI-Nspire™ CAS TI-Nspire™ CX CAS Reference Guide This guidebook applies to TI-Nspire™ software version 3.2. To obtain the latest version of the documentation, go to education.ti.com/guides. Important Information Except as otherwise expressly stated in the License that accompanies a program, Texas Instruments makes no warranty, either express or implied, including but not limited to any implied warranties of merchantability and fitness for a particular purpose, regarding any programs or book materials and makes such materials available solely on an "as-is" basis. In no event shall Texas Instruments be liable to anyone for special, collateral, incidental, or consequential damages in connection with or arising out of the purchase or use of these materials, and the sole and exclusive liability of Texas Instruments, regardless of the form of action, shall not exceed the amount set forth in the license for the program. 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License Please see the complete license installed in C:\Program Files\TI Education\<TI-Nspire™ Product Name>\license. © 2006 - 2012 Texas Instruments Incorporated ii Contents Expression Templates Fraction template ........................................ 1 Exponent template ...................................... 1 Square root template .................................. 1 Nth root template ........................................ 1 e exponent template ................................... 2 Log template ................................................ 2 Piecewise template (2-piece) ....................... 2 Piecewise template (N-piece) ...................... 2 System of 2 equations template ................. 3 System of N equations template ................. 3 Absolute value template ............................. 3 dd°mm’ss.ss’’ template ................................3 Matrix template (2 x 2) ................................3 Matrix template (1 x 2) ................................4 Matrix template (2 x 1) ................................4 Matrix template (m x n) .............................. 4 Sum template (G) ......................................... 4 Product template (Π) ................................... 4 First derivative template ............................. 5 Second derivative template ........................5 Nth derivative template .............................. 5 Definite integral template .......................... 5 Indefinite integral template ....................... 5 Limit template .............................................. 6 Alphabetical Listing A abs() .............................................................. 7 amortTbl() .................................................... 7 and ................................................................ 7 angle() ..........................................................8 ANOVA ......................................................... 8 ANOVA2way ................................................ 9 Ans .............................................................. 11 approx() ...................................................... 11 4approxFraction() ....................................... 11 approxRational() ........................................ 11 arccos() ........................................................11 arccosh() ..................................................... 12 arccot() ........................................................12 arccoth() ..................................................... 12 arccsc() ........................................................12 arccsch() ...................................................... 12 arcLen() ....................................................... 12 arcsec() ........................................................12 arcsech() ...................................................... 12 arcsin() ........................................................12 arcsinh() ...................................................... 12 arctan() ....................................................... 12 arctanh() ..................................................... 12 augment() ...................................................12 avgRC() ....................................................... 13 B bal() ............................................................. 13 4Base2 ......................................................... 14 4Base10 ....................................................... 14 4Base16 ....................................................... 15 binomCdf() ................................................. 15 binomPdf() ................................................. 15 C ceiling() ...................................................... 15 centralDiff() ............................................... 16 cFactor() ..................................................... 16 char() .......................................................... 17 charPoly() ................................................... 17 c22way ........................................................ 17 c2Cdf() ........................................................ 17 c2GOF ......................................................... 18 c2Pdf() ........................................................ 18 ClearAZ ....................................................... 18 ClrErr .......................................................... 19 colAugment() ............................................. 19 colDim() ...................................................... 19 colNorm() ................................................... 19 comDenom() .............................................. 19 completeSquare() ...................................... 20 conj() .......................................................... 21 constructMat() ........................................... 21 CopyVar ...................................................... 21 corrMat() .................................................... 22 4cos ............................................................. 22 cos() ............................................................ 22 cos/() .......................................................... 23 cosh() .......................................................... 24 cosh/() ........................................................ 24 cot() ............................................................ 24 cot/() .......................................................... 25 coth() .......................................................... 25 coth/() ........................................................ 25 count() ........................................................ 25 countif() ..................................................... 26 cPolyRoots() ............................................... 26 crossP() ....................................................... 26 csc() ............................................................. 27 csc/() ........................................................... 27 csch() ........................................................... 27 csch/() ......................................................... 27 cSolve() ....................................................... 28 CubicReg .................................................... 30 cumulativeSum() ........................................ 30 Cycle ........................................................... 31 4Cylind ........................................................ 31 cZeros() ....................................................... 31 D dbd() ........................................................... 33 4DD ............................................................. 33 4Decimal ..................................................... 33 Define ......................................................... 34 Define LibPriv ............................................ 34 Define LibPub ............................................ 35 deltaList() ................................................... 35 deltaTmpCnv() ........................................... 35 DelVar ........................................................ 35 delVoid() .................................................... 35 iii derivative() .................................................35 deSolve() .....................................................36 det() ............................................................37 diag() ...........................................................37 dim() ............................................................37 Disp .............................................................38 4DMS ...........................................................38 domain() .....................................................38 dominantTerm() .........................................39 dotP() ..........................................................39 E e^() ..............................................................40 eff() .............................................................40 eigVc() .........................................................40 eigVl() .........................................................41 Else ..............................................................41 ElseIf ............................................................41 EndFor .........................................................41 EndFunc ......................................................41 EndIf ............................................................41 EndLoop ......................................................41 EndPrgm .....................................................41 EndTry .........................................................41 EndWhile ....................................................42 euler() .........................................................42 exact() .........................................................42 Exit ..............................................................43 4exp .............................................................43 exp() ............................................................43 exp4list() ......................................................44 expand() ......................................................44 expr() ...........................................................45 ExpReg ........................................................45 F factor() ........................................................46 FCdf() ..........................................................47 Fill ................................................................47 FiveNumSummary ......................................48 floor() ..........................................................48 fMax() .........................................................48 fMin() ..........................................................49 For ...............................................................49 format() ......................................................50 fPart() ..........................................................50 FPdf() ..........................................................50 freqTable4list() ............................................50 frequency() .................................................51 FTest_2Samp ..............................................51 Func .............................................................52 G gcd() ............................................................52 geomCdf() ...................................................52 geomPdf() ...................................................53 getDenom() ................................................53 getLangInfo() .............................................53 getLockInfo() ..............................................53 getMode() ...................................................54 getNum() ....................................................54 getType() ....................................................55 getVarInfo() ................................................55 iv Goto ............................................................ 56 4Grad ........................................................... 56 I identity() ..................................................... 56 If .................................................................. 57 ifFn() ........................................................... 58 imag() ......................................................... 58 impDif() ...................................................... 58 Indirection .................................................. 58 inString() .................................................... 59 int() ............................................................. 59 intDiv() ........................................................ 59 integral ....................................................... 59 interpolate() ............................................... 60 invc2() ......................................................... 60 invF() .......................................................... 60 invNorm() ................................................... 60 invt() ........................................................... 60 iPart() .......................................................... 61 irr() .............................................................. 61 isPrime() ...................................................... 61 isVoid() ....................................................... 61 L Lbl ............................................................... 62 lcm() ............................................................ 62 left() ............................................................ 62 libShortcut() ............................................... 63 limit() or lim() ............................................. 63 LinRegBx ..................................................... 64 LinRegMx ................................................... 64 LinRegtIntervals ......................................... 65 LinRegtTest ................................................ 66 linSolve() ..................................................... 67 @List() .......................................................... 67 list4mat() ..................................................... 68 4ln ................................................................ 68 ln() .............................................................. 68 LnReg .......................................................... 69 Local ........................................................... 70 Lock ............................................................ 70 log() ............................................................ 71 4logbase ...................................................... 71 Logistic ....................................................... 72 LogisticD ..................................................... 72 Loop ............................................................ 73 LU ................................................................ 74 M mat4list() ..................................................... 74 max() ........................................................... 75 mean() ........................................................ 75 median() ..................................................... 75 MedMed ..................................................... 76 mid() ........................................................... 76 min() ........................................................... 77 mirr() ........................................................... 77 mod() .......................................................... 78 mRow() ....................................................... 78 mRowAdd() ................................................ 78 MultReg ...................................................... 78 MultRegIntervals ....................................... 79 MultRegTests .............................................. 79 N nand ............................................................ 80 nCr() ............................................................ 81 nDerivative() ............................................... 81 newList() ..................................................... 81 newMat() .................................................... 81 nfMax() ....................................................... 82 nfMin() ........................................................82 nInt() ........................................................... 82 nom() .......................................................... 82 nor .............................................................. 83 norm() ......................................................... 83 normalLine() ............................................... 83 normCdf() ...................................................83 normPdf() ...................................................84 not .............................................................. 84 nPr() ............................................................ 84 npv() ............................................................ 85 nSolve() ....................................................... 85 O OneVar ....................................................... 86 or ................................................................. 87 ord() ............................................................ 87 P P4Rx() ........................................................... 87 P4Ry() ........................................................... 88 PassErr ......................................................... 88 piecewise() .................................................. 88 poissCdf() .................................................... 88 poissPdf() .................................................... 88 4Polar .......................................................... 89 polyCoeffs() ................................................ 89 polyDegree() .............................................. 90 polyEval() .................................................... 90 polyGcd() .................................................... 90 polyQuotient() ...........................................91 polyRemainder() ........................................ 91 polyRoots() ................................................. 91 PowerReg ...................................................92 Prgm ........................................................... 93 prodSeq() .................................................... 93 Product (PI) ................................................. 93 product() ..................................................... 93 propFrac() ...................................................94 Q QR ............................................................... 94 QuadReg ..................................................... 95 QuartReg .................................................... 96 R R4Pq() .......................................................... 97 R4Pr() ........................................................... 97 4Rad ............................................................. 97 rand() .......................................................... 97 randBin() ..................................................... 98 randInt() ..................................................... 98 randMat() ...................................................98 randNorm() ................................................. 98 randPoly() ................................................... 98 randSamp() ................................................ 98 RandSeed ................................................... 99 real() ........................................................... 99 4Rect ........................................................... 99 ref() ........................................................... 100 remain() .................................................... 100 Request .................................................... 101 RequestStr ................................................ 102 Return ...................................................... 102 right() ....................................................... 102 rk23() ........................................................ 103 root() ........................................................ 103 rotate() ..................................................... 104 round() ..................................................... 104 rowAdd() .................................................. 105 rowDim() .................................................. 105 rowNorm() ............................................... 105 rowSwap() ................................................ 105 rref() ......................................................... 105 S sec() .......................................................... 106 sec/() ......................................................... 106 sech() ........................................................ 106 sech/() ...................................................... 107 seq() .......................................................... 107 seqGen() ................................................... 108 seqn() ........................................................ 108 series() ...................................................... 109 setMode() ................................................. 110 shift() ........................................................ 111 sign() ......................................................... 111 simult() ..................................................... 112 4sin ............................................................ 112 sin() ........................................................... 113 sin/() ......................................................... 113 sinh() ......................................................... 114 sinh/() ....................................................... 114 SinReg ...................................................... 115 solve() ....................................................... 115 SortA ........................................................ 118 SortD ........................................................ 118 4Sphere ..................................................... 119 sqrt() ......................................................... 119 stat.results ................................................ 120 stat.values ................................................ 121 stDevPop() ................................................ 121 stDevSamp() ............................................. 121 Stop .......................................................... 122 Store ......................................................... 122 string() ...................................................... 122 subMat() ................................................... 122 Sum (Sigma) ............................................. 122 sum() ......................................................... 123 sumIf() ...................................................... 123 sumSeq() ................................................... 123 system() .................................................... 123 T T (transpose) ............................................ 124 tan() .......................................................... 124 tan/() ........................................................ 125 v tangentLine() ............................................125 tanh() ........................................................125 tanh/() ......................................................126 taylor() ......................................................126 tCdf() .........................................................126 tCollect() ...................................................127 tExpand() ..................................................127 Text ...........................................................127 Then ..........................................................127 tInterval ....................................................128 tInterval_2Samp .......................................128 tmpCnv() ...................................................129 @tmpCnv() .................................................129 tPdf() .........................................................129 trace() ........................................................130 Try .............................................................130 tTest ..........................................................131 tTest_2Samp .............................................131 tvmFV() .....................................................132 tvmI() .........................................................132 tvmN() .......................................................132 tvmPmt() ...................................................132 tvmPV() .....................................................132 TwoVar .....................................................133 U unitV() .......................................................134 unLock ......................................................135 V varPop() ....................................................135 varSamp() ..................................................135 W warnCodes() .............................................136 when() .......................................................136 While .........................................................136 X .^ (dot power) .......................................... 147 L(negate) ................................................... 147 % (percent) .............................................. 147 = (equal) ................................................... 148 ƒ (not equal) ............................................ 148 < (less than) .............................................. 148 { (less or equal) ........................................ 149 > (greater than) ....................................... 149 | (greater or equal) ................................. 149 (logical implication) ............................ 149 ⇔ (logical double implication, XNOR) ... 150 ! (factorial) ............................................... 150 & (append) ............................................... 150 d() (derivative) ......................................... 150 ‰() (integral) .............................................. 151 ‡() (square root) ...................................... 152 Π() (prodSeq) ............................................ 152 G() (sumSeq) ............................................. 153 GInt() ......................................................... 154 GPrn() ........................................................ 154 # (indirection) .......................................... 155 E (scientific notation) ............................... 155 g (gradian) ............................................... 155 R(radian) .................................................... 155 ¡ (degree) ................................................. 156 ¡, ', '' (degree/minute/second) ................. 156 ± (angle) .................................................. 156 ' (prime) .................................................... 157 _ (underscore as an empty element) ...... 157 _ (underscore as unit designator) ........... 157 4 (convert) ................................................. 158 10^() .......................................................... 158 ^/(reciprocal) ........................................... 158 | (constraint operator) ............................. 159 & (store) ................................................... 160 := (assign) ................................................. 160 © (comment) ............................................ 160 0b, 0h ........................................................ 161 xor .............................................................137 Empty (Void) Elements Z Calculations involving void elements ..... 162 List arguments containing void elements ................................................... 162 zeros() .......................................................137 zInterval ....................................................139 zInterval_1Prop ........................................139 zInterval_2Prop ........................................140 zInterval_2Samp .......................................140 zTest ..........................................................141 zTest_1Prop ..............................................141 zTest_2Prop ..............................................142 zTest_2Samp .............................................142 Symbols + (add) .......................................................143 N(subtract) ................................................143 ·(multiply) ...............................................144 à (divide) ...................................................144 ^ (power) ..................................................145 x2 (square) ................................................146 .+ (dot add) ...............................................146 .. (dot subt.) ..............................................146 .·(dot mult.) .............................................146 . / (dot divide) ...........................................147 vi Shortcuts for Entering Math Expressions EOS™ (Equation Operating System) Hierarchy Error Codes and Messages Texas Instruments Support and Service Service and Warranty Information TI-Nspire™ CAS Reference Guide This guide lists the templates, functions, commands, and operators available for evaluating math expressions. Expression Templates Expression templates give you an easy way to enter math expressions in standard mathematical notation. When you insert a template, it appears on the entry line with small blocks at positions where you can enter elements. A cursor shows which element you can enter. Use the arrow keys or press e to move the cursor to each element’s position, and type a value or expression for the element. Press · or /· to evaluate the expression. /p keys Fraction template Example: Note: See also / (divide), page 144. l key Exponent template Example: Note: Type the first value, press l, and then type the exponent. ¢ To return the cursor to the baseline, press right arrow ( ). Note: See also ^ (power), page 145. /q keys Square root template Example: Note: See also ‡() (square root), page 152. /l keys Nth root template Example: Note: See also root(), page 103. TI-Nspire™ CAS Reference Guide 1 e exponent template u keys Example: Natural exponential e raised to a power Note: See also e^(), page 40. /s key Log template Example: Calculates log to a specified base. For a default of base 10, omit the base. Note: See also log(), page 71. Piecewise template (2-piece) Catalog > Example: Lets you create expressions and conditions for a two-piece piecewise function. To add a piece, click in the template and repeat the template. Note: See also piecewise(), page 88. Piecewise template (N-piece) Lets you create expressions and conditions for an N-piece piecewise function. Prompts for N. Note: See also piecewise(), page 88. 2 TI-Nspire™ CAS Reference Guide Catalog > Example: See the example for Piecewise template (2-piece). System of 2 equations template Catalog > Example: Creates a system of two equations. To add a row to an existing system, click in the template and repeat the template. Note: See also system(), page 123. System of N equations template Catalog > Lets you create a system of N equations. Prompts for N. Example: See the example for System of equations template (2-equation). Note: See also system(), page 123. Absolute value template Catalog > Example: Note: See also abs(), page 7. dd°mm’ss.ss’’ template Catalog > Example: Lets you enter angles in dd°mm’ss.ss’’ format, where dd is the number of decimal degrees, mm is the number of minutes, and ss.ss is the number of seconds. Matrix template (2 x 2) Catalog > Example: Creates a 2 x 2 matrix. TI-Nspire™ CAS Reference Guide 3 Matrix template (1 x 2) Catalog > Example: . Matrix template (2 x 1) Catalog > Example: Matrix template (m x n) The template appears after you are prompted to specify the number of rows and columns. Catalog > Example: Note: If you create a matrix with a large number of rows and columns, it may take a few moments to appear. Sum template (G) Catalog > Example: Note: See also G() (sumSeq), page 153. Product template (Π) Catalog > Example: Note: See also Π() (prodSeq), page 152. 4 TI-Nspire™ CAS Reference Guide First derivative template Catalog > Example: The first derivative template can also be used to calculate first derivative at a point. Note: See also d() (derivative), page 150. Second derivative template Catalog > Example: The second derivative template can also be used to calculate second derivative at a point. Note: See also d() (derivative), page 150. Nth derivative template Catalog > Example: The nth derivative template can be used to calculate the nth derivative. Note: See also d() (derivative), page 150. Definite integral template Catalog > Example: Note: See also ‰() integral(), page 151. Indefinite integral template Catalog > Example: Note: See also ‰() integral(), page 151. TI-Nspire™ CAS Reference Guide 5 Limit template Catalog > Example: Use N or (N) for left hand limit. Use + for right hand limit. Note: See also limit(), page 63. 6 TI-Nspire™ CAS Reference Guide Alphabetical Listing Items whose names are not alphabetic (such as +, !, and >) are listed at the end of this section, starting on page 143. Unless otherwise specified, all examples in this section were performed in the default reset mode, and all variables are assumed to be undefined. A abs() Catalog > abs(Expr1) expression abs(List1) list abs(Matrix1) matrix Returns the absolute value of the argument. Note: See also Absolute value template, page 3. If the argument is a complex number, returns the number’s modulus. Note: All undefined variables are treated as real variables. amortTbl() Catalog > amortTbl(NPmt,N,I,PV, [Pmt], [FV], [PpY], [CpY], [PmtAt], [roundValue]) matrix Amortization function that returns a matrix as an amortization table for a set of TVM arguments. NPmt is the number of payments to be included in the table. The table starts with the first payment. N, I, PV, Pmt, FV, PpY, CpY, and PmtAt are described in the table of TVM arguments, page 132. • • • If you omit Pmt, it defaults to Pmt=tvmPmt(N,I,PV,FV,PpY,CpY,PmtAt). If you omit FV, it defaults to FV=0. The defaults for PpY, CpY, and PmtAt are the same as for the TVM functions. roundValue specifies the number of decimal places for rounding. Default=2. The columns in the result matrix are in this order: Payment number, amount paid to interest, amount paid to principal, and balance. The balance displayed in row n is the balance after payment n. You can use the output matrix as input for the other amortization functions GInt() and GPrn(), page 154, and bal(), page 13. and Catalog > BooleanExpr1 and BooleanExpr2 Boolean expression BooleanList1 and BooleanList2 Boolean list BooleanMatrix1 and BooleanMatrix2 Boolean matrix Returns true or false or a simplified form of the original entry. TI-Nspire™ CAS Reference Guide 7 and Catalog > Integer1 and Integer2 integer Compares two real integers bit-by-bit using an and operation. Internally, both integers are converted to signed, 64-bit binary numbers. When corresponding bits are compared, the result is 1 if both bits are 1; otherwise, the result is 0. The returned value represents the bit results, and is displayed according to the Base mode. You can enter the integers in any number base. For a binary or hexadecimal entry, you must use the 0b or 0h prefix, respectively. Without a prefix, integers are treated as decimal (base 10). In Hex base mode: Important: Zero, not the letter O. In Bin base mode: In Dec base mode: Note: A binary entry can have up to 64 digits (not counting the 0b prefix). A hexadecimal entry can have up to 16 digits. angle() angle(Expr1) Catalog > expression In Degree angle mode: Returns the angle of the argument, interpreting the argument as a complex number. Note: All undefined variables are treated as real variables. In Gradian angle mode: In Radian angle mode: angle(List1) list angle(Matrix1) matrix Returns a list or matrix of angles of the elements in List1 or Matrix1, interpreting each element as a complex number that represents a two-dimensional rectangular coordinate point. ANOVA Catalog > ANOVA List1,List2[,List3,...,List20][,Flag] Performs a one-way analysis of variance for comparing the means of two to 20 populations. A summary of results is stored in the stat.results variable. (See page 120.) Flag=0 for Data, Flag=1 for Stats 8 Output variable Description stat.F Value of the F statistic stat.PVal Smallest level of significance at which the null hypothesis can be rejected stat.df Degrees of freedom of the groups stat.SS Sum of squares of the groups TI-Nspire™ CAS Reference Guide Output variable Description stat.MS Mean squares for the groups stat.dfError Degrees of freedom of the errors stat.SSError Sum of squares of the errors stat.MSError Mean square for the errors stat.sp Pooled standard deviation stat.xbarlist Mean of the input of the lists stat.CLowerList 95% confidence intervals for the mean of each input list stat.CUpperList 95% confidence intervals for the mean of each input list ANOVA2way Catalog > ANOVA2way List1,List2[,List3,…,List10][,levRow] Computes a two-way analysis of variance for comparing the means of two to 10 populations. A summary of results is stored in the stat.results variable. (See page 120.) LevRow=0 for Block LevRow=2,3,...,Len-1, for Two Factor, where Len=length(List1)=length(List2) = … = length(List10) and Len / LevRow ∈ {2,3,…} Outputs: Block Design Output variable Description stat.F F statistic of the column factor stat.PVal Smallest level of significance at which the null hypothesis can be rejected stat.df Degrees of freedom of the column factor stat.SS Sum of squares of the column factor stat.MS Mean squares for column factor stat.FBlock F statistic for factor stat.PValBlock Least probability at which the null hypothesis can be rejected stat.dfBlock Degrees of freedom for factor stat.SSBlock Sum of squares for factor stat.MSBlock Mean squares for factor stat.dfError Degrees of freedom of the errors stat.SSError Sum of squares of the errors stat.MSError Mean squares for the errors stat.s Standard deviation of the error TI-Nspire™ CAS Reference Guide 9 COLUMN FACTOR Outputs Output variable Description stat.Fcol F statistic of the column factor stat.PValCol Probability value of the column factor stat.dfCol Degrees of freedom of the column factor stat.SSCol Sum of squares of the column factor stat.MSCol Mean squares for column factor ROW FACTOR Outputs Output variable Description stat.FRow F statistic of the row factor stat.PValRow Probability value of the row factor stat.dfRow Degrees of freedom of the row factor stat.SSRow Sum of squares of the row factor stat.MSRow Mean squares for row factor INTERACTION Outputs Output variable Description stat.FInteract F statistic of the interaction stat.PValInteract Probability value of the interaction stat.dfInteract Degrees of freedom of the interaction stat.SSInteract Sum of squares of the interaction stat.MSInteract Mean squares for interaction ERROR Outputs Output variable Description stat.dfError Degrees of freedom of the errors stat.SSError Sum of squares of the errors stat.MSError Mean squares for the errors s Standard deviation of the error 10 TI-Nspire™ CAS Reference Guide /v keys Ans Ans value Returns the result of the most recently evaluated expression. approx() approx(Expr1) Catalog > expression Returns the evaluation of the argument as an expression containing decimal values, when possible, regardless of the current Auto or Approximate mode. This is equivalent to entering the argument and pressing / ·. approx(List1) list approx(Matrix1) matrix Returns a list or matrix where each element has been evaluated to a decimal value, when possible. 4approxFraction() Catalog > Expr 4approxFraction([Tol]) expression List 4approxFraction([Tol]) list Matrix 4approxFraction([Tol]) matrix Returns the input as a fraction, using a tolerance of Tol. If Tol is omitted, a tolerance of 5.E-14 is used. Note: You can insert this function from the computer keyboard by typing @>approxFraction(...). approxRational() Catalog > expression approxRational(List[, Tol]) list approxRational(Matrix[, Tol]) matrix approxRational(Expr[, Tol]) Returns the argument as a fraction using a tolerance of Tol. If Tol is omitted, a tolerance of 5.E-14 is used. arccos() See cos/(), page 23. TI-Nspire™ CAS Reference Guide 11 See cosh/(), page 24. arccosh() See cot/(), page 25. arccot() See coth/(), page 25. arccoth() See csc/(), page 27. arccsc() See csch/(), page 27. arccsch() arcLen() Catalog > arcLen(Expr1,Var,Start,End) expression Returns the arc length of Expr1 from Start to End with respect to variable Var. Arc length is calculated as an integral assuming a function mode definition. arcLen(List1,Var,Start,End) list Returns a list of the arc lengths of each element of List1 from Start to End with respect to Var. See sec/(), page 106. arcsec() See sech/(), page 107. arcsech() See sin/(), page 113. arcsin() arcsinh() See sinh/(), page 114. arctan() See tan/(), page 125. See tanh/(), page 126. arctanh() augment() augment(List1, List2) Catalog > list Returns a new list that is List2 appended to the end of List1. 12 TI-Nspire™ CAS Reference Guide augment() Catalog > augment(Matrix1, Matrix2) matrix Returns a new matrix that is Matrix2 appended to Matrix1. When the “,” character is used, the matrices must have equal row dimensions, and Matrix2 is appended to Matrix1 as new columns. Does not alter Matrix1 or Matrix2. avgRC() Catalog > expression avgRC(Expr1, Var [=Value] [, List1]) list avgRC(List1, Var [=Value] [, Step]) list avgRC(Matrix1, Var [=Value] [, Step]) matrix avgRC(Expr1, Var [=Value] [, Step]) Returns the forward-difference quotient (average rate of change). Expr1 can be a user-defined function name (see Func). When Value is specified, it overrides any prior variable assignment or any current “|” substitution for the variable. Step is the step value. If Step is omitted, it defaults to 0.001. Note that the similar function centralDiff() uses the centraldifference quotient. B bal() Catalog > bal(NPmt,N,I,PV ,[Pmt], [FV], [PpY], [CpY], [PmtAt], [roundValue]) value bal(NPmt,amortTable) value Amortization function that calculates schedule balance after a specified payment. N, I, PV, Pmt, FV, PpY, CpY, and PmtAt are described in the table of TVM arguments, page 132. NPmt specifies the payment number after which you want the data calculated. N, I, PV, Pmt, FV, PpY, CpY, and PmtAt are described in the table of TVM arguments, page 132. • • • If you omit Pmt, it defaults to Pmt=tvmPmt(N,I,PV,FV,PpY,CpY,PmtAt). If you omit FV, it defaults to FV=0. The defaults for PpY, CpY, and PmtAt are the same as for the TVM functions. roundValue specifies the number of decimal places for rounding. Default=2. bal(NPmt,amortTable) calculates the balance after payment number NPmt, based on amortization table amortTable. The amortTable argument must be a matrix in the form described under amortTbl(), page 7. Note: See also GInt() and GPrn(), page 154. TI-Nspire™ CAS Reference Guide 13 4Base2 Catalog > Integer1 4Base2 integer Note: You can insert this operator from the computer keyboard by typing @>Base2. Converts Integer1 to a binary number. Binary or hexadecimal numbers always have a 0b or 0h prefix, respectively. Zero, not the letter O, followed by b or h. 0b binaryNumber 0h hexadecimalNumber A binary number can have up to 64 digits. A hexadecimal number can have up to 16. Without a prefix, Integer1 is treated as decimal (base 10). The result is displayed in binary, regardless of the Base mode. Negative numbers are displayed in “two's complement” form. For example, N1 is displayed as 0hFFFFFFFFFFFFFFFF in Hex base mode 0b111...111 (64 1’s) in Binary base mode N263 is displayed as 0h8000000000000000 in Hex base mode 0b100...000 (63 zeros) in Binary base mode If you enter a decimal integer that is outside the range of a signed, 64-bit binary form, a symmetric modulo operation is used to bring the value into the appropriate range. Consider the following examples of values outside the range. 263 becomes N263 and is displayed as 0h8000000000000000 in Hex base mode 0b100...000 (63 zeros) in Binary base mode 264 becomes 0 and is displayed as 0h0 in Hex base mode 0b0 in Binary base mode N263 N 1 becomes 263 N 1 and is displayed as 0h7FFFFFFFFFFFFFFF in Hex base mode 0b111...111 (64 1’s) in Binary base mode 4Base10 Integer1 4Base10 integer Note: You can insert this operator from the computer keyboard by typing @>Base10. Converts Integer1 to a decimal (base 10) number. A binary or hexadecimal entry must always have a 0b or 0h prefix, respectively. 0b binaryNumber 0h hexadecimalNumber Zero, not the letter O, followed by b or h. A binary number can have up to 64 digits. A hexadecimal number can have up to 16. Without a prefix, Integer1 is treated as decimal. The result is displayed in decimal, regardless of the Base mode. 14 TI-Nspire™ CAS Reference Guide Catalog > 4Base16 Catalog > Integer1 4Base16 integer Note: You can insert this operator from the computer keyboard by typing @>Base16. Converts Integer1 to a hexadecimal number. Binary or hexadecimal numbers always have a 0b or 0h prefix, respectively. 0b binaryNumber 0h hexadecimalNumber Zero, not the letter O, followed by b or h. A binary number can have up to 64 digits. A hexadecimal number can have up to 16. Without a prefix, Integer1 is treated as decimal (base 10). The result is displayed in hexadecimal, regardless of the Base mode. If you enter a decimal integer that is too large for a signed, 64-bit binary form, a symmetric modulo operation is used to bring the value into the appropriate range. For more information, see 4Base2, page 14. binomCdf() binomCdf(n,p) Catalog > number binomCdf(n,p,lowBound,upBound) number if lowBound and upBound are numbers, list if lowBound and upBound are lists binomCdf(n,p,upBound) for P(0{X{upBound) number if upBound is a number, list if upBound is a list Computes a cumulative probability for the discrete binomial distribution with n number of trials and probability p of success on each trial. For P(X { upBound), set lowBound=0 binomPdf() binomPdf(n,p) Catalog > number number if XVal is a number, list if binomPdf(n,p,XVal) XVal is a list Computes a probability for the discrete binomial distribution with n number of trials and probability p of success on each trial. C ceiling() ceiling(Expr1) Catalog > integer Returns the nearest integer that is | the argument. The argument can be a real or a complex number. Note: See also floor(). ceiling(List1) list ceiling(Matrix1) matrix Returns a list or matrix of the ceiling of each element. TI-Nspire™ CAS Reference Guide 15 centralDiff() Catalog > 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 centralDiff(Expr1,Var [=Value][,Step]) Returns the numerical derivative using the central difference quotient formula. When Value is specified, it overrides any prior variable assignment or any current “|” substitution for the variable. Step is the step value. If Step is omitted, it defaults to 0.001. When using List1 or Matrix1, the operation gets mapped across the values in the list or across the matrix elements. Note: See also avgRC() and d(). cFactor() Catalog > cFactor(Expr1[,Var]) expression cFactor(List1[,Var]) list cFactor(Matrix1[,Var]) matrix cFactor(Expr1) returns Expr1 factored with respect to all of its variables over a common denominator. Expr1 is factored as much as possible toward linear rational factors even if this introduces new non-real numbers. This alternative is appropriate if you want factorization with respect to more than one variable. cFactor(Expr1,Var) returns Expr1 factored with respect to variable Var. Expr1 is factored as much as possible toward factors that are linear in Var, with perhaps non-real constants, even if it introduces irrational constants or subexpressions that are irrational in other variables. The factors and their terms are sorted with Var as the main variable. Similar powers of Var are collected in each factor. Include Var if factorization is needed with respect to only that variable and you are willing to accept irrational expressions in any other variables to increase factorization with respect to Var. There might be some incidental factoring with respect to other variables. For the Auto setting of the Auto or Approximate mode, including Var also permits approximation with floating-point coefficients where irrational coefficients cannot be explicitly expressed concisely in terms of the built-in functions. Even when there is only one variable, including Var might yield more complete factorization. Note: See also factor(). To see the entire result, press move the cursor. 16 TI-Nspire™ CAS Reference Guide £ and then use ¡ and ¢ to char() char(Integer) Catalog > character Returns a character string containing the character numbered Integer from the handheld character set. The valid range for Integer is 0– 65535. charPoly() Catalog > polynomial expression charPoly(squareMatrix,Expr) polynomial expression charPoly(squareMatrix1,Matrix2) polynomial expression charPoly(squareMatrix,Var) Returns the characteristic polynomial of squareMatrix. The characteristic polynomial of n×n matrix A, denoted by pA(l), is the polynomial defined by pA(l) = det(l• I NA) where I denotes the n×n identity matrix. squareMatrix1 and squareMatrix2 must have the equal dimensions. c22way c 2 Catalog > 2way obsMatrix chi22way obsMatrix Computes a c2 test for association on the two-way table of counts in the observed matrix obsMatrix. A summary of results is stored in the stat.results variable. (See page 120.) For information on the effect of empty elements in a matrix, see “Empty (Void) Elements” on page 162. Output variable Description stat.c2 Chi square stat: sum (observed - expected)2/expected stat.PVal Smallest level of significance at which the null hypothesis can be rejected stat.df Degrees of freedom for the chi square statistics stat.ExpMat Matrix of expected elemental count table, assuming null hypothesis stat.CompMat Matrix of elemental chi square statistic contributions c2Cdf() Catalog > c2Cdf(lowBound,upBound,df) number if lowBound and upBound are numbers, list if lowBound and upBound are lists chi2Cdf(lowBound,upBound,df) number if lowBound and upBound are numbers, list if lowBound and upBound are lists Computes the c2 distribution probability between lowBound and upBound for the specified degrees of freedom df. For P(X { upBound), set lowBound = 0. For information on the effect of empty elements in a list, see “Empty (Void) Elements” on page 162. TI-Nspire™ CAS Reference Guide 17 c2GOF c 2 Catalog > GOF obsList,expList,df chi2GOF obsList,expList,df Performs a test to confirm that sample data is from a population that conforms to a specified distribution. obsList is a list of counts and must contain integers. A summary of results is stored in the stat.results variable. (See page 120.) For information on the effect of empty elements in a list, see “Empty (Void) Elements” on page 162. Output variable Description stat.c2 Chi square stat: sum((observed - expected)2/expected stat.PVal Smallest level of significance at which the null hypothesis can be rejected stat.df Degrees of freedom for the chi square statistics stat.CompList Elemental chi square statistic contributions c2Pdf() Catalog > c2Pdf(XVal,df) number if XVal is a number, list if XVal is a list chi2Pdf(XVal,df) a list number if XVal is a number, list if XVal is Computes the probability density function (pdf) for the c2 distribution at a specified XVal value for the specified degrees of freedom df. For information on the effect of empty elements in a list, see “Empty (Void) Elements” on page 162. ClearAZ ClearAZ Clears all single-character variables in the current problem space. If one or more of the variables are locked, this command displays an error message and deletes only the unlocked variables. See unLock, page 135. 18 TI-Nspire™ CAS Reference Guide Catalog > ClrErr Catalog > For an example of ClrErr, See Example 2 under the Try command, page 130. ClrErr Clears the error status and sets system variable errCode to zero. The Else clause of the Try...Else...EndTry block should use ClrErr or PassErr. If the error is to be processed or ignored, use ClrErr. If what to do with the error is not known, use PassErr to send it to the next error handler. If there are no more pending Try...Else...EndTry error handlers, the error dialog box will be displayed as normal. Note: See also PassErr, page 88, and Try, page 130. Note for entering the example: In the Calculator application on the handheld, you can enter multi-line definitions by pressing @ · instead of at the end of each line. On the computer keyboard, hold down Alt and press Enter. colAugment() Catalog > colAugment(Matrix1, Matrix2) matrix Returns a new matrix that is Matrix2 appended to Matrix1. The matrices must have equal column dimensions, and Matrix2 is appended to Matrix1 as new rows. Does not alter Matrix1 or Matrix2. colDim() colDim(Matrix) Catalog > expression Returns the number of columns contained in Matrix. Note: See also rowDim(). colNorm() colNorm(Matrix) Catalog > expression Returns the maximum of the sums of the absolute values of the elements in the columns in Matrix. Note: Undefined matrix elements are not allowed. See also rowNorm(). comDenom() Catalog > comDenom(Expr1[,Var]) expression comDenom(List1[,Var]) list comDenom(Matrix1[,Var]) matrix comDenom(Expr1) returns a reduced ratio of a fully expanded numerator over a fully expanded denominator. TI-Nspire™ CAS Reference Guide 19 comDenom() Catalog > comDenom(Expr1,Var) returns a reduced ratio of numerator and denominator expanded with respect to Var. The terms and their factors are sorted with Var as the main variable. Similar powers of Var are collected. There might be some incidental factoring of the collected coefficients. Compared to omitting Var, this often saves time, memory, and screen space, while making the expression more comprehensible. It also makes subsequent operations on the result faster and less likely to exhaust memory. If Var does not occur in Expr1, comDenom(Expr1,Var) returns a reduced ratio of an unexpanded numerator over an unexpanded denominator. Such results usually save even more time, memory, and screen space. Such partially factored results also make subsequent operations on the result much faster and much less likely to exhaust memory. Even when there is no denominator, the comden function is often a fast way to achieve partial factorization if factor() is too slow or if it exhausts memory. Hint: Enter this comden() function definition and routinely try it as an alternative to comDenom() and factor(). completeSquare() completeSquare(ExprOrEqn, Var) Catalog > expression or equation completeSquare(ExprOrEqn, Var^Power) equation completeSquare(ExprOrEqn, Var1, Var2 [,...]) equation expression or completeSquare(ExprOrEqn, {Var1, Var2 [,...]}) or equation expression or expression Converts a quadratic polynomial expression of the form a·x2+b·x+c into the form a·(x-h)2+k - or Converts a quadratic equation of the form a·x2+b·x+c=d into the form a·(x-h)2=k The first argument must be a quadratic expression or equation in standard form with respect to the second argument. The Second argument must be a single univariate term or a single univariate term raised to a rational power, for example x, y2, or z(1/3). The third and fourth syntax attempt to complete the square with respect to variables Var1, Var2 [,… ]). 20 TI-Nspire™ CAS Reference Guide conj() Catalog > conj(Expr1) expression conj(List1) list conj(Matrix1) matrix Returns the complex conjugate of the argument. Note: All undefined variables are treated as real variables. constructMat() Catalog > constructMat(Expr,Var1,Var2,numRows,numCols) matrix Returns a matrix based on the arguments. Expr is an expression in variables Var1 and Var2. Elements in the resulting matrix are formed by evaluating Expr for each incremented value of Var1 and Var2. Var1 is automatically incremented from 1 through numRows. Within each row, Var2 is incremented from 1 through numCols. CopyVar Catalog > CopyVar Var1, Var2 CopyVar Var1. , Var2. CopyVar Var1, Var2 copies the value of variable Var1 to variable Var2, creating Var2 if necessary. Variable Var1 must have a value. If Var1 is the name of an existing user-defined function, copies the definition of that function to function Var2. Function Var1 must be defined. Var1 must meet the variable-naming requirements or must be an indirection expression that simplifies to a variable name meeting the requirements. CopyVar Var1. , Var2. copies all members of the Var1. variable group to the Var2. group, creating Var2. if necessary. Var1. must be the name of an existing variable group, such as the statistics stat.nn results, or variables created using the LibShortcut() function. If Var2. already exists, this command replaces all members that are common to both groups and adds the members that do not already exist. If one or more members of Var2. are locked, all members of Var2. are left unchanged. TI-Nspire™ CAS Reference Guide 21 corrMat() Catalog > corrMat(List1,List2[,…[,List20]]) Computes the correlation matrix for the augmented matrix [List1, List2, ..., List20]. 4cos Catalog > Expr 4cos Note: You can insert this operator from the computer keyboard by typing @>cos. Represents Expr in terms of cosine. This is a display conversion operator. It can be used only at the end of the entry line. 4cos reduces all powers of sin(...) modulo 1Ncos(...)^2 so that any remaining powers of cos(...) have exponents in the range (0, 2). Thus, the result will be free of sin(...) if and only if sin(...) occurs in the given expression only to even powers. Note: This conversion operator is not supported in Degree or Gradian Angle modes. Before using it, make sure that the Angle mode is set to Radians and that Expr does not contain explicit references to degree or gradian angles. μ key cos() expression cos(List1) list cos(Expr1) In Degree angle mode: cos(Expr1) returns the cosine of the argument as an expression. cos(List1) returns a list of the cosines of all elements in List1. Note: The argument is interpreted as a degree, gradian or radian angle, according to the current angle mode setting. You can use ¡, G, or R to override the angle mode temporarily. In Gradian angle mode: In Radian angle mode: 22 TI-Nspire™ CAS Reference Guide μ key cos() cos(squareMatrix1) squareMatrix In Radian angle mode: Returns the matrix cosine of squareMatrix1. This is not the same as calculating the cosine of each element. When a scalar function f(A) operates on squareMatrix1 (A), the result is calculated by the algorithm: Compute the eigenvalues (li) and eigenvectors (Vi) of A. squareMatrix1 must be diagonalizable. Also, it cannot have symbolic variables that have not been assigned a value. Form the matrices: Then A = X B X/and f(A) = X f(B) X/. For example, cos(A) = X cos(B) X/ where: cos(B) = All computations are performed using floating-point arithmetic. μ key cos /() cos/(Expr1) expression cos/(List1) list In Degree angle mode: cos/(Expr1) returns the angle whose cosine is Expr1 as an expression. In Gradian angle mode: cos/(List1) returns a list of the inverse cosines of each element of List1. In Radian angle mode: Note: The result is returned as a degree, gradian or radian angle, according to the current angle mode setting. Note: You can insert this function from the keyboard by typing arccos(...). cos/(squareMatrix1) squareMatrix In Radian angle mode and Rectangular Complex Format: Returns the matrix inverse cosine of squareMatrix1. This is not the same as calculating the inverse cosine of each element. For information about the calculation method, refer to cos(). squareMatrix1 must be diagonalizable. The result always contains floating-point numbers. To see the entire result, press move the cursor. £ and then use ¡ and ¢ to TI-Nspire™ CAS Reference Guide 23 cosh() Catalog > cosh(Expr1) expression cosh(List1) list cosh(Expr1) returns the hyperbolic cosine of the argument as an expression. cosh(List1) returns a list of the hyperbolic cosines of each element of List1. cosh(squareMatrix1) squareMatrix In Radian angle mode: Returns the matrix hyperbolic cosine of squareMatrix1. This is not the same as calculating the hyperbolic cosine of each element. For information about the calculation method, refer to cos(). squareMatrix1 must be diagonalizable. The result always contains floating-point numbers. cosh /() Catalog > cosh/(Expr1) expression cosh/(List1) list cosh/(Expr1) returns the inverse hyperbolic cosine of the argument as an expression. cosh/(List1) returns a list of the inverse hyperbolic cosines of each element of List1. Note: You can insert this function from the keyboard by typing arccosh(...). cosh/(squareMatrix1) squareMatrix In Radian angle mode and In Rectangular Complex Format: Returns the matrix inverse hyperbolic cosine of squareMatrix1. This is not the same as calculating the inverse hyperbolic cosine of each element. For information about the calculation method, refer to cos(). squareMatrix1 must be diagonalizable. The result always contains floating-point numbers. To see the entire result, press move the cursor. μ key cot() cot(Expr1) expression cot(List1) list In Degree angle mode: Returns the cotangent of Expr1 or returns a list of the cotangents of all elements in List1. In Gradian angle mode: Note: The argument is interpreted as a degree, gradian or radian G angle, according to the current angle mode setting. You can use ¡, , or R to override the angle mode temporarily. In Radian angle mode: 24 £ and then use ¡ and ¢ to TI-Nspire™ CAS Reference Guide μ key cot /() cot/(Expr1) expression cot/(List1) list In Degree angle mode: Returns the angle whose cotangent is Expr1 or returns a list containing the inverse cotangents of each element of List1. In Gradian angle mode: Note: The result is returned as a degree, gradian or radian angle, according to the current angle mode setting. Note: You can insert this function from the keyboard by typing In Radian angle mode: arccot(...). coth() Catalog > coth(Expr1) expression coth(List1) list Returns the hyperbolic cotangent of Expr1 or returns a list of the hyperbolic cotangents of all elements of List1. coth/() Catalog > coth/(Expr1) expression coth/(List1) list Returns the inverse hyperbolic cotangent of Expr1 or returns a list containing the inverse hyperbolic cotangents of each element of List1. Note: You can insert this function from the keyboard by typing arccoth(...). count() count(Value1orList1 [,Value2orList2 [,...]]) Catalog > value Returns the accumulated count of all elements in the arguments that evaluate to numeric values. Each argument can be an expression, value, list, or matrix. You can mix data types and use arguments of various dimensions. For a list, matrix, or range of cells, each element is evaluated to determine if it should be included in the count. Within the Lists & Spreadsheet application, you can use a range of cells in place of any argument. Empty (void) elements are ignored. For more information on empty elements, see page 162. In the last example, only 1/2 and 3+4*i are counted. The remaining arguments, assuming x is undefined, do not evaluate to numeric values. TI-Nspire™ CAS Reference Guide 25 countif() Catalog > countif(List,Criteria) value Returns the accumulated count of all elements in List that meet the specified Criteria. Counts the number of elements equal to 3. Criteria can be: • • A value, expression, or string. For example, 3 counts only those elements in List that simplify to the value 3. A Boolean expression containing the symbol ? as a placeholder for each element. For example, ?<5 counts only those elements in List that are less than 5. Within the Lists & Spreadsheet application, you can use a range of cells in place of List. Counts the number of elements equal to “def.” Counts the number of elements equal to x; this example assumes the variable x is undefined. Empty (void) elements in the list are ignored. For more information on empty elements, see page 162. Note: See also sumIf(), page 123, and frequency(), page 51. Counts 1 and 3. Counts 3, 5, and 7. Counts 1, 3, 7, and 9. cPolyRoots() Catalog > list cPolyRoots(ListOfCoeffs) list cPolyRoots(Poly,Var) The first syntax, cPolyRoots(Poly,Var), returns a list of complex roots of polynomial Poly with respect to variable Var. Poly must be a polynomial in one variable. The second syntax, cPolyRoots(ListOfCoeffs), returns a list of complex roots for the coefficients in ListOfCoeffs. Note: See also polyRoots(), page 91. crossP() crossP(List1, List2) Catalog > list Returns the cross product of List1 and List2 as a list. List1 and List2 must have equal dimension, and the dimension must be either 2 or 3. crossP(Vector1, Vector2) vector Returns a row or column vector (depending on the arguments) that is the cross product of Vector1 and Vector2. Both Vector1 and Vector2 must be row vectors, or both must be column vectors. Both vectors must have equal dimension, and the dimension must be either 2 or 3. 26 TI-Nspire™ CAS Reference Guide μ key csc() csc(Expr1) expression csc(List1) list In Degree angle mode: Returns the cosecant of Expr1 or returns a list containing the cosecants of all elements in List1. In Gradian angle mode: In Radian angle mode: μ key csc/() csc /(Expr1) expression csc /(List1) list In Degree angle mode: Returns the angle whose cosecant is Expr1 or returns a list containing the inverse cosecants of each element of List1. In Gradian angle mode: Note: The result is returned as a degree, gradian or radian angle, according to the current angle mode setting. Note: You can insert this function from the keyboard by typing In Radian angle mode: arccsc(...). csch() Catalog > expression list csch(Expr1) csch(List1) Returns the hyperbolic cosecant of Expr1 or returns a list of the hyperbolic cosecants of all elements of List1. csch/() Catalog > csch/(Expr1) expression csch/(List1) list Returns the inverse hyperbolic cosecant of Expr1 or returns a list containing the inverse hyperbolic cosecants of each element of List1. Note: You can insert this function from the keyboard by typing arccsch(...). TI-Nspire™ CAS Reference Guide 27 cSolve() Catalog > Boolean expression cSolve(Equation, Var=Guess) Boolean expression cSolve(Inequality, Var) Boolean expression cSolve(Equation, Var) Returns candidate complex solutions of an equation or inequality for Var. The goal is to produce candidates for all real and non-real solutions. Even if Equation is real, cSolve() allows non-real results in Real result Complex Format. Although all undefined variables that do not end with an underscore (_) are processed as if they were real, cSolve() can solve polynomial equations for complex solutions. cSolve() temporarily sets the domain to complex during the solution even if the current domain is real. In the complex domain, fractional powers having odd denominators use the principal rather than the real branch. Consequently, solutions from solve() to equations involving such fractional powers are not necessarily a subset of those from cSolve(). cSolve() starts with exact symbolic methods. cSolve() also uses iterative approximate complex polynomial factoring, if necessary. In Display Digits mode of Fix 2: Note: See also cZeros(), solve(), and zeros(). Note: If Equation is non-polynomial with functions such as abs(), angle(), conj(), real(), or imag(), you should place an underscore /_) at the end of Var. By default, a variable is treated (press as a real value. To see the entire result, press the cursor. If you use var_ , the variable is treated as complex. £ and then use ¡ and ¢ to move z is treated as real: You should also use var_ for any other variables in Equation that might have unreal values. Otherwise, you may receive unexpected results. z_ is treated as complex: cSolve(Eqn1 and Eqn2 [and …], VarOrGuess1, VarOrGuess2 [, … ]) Boolean expression cSolve(SystemOfEqns, VarOrGuess1, VarOrGuess2 [, …]) Boolean expression Returns candidate complex solutions to the simultaneous algebraic equations, where each varOrGuess specifies a variable that you want to solve for. Optionally, you can specify an initial guess for a variable. Each varOrGuess must have the form: variable – or – variable = real or non-real number For example, x is valid and so is x=3+i. If all of the equations are polynomials and if you do NOT specify any initial guesses, cSolve() uses the lexical Gröbner/Buchberger elimination method to attempt to determine all complex solutions. 28 TI-Nspire™ CAS Reference Guide Note: The following examples use an underscore (press _) so that the variables will be treated as complex. / cSolve() Catalog > Complex solutions can include both real and non-real solutions, as in the example to the right. To see the entire result, press the cursor. £ and then use ¡ and ¢ to move To see the entire result, press the cursor. £ and then use ¡ and ¢ to move Simultaneous polynomial equations can have extra variables that have no values, but represent given numeric values that could be substituted later. You can also include solution variables that do not appear in the equations. These solutions show how families of solutions might contain arbitrary constants of the form ck, where k is an integer suffix from 1 through 255. For polynomial systems, computation time or memory exhaustion may depend strongly on the order in which you list solution variables. To see the entire result, press If your initial choice exhausts memory or your patience, try the cursor. rearranging the variables in the equations and/or varOrGuess list. £ and then use ¡ and ¢ to move If you do not include any guesses and if any equation is nonpolynomial in any variable but all equations are linear in all solution variables, cSolve() uses Gaussian elimination to attempt to determine all solutions. If a system is neither polynomial in all of its variables nor linear in its solution variables, cSolve() determines at most one solution using an approximate iterative method. To do so, the number of solution variables must equal the number of equations, and all other variables in the equations must simplify to numbers. A non-real guess is often necessary to determine a non-real solution. For convergence, a guess might have to be rather close to a solution. To see the entire result, press the cursor. £ and then use ¡ and ¢ to move TI-Nspire™ CAS Reference Guide 29 CubicReg Catalog > CubicReg X, Y[, [Freq] [, Category, Include]] Computes the cubic polynomial regression y = a·x3+b· x2+c·x+d on lists X and Y with frequency Freq. A summary of results is stored in the stat.results variable. (See page 120.) All the lists must have equal dimension except for Include. X and Y are lists of independent and dependent variables. Freq is an optional list of frequency values. Each element in Freq specifies the frequency of occurrence for each corresponding X and Y data point. The default value is 1. All elements must be integers | 0. Category is a list of category codes for the corresponding X and Y data. Include is a list of one or more of the category codes. Only those data items whose category code is included in this list are included in the calculation. For information on the effect of empty elements in a list, see “Empty (Void) Elements” on page 162. Output variable Description stat.RegEqn Regression equation: 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 the modified X List actually used in the regression based on restrictions of Freq, Category List, and Include Categories stat.YReg List of data points in the modified Y List actually used in the regression based on restrictions of Freq, Category List, and Include Categories stat.FreqReg List of frequencies corresponding to stat.XReg and stat.YReg cumulativeSum() cumulativeSum(List1) Catalog > list Returns a list of the cumulative sums of the elements in List1, starting at element 1. cumulativeSum(Matrix1) matrix Returns a matrix of the cumulative sums of the elements in Matrix1. Each element is the cumulative sum of the column from top to bottom. An empty (void) element in List1 or Matrix1 produces a void element in the resulting list or matrix. For more information on empty elements, see page 162. 30 TI-Nspire™ CAS Reference Guide Cycle Catalog > Cycle Transfers control immediately to the next iteration of the current loop (For, While, or Loop). Function listing that sums the integers from 1 to 100 skipping 50. Cycle is not allowed outside the three looping structures (For, While, or Loop). Note for entering the example: In the Calculator application on the handheld, you can enter multi-line definitions by pressing @ · instead of at the end of each line. On the computer keyboard, hold down Alt and press Enter. 4Cylind Catalog > Vector 4Cylind Note: You can insert this operator from the computer keyboard by typing @>Cylind. Displays the row or column vector in cylindrical form [r,±q, z]. Vector must have exactly three elements. It can be either a row or a column. cZeros() cZeros(Expr, Var) Catalog > list In Display Digits mode of Fix 3: Returns a list of candidate real and non-real values of Var that make Expr=0. cZeros() does this by computing exp4list(cSolve(Expr=0,Var),Var). Otherwise, cZeros() is similar to zeros(). Note: See also cSolve(), solve(), and zeros(). To see the entire result, press move the cursor. Note: If Expr is non-polynomial with functions such as abs(), z is treated as real: £ and then use ¡ and ¢ to angle(), conj(), real(), or imag(), you should place an underscore /_ (press ) at the end of Var. By default, a variable is treated as a real value. If you use var_ , the variable is treated as complex. You should also use var_ for any other variables in Expr that might have unreal values. Otherwise, you may receive unexpected results. cZeros({Expr1, Expr2 [, … ] }, {VarOrGuess1,VarOrGuess2 [, … ] }) z_ is treated as complex: matrix Returns candidate positions where the expressions are zero simultaneously. Each VarOrGuess specifies an unknown whose value you seek. Optionally, you can specify an initial guess for a variable. Each VarOrGuess must have the form: variable – or – variable = real or non-real number For example, x is valid and so is x=3+i. TI-Nspire™ CAS Reference Guide 31 cZeros() If all of the expressions are polynomials and you do NOT specify any initial guesses, cZeros() uses the lexical Gröbner/Buchberger elimination method to attempt to determine all complex zeros. Catalog > Note: The following examples use an underscore _ (press /_) so that the variables will be treated as complex. Complex zeros can include both real and non-real zeros, as in the example to the right. Each row of the resulting matrix represents an alternate zero, with the components ordered the same as the VarOrGuess list. To extract a row, index the matrix by [row]. Extract row 2: Simultaneous polynomials can have extra variables that have no values, but represent given numeric values that could be substituted later. You can also include unknown variables that do not appear in the expressions. These zeros show how families of zeros might contain arbitrary constants of the form ck, where k is an integer suffix from 1 through 255. For polynomial systems, computation time or memory exhaustion may depend strongly on the order in which you list unknowns. If your initial choice exhausts memory or your patience, try rearranging the variables in the expressions and/or VarOrGuess list. If you do not include any guesses and if any expression is nonpolynomial in any variable but all expressions are linear in all unknowns, cZeros() uses Gaussian elimination to attempt to determine all zeros. If a system is neither polynomial in all of its variables nor linear in its unknowns, cZeros() determines at most one zero using an approximate iterative method. To do so, the number of unknowns must equal the number of expressions, and all other variables in the expressions must simplify to numbers. A non-real guess is often necessary to determine a non-real zero. For convergence, a guess might have to be rather close to a zero. 32 TI-Nspire™ CAS Reference Guide D dbd() dbd(date1,date2) Catalog > value Returns the number of days between date1 and date2 using the actual-day-count method. date1 and date2 can be numbers or lists of numbers within the range of the dates on the standard calendar. If both date1 and date2 are lists, they must be the same length. date1 and date2 must be between the years 1950 through 2049. You can enter the dates in either of two formats. The decimal placement differentiates between the date formats. MM.DDYY (format used commonly in the United States) DDMM.YY (format use commonly in Europe) 4DD Catalog > Expr1 4DD value List1 4DD list Matrix1 4DD matrix In Degree angle mode: Note: You can insert this operator from the computer keyboard by typing @>DD. Returns the decimal equivalent of the argument expressed in degrees. The argument is a number, list, or matrix that is interpreted by the Angle mode setting in gradians, radians or degrees. In Gradian angle mode: In Radian angle mode: 4Decimal Catalog > Expression1 4Decimal expression List1 4Decimal expression Matrix1 4Decimal expression Note: You can insert this operator from the computer keyboard by typing @>Decimal. Displays the argument in decimal form. This operator can be used only at the end of the entry line. TI-Nspire™ CAS Reference Guide 33 Define Catalog > Define Var = Expression Define Function(Param1, Param2, ...) = Expression Defines the variable Var or the user-defined function Function. Parameters, such as Param1, provide placeholders for passing arguments to the function. When calling a user-defined function, you must supply arguments (for example, values or variables) that correspond to the parameters. When called, the function evaluates Expression using the supplied arguments. Var and Function cannot be the name of a system variable or built-in function or command. Note: This form of Define is equivalent to executing the expression: expression & Function(Param1,Param2). Define Function(Param1, Param2, ...) = Func Block EndFunc Define Program(Param1, Param2, ...) = Prgm Block EndPrgm In this form, the user-defined function or program can execute a block of multiple statements. Block can be either a single statement or a series of statements on separate lines. Block also can include expressions and instructions (such as If, Then, Else, and For). Note for entering the example: In the Calculator application on the handheld, you can enter multi-line definitions by pressing @ · instead of at the end of each line. On the computer keyboard, hold down Alt and press Enter. Note: See also Define LibPriv, page 34, and Define LibPub, page 35. Define LibPriv Define LibPriv Var = Expression Define LibPriv Function(Param1, Param2, ...) = Expression Define LibPriv Function(Param1, Param2, ...) = Func Block EndFunc Define LibPriv Program(Param1, Param2, ...) = Prgm Block EndPrgm Operates the same as Define, except defines a private library variable, function, or program. Private functions and programs do not appear in the Catalog. Note: See also Define, page 34, and Define LibPub, page 35. 34 TI-Nspire™ CAS Reference Guide Catalog > Define LibPub Catalog > Define LibPub Var = Expression Define LibPub Function(Param1, Param2, ...) = Expression Define LibPub Function(Param1, Param2, ...) = Func Block EndFunc Define LibPub Program(Param1, Param2, ...) = Prgm Block EndPrgm Operates the same as Define, except defines a public library variable, function, or program. Public functions and programs appear in the Catalog after the library has been saved and refreshed. Note: See also Define, page 34, and Define LibPriv, page 34. See @List(), page 67. deltaList() See @tmpCnv(), page 129. deltaTmpCnv() DelVar Catalog > DelVar Var1[, Var2] [, Var3] ... DelVar Var. Deletes the specified variable or variable group from memory. If one or more of the variables are locked, this command displays an error message and deletes only the unlocked variables. See unLock, page 135. DelVar Var. deletes all members of the Var. variable group (such as the statistics stat.nn results or variables created using the LibShortcut() function). The dot (.) in this form of the DelVar command limits it to deleting a variable group; the simple variable Var is not affected. delVoid() delVoid(List1) Catalog > list Returns a list that has the contents of List1 with all empty (void) elements removed. For more information on empty elements, see page 162. derivative() See d(), page 150. TI-Nspire™ CAS Reference Guide 35 deSolve() Catalog > deSolve(1stOr2ndOrderODE, Var, depVar) a general solution Returns an equation that explicitly or implicitly specifies a general solution to the 1st- or 2nd-order ordinary differential equation (ODE). In the ODE: • • º Use a prime symbol (press ) to denote the 1st derivative of the dependent variable with respect to the independent variable. Use two prime symbols to denote the corresponding second derivative. The prime symbol is used for derivatives within deSolve() only. In other cases, use d(). The general solution of a 1st-order equation contains an arbitrary constant of the form ck, where k is an integer suffix from 1 through 255. The solution of a 2nd-order equation contains two such constants. Apply solve() to an implicit solution if you want to try to convert it to one or more equivalent explicit solutions. When comparing your results with textbook or manual solutions, be aware that different methods introduce arbitrary constants at different points in the calculation, which may produce different general solutions. deSolve(1stOrderODE and initCond, Var, depVar) a particular solution Returns a particular solution that satisfies 1stOrderODE and initCond. This is usually easier than determining a general solution, substituting initial values, solving for the arbitrary constant, and then substituting that value into the general solution. initCond is an equation of the form: depVar (initialIndependentValue) = initialDependentValue The initialIndependentValue and initialDependentValue can be variables such as x0 and y0 that have no stored values. Implicit differentiation can help verify implicit solutions. deSolve(2ndOrderODE and initCond1 and initCond2, Var, depVar) a particular solution Returns a particular solution that satisfies 2nd Order ODE and has a specified value of the dependent variable and its first derivative at one point. For initCond1, use the form: depVar (initialIndependentValue) = initialDependentValue For initCond2, use the form: depVar (initialIndependentValue) = initial1stDerivativeValue 36 TI-Nspire™ CAS Reference Guide deSolve() Catalog > deSolve(2ndOrderODE and bndCond1 and bndCond2, Var, depVar) a particular solution Returns a particular solution that satisfies 2ndOrderODE and has specified values at two different points. det() Catalog > det(squareMatrix[, Tolerance]) expression Returns the determinant of squareMatrix. Optionally, any matrix element is treated as zero if its absolute value is less than Tolerance. This tolerance is used only if the matrix has floating-point entries and does not contain any symbolic variables that have not been assigned a value. Otherwise, Tolerance is ignored. • • /· or set the Auto or Approximate If you use mode to Approximate, computations are done using floatingpoint arithmetic. If Tolerance is omitted or not used, the default tolerance is calculated as: 5EM14 ·max(dim(squareMatrix))· rowNorm(squareMatrix) diag() Catalog > diag(List) matrix diag(rowMatrix) matrix diag(columnMatrix) matrix Returns a matrix with the values in the argument list or matrix in its main diagonal. diag(squareMatrix) rowMatrix Returns a row matrix containing the elements from the main diagonal of squareMatrix. squareMatrix must be square. dim() dim(List) Catalog > integer Returns the dimension of List. dim(Matrix) list Returns the dimensions of matrix as a two-element list {rows, columns}. dim(String) integer Returns the number of characters contained in character string String. TI-Nspire™ CAS Reference Guide 37 Disp Catalog > Disp [exprOrString1] [, exprOrString2] ... Displays the arguments in the Calculator history. The arguments are displayed in succession, with thin spaces as separators. Useful mainly in programs and functions to ensure the display of intermediate calculations. Note for entering the example: In the Calculator application on the handheld, you can enter multi-line definitions by pressing @ · at the end of each line. On the computer keyboard, instead of hold down Alt and press Enter. 4DMS Catalog > Expr 4DMS List 4DMS Matrix 4DMS In Degree angle mode: Note: You can insert this operator from the computer keyboard by typing @>DMS. Interprets the argument as an angle and displays the equivalent DMS (DDDDDD¡MM'SS.ss'') number. See ¡, ', '' on page 156 for DMS (degree, minutes, seconds) format. Note: 4DMS will convert from radians to degrees when used in radian mode. If the input is followed by a degree symbol ¡ , no conversion will occur. You can use 4DMS only at the end of an entry line. domain() domain(Expr1, Var) Catalog > expression Returns the domain of Expr1 with respect to Var. domain() can be used to examine domains of functions. It is restricted to real and finite domain. This functionality has limitations due to shortcomings of computer algebra simplification and solver algorithms. Certain functions cannot be used as arguments for domain(), regardless of whether they appear explicitly or within user-defined variables and functions. In the following example, the expression cannot be simplified because ‰() is a disallowed function. 38 TI-Nspire™ CAS Reference Guide dominantTerm() Catalog > dominantTerm(Expr1, Var [, Point]) expression dominantTerm(Expr1, Var [, Point]) | Var>Point expression dominantTerm(Expr1, Var [, Point]) | Var<Point expression Returns the dominant term of a power series representation of Expr1 expanded about Point. The dominant term is the one whose magnitude grows most rapidly near Var = Point. The resulting power of (Var N Point) can have a negative and/or fractional exponent. The coefficient of this power can include logarithms of (Var N Point) and other functions of Var that are dominated by all powers of (Var N Point) having the same exponent sign. Point defaults to 0. Point can be ˆ or Nˆ, in which cases the dominant term will be the term having the largest exponent of Var rather than the smallest exponent of Var. dominantTerm(…) returns “dominantTerm(…)” if it is unable to determine such a representation, such as for essential singularities such as sin(1/z) at z=0, eN1/z at z=0, or ez at z = ˆ or Nˆ. If the series or one of its derivatives has a jump discontinuity at Point, the result is likely to contain sub-expressions of the form sign(…) or abs(…) for a real expansion variable or (-1)floor(…angle(…)…) for a complex expansion variable, which is one ending with “_”. If you intend to use the dominant term only for values on one side of Point, then append to dominantTerm(...) the appropriate one of “| Var > Point”, “| Var < Point”, “| “Var | Point”, or “Var { Point” to obtain a simpler result. dominantTerm() distributes over 1st-argument lists and matrices. dominantTerm() is useful when you want to know the simplest possible expression that is asymptotic to another expression as Var " Point. dominantTerm() is also useful when it isn’t obvious what the degree of the first non-zero term of a series will be, and you don’t want to iteratively guess either interactively or by a program loop. Note: See also series(), page 109. dotP() dotP(List1, List2) Catalog > expression Returns the “dot” product of two lists. dotP(Vector1, Vector2) expression Returns the “dot” product of two vectors. Both must be row vectors, or both must be column vectors. TI-Nspire™ CAS Reference Guide 39 E u key e^() e^(Expr1) expression Returns e raised to the Expr1 power. Note: See also e exponent template, page 2. u to display e^( is different from pressing the E on the keyboard. Note: Pressing character You can enter a complex number in rei q polar form. However, use this form in Radian angle mode only; it causes a Domain error in Degree or Gradian angle mode. e^(List1) list Returns e raised to the power of each element in List1. e^(squareMatrix1) squareMatrix Returns the matrix exponential of squareMatrix1. This is not the same as calculating e raised to the power of each element. For information about the calculation method, refer to cos(). squareMatrix1 must be diagonalizable. The result always contains floating-point numbers. eff() Catalog > eff(nominalRate,CpY) value Financial function that converts the nominal interest rate nominalRate to an annual effective rate, given CpY as the number of compounding periods per year. nominalRate must be a real number, and CpY must be a real number > 0. Note: See also nom(), page 82. eigVc() eigVc(squareMatrix) Catalog > matrix In Rectangular Complex Format: Returns a matrix containing the eigenvectors for a real or complex squareMatrix, where each column in the result corresponds to an eigenvalue. Note that an eigenvector is not unique; it may be scaled by any constant factor. The eigenvectors are normalized, meaning that if V = [x 1, x 2, … , x n], then: x 12 + x 22 + … + x n2 = 1 squareMatrix is first balanced with similarity transformations until the row and column norms are as close to the same value as possible. The squareMatrix is then reduced to upper Hessenberg form and the eigenvectors are computed via a Schur factorization. To see the entire result, press move the cursor. 40 TI-Nspire™ CAS Reference Guide £ and then use ¡ and ¢ to eigVl() Catalog > eigVl(squareMatrix) list In Rectangular complex format mode: Returns a list of the eigenvalues of a real or complex squareMatrix. squareMatrix is first balanced with similarity transformations until the row and column norms are as close to the same value as possible. The squareMatrix is then reduced to upper Hessenberg form and the eigenvalues are computed from the upper Hessenberg matrix. To see the entire result, press move the cursor. Else £ and then use ¡ and ¢ to See If, page 57. ElseIf Catalog > If BooleanExpr1 Then Block1 ElseIf BooleanExpr2 Then Block2 © ElseIf BooleanExprN Then BlockN EndIf © Note for entering the example: In the Calculator application on the handheld, you can enter multi-line definitions by pressing @ · instead of at the end of each line. On the computer keyboard, hold down Alt and press Enter. EndFor EndFunc EndIf See For, page 49. See Func, page 52. See If, page 57. EndLoop See Loop, page 73. EndPrgm See Prgm, page 93. EndTry See Try, page 130. TI-Nspire™ CAS Reference Guide 41 EndWhile See While, page 136. euler() 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 Catalog > Differential equation: y'=0.001*y*(100-y) and y(0)=10 Uses the Euler method to solve the system £ and then use ¡ and ¢ to d depVar ---------------------- = Expr(Var, depVar) d Var To see the entire result, press move the cursor. with depVar(Var0)=depVar0 on the interval [Var0,VarMax]. Returns a matrix whose first row defines the Var output values and whose second row defines the value of the first solution component at the corresponding Var values, and so on. Compare above result with CAS exact solution obtained using deSolve() and seqGen(): Expr is the right-hand side that defines the ordinary differential equation (ODE). SystemOfExpr is the system of right-hand sides that define the system of ODEs (corresponds to order of dependent variables in ListOfDepVars). ListOfExpr is a list of right-hand sides that define the system of ODEs (corresponds to the order of dependent variables in ListOfDepVars). Var is the independent variable. ListOfDepVars is a list of dependent variables. {Var0, VarMax} is a two-element list that tells the function to integrate from Var0 to VarMax. System of equations: ListOfDepVars0 is a list of initial values for dependent variables. VarStep is a nonzero number such that sign(VarStep) = sign(VarMax-Var0) and solutions are returned at Var0+i·VarStep for with y1(0)=2 and y2(0)=5 all i=0,1,2,… such that Var0+i·VarStep is in [var0,VarMax] (there may not be a solution value at VarMax). eulerStep is a positive integer (defaults to 1) that defines the number of euler steps between output values. The actual step size used by the euler method is VarStep àeulerStep. exact() exact( Expr1 [, Tolerance]) expression exact( List1 [, Tolerance]) list exact( Matrix1 [, Tolerance]) matrix Uses Exact mode arithmetic to return, when possible, the rationalnumber equivalent of the argument. Tolerance specifies the tolerance for the conversion; the default is 0 (zero). 42 TI-Nspire™ CAS Reference Guide Catalog > Exit Catalog > Function listing: Exit Exits the current For, While, or Loop block. Exit is not allowed outside the three looping structures (For, While, or Loop). Note for entering the example: In the Calculator application on the handheld, you can enter multi-line definitions by pressing @ · instead of at the end of each line. On the computer keyboard, hold down Alt and press Enter. 4exp Catalog > Expr 4exp Represents Expr in terms of the natural exponential e. This is a display conversion operator. It can be used only at the end of the entry line. Note: You can insert this operator from the computer keyboard by typing @>exp. u key exp() exp(Expr1) expression Returns e raised to the Expr1 power. Note: See also e exponent template, page 2. You can enter a complex number in rei q polar form. However, use this form in Radian angle mode only; it causes a Domain error in Degree or Gradian angle mode. exp(List1) list Returns e raised to the power of each element in List1. exp(squareMatrix1) squareMatrix Returns the matrix exponential of squareMatrix1. This is not the same as calculating e raised to the power of each element. For information about the calculation method, refer to cos(). squareMatrix1 must be diagonalizable. The result always contains floating-point numbers. TI-Nspire™ CAS Reference Guide 43 exp4list() exp4list(Expr,Var) Catalog > list Examines Expr for equations that are separated by the word “or,” and returns a list containing the right-hand sides of the equations of the form Var=Expr. This gives you an easy way to extract some solution values embedded in the results of the solve(), cSolve(), fMin(), and fMax() functions. Note: exp4list() is not necessary with the zeros() and cZeros() functions because they return a list of solution values directly. You can insert this function from the keyboard by typing exp@>list(...). expand() expression list expand(Matrix1 [,Var]) matrix expand(Expr1 [, Var]) expand(List1 [,Var]) expand(Expr1) returns Expr1 expanded with respect to all its variables. The expansion is polynomial expansion for polynomials and partial fraction expansion for rational expressions. The goal of expand() is to transform Expr1 into a sum and/or difference of simple terms. In contrast, the goal of factor() is to transform Expr1 into a product and/or quotient of simple factors. expand(Expr1,Var) returns Expr1 expanded with respect to Var. Similar powers of Var are collected. The terms and their factors are sorted with Var as the main variable. There might be some incidental factoring or expansion of the collected coefficients. Compared to omitting Var, this often saves time, memory, and screen space, while making the expression more comprehensible. Even when there is only one variable, using Var might make the denominator factorization used for partial fraction expansion more complete. Hint: For rational expressions, propFrac() is a faster but less extreme alternative to expand(). Note: See also comDenom() for an expanded numerator over an expanded denominator. 44 TI-Nspire™ CAS Reference Guide Catalog > expand() Catalog > expand(Expr1,[Var]) also distributes logarithms and fractional powers regardless of Var. For increased distribution of logarithms and fractional powers, inequality constraints might be necessary to guarantee that some factors are nonnegative. expand(Expr1, [Var]) also distributes absolute values, sign(), and exponentials, regardless of Var. Note: See also tExpand() for trigonometric angle-sum and multiple-angle expansion. expr() expr(String) Catalog > expression Returns the character string contained in String as an expression and immediately executes it. ExpReg Catalog > ExpReg X, Y [, [Freq] [, Category, Include]] Computes the exponential regression y = a·(b)x on lists X and Y with frequency Freq. A summary of results is stored in the stat.results variable. (See page 120.) All the lists must have equal dimension except for Include. X and Y are lists of independent and dependent variables. Freq is an optional list of frequency values. Each element in Freq specifies the frequency of occurrence for each corresponding X and Y data point. The default value is 1. All elements must be integers | 0. Category is a list of category codes for the corresponding X and Y data. Include is a list of one or more of the category codes. Only those data items whose category code is included in this list are included in the calculation. For information on the effect of empty elements in a list, see “Empty (Void) Elements” on page 162. Output variable Description stat.RegEqn Regression equation: a·(b)x stat.a, stat.b Regression coefficients stat.r2 Coefficient of linear determination for transformed data TI-Nspire™ CAS Reference Guide 45 Output variable Description stat.r Correlation coefficient for transformed data (x, ln(y)) stat.Resid Residuals associated with the exponential model stat.ResidTrans Residuals associated with linear fit of transformed data stat.XReg List of data points in the modified X List actually used in the regression based on restrictions of Freq, Category List, and Include Categories stat.YReg List of data points in the modified Y List actually used in the regression based on restrictions of Freq, Category List, and Include Categories stat.FreqReg List of frequencies corresponding to stat.XReg and stat.YReg F factor() expression factor(List1[,Var]) list factor(Matrix1[,Var]) matrix factor(Expr1[, Var]) factor(Expr1) returns Expr1 factored with respect to all of its variables over a common denominator. Expr1 is factored as much as possible toward linear rational factors without introducing new non-real subexpressions. This alternative is appropriate if you want factorization with respect to more than one variable. factor(Expr1,Var) returns Expr1 factored with respect to variable Var. Expr1 is factored as much as possible toward real factors that are linear in Var, even if it introduces irrational constants or subexpressions that are irrational in other variables. The factors and their terms are sorted with Var as the main variable. Similar powers of Var are collected in each factor. Include Var if factorization is needed with respect to only that variable and you are willing to accept irrational expressions in any other variables to increase factorization with respect to Var. There might be some incidental factoring with respect to other variables. For the Auto setting of the Auto or Approximate mode, including Var permits approximation with floating-point coefficients where irrational coefficients cannot be explicitly expressed concisely in terms of the built-in functions. Even when there is only one variable, including Var might yield more complete factorization. Note: See also comDenom() for a fast way to achieve partial factoring when factor() is not fast enough or if it exhausts memory. Note: See also cFactor() for factoring all the way to complex coefficients in pursuit of linear factors. 46 TI-Nspire™ CAS Reference Guide Catalog > factor() Catalog > factor(rationalNumber) returns the rational number factored into primes. For composite numbers, the computing time grows exponentially with the number of digits in the second-largest factor. For example, factoring a 30-digit integer could take more than a day, and factoring a 100-digit number could take more than a century. To stop a calculation manually, • • • Windows®: Hold down the F12 key and press Enter repeatedly. Macintosh®: Hold down the F5 key and press Enter repeatedly. Handheld: Hold down the repeatedly. c key and press · If you merely want to determine if a number is prime, use isPrime() instead. It is much faster, particularly if rationalNumber is not prime and if the second-largest factor has more than five digits. FCdf() Catalog > FCdf(lowBound,upBound,dfNumer,dfDenom) number if lowBound and upBound are numbers, list if lowBound and upBound are lists FCdf(lowBound,upBound,dfNumer,dfDenom) number if lowBound and upBound are numbers, list if lowBound and upBound are lists Computes the F distribution probability between lowBound and upBound for the specified dfNumer (degrees of freedom) and dfDenom. For P(X { upBound), set lowBound = 0. Fill Catalog > Fill Expr, matrixVar matrix Replaces each element in variable matrixVar with Expr. matrixVar must already exist. Fill Expr, listVar list Replaces each element in variable listVar with Expr. listVar must already exist. TI-Nspire™ CAS Reference Guide 47 FiveNumSummary Catalog > FiveNumSummary X[,[Freq][,Category,Include]] Provides an abbreviated version of the 1-variable statistics on list X. A summary of results is stored in the stat.results variable. (See page 120.) X represents a list containing the data. Freq is an optional list of frequency values. Each element in Freq specifies the frequency of occurrence for each corresponding X and Y data point. The default value is 1. Category is a list of numeric category codes for the corresponding X data. Include is a list of one or more of the category codes. Only those data items whose category code is included in this list are included in the calculation. An empty (void) element in any of the lists X, Freq, or Category results in a void for the corresponding element of all those lists. For more information on empty elements, see page 162. Output variable Description stat.MinX Minimum of x values. stat.Q1X 1st Quartile of x. stat.MedianX Median of x. stat.Q3X 3rd Quartile of x. stat.MaxX Maximum of x values. floor() floor(Expr1) Catalog > integer Returns the greatest integer that is { the argument. This function is identical to int(). The argument can be a real or a complex number. floor(List1) list floor(Matrix1) matrix Returns a list or matrix of the floor of each element. Note: See also ceiling() and int(). fMax() fMax(Expr, Var) Boolean expression fMax(Expr, Var,lowBound) fMax(Expr, Var,lowBound,upBound) fMax(Expr, Var) | lowBound{Var{upBound Returns a Boolean expression specifying candidate values of Var that maximize Expr or locate its least upper bound. 48 TI-Nspire™ CAS Reference Guide Catalog > fMax() Catalog > You can use the constraint (“|”) operator to restrict the solution interval and/or specify other constraints. For the Approximate setting of the Auto or Approximate mode, fMax() iteratively searches for one approximate local maximum. This is often faster, particularly if you use the “|” operator to constrain the search to a relatively small interval that contains exactly one local maximum. Note: See also fMin() and max(). fMin() Catalog > fMin(Expr, Var) Boolean expression fMin(Expr, Var,lowBound) fMin(Expr, Var,lowBound,upBound) fMin(Expr, Var) | lowBound{Var{upBound Returns a Boolean expression specifying candidate values of Var that minimize Expr or locate its greatest lower bound. You can use the constraint (“|”) operator to restrict the solution interval and/or specify other constraints. For the Approximate setting of the Auto or Approximate mode, fMin() iteratively searches for one approximate local minimum. This is often faster, particularly if you use the “|” operator to constrain the search to a relatively small interval that contains exactly one local minimum. Note: See also fMax() and min(). For Catalog > For Var, Low, High [, Step] Block EndFor Executes the statements in Block iteratively for each value of Var, from Low to High, in increments of Step. Var must not be a system variable. Step can be positive or negative. The default value is 1. Block can be either a single statement or a series of statements separated with the “:” character. Note for entering the example: In the Calculator application on the handheld, you can enter multi-line definitions by pressing @ · instead of at the end of each line. On the computer keyboard, hold down Alt and press Enter. TI-Nspire™ CAS Reference Guide 49 format() format(Expr[, formatString]) Catalog > string Returns Expr as a character string based on the format template. Expr must simplify to a number. formatString is a string and must be in the form: “F[n]”, “S[n]”, “E[n]”, “G[n][c]”, where [ ] indicate optional portions. F[n]: Fixed format. n is the number of digits to display after the decimal point. S[n]: Scientific format. n is the number of digits to display after the decimal point. E[n]: Engineering format. n is the number of digits after the first significant digit. The exponent is adjusted to a multiple of three, and the decimal point is moved to the right by zero, one, or two digits. G[n][c]: Same as fixed format but also separates digits to the left of the radix into groups of three. c specifies the group separator character and defaults to a comma. If c is a period, the radix will be shown as a comma. [Rc]: Any of the above specifiers may be suffixed with the Rc radix flag, where c is a single character that specifies what to substitute for the radix point. fPart() Catalog > fPart(Expr1) expression fPart(List1) list fPart(Matrix1) matrix Returns the fractional part of the argument. For a list or matrix, returns the fractional parts of the elements. The argument can be a real or a complex number. FPdf() Catalog > FPdf(XVal,dfNumer,dfDenom) number if XVal is a number, list if XVal is a list Computes the F distribution probability at XVal for the specified dfNumer (degrees of freedom) and dfDenom. freqTable4list() freqTable4list(List1, freqIntegerList) Catalog > list Returns a list containing the elements from List1 expanded according to the frequencies in freqIntegerList. This function can be used for building a frequency table for the Data & Statistics application. List1 can be any valid list. freqIntegerList must have the same dimension as List1 and must contain non-negative integer elements only. Each element specifies the number of times the corresponding List1 element will be repeated in the result list. A value of zero excludes the corresponding List1 element. Note: You can insert this function from the computer keyboard by typing freqTable@>list(...). Empty (void) elements are ignored. For more information on empty elements, see page 162. 50 TI-Nspire™ CAS Reference Guide frequency() frequency(List1,binsList) Catalog > list Returns a list containing counts of the elements in List1. The counts are based on ranges (bins) that you define in binsList. If binsList is {b(1), b(2), …, b(n)}, the specified ranges are {?{b(1), b(1)<?{b(2),…,b(n-1)<?{b(n), b(n)>?}. The resulting list is one element longer than binsList. Each element of the result corresponds to the number of elements from List1 that are in the range of that bin. Expressed in terms of the countIf() function, the result is { countIf(list, ?{b(1)), countIf(list, b(1)<?{b(2)), …, countIf(list, b(n-1)<?{b(n)), countIf(list, b(n)>?)}. Elements of List1 that cannot be “placed in a bin” are ignored. Empty (void) elements are also ignored. For more information on empty elements, see page 162. Explanation of result: 2 elements from Datalist are {2.5 4 elements from Datalist are >2.5 and {4.5 3 elements from Datalist are >4.5 The element “hello” is a string and cannot be placed in any of the defined bins. Within the Lists & Spreadsheet application, you can use a range of cells in place of both arguments. Note: See also countIf(), page 26. FTest_2Samp Catalog > FTest_2Samp List1,List2[,Freq1[,Freq2[,Hypoth]]] FTest_2Samp List1,List2[,Freq1[,Freq2[,Hypoth]]] (Data list input) FTest_2Samp sx1,n1,sx2,n2[,Hypoth] FTest_2Samp sx1,n1,sx2,n2[,Hypoth] (Summary stats input) Performs a two-sample F test. A summary of results is stored in the stat.results variable. (See page 120.) For Ha: s1 > s2, set Hypoth>0 For Ha: s1 ƒ s2 (default), set Hypoth =0 For Ha: s1 < s2, set Hypoth<0 For information on the effect of empty elements in a list, see “Empty (Void) Elements” on page 162. Output variable Description stat.F Calculated F statistic for the data sequence stat.PVal Smallest level of significance at which the null hypothesis can be rejected stat.dfNumer numerator degrees of freedom = n1-1 stat.dfDenom denominator degrees of freedom = n2-1 stat.sx1, stat.sx2 Sample standard deviations of the data sequences in List 1 and List 2 stat.x1_bar stat.x2_bar Sample means of the data sequences in List 1 and List 2 stat.n1, stat.n2 Size of the samples TI-Nspire™ CAS Reference Guide 51 Func Catalog > Define a piecewise function: Func Block EndFunc Template for creating a user-defined function. Block can be a single statement, a series of statements separated with the “:” character, or a series of statements on separate lines. The function can use the Return instruction to return a specific result. Note for entering the example: In the Calculator application on the handheld, you can enter multi-line definitions by pressing @ · instead of at the end of each line. On the computer keyboard, hold down Alt and press Enter. Result of graphing g(x) G gcd() Catalog > gcd(Number1, Number2) expression Returns the greatest common divisor of the two arguments. The gcd of two fractions is the gcd of their numerators divided by the lcm of their denominators. In Auto or Approximate mode, the gcd of fractional floating-point numbers is 1.0. gcd(List1, List2) list Returns the greatest common divisors of the corresponding elements in List1 and List2. gcd(Matrix1, Matrix2) matrix Returns the greatest common divisors of the corresponding elements in Matrix1 and Matrix2. geomCdf() Catalog > geomCdf(p,lowBound,upBound) number if lowBound and upBound are numbers, list if lowBound and upBound are lists geomCdf(p,upBound) for P(1{X{upBound) upBound is a number, list if upBound is a list number if Computes a cumulative geometric probability from lowBound to upBound with the specified probability of success p. For P(X { upBound), set lowBound = 1. 52 TI-Nspire™ CAS Reference Guide geomPdf() Catalog > geomPdf(p,XVal) is a list number if XVal is a number, list if XVal Computes a probability at XVal, the number of the trial on which the first success occurs, for the discrete geometric distribution with the specified probability of success p. getDenom() Catalog > getDenom(Expr1) expression Transforms the argument into an expression having a reduced common denominator, and then returns its denominator. getLangInfo() getLangInfo() Catalog > string Returns a string that corresponds to the short name of the currently active language. You can, for example, use it in a program or function to determine the current language. English = “en” Danish = “da” German = “de” Finnish = “fi” French = “fr” Italian = “it” Dutch = “nl” Belgian Dutch = “nl_BE” Norwegian = “no” Portuguese = “pt” Spanish = “es” Swedish = “sv” getLockInfo() getLockInfo(Var) Catalog > value Returns the current locked/unlocked state of variable Var. value =0: Var is unlocked or does not exist. value =1: Var is locked and cannot be modified or deleted. See Lock, page 70, and unLock, page 135. TI-Nspire™ CAS Reference Guide 53 getMode() Catalog > getMode(ModeNameInteger) getMode(0) value list getMode(ModeNameInteger) returns a value representing the current setting of the ModeNameInteger mode. getMode(0) returns a list containing number pairs. Each pair consists of a mode integer and a setting integer. For a listing of the modes and their settings, refer to the table below. If you save the settings with getMode(0) & var, you can use setMode(var) in a function or program to temporarily restore the settings within the execution of the function or program only. See setMode(), page 110. Mode Name Mode Integer Display Digits 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 Exponential Format 3 1=Normal, 2=Scientific, 3=Engineering Real or Complex 4 1=Real, 2=Rectangular, 3=Polar Setting Integers Auto or Approx. 5 1=Auto, 2=Approximate, 3=Exact Vector Format 6 1=Rectangular, 2=Cylindrical, 3=Spherical Base 7 1=Decimal, 2=Hex, 3=Binary Unit system 8 1=SI, 2=Eng/US getNum() getNum(Expr1) Catalog > expression Transforms the argument into an expression having a reduced common denominator, and then returns its numerator. 54 TI-Nspire™ CAS Reference Guide getType() getType(var) Catalog > string Returns a string that indicates the data type of variable var. If var has not been defined, returns the string "NONE". getVarInfo() Catalog > matrix or string getVarInfo(LibNameString) matrix or string getVarInfo() getVarInfo() returns a matrix of information (variable name, type, library accessibility, and locked/unlocked state) for all variables and library objects defined in the current problem. If no variables are defined, getVarInfo() returns the string "NONE". getVarInfo(LibNameString) returns a matrix of information for all library objects defined in library LibNameString. LibNameString must be a string (text enclosed in quotation marks) or a string variable. If the library LibNameString does not exist, an error occurs. Note the example, in which the result of getVarInfo() is assigned to variable vs. Attempting to display row 2 or row 3 of vs returns an “Invalid list or matrix” error because at least one of elements in those rows (variable b, for example) revaluates to a matrix. This error could also occur when using Ans to reevaluate a getVarInfo() result. The system gives the above error because the current version of the software does not support a generalized matrix structure where an element of a matrix can be either a matrix or a list. TI-Nspire™ CAS Reference Guide 55 Goto Catalog > Goto labelName Transfers control to the label labelName. labelName must be defined in the same function using a Lbl instruction. Note for entering the example: In the Calculator application on the handheld, you can enter multi-line definitions by pressing @ · at the end of each line. On the computer keyboard, instead of hold down Alt and press Enter. 4Grad Catalog > Expr1 4 Grad expression In Degree angle mode: Converts Expr1 to gradian angle measure. Note: You can insert this operator from the computer keyboard by typing @>Grad. In Radian angle mode: I identity() identity(Integer) Catalog > matrix Returns the identity matrix with a dimension of Integer. Integer must be a positive integer. 56 TI-Nspire™ CAS Reference Guide If Catalog > If BooleanExpr Statement If BooleanExpr Then Block EndIf If BooleanExpr evaluates to true, executes the single statement Statement or the block of statements Block before continuing execution. If BooleanExpr evaluates to false, continues execution without executing the statement or block of statements. Block can be either a single statement or a sequence of statements separated with the “:” character. Note for entering the example: In the Calculator application on the handheld, you can enter multi-line definitions by pressing @ · instead of at the end of each line. On the computer keyboard, hold down Alt and press Enter. If BooleanExpr Then Block1 Else Block2 EndIf If BooleanExpr evaluates to true, executes Block1 and then skips Block2. If BooleanExpr evaluates to false, skips Block1 but executes Block2. Block1 and Block2 can be a single statement. If BooleanExpr1 Then Block1 ElseIf BooleanExpr2 Then Block2 © ElseIf BooleanExprN Then BlockN EndIf Allows for branching. If BooleanExpr1 evaluates to true, executes Block1. If BooleanExpr1 evaluates to false, evaluates BooleanExpr2, and so on. TI-Nspire™ CAS Reference Guide 57 ifFn() Catalog > ifFn(BooleanExpr,Value_If_true [,Value_If_false [,Value_If_unknown]]) expression, list, or matrix Evaluates the boolean expression BooleanExpr (or each element from BooleanExpr ) and produces a result based on the following rules: • • • • • BooleanExpr can test a single value, a list, or a matrix. If an element of BooleanExpr evaluates to true, returns the corresponding element from Value_If_true. If an element of BooleanExpr evaluates to false, returns the corresponding element from Value_If_false. If you omit Value_If_false, returns undef. If an element of BooleanExpr is neither true nor false, returns the corresponding element Value_If_unknown. If you omit Value_If_unknown, returns undef. If the second, third, or fourth argument of the ifFn() function is a single expression, the Boolean test is applied to every position in BooleanExpr. Test value of 1 is less than 2.5, so its corresponding Value_If_True element of 5 is copied to the result list. Test value of 2 is less than 2.5, so its corresponding Value_If_True element of 6 is copied to the result list. Test value of 3 is not less than 2.5, so its corresponding Value_If_False element of 10 is copied to the result list. Value_If_true is a single value and corresponds to any selected position. Note: If the simplified BooleanExpr statement involves a list or matrix, all other list or matrix arguments must have the same dimension(s), and the result will have the same dimension(s). Value_If_false is not specified. Undef is used. One element selected from Value_If_true. One element selected from Value_If_unknown. imag() Catalog > expression imag(Expr1) Returns the imaginary part of the argument. Note: All undefined variables are treated as real variables. See also real(), page 99 imag(List1) list Returns a list of the imaginary parts of the elements. imag(Matrix1) matrix Returns a matrix of the imaginary parts of the elements. impDif() Catalog > impDif(Equation, Var, dependVar[,Ord]) expression where the order Ord defaults to 1. Computes the implicit derivative for equations in which one variable is defined implicitly in terms of another. Indirection 58 TI-Nspire™ CAS Reference Guide See #(), page 155. inString() inString(srcString, subString[, Start]) Catalog > integer Returns the character position in string srcString at which the first occurrence of string subString begins. Start, if included, specifies the character position within srcString where the search begins. Default = 1 (the first character of srcString). If srcString does not contain subString or Start is > the length of srcString, returns zero. int() Catalog > int(Expr) integer int(List1) list int(Matrix1) matrix Returns the greatest integer that is less than or equal to the argument. This function is identical to floor(). The argument can be a real or a complex number. For a list or matrix, returns the greatest integer of each of the elements. intDiv() Catalog > intDiv(Number1, Number2) integer intDiv(List1, List2) list intDiv(Matrix1, Matrix2) matrix Returns the signed integer part of (Number1 ÷ Number2). For lists and matrices, returns the signed integer part of (argument 1 ÷ argument 2) for each element pair. integral See ‰(), page 151. TI-Nspire™ CAS Reference Guide 59 interpolate() interpolate(xValue, xList, yList, yPrimeList) Catalog > list This function does the following: Differential equation: y'=-3·y+6·t+5 and y(0)=5 Given xList, yList=f(xList), and yPrimeList=f'(xList) for some unknown function f, a cubic interpolant is used to approximate the function f at xValue. It is assumed that xList is a list of monotonically increasing or decreasing numbers, but this function may return a value even when it is not. This function walks through xList looking To see the entire result, press and then use and to for an interval [xList[i], xList[i+1]] that contains xValue. If it finds such move the cursor. an interval, it returns an interpolated value for f(xValue); otherwise, it returns undef. Use the interpolate() function to calculate the function values for the xvaluelist: xList, yList, and yPrimeList must be of equal dimension | 2 and contain expressions that simplify to numbers. £ ¡ ¢ xValue can be an undefined variable, a number, or a list of numbers. invc2() Catalog > invc2(Area,df) invChi2(Area,df) Computes the Inverse cumulative c2 (chi-square) probability function specified by degree of freedom, df for a given Area under the curve. invF() Catalog > invF(Area,dfNumer,dfDenom) invF(Area,dfNumer,dfDenom) computes the Inverse cumulative F distribution function specified by dfNumer and dfDenom for a given Area under the curve. invNorm() Catalog > invNorm(Area[,m[,s]]) Computes the inverse cumulative normal distribution function for a given Area under the normal distribution curve specified by m and s. invt() Catalog > invt(Area,df) Computes the inverse cumulative student-t probability function specified by degree of freedom, df for a given Area under the curve. 60 TI-Nspire™ CAS Reference Guide iPart() Catalog > iPart(Number) integer iPart(List1) list iPart(Matrix1) matrix Returns the integer part of the argument. For lists and matrices, returns the integer part of each element. The argument can be a real or a complex number. irr() Catalog > irr(CF0,CFList [,CFFreq]) value Financial function that calculates internal rate of return of an investment. CF0 is the initial cash flow at time 0; it must be a real number. CFList is a list of cash flow amounts after the initial cash flow CF0. CFFreq is an optional list in which each element specifies the frequency of occurrence for a grouped (consecutive) cash flow amount, which is the corresponding element of CFList. The default is 1; if you enter values, they must be positive integers < 10,000. Note: See also mirr(), page 77. isPrime() isPrime(Number) Catalog > Boolean constant expression Returns true or false to indicate if number is a whole number | 2 that is evenly divisible only by itself and 1. If Number exceeds about 306 digits and has no factors {1021, isPrime(Number) displays an error message. Function to find the next prime after a specified number: If you merely want to determine if Number is prime, use isPrime() instead of factor(). It is much faster, particularly if Number is not prime and has a second-largest factor that exceeds about five digits. Note for entering the example: In the Calculator application on the handheld, you can enter multi-line definitions by pressing @ · instead of at the end of each line. On the computer keyboard, hold down Alt and press Enter. isVoid() Catalog > isVoid(Var) Boolean constant expression isVoid(Expr) Boolean constant expression isVoid(List) list of Boolean constant expressions Returns true or false to indicate if the argument is a void data type. For more information on void elements, see page 162. TI-Nspire™ CAS Reference Guide 61 L Lbl Catalog > Lbl labelName Defines a label with the name labelName within a function. You can use a Goto labelName instruction to transfer control to the instruction immediately following the label. labelName must meet the same naming requirements as a variable name. Note for entering the example: In the Calculator application on the handheld, you can enter multi-line definitions by pressing @ · at the end of each line. On the computer keyboard, instead of hold down Alt and press Enter. lcm() Catalog > lcm(Number1, Number2) expression lcm(List1, List2) list lcm(Matrix1, Matrix2) matrix Returns the least common multiple of the two arguments. The lcm of two fractions is the lcm of their numerators divided by the gcd of their denominators. The lcm of fractional floating-point numbers is their product. For two lists or matrices, returns the least common multiples of the corresponding elements. left() Catalog > left(sourceString[, Num]) string Returns the leftmost Num characters contained in character string sourceString. If you omit Num, returns all of sourceString. left(List1[, Num]) list Returns the leftmost Num elements contained in List1. If you omit Num, returns all of List1. left(Comparison) expression Returns the left-hand side of an equation or inequality. 62 TI-Nspire™ CAS Reference Guide libShortcut() Catalog > libShortcut(LibNameString, ShortcutNameString [, LibPrivFlag]) list of variables Creates a variable group in the current problem that contains references to all the objects in the specified library document libNameString. Also adds the group members to the Variables menu. You can then refer to each object using its ShortcutNameString. This example assumes a properly stored and refreshed library document named linalg2 that contains objects defined as clearmat, gauss1, and gauss2. Set LibPrivFlag=0 to exclude private library objects (default) Set LibPrivFlag=1 to include private library objects To copy a variable group, see CopyVar on page 21. To delete a variable group, see DelVar on page 35. limit() or lim() Catalog > limit(Expr1, Var, Point [,Direction]) expression limit(List1, Var, Point [, Direction]) list limit(Matrix1, Var, Point [, Direction]) matrix Returns the limit requested. Note: See also Limit template, page 6. Direction: negative=from left, positive=from right, otherwise=both. (If omitted, Direction defaults to both.) Limits at positive ˆ and at negative ˆ are always converted to onesided limits from the finite side. Depending on the circumstances, limit() returns itself or undef when it cannot determine a unique limit. This does not necessarily mean that a unique limit does not exist. undef means that the result is either an unknown number with finite or infinite magnitude, or it is the entire set of such numbers. limit() uses methods such as L’Hopital’s rule, so there are unique limits that it cannot determine. If Expr1 contains undefined variables other than Var, you might have to constrain them to obtain a more concise result. Limits can be very sensitive to rounding error. When possible, avoid the Approximate setting of the Auto or Approximate mode and approximate numbers when computing limits. Otherwise, limits that should be zero or have infinite magnitude probably will not, and limits that should have finite non-zero magnitude might not. TI-Nspire™ CAS Reference Guide 63 LinRegBx Catalog > LinRegBx X,Y[,[Freq][,Category,Include]] Computes the linear regression y = a+b·x on lists X and Y with frequency Freq. A summary of results is stored in the stat.results variable. (See page 120.) All the lists must have equal dimension except for Include. X and Y are lists of independent and dependent variables. Freq is an optional list of frequency values. Each element in Freq specifies the frequency of occurrence for each corresponding X and Y data point. The default value is 1. All elements must be integers | 0. Category is a list of category codes for the corresponding X and Y data. Include is a list of one or more of the category codes. Only those data items whose category code is included in this list are included in the calculation. For information on the effect of empty elements in a list, see “Empty (Void) Elements” on page 162. Output variable Description stat.RegEqn Regression Equation: a+b·x stat.a, stat.b Regression coefficients stat.r2 Coefficient of determination stat.r Correlation coefficient stat.Resid Residuals from the regression stat.XReg List of data points in the modified X List actually used in the regression based on restrictions of Freq, Category List, and Include Categories stat.YReg List of data points in the modified Y List actually used in the regression based on restrictions of Freq, Category List, and Include Categories stat.FreqReg List of frequencies corresponding to stat.XReg and stat.YReg LinRegMx LinRegMx X,Y[,[Freq][,Category,Include]] Computes the linear regression y = m·x+b on lists X and Y with frequency Freq. A summary of results is stored in the stat.results variable. (See page 120.) All the lists must have equal dimension except for Include. X and Y are lists of independent and dependent variables. Freq is an optional list of frequency values. Each element in Freq specifies the frequency of occurrence for each corresponding X and Y data point. The default value is 1. All elements must be integers | 0. Category is a list of category codes for the corresponding X and Y data. Include is a list of one or more of the category codes. Only those data items whose category code is included in this list are included in the calculation. For information on the effect of empty elements in a list, see “Empty (Void) Elements” on page 162. 64 TI-Nspire™ CAS Reference Guide Catalog > Output variable Description stat.RegEqn Regression Equation: y = m·x+b stat.m, stat.b Regression coefficients stat.r2 Coefficient of determination stat.r Correlation coefficient stat.Resid Residuals from the regression stat.XReg List of data points in the modified X List actually used in the regression based on restrictions of Freq, Category List, and Include Categories stat.YReg List of data points in the modified Y List actually used in the regression based on restrictions of Freq, Category List, and Include Categories stat.FreqReg List of frequencies corresponding to stat.XReg and stat.YReg LinRegtIntervals Catalog > LinRegtIntervals X,Y[,F[,0[,CLev]]] For Slope. Computes a level C confidence interval for the slope. LinRegtIntervals X,Y[,F[,1,Xval[,CLev]]] For Response. Computes a predicted y-value, a level C prediction interval for a single observation, and a level C confidence interval for the mean response. A summary of results is stored in the stat.results variable. (See page 120.) All the lists must have equal dimension. X and Y are lists of independent and dependent variables. F is an optional list of frequency values. Each element in F specifies the frequency of occurrence for each corresponding X and Y data point. The default value is 1. All elements must be integers | 0. For information on the effect of empty elements in a list, see “Empty (Void) Elements” on page 162. Output variable Description stat.RegEqn Regression Equation: a+b·x stat.a, stat.b Regression coefficients stat.df Degrees of freedom stat.r2 Coefficient of determination stat.r Correlation coefficient stat.Resid Residuals from the regression TI-Nspire™ CAS Reference Guide 65 For Slope type only Output variable Description [stat.CLower, stat.CUpper] Confidence interval for the slope stat.ME Confidence interval margin of error stat.SESlope Standard error of slope stat.s Standard error about the line For Response type only Output variable Description [stat.CLower, stat.CUpper] Confidence interval for the mean response stat.ME Confidence interval margin of error stat.SE Standard error of mean response [stat.LowerPred, stat.UpperPred] Prediction interval for a single observation stat.MEPred Prediction interval margin of error stat.SEPred Standard error for prediction y a + b·XVal stat. LinRegtTest LinRegtTest X,Y[,Freq[,Hypoth]] Computes a linear regression on the X and Y lists and a t test on the value of slope b and the correlation coefficient r for the equation y=a+bx. It tests the null hypothesis H0:b=0 (equivalently, r=0) against one of three alternative hypotheses. All the lists must have equal dimension. X and Y are lists of independent and dependent variables. Freq is an optional list of frequency values. Each element in Freq specifies the frequency of occurrence for each corresponding X and Y data point. The default value is 1. All elements must be integers | 0. Hypoth is an optional value specifying one of three alternative hypotheses against which the null hypothesis (H0:b=r=0) will be tested. For Ha: bƒ0 and rƒ0 (default), set Hypoth=0 For Ha: b<0 and r<0, set Hypoth<0 For Ha: b>0 and r>0, set Hypoth>0 A summary of results is stored in the stat.results variable. (See page 120.) For information on the effect of empty elements in a list, see “Empty (Void) Elements” on page 162. 66 TI-Nspire™ CAS Reference Guide Catalog > Output variable Description stat.RegEqn Regression equation: a + b·x stat.t t-Statistic for significance test stat.PVal Smallest level of significance at which the null hypothesis can be rejected stat.df Degrees of freedom stat.a, stat.b Regression coefficients stat.s Standard error about the line stat.SESlope Standard error of slope stat.r2 Coefficient of determination stat.r Correlation coefficient stat.Resid Residuals from the regression linSolve() linSolve( SystemOfLinearEqns, Var1, Var2, ...) Catalog > 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 variables Var1, Var2, ... The first argument must evaluate to a system of linear equations or a single linear equation. Otherwise, an argument error occurs. For example, evaluating linSolve(x=1 and x=2,x) produces an “Argument Error” result. @List() Catalog > @List(List1) list Note: You can insert this function from the keyboard by typing deltaList(...). Returns a list containing the differences between consecutive elements in List1. Each element of List1 is subtracted from the next element of List1. The resulting list is always one element shorter than the original List1. TI-Nspire™ CAS Reference Guide 67 list4mat() Catalog > list4mat( List [, elementsPerRow]) matrix Returns a matrix filled row-by-row with the elements from List. elementsPerRow, if included, specifies the number of elements per row. Default is the number of elements in List (one row). If List does not fill the resulting matrix, zeros are added. Note: You can insert this function from the computer keyboard by typing list@>mat(...). 4ln Catalog > Expr 4ln expression Causes the input Expr to be converted to an expression containing only natural logs (ln). Note: You can insert this operator from the computer keyboard by typing @>ln. /u keys ln() ln(Expr1) expression ln(List1) list Returns the natural logarithm of the argument. If complex format mode is Real: For a list, returns the natural logarithms of the elements. If complex format mode is Rectangular: ln(squareMatrix1) squareMatrix In Radian angle mode and Rectangular complex format: Returns the matrix natural logarithm of squareMatrix1. This is not the same as calculating the natural logarithm of each element. For information about the calculation method, refer to cos() on. squareMatrix1 must be diagonalizable. The result always contains floating-point numbers. To see the entire result, press move the cursor. 68 TI-Nspire™ CAS Reference Guide £ and then use ¡ and ¢ to LnReg Catalog > LnReg X, Y[, [Freq] [, Category, Include]] Computes the logarithmic regression y = a+b·ln(x) on lists X and Y with frequency Freq. A summary of results is stored in the stat.results variable. (See page 120.) All the lists must have equal dimension except for Include. X and Y are lists of independent and dependent variables. Freq is an optional list of frequency values. Each element in Freq specifies the frequency of occurrence for each corresponding X and Y data point. The default value is 1. All elements must be integers | 0. Category is a list of category codes for the corresponding X and Y data. Include is a list of one or more of the category codes. Only those data items whose category code is included in this list are included in the calculation. For information on the effect of empty elements in a list, see “Empty (Void) Elements” on page 162. Output variable Description stat.RegEqn Regression equation: a+b·ln(x) stat.a, stat.b Regression coefficients 2 stat.r Coefficient of linear determination for transformed data stat.r Correlation coefficient for transformed data (ln(x), y) stat.Resid Residuals associated with the logarithmic model stat.ResidTrans Residuals associated with linear fit of transformed data stat.XReg List of data points in the modified X List actually used in the regression based on restrictions of Freq, Category List, and Include Categories stat.YReg List of data points in the modified Y List actually used in the regression based on restrictions of Freq, Category List, and Include Categories stat.FreqReg List of frequencies corresponding to stat.XReg and stat.YReg TI-Nspire™ CAS Reference Guide 69 Local Catalog > Local Var1[, Var2] [, Var3] ... Declares the specified vars as local variables. Those variables exist only during evaluation of a function and are deleted when the function finishes execution. Note: Local variables save memory because they only exist temporarily. Also, they do not disturb any existing global variable values. Local variables must be used for For loops and for temporarily saving values in a multi-line function since modifications on global variables are not allowed in a function. Note for entering the example: In the Calculator application on the handheld, you can enter multi-line definitions by pressing @ · instead of at the end of each line. On the computer keyboard, hold down Alt and press Enter. Lock Catalog > Lock Var1[, Var2] [, Var3] ... Lock Var. Locks the specified variables or variable group. Locked variables cannot be modified or deleted. You cannot lock or unlock the system variable Ans, and you cannot lock the system variable groups stat. or tvm. Note: The Lock command clears the Undo/Redo history when applied to unlocked variables. See unLock, page 135, and getLockInfo(), page 53. 70 TI-Nspire™ CAS Reference Guide /s keys log() log(Expr1[,Expr2]) expression log(List1[,Expr2]) list Returns the base-Expr2 logarithm of the first argument. Note: See also Log template, page 2. For a list, returns the base-Expr2 logarithm of the elements. If the second argument is omitted, 10 is used as the base. If complex format mode is Real: If complex format mode is Rectangular: log(squareMatrix1[,Expr]) squareMatrix In Radian angle mode and Rectangular complex format: Returns the matrix base-Expr logarithm of squareMatrix1. This is not the same as calculating the base-Expr logarithm of each element. For information about the calculation method, refer to cos(). squareMatrix1 must be diagonalizable. The result always contains floating-point numbers. If the base argument is omitted, 10 is used as base. To see the entire result, press move the cursor. 4logbase £ and then use ¡ and ¢ to Catalog > Expr 4logbase(Expr1) expression Causes the input Expression to be simplified to an expression using base Expr1. Note: You can insert this operator from the computer keyboard by typing @>logbase(...). TI-Nspire™ CAS Reference Guide 71 Logistic Catalog > Logistic X, Y[, [Freq] [, Category, Include]] Computes the logistic regression y = (c/(1+a·e-bx)) on lists X and Y with frequency Freq. A summary of results is stored in the stat.results variable. (See page 120.) All the lists must have equal dimension except for Include. X and Y are lists of independent and dependent variables. Freq is an optional list of frequency values. Each element in Freq specifies the frequency of occurrence for each corresponding X and Y data point. The default value is 1. All elements must be integers | 0. Category is a list of category codes for the corresponding X and Y data. Include is a list of one or more of the category codes. Only those data items whose category code is included in this list are included in the calculation. For information on the effect of empty elements in a list, see “Empty (Void) Elements” on page 162. Output variable Description stat.RegEqn Regression equation: c/(1+a·e-bx) stat.a, stat.b, stat.c Regression coefficients stat.Resid Residuals from the regression stat.XReg List of data points in the modified X List actually used in the regression based on restrictions of Freq, Category List, and Include Categories stat.YReg List of data points in the modified Y List actually used in the regression based on restrictions of Freq, Category List, and Include Categories stat.FreqReg List of frequencies corresponding to stat.XReg and stat.YReg LogisticD LogisticD X, Y [ , [Iterations] , [Freq] [, Category, Include] ] Computes the logistic regression y = (c/(1+a·e-bx)+d) on lists X and Y with frequency Freq, using a specified number of Iterations. A summary of results is stored in the stat.results variable. (See page 120.) All the lists must have equal dimension except for Include. X and Y are lists of independent and dependent variables. Freq is an optional list of frequency values. Each element in Freq specifies the frequency of occurrence for each corresponding X and Y data point. The default value is 1. All elements must be integers | 0. Category is a list of category codes for the corresponding X and Y data. Include is a list of one or more of the category codes. Only those data items whose category code is included in this list are included in the calculation. For information on the effect of empty elements in a list, see “Empty (Void) Elements” on page 162. 72 TI-Nspire™ CAS Reference Guide Catalog > Output variable Description stat.RegEqn Regression equation: c/(1+a·e-bx)+d) stat.a, stat.b, stat.c, stat.d Regression coefficients stat.Resid Residuals from the regression stat.XReg List of data points in the modified X List actually used in the regression based on restrictions of Freq, Category List, and Include Categories stat.YReg List of data points in the modified Y List actually used in the regression based on restrictions of Freq, Category List, and Include Categories stat.FreqReg List of frequencies corresponding to stat.XReg and stat.YReg Loop Catalog > Loop Block EndLoop Repeatedly executes the statements in Block. Note that the loop will be executed endlessly, unless a Goto or Exit instruction is executed within Block. Block is a sequence of statements separated with the “:” character. Note for entering the example: In the Calculator application on the handheld, you can enter multi-line definitions by pressing @ · at the end of each line. On the computer keyboard, instead of hold down Alt and press Enter. TI-Nspire™ CAS Reference Guide 73 LU Catalog > LU Matrix, lMatrix, uMatrix, pMatrix[,Tol] Calculates the Doolittle LU (lower-upper) decomposition of a real or complex matrix. The lower triangular matrix is stored in lMatrix, the upper triangular matrix in uMatrix, and the permutation matrix (which describes the row swaps done during the calculation) in pMatrix. lMatrix · uMatrix = pMatrix · matrix Optionally, any matrix element is treated as zero if its absolute value is less than Tol. This tolerance is used only if the matrix has floatingpoint entries and does not contain any symbolic variables that have not been assigned a value. Otherwise, Tol is ignored. • • /· or set the Auto or Approximate If you use mode to Approximate, computations are done using floatingpoint arithmetic. If Tol is omitted or not used, the default tolerance is calculated as: 5EM14 ·max(dim(Matrix)) ·rowNorm(Matrix) The LU factorization algorithm uses partial pivoting with row interchanges. M mat4list() mat4list(Matrix) Catalog > list Returns a list filled with the elements in Matrix. The elements are copied from Matrix row by row. Note: You can insert this function from the computer keyboard by typing mat@>list(...). 74 TI-Nspire™ CAS Reference Guide max() Catalog > max(Expr1, Expr2) expression max(List1, List2) list max(Matrix1, Matrix2) matrix Returns the maximum of the two arguments. If the arguments are two lists or matrices, returns a list or matrix containing the maximum value of each pair of corresponding elements. max(List) expression Returns the maximum element in list. max(Matrix1) matrix Returns a row vector containing the maximum element of each column in Matrix1. Empty (void) elements are ignored. For more information on empty elements, see page 162. Note: See also fMax() and min(). mean() mean(List[, freqList]) Catalog > expression Returns the mean of the elements in List. Each freqList element counts the number of consecutive occurrences of the corresponding element in List. mean(Matrix1[, freqMatrix]) matrix In Rectangular vector format: Returns a row vector of the means of all the columns in Matrix1. Each freqMatrix element counts the number of consecutive occurrences of the corresponding element in Matrix1. Empty (void) elements are ignored. For more information on empty elements, see page 162. median() median(List[, freqList]) Catalog > expression Returns the median of the elements in List. Each freqList element counts the number of consecutive occurrences of the corresponding element in List. TI-Nspire™ CAS Reference Guide 75 median() Catalog > median(Matrix1[, freqMatrix]) matrix Returns a row vector containing the medians of the columns in Matrix1. Each freqMatrix element counts the number of consecutive occurrences of the corresponding element in Matrix1. Notes: • • All entries in the list or matrix must simplify to numbers. Empty (void) elements in the list or matrix are ignored. For more information on empty elements, see page 162. MedMed Catalog > MedMed X,Y [, Freq] [, Category, Include]] Computes the median-median line y = (m·x+b) on lists X and Y with frequency Freq. A summary of results is stored in the stat.results variable. (See page 120.) All the lists must have equal dimension except for Include. X and Y are lists of independent and dependent variables. Freq is an optional list of frequency values. Each element in Freq specifies the frequency of occurrence for each corresponding X and Y data point. The default value is 1. All elements must be integers | 0. Category is a list of category codes for the corresponding X and Y data. Include is a list of one or more of the category codes. Only those data items whose category code is included in this list are included in the calculation. For information on the effect of empty elements in a list, see “Empty (Void) Elements” on page 162. Output variable Description stat.RegEqn Median-median line equation: m·x+b stat.m, stat.b Model coefficients stat.Resid Residuals from the median-median line stat.XReg List of data points in the modified X List actually used in the regression based on restrictions of Freq, Category List, and Include Categories stat.YReg List of data points in the modified Y List actually used in the regression based on restrictions of Freq, Category List, and Include Categories stat.FreqReg List of frequencies corresponding to stat.XReg and stat.YReg mid() Catalog > mid(sourceString, Start[, Count]) string Returns Count characters from character string sourceString, beginning with character number Start. If Count is omitted or is greater than the dimension of sourceString, returns all characters from sourceString, beginning with character number Start. Count must be | 0. If Count = 0, returns an empty string. 76 TI-Nspire™ CAS Reference Guide mid() Catalog > mid(sourceList, Start [, Count]) list Returns Count elements from sourceList, beginning with element number Start. If Count is omitted or is greater than the dimension of sourceList, returns all elements from sourceList, beginning with element number Start. Count must be | 0. If Count = 0, returns an empty list. mid(sourceStringList, Start[, Count]) list Returns Count strings from the list of strings sourceStringList, beginning with element number Start. min() Catalog > min(Expr1, Expr2) expression min(List1, List2) list min(Matrix1, Matrix2) matrix Returns the minimum of the two arguments. If the arguments are two lists or matrices, returns a list or matrix containing the minimum value of each pair of corresponding elements. min(List) expression Returns the minimum element of List. min(Matrix1) matrix Returns a row vector containing the minimum element of each column in Matrix1. Note: See also fMin() and max(). mirr() Catalog > mirr(financeRate,reinvestRate,CF0,CFList[,CFFreq]) Financial function that returns the modified internal rate of return of an investment. financeRate is the interest rate that you pay on the cash flow amounts. reinvestRate is the interest rate at which the cash flows are reinvested. CF0 is the initial cash flow at time 0; it must be a real number. CFList is a list of cash flow amounts after the initial cash flow CF0. CFFreq is an optional list in which each element specifies the frequency of occurrence for a grouped (consecutive) cash flow amount, which is the corresponding element of CFList. The default is 1; if you enter values, they must be positive integers < 10,000. Note: See also irr(), page 61. TI-Nspire™ CAS Reference Guide 77 mod() Catalog > mod(Expr1, Expr2) expression mod(List1, List2) list mod(Matrix1, Matrix2) matrix Returns the first argument modulo the second argument as defined by the identities: mod(x,0) = x mod(x,y) = x - y floor(x/y) When the second argument is non-zero, the result is periodic in that argument. The result is either zero or has the same sign as the second argument. If the arguments are two lists or two matrices, returns a list or matrix containing the modulo of each pair of corresponding elements. Note: See also remain(), page 100 mRow() Catalog > mRow(Expr, Matrix1, Index) matrix Returns a copy of Matrix1 with each element in row Index of Matrix1 multiplied by Expr. mRowAdd() Catalog > mRowAdd(Expr, Matrix1, Index1, Index2) matrix Returns a copy of Matrix1 with each element in row Index2 of Matrix1 replaced with: Expr · row Index1 + row Index2 MultReg Catalog > MultReg Y, X1[,X2[,X3,…[,X10]]] Calculates multiple linear regression of list Y on lists X1, X2, …, X10. A summary of results is stored in the stat.results variable. (See page 120.) All the lists must have equal dimension. For information on the effect of empty elements in a list, see “Empty (Void) Elements” on page 162. Output variable Description stat.RegEqn Regression Equation: b0+b1·x1+b2·x2+ ... stat.b0, stat.b1, ... Regression coefficients stat.R2 Coefficient of multiple determination stat. List y yList = b0+b1·x1+ ... stat.Resid Residuals from the regression 78 TI-Nspire™ CAS Reference Guide MultRegIntervals Catalog > MultRegIntervals Y, X1[,X2[,X3,…[,X10]]],XValList[,CLevel] Computes a predicted y-value, a level C prediction interval for a single observation, and a level C confidence interval for the mean response. A summary of results is stored in the stat.results variable. (See page 120.) All the lists must have equal dimension. For information on the effect of empty elements in a list, see “Empty (Void) Elements” on page 162. Output variable Description stat.RegEqn Regression Equation: b0+b1·x1+b2·x2+ ... y y = b0 + b1 · xl + ... for XValList stat. A point estimate: stat.dfError Error degrees of freedom stat.CLower, stat.CUpper Confidence interval for a mean response stat.ME Confidence interval margin of error stat.SE Standard error of mean response stat.LowerPred, stat.UpperrPred Prediction interval for a single observation stat.MEPred Prediction interval margin of error stat.SEPred Standard error for prediction stat.bList List of regression coefficients, {b0,b1,b2,...} stat.Resid Residuals from the regression MultRegTests Catalog > MultRegTests Y, X1[,X2[,X3,…[,X10]]] Multiple linear regression test computes a multiple linear regression on the given data and provides the global F test statistic and t test statistics for the coefficients. A summary of results is stored in the stat.results variable. (See page 120.) For information on the effect of empty elements in a list, see “Empty (Void) Elements” on page 162. Outputs Output variable Description stat.RegEqn Regression Equation: b0+b1·x1+b2·x2+ ... stat.F Global F test statistic stat.PVal P-value associated with global F statistic stat.R2 Coefficient of multiple determination TI-Nspire™ CAS Reference Guide 79 Output variable Description stat.AdjR2 Adjusted coefficient of multiple determination stat.s Standard deviation of the error stat.DW Durbin-Watson statistic; used to determine whether first-order auto correlation is present in the model stat.dfReg Regression degrees of freedom stat.SSReg Regression sum of squares stat.MSReg Regression mean square stat.dfError Error degrees of freedom stat.SSError Error sum of squares stat.MSError Error mean square stat.bList {b0,b1,...} List of coefficients stat.tList List of t statistics, one for each coefficient in the bList stat.PList List P-values for each t statistic stat.SEList List of standard errors for coefficients in bList stat. List yList = b0+b1·x1+ . . . stat.Resid y Residuals from the regression stat.sResid Standardized residuals; obtained by dividing a residual by its standard deviation stat.CookDist Cook’s distance; measure of the influence of an observation based on the residual and leverage stat.Leverage Measure of how far the values of the independent variable are from their mean values N /= keys nand BooleanExpr1 nand BooleanExpr2 returns Boolean expression BooleanList1 nand BooleanList2 returns Boolean list BooleanMatrix1 nand BooleanMatrix2 returns Boolean matrix Returns the negation of a logical and operation on the two arguments. Returns true, false, or a simplified form of the equation. For lists and matrices, returns comparisons element by element. Integer1 nand Integer2 integer Compares two real integers bit-by-bit using a nand operation. Internally, both integers are converted to signed, 64-bit binary numbers. When corresponding bits are compared, the result is 1 if both bits are 1; otherwise, the result is 0. The returned value represents the bit results, and is displayed according to the Base mode. You can enter the integers in any number base. For a binary or hexadecimal entry, you must use the 0b or 0h prefix, respectively. Without a prefix, integers are treated as decimal (base 10). 80 TI-Nspire™ CAS Reference Guide nCr() Catalog > nCr(Expr1, Expr2) expression For integer Expr1 and Expr2 with Expr1 | Expr2 | 0, nCr() is the number of combinations of Expr1 things taken Expr2 at a time. (This is also known as a binomial coefficient.) Both arguments can be integers or symbolic expressions. nCr(Expr, 0) 1 nCr(Expr, negInteger) nCr(Expr, posInteger) Expr·(ExprN1)... 0 (ExprNposInteger+1)/ posInteger! expression!/ nCr(Expr, nonInteger) ((ExprNnonInteger)!·nonInteger!) nCr(List1, List2) list Returns a list of combinations based on the corresponding element pairs in the two lists. The arguments must be the same size list. nCr(Matrix1, Matrix2) matrix Returns a matrix of combinations based on the corresponding element pairs in the two matrices. The arguments must be the same size matrix. nDerivative() Catalog > value nDerivative(Expr1,Var [,Order]) | Var=Value value nDerivative(Expr1,Var=Value[,Order]) Returns the numerical derivative calculated using auto differentiation methods. When Value is specified, it overrides any prior variable assignment or any current “|” substitution for the variable. Order of the derivative must be 1 or 2. newList() newList(numElements) Catalog > list Returns a list with a dimension of numElements. Each element is zero. newMat() newMat(numRows, numColumns) Catalog > matrix Returns a matrix of zeros with the dimension numRows by numColumns. TI-Nspire™ CAS Reference Guide 81 nfMax() Catalog > nfMax(Expr, Var) value nfMax(Expr, Var, lowBound) value nfMax(Expr, Var, lowBound, upBound) value value nfMax(Expr, Var) | lowBound{Var{upBound Returns a candidate numerical value of variable Var where the local maximum of Expr occurs. If you supply lowBound and upBound, the function looks in the closed interval [lowBound,upBound] for the local maximum. Note: See also fMax() and d(). nfMin() Catalog > nfMin(Expr, Var) value nfMin(Expr, Var, lowBound) value nfMin(Expr, Var, lowBound, upBound) value value nfMin(Expr, Var) | lowBound{Var{upBound Returns a candidate numerical value of variable Var where the local minimum of Expr occurs. If you supply lowBound and upBound, the function looks in the closed interval [lowBound,upBound] for the local minimum. Note: See also fMin() and d(). nInt() Catalog > nInt(Expr1, Var, Lower, Upper) expression If the integrand Expr1 contains no variable other than Var, and if Lower and Upper are constants, positive ˆ, or negative ˆ, then nInt() returns an approximation of ‰(Expr1, Var, Lower, Upper). This approximation is a weighted average of some sample values of the integrand in the interval Lower<Var<Upper. The goal is six significant digits. The adaptive algorithm terminates when it seems likely that the goal has been achieved, or when it seems unlikely that additional samples will yield a worthwhile improvement. A warning is displayed (“Questionable accuracy”) when it seems that the goal has not been achieved. Nest nInt() to do multiple numeric integration. Integration limits can depend on integration variables outside them. Note: See also ‰(), page 151. nom() Catalog > nom(effectiveRate,CpY) value Financial function that converts the annual effective interest rate effectiveRate to a nominal rate, given CpY as the number of compounding periods per year. effectiveRate must be a real number, and CpY must be a real number > 0. Note: See also eff(), page 40. 82 TI-Nspire™ CAS Reference Guide /= keys nor BooleanExpr1 nor BooleanExpr2 returns Boolean expression BooleanList1 nor BooleanList2 returns Boolean list BooleanMatrix1 nor BooleanMatrix2 returns Boolean matrix Returns the negation of a logical or operation on the two arguments. Returns true, false, or a simplified form of the equation. For lists and matrices, returns comparisons element by element. Integer1 nor Integer2 integer Compares two real integers bit-by-bit using a nor operation. Internally, both integers are converted to signed, 64-bit binary numbers. When corresponding bits are compared, the result is 1 if both bits are 1; otherwise, the result is 0. The returned value represents the bit results, and is displayed according to the Base mode. You can enter the integers in any number base. For a binary or hexadecimal entry, you must use the 0b or 0h prefix, respectively. Without a prefix, integers are treated as decimal (base 10). norm() Catalog > expression norm(Vector) expression norm(Matrix) Returns the Frobenius norm. normalLine() Catalog > expression normalLine(Expr1,Var=Point) expression normalLine(Expr1,Var,Point) Returns the normal line to the curve represented by Expr1 at the point specified in Var=Point. Make sure that the independent variable is not defined. For example, If f1(x):=5 and x:=3, then normalLine(f1(x),x,2) returns “false.” normCdf() Catalog > normCdf(lowBound,upBound[,m[,s]]) number if lowBound and upBound are numbers, list if lowBound and upBound are lists Computes the normal distribution probability between lowBound and upBound for the specified m (default=0) and s (default=1). For P(X {Å upBound), set lowBound = .ˆ. TI-Nspire™ CAS Reference Guide 83 normPdf() Catalog > number if XVal is a number, list if normPdf(XVal[,m[,s]]) XVal is a list Computes the probability density function for the normal distribution at a specified XVal value for the specified m and s. not Catalog > not BooleanExpr Boolean expression Returns true, false, or a simplified form of the argument. not Integer1 integer In Hex base mode: Returns the one’s complement of a real integer. Internally, Integer1 is converted to a signed, 64-bit binary number. The value of each bit is flipped (0 becomes 1, and vice versa) for the one’s complement. Results are displayed according to the Base mode. You can enter the integer in any number base. For a binary or hexadecimal entry, you must use the 0b or 0h prefix, respectively. Without a prefix, the integer is treated as decimal (base 10). Important: Zero, not the letter O. In Bin base mode: If you enter a decimal integer that is too large for a signed, 64-bit binary form, a symmetric modulo operation is used to bring the value into the appropriate range. For more information, see 4Base2, page 14. £ ¡ ¢ To see the entire result, press and then use and to move the cursor. Note: A binary entry can have up to 64 digits (not counting the 0b prefix). A hexadecimal entry can have up to 16 digits. nPr() Catalog > nPr(Expr1, Expr2) expression For integer Expr1 and Expr2 with Expr1 | Expr2 | 0, nPr() is the number of permutations of Expr1 things taken Expr2 at a time. Both arguments can be integers or symbolic expressions. nPr(Expr, 0) 1 nPr(Expr, negInteger) 1/((Expr+1)·(Expr+2)... (expressionNnegInteger)) nPr(Expr, posInteger) Expr·(ExprN1)... (ExprNposInteger+1) nPr(Expr, nonInteger) nPr(List1, List2) Expr! / (ExprNnonInteger)! list Returns a list of permutations based on the corresponding element pairs in the two lists. The arguments must be the same size list. nPr(Matrix1, Matrix2) matrix Returns a matrix of permutations based on the corresponding element pairs in the two matrices. The arguments must be the same size matrix. 84 TI-Nspire™ CAS Reference Guide npv() Catalog > npv(InterestRate,CFO,CFList[,CFFreq]) Financial function that calculates net present value; the sum of the present values for the cash inflows and outflows. A positive result for npv indicates a profitable investment. InterestRate is the rate by which to discount the cash flows (the cost of money) over one period. CF0 is the initial cash flow at time 0; it must be a real number. CFList is a list of cash flow amounts after the initial cash flow CF0. CFFreq is a list in which each element specifies the frequency of occurrence for a grouped (consecutive) cash flow amount, which is the corresponding element of CFList. The default is 1; if you enter values, they must be positive integers < 10,000. nSolve() nSolve(Equation,Var[=Guess]) Catalog > number or error_string nSolve(Equation,Var[=Guess],lowBound) number or error_string nSolve(Equation,Var[=Guess],lowBound,upBound) number or error_string nSolve(Equation,Var[=Guess]) | lowBound{Var{upBound number or error_string Note: If there are multiple solutions, you can use a guess to help find a particular solution. Iteratively searches for one approximate real numeric solution to Equation for its one variable. Specify the variable as: variable – or – variable = real number For example, x is valid and so is x=3. nSolve() is often much faster than solve() or zeros(), particularly if the “|” operator is used to constrain the search to a small interval containing exactly one simple solution. nSolve() attempts to determine either one point where the residual is zero or two relatively close points where the residual has opposite signs and the magnitude of the residual is not excessive. If it cannot achieve this using a modest number of sample points, it returns the string “no solution found.” Note: See also cSolve(), cZeros(), solve(), and zeros(). TI-Nspire™ CAS Reference Guide 85 O OneVar Catalog > OneVar [1,]X[,[Freq][,Category,Include]] OneVar [n,]X1,X2[X3[,…[,X20]]] Calculates 1-variable statistics on up to 20 lists. A summary of results is stored in the stat.results variable. (See page 120.) All the lists must have equal dimension except for Include. Freq is an optional list of frequency values. Each element in Freq specifies the frequency of occurrence for each corresponding X and Y data point. The default value is 1. All elements must be integers | 0. Category is a list of numeric category codes for the corresponding X values. Include is a list of one or more of the category codes. Only those data items whose category code is included in this list are included in the calculation. An empty (void) element in any of the lists X, Freq, or Category results in a void for the corresponding element of all those lists. An empty element in any of the lists X1 through X20 results in a void for the corresponding element of all those lists. For more information on empty elements, see page 162. Output variable Description stat.v Mean of x values stat.Gx stat.Gx Sum of x values 2 Sum of x2 values stat.sx Sample standard deviation of x stat.sx Population standard deviation of x stat.n Number of data points stat.MinX Minimum of x values stat.Q1X 1st Quartile of x stat.MedianX Median of x stat.Q3X 3rd Quartile of x stat.MaxX Maximum of x values stat.SSX Sum of squares of deviations from the mean of x 86 TI-Nspire™ CAS Reference Guide or Catalog > BooleanExpr1 or BooleanExpr2 returns Boolean expression BooleanList1 or BooleanList2 returns Boolean list BooleanMatrix1 or BooleanMatrix2 returns Boolean matrix Returns true or false or a simplified form of the original entry. Returns true if either or both expressions simplify to true. Returns false only if both expressions evaluate to false. Note: See xor. Note for entering the example: In the Calculator application on the handheld, you can enter multi-line definitions by pressing @ · instead of at the end of each line. On the computer keyboard, hold down Alt and press Enter. Integer1 or Integer2 integer In Hex base mode: Compares two real integers bit-by-bit using an or operation. Internally, both integers are converted to signed, 64-bit binary Important: Zero, not the letter O. numbers. When corresponding bits are compared, the result is 1 if either bit is 1; the result is 0 only if both bits are 0. The returned value In Bin base mode: represents the bit results, and is displayed according to the Base mode. You can enter the integers in any number base. For a binary or hexadecimal entry, you must use the 0b or 0h prefix, respectively. Without a prefix, integers are treated as decimal (base 10). Note: A binary entry can have up to 64 digits (not counting the 0b prefix). A hexadecimal entry can have up to 16 digits. If you enter a decimal integer that is too large for a signed, 64-bit binary form, a symmetric modulo operation is used to bring the value into the appropriate range. For more information, see 4Base2, page 14. Note: See xor. ord() Catalog > ord(String) integer ord(List1) list Returns the numeric code of the first character in character string String, or a list of the first characters of each list element. P P4Rx() Catalog > P4Rx(rExpr, qExpr) expression P4Rx(rList, qList) list P4Rx(rMatrix, qMatrix) matrix In Radian angle mode: Returns the equivalent x-coordinate of the (r, q) pair. Note: The q argument is interpreted as either a degree, gradian or radian angle, according to the current angle mode. If the argument is an expression, you can use ¡, G or R to override the angle mode setting temporarily. Note: You can insert this function from the computer keyboard by typing P@>Rx(...). TI-Nspire™ CAS Reference Guide 87 P4Ry() Catalog > P4Ry(rExpr, qExpr) expression P4Ry(rList, qList) list P4Ry(rMatrix, qMatrix) matrix In Radian angle mode: Returns the equivalent y-coordinate of the (r, q) pair. Note: The q argument is interpreted as either a degree, radian or gradian angle, according to the current angle mode. If the argument is an expression, you can use ¡, G or R to override the angle mode setting temporarily. Note: You can insert this function from the computer keyboard by typing P@>Ry(...). PassErr Catalog > For an example of PassErr, See Example 2 under the Try command, page 130. PassErr Passes an error to the next level. If system variable errCode is zero, PassErr does not do anything. The Else clause of the Try...Else...EndTry block should use ClrErr or PassErr. If the error is to be processed or ignored, use ClrErr. If what to do with the error is not known, use PassErr to send it to the next error handler. If there are no more pending Try...Else...EndTry error handlers, the error dialog box will be displayed as normal. Note: See also ClrErr, page 19, and Try, page 130. Note for entering the example: In the Calculator application on the handheld, you can enter multi-line definitions by pressing @ · instead of at the end of each line. On the computer keyboard, hold down Alt and press Enter. piecewise() Catalog > piecewise(Expr1 [, Cond1 [, Expr2 [, Cond2 [, … ]]]]) Returns definitions for a piecewise function in the form of a list. You can also create piecewise definitions by using a template. Note: See also Piecewise template, page 2. poissCdf() Catalog > poissCdf(l,lowBound,upBound) number if lowBound and upBound are numbers, list if lowBound and upBound are lists poissCdf(l,upBound) for P(0{X{upBound) upBound is a number, list if upBound is a list number if Computes a cumulative probability for the discrete Poisson distribution with specified mean l. For P(X { upBound), set lowBound=0 poissPdf() poissPdf(l,XVal) a list Catalog > number if XVal is a number, list if XVal is Computes a probability for the discrete Poisson distribution with the specified mean l. 88 TI-Nspire™ CAS Reference Guide 4Polar Catalog > Vector 4Polar Note: You can insert this operator from the computer keyboard by typing @>Polar. Displays vector in polar form [r ±q]. The vector must be of dimension 2 and can be a row or a column. Note: 4Polar is a display-format instruction, not a conversion function. You can use it only at the end of an entry line, and it does not update ans. Note: See also 4Rect, page 99. complexValue 4Polar In Radian angle mode: Displays complexVector in polar form. • Degree angle mode returns (r±q). • Radian angle mode returns reiq. complexValue can have any complex form. However, an reiq entry causes an error in Degree angle mode. Note: You must use the parentheses for an (r±q) polar entry. In Gradian angle mode: In Degree angle mode: polyCoeffs() polyCoeffs(Poly [,Var]) Catalog > list Returns a list of the coefficients of polynomial Poly with respect to variable Var. Poly must be a polynomial expression in Var. We recommend that you do not omit Var unless Poly is an expression in a single variable. Expands the polynomial and selects x for the omitted Var. TI-Nspire™ CAS Reference Guide 89 polyDegree() Catalog > polyDegree(Poly [,Var]) value Returns the degree of polynomial expression Poly with respect to variable Var. If you omit Var, the polyDegree() function selects a default from the variables contained in the polynomial Poly. Poly must be a polynomial expression in Var. We recommend that you do not omit Var unless Poly is an expression in a single variable. Constant polynomials The degree can be extracted even though the coefficients cannot. This is because the degree can be extracted without expanding the polynomial. polyEval() Catalog > polyEval(List1, Expr1) expression polyEval(List1, List2) expression Interprets the first argument as the coefficient of a descending-degree polynomial, and returns the polynomial evaluated for the value of the second argument. polyGcd() polyGcd(Expr1,Expr2) Catalog > expression Returns greatest common divisor of the two arguments. Expr1 and Expr2 must be polynomial expressions. List, matrix, and Boolean arguments are not allowed. 90 TI-Nspire™ CAS Reference Guide polyQuotient() polyQuotient(Poly1,Poly2 [,Var]) Catalog > expression Returns the quotient of polynomial Poly1 divided by polynomial Poly2 with respect to the specified variable Var. Poly1 and Poly2 must be polynomial expressions in Var. We recommend that you do not omit Var unless Poly1 and Poly2 are expressions in the same single variable. polyRemainder() polyRemainder(Poly1,Poly2 [,Var]) Catalog > expression Returns the remainder of polynomial Poly1 divided by polynomial Poly2 with respect to the specified variable Var. Poly1 and Poly2 must be polynomial expressions in Var. We recommend that you do not omit Var unless Poly1 and Poly2 are expressions in the same single variable. polyRoots() Catalog > list polyRoots(ListOfCoeffs) list polyRoots(Poly,Var) The first syntax, polyRoots(Poly,Var), returns a list of real roots of polynomial Poly with respect to variable Var. If no real roots exist, returns an empty list: { }. Poly must be a polynomial in one variable. The second syntax, polyRoots(ListOfCoeffs), returns a list of real roots for the coefficients in ListOfCoeffs. Note: See also cPolyRoots(), page 26. TI-Nspire™ CAS Reference Guide 91 PowerReg Catalog > PowerReg X,Y [, Freq] [, Category, Include]] Computes the power regression y = (a·(x)b) on lists X and Y with frequency Freq. A summary of results is stored in the stat.results variable. (See page 120.) All the lists must have equal dimension except for Include. X and Y are lists of independent and dependent variables. Freq is an optional list of frequency values. Each element in Freq specifies the frequency of occurrence for each corresponding X and Y data point. The default value is 1. All elements must be integers | 0. Category is a list of category codes for the corresponding X and Y data. Include is a list of one or more of the category codes. Only those data items whose category code is included in this list are included in the calculation. For information on the effect of empty elements in a list, see “Empty (Void) Elements” on page 162. Output variable Description stat.RegEqn Regression equation: a·(x)b stat.a, stat.b Regression coefficients stat.r Coefficient of linear determination for transformed data stat.r Correlation coefficient for transformed data (ln(x), ln(y)) 2 stat.Resid Residuals associated with the power model stat.ResidTrans Residuals associated with linear fit of transformed data stat.XReg List of data points in the modified X List actually used in the regression based on restrictions of Freq, Category List, and Include Categories stat.YReg List of data points in the modified Y List actually used in the regression based on restrictions of Freq, Category List, and Include Categories stat.FreqReg List of frequencies corresponding to stat.XReg and stat.YReg 92 TI-Nspire™ CAS Reference Guide Prgm Catalog > Calculate GCD and display intermediate results. Prgm Block EndPrgm Template for creating a user-defined program. Must be used with the Define, Define LibPub, or Define LibPriv command. Block can be a single statement, a series of statements separated with the “:” character, or a series of statements on separate lines. Note for entering the example: In the Calculator application on the handheld, you can enter multi-line definitions by pressing @ · instead of at the end of each line. On the computer keyboard, hold down Alt and press Enter. prodSeq() See Π( ), page 152. Product (PI) See Π( ), page 152. product() product(List[, Start[, End]]) Catalog > expression Returns the product of the elements contained in List. Start and End are optional. They specify a range of elements. product(Matrix1[, Start[, End]]) matrix Returns a row vector containing the products of the elements in the columns of Matrix1. Start and end are optional. They specify a range of rows. Empty (void) elements are ignored. For more information on empty elements, see page 162. TI-Nspire™ CAS Reference Guide 93 propFrac() Catalog > propFrac(Expr1[, Var]) expression propFrac(rational_number) returns rational_number as the sum of an integer and a fraction having the same sign and a greater denominator magnitude than numerator magnitude. propFrac(rational_expression,Var) returns the sum of proper ratios and a polynomial with respect to Var. The degree of Var in the denominator exceeds the degree of Var in the numerator in each proper ratio. Similar powers of Var are collected. The terms and their factors are sorted with Var as the main variable. If Var is omitted, a proper fraction expansion is done with respect to the most main variable. The coefficients of the polynomial part are then made proper with respect to their most main variable first and so on. For rational expressions, propFrac() is a faster but less extreme alternative to expand(). You can use the propFrac() function to represent mixed fractions and demonstrate addition and subtraction of mixed fractions. Q QR Catalog > QR Matrix, qMatrix, rMatrix[, Tol] Calculates the Householder QR factorization of a real or complex matrix. The resulting Q and R matrices are stored to the specified Matrix. The Q matrix is unitary. The R matrix is upper triangular. Optionally, any matrix element is treated as zero if its absolute value is less than Tol. This tolerance is used only if the matrix has floatingpoint entries and does not contain any symbolic variables that have not been assigned a value. Otherwise, Tol is ignored. • • 94 /· If you use or set the Auto or Approximate mode to Approximate, computations are done using floatingpoint arithmetic. If Tol is omitted or not used, the default tolerance is calculated as: 5EL14 ·max(dim(Matrix)) ·rowNorm(Matrix) TI-Nspire™ CAS Reference Guide The floating-point number (9.) in m1 causes results to be calculated in floating-point form. QR Catalog > The QR factorization is computed numerically using Householder transformations. The symbolic solution is computed using GramSchmidt. The columns in qMatName are the orthonormal basis vectors that span the space defined by matrix. QuadReg Catalog > QuadReg X,Y [, Freq] [, Category, Include]] Computes the quadratic polynomial regression y = a·x2+b·x+c on lists X and Y with frequency Freq. A summary of results is stored in the stat.results variable. (See page 120.) All the lists must have equal dimension except for Include. X and Y are lists of independent and dependent variables. Freq is an optional list of frequency values. Each element in Freq specifies the frequency of occurrence for each corresponding X and Y data point. The default value is 1. All elements must be integers | 0. Category is a list of category codes for the corresponding X and Y data. Include is a list of one or more of the category codes. Only those data items whose category code is included in this list are included in the calculation. For information on the effect of empty elements in a list, see “Empty (Void) Elements” on page 162. Output variable Description stat.RegEqn Regression equation: a·x2+b·x+c stat.a, stat.b, stat.c Regression coefficients stat.R2 Coefficient of determination stat.Resid Residuals from the regression stat.XReg List of data points in the modified X List actually used in the regression based on restrictions of Freq, Category List, and Include Categories stat.YReg List of data points in the modified Y List actually used in the regression based on restrictions of Freq, Category List, and Include Categories stat.FreqReg List of frequencies corresponding to stat.XReg and stat.YReg TI-Nspire™ CAS Reference Guide 95 QuartReg Catalog > QuartReg X,Y [, Freq] [, Category, Include]] Computes the quartic polynomial regression y = a·x4+b·x3+c· x2+d·x+e on lists X and Y with frequency Freq. A summary of results is stored in the stat.results variable. (See page 120.) All the lists must have equal dimension except for Include. X and Y are lists of independent and dependent variables. Freq is an optional list of frequency values. Each element in Freq specifies the frequency of occurrence for each corresponding X and Y data point. The default value is 1. All elements must be integers | 0. Category is a list of category codes for the corresponding X and Y data. Include is a list of one or more of the category codes. Only those data items whose category code is included in this list are included in the calculation. For information on the effect of empty elements in a list, see “Empty (Void) Elements” on page 162. Output variable Description stat.RegEqn Regression equation: a·x4+b·x3+c· x2+d·x+e stat.a, stat.b, stat.c, stat.d, stat.e Regression coefficients stat.R2 Coefficient of determination stat.Resid Residuals from the regression stat.XReg List of data points in the modified X List actually used in the regression based on restrictions of Freq, Category List, and Include Categories stat.YReg List of data points in the modified Y List actually used in the regression based on restrictions of Freq, Category List, and Include Categories stat.FreqReg List of frequencies corresponding to stat.XReg and stat.YReg 96 TI-Nspire™ CAS Reference Guide R R4Pq() Catalog > R4Pq (xExpr, yExpr) expression R4Pq (xList, yList) list R4Pq (xMatrix, yMatrix) matrix In Degree angle mode: Returns the equivalent q-coordinate of the (x,y) pair arguments. In Gradian angle mode: Note: The result is returned as a degree, gradian or radian angle, according to the current angle mode setting. Note: You can insert this function from the computer keyboard by typing R@>Ptheta(...). In Radian angle mode: R4Pr() Catalog > R4Pr (xExpr, yExpr) expression R4Pr (xList, yList) list R4Pr (xMatrix, yMatrix) matrix In Radian angle mode: Returns the equivalent r-coordinate of the (x,y) pair arguments. Note: You can insert this function from the computer keyboard by typing R@>Pr(...). 4Rad Catalog > Expr14Rad expression In Degree angle mode: Converts the argument to radian angle measure. Note: You can insert this operator from the computer keyboard by typing @>Rad. In Gradian angle mode: rand() rand() expression rand(#Trials) list Catalog > Sets the random-number seed. rand() returns a random value between 0 and 1. rand(#Trials) returns a list containing #Trials random values between 0 and 1. TI-Nspire™ CAS Reference Guide 97 randBin() Catalog > randBin(n, p) expression randBin(n, p, #Trials) list randBin(n, p) returns a random real number from a specified Binomial distribution. randBin(n, p, #Trials) returns a list containing #Trials random real numbers from a specified Binomial distribution. randInt() Catalog > randInt(lowBound,upBound) expression randInt(lowBound,upBound ,#Trials) list randInt(lowBound,upBound) returns a random integer within the range specified by lowBound and upBound integer bounds. randInt(lowBound,upBound ,#Trials) returns a list containing #Trials random integers within the specified range. randMat() Catalog > randMat(numRows, numColumns) matrix Returns a matrix of integers between -9 and 9 of the specified dimension. Both arguments must simplify to integers. Note: The values in this matrix will change each time you press ·. randNorm() randNorm(m, randNorm(m, Catalog > s) expression s, #Trials) list randNorm(m, s) returns a decimal number from the specified normal distribution. It could be any real number but will be heavily concentrated in the interval [mN3·s, m+3·s]. randNorm(m, s, #Trials) returns a list containing #Trials decimal numbers from the specified normal distribution. randPoly() randPoly(Var, Order) Catalog > expression Returns a polynomial in Var of the specified Order. The coefficients are random integers in the range L9 through 9. The leading coefficient will not be zero. Order must be 0–99. randSamp() randSamp(List,#Trials[,noRepl]) Catalog > list Returns a list containing a random sample of #Trials trials from List with an option for sample replacement (noRepl=0), or no sample replacement (noRepl=1). The default is with sample replacement. 98 TI-Nspire™ CAS Reference Guide RandSeed Catalog > RandSeed Number If Number = 0, sets the seeds to the factory defaults for the randomnumber generator. If Number ƒ 0, it is used to generate two seeds, which are stored in system variables seed1 and seed2. real() Catalog > expression real( Expr1) Returns the real part of the argument. Note: All undefined variables are treated as real variables. See also imag(), page 58. real( List1) list Returns the real parts of all elements. real( Matrix1) matrix Returns the real parts of all elements. 4Rect Catalog > Vector 4Rect Note: You can insert this operator from the computer keyboard by typing @>Rect. Displays Vector in rectangular form [x, y, z]. The vector must be of dimension 2 or 3 and can be a row or a column. Note: 4Rect is a display-format instruction, not a conversion function. You can use it only at the end of an entry line, and it does not update ans. Note: See also 4Polar, page 89. complexValue 4Rect In Radian angle mode: Displays complexValue in rectangular form a+bi. The complexValue can have any complex form. However, an reiq entry causes an error in Degree angle mode. Note: You must use parentheses for an (r±q) polar entry. In Gradian angle mode: In Degree angle mode: Note: To type ±, select it from the symbol list in the Catalog. TI-Nspire™ CAS Reference Guide 99 ref() Catalog > ref( Matrix1[, Tol]) matrix Returns the row echelon form of Matrix1. Optionally, any matrix element is treated as zero if its absolute value is less than Tol. This tolerance is used only if the matrix has floatingpoint entries and does not contain any symbolic variables that have not been assigned a value. Otherwise, Tol is ignored. • • /· or set the Auto or Approximate If you use mode to Approximate, computations are done using floatingpoint arithmetic. If Tol is omitted or not used, the default tolerance is calculated as: 5EL14 ·max(dim(Matrix1)) ·rowNorm(Matrix1) Avoid undefined elements in Matrix1. They can lead to unexpected results. For example, if a is undefined in the following expression, a warning message appears and the result is shown as: The warning appears because the generalized element 1/a would not be valid for a=0. You can avoid this by storing a value to a beforehand or by using the constraint (“|”) operator to substitute a value, as shown in the following example. Note: See also rref(), page 105. remain() remain(Expr1, Expr2) expression remain(List1, List2) list remain(Matrix1, Matrix2) matrix Returns the remainder of the first argument with respect to the second argument as defined by the identities: remain(x,0) ? x remain(x,y) ? xNy·iPart(x/y) As a consequence, note that remain(Nx,y) ? Nremain(x,y). The result is either zero or it has the same sign as the first argument. Note: See also mod(), page 78. 100 TI-Nspire™ CAS Reference Guide Catalog > Request Catalog > Request promptString, var [, DispFlag [, statusVar]] Request promptString, func ( arg1, ...argn ) [, DispFlag [, statusVar]] Programming command: Pauses the program and displays a dialog box containing the message promptString and an input box for the user’s response. When the user types a response and clicks OK, the contents of the input box are assigned to variable var. Define a program: Define request_demo()=Prgm Request “Radius: ”,r Disp “Area = “,pi*r2 EndPrgm Run the program and type a response: request_demo() If the user clicks Cancel, the program proceeds without accepting any input. The program uses the previous value of var if var was already defined. The optional DispFlag argument can be any expression. • • If DispFlag is omitted or evaluates to 1, the prompt message and user’s response are displayed in the Calculator history. If DispFlag evaluates to 0, the prompt and response are not displayed in the history. Result after selecting OK: Radius: 6/2 Area= 28.2743 Define a program: The optional statusVar argument gives the program a way to determine how the user dismissed the dialog box. Note that statusVar Define polynomial()=Prgm Request "Enter a polynomial in x:",p(x) requires the DispFlag argument. Disp "Real roots are:",polyRoots(p(x),x) • If the user clicked OK or pressed Enter or Ctrl+Enter, variable EndPrgm statusVar is set to a value of 1. Run the program and type a response: • Otherwise, variable statusVar is set to a value of 0. polynomial() The func() argument allows a program to store the user’s response as a function definition. This syntax operates as if the user executed the command: Define func(arg1, ...argn) = user’s response The program can then use the defined function func(). The promptString should guide the user to enter an appropriate user’s response that completes the function definition. Note: You can use the Request command within a user-defined program but not within a function. Result after selecting OK: Enter a polynomial in x: x^3+3x+1 Real roots are: {-0.322185} To stop a program that contains a Request command inside an infinite loop: • • • Windows®: Hold down the F12 key and press Enter repeatedly. Macintosh®: Hold down the F5 key and press Enter repeatedly. Handheld: Hold down the repeatedly. c key and press · Note: See also RequestStr, page 102. TI-Nspire™ CAS Reference Guide 101 RequestStr Catalog > RequestStr promptString, var [, DispFlag] Define a program: Define requestStr_demo()=Prgm Programming command: Operates identically to the first syntax of the RequestStr “Your name:”,name,0 Request command, except that the user’s response is always Disp “Response has “,dim(name),” characters.” interpreted as a string. By contrast, the Request command interprets EndPrgm the response as an expression unless the user encloses it in quotation Run the program and type a response: marks (““). requestStr_demo() Note: You can use the RequestStr command within a userdefined program but not within a function. To stop a program that contains a RequestStr command inside an infinite loop: • • • Windows®: Hold down the F12 key and press Enter repeatedly. Macintosh®: Hold down the F5 key and press Enter repeatedly. Handheld: Hold down the repeatedly. c key and press · Result after selecting OK (Note that the DispFlag argument of 0 omits the prompt and response from the history): requestStr_demo() Response has 5 characters. Note: See also Request, page 101. Return Catalog > Return [Expr] Returns Expr as the result of the function. Use within a Func...EndFunc block. Note: Use Return without an argument within a Prgm...EndPrgm block to exit a program. Note for entering the example: In the Calculator application on the handheld, you can enter multi-line definitions by pressing @ · instead of at the end of each line. On the computer keyboard, hold down Alt and press Enter. right() Catalog > right(List1[, Num]) list Returns the rightmost Num elements contained in List1. If you omit Num, returns all of List1. right(sourceString[, Num]) string Returns the rightmost Num characters contained in character string sourceString. If you omit Num, returns all of sourceString. right(Comparison) expression Returns the right side of an equation or inequality. 102 TI-Nspire™ CAS Reference Guide rk23() Catalog > rk23(Expr, Var, depVar, {Var0, VarMax}, depVar0, VarStep [, diftol]) matrix rk23(SystemOfExpr, Var, ListOfDepVars, {Var0, VarMax}, ListOfDepVars0, VarStep [, diftol]) matrix rk23(ListOfExpr, Var, ListOfDepVars, {Var0, VarMax}, ListOfDepVars0, VarStep [, diftol]) matrix Differential equation: y'=0.001*y*(100-y) and y(0)=10 Uses the Runge-Kutta method to solve the system d depVar ---------------------- = Expr(Var, depVar) d Var To see the entire result, press move the cursor. with depVar(Var0)=depVar0 on the interval [Var0,VarMax]. Returns a matrix whose first row defines the Var output values as defined by VarStep. The second row defines the value of the first solution component at the corresponding Var values, and so on. £ and then use ¡ and ¢ to Same equation with diftol set to 1.E•6 Expr is the right hand side that defines the ordinary differential equation (ODE). SystemOfExpr is a system of right-hand sides that define the system of ODEs (corresponds to order of dependent variables in ListOfDepVars). Compare above result with CAS exact solution obtained using deSolve() and seqGen(): ListOfExpr is a list of right-hand sides that define the system of ODEs (corresponds to order of dependent variables in ListOfDepVars). Var is the independent variable. ListOfDepVars is a list of dependent variables. {Var0, VarMax} is a two-element list that tells the function to integrate from Var0 to VarMax. ListOfDepVars0 is a list of initial values for dependent variables. If VarStep evaluates to a nonzero number: sign(VarStep) = sign(VarMax-Var0) and solutions are returned at Var0+i*VarStep for all i=0,1,2,… such that Var0+i*VarStep is in [var0,VarMax] (may not get a solution value at VarMax). System of equations: if VarStep evaluates to zero, solutions are returned at the "RungeKutta" Var values. with y1(0)=2 and y2(0)=5 diftol is the error tolerance (defaults to 0.001). root() root(Expr) Catalog > root root root(Expr1, Expr2) root(Expr) returns the square root of Expr. root(Expr1, Expr2) returns the Expr2 root of Expr1. Expr1 can be a real or complex floating point constant, an integer or complex rational constant, or a general symbolic expression. Note: See also Nth root template, page 1. TI-Nspire™ CAS Reference Guide 103 rotate() Catalog > rotate(Integer1[,#ofRotations]) integer In Bin base mode: Rotates the bits in a binary integer. You can enter Integer1 in any number base; it is converted automatically to a signed, 64-bit binary form. If the magnitude of Integer1 is too large for this form, a symmetric modulo operation brings it within the range. For more information, see 4Base2, page 14. To see the entire result, press move the cursor. If #ofRotations is positive, the rotation is to the left. If #ofRotations is negative, the rotation is to the right. The default is L1 (rotate right one bit). £ and then use ¡ and ¢ to In Hex base mode: For example, in a right rotation: Each bit rotates right. 0b00000000000001111010110000110101 Important: To enter a binary or hexadecimal number, always use the 0b or 0h prefix (zero, not the letter O). Rightmost bit rotates to leftmost. produces: 0b10000000000000111101011000011010 The result is displayed according to the Base mode. rotate(List1[,#ofRotations]) list In Dec base mode: Returns a copy of List1 rotated right or left by #of Rotations elements. Does not alter List1. If #ofRotations is positive, the rotation is to the left. If #of Rotations is negative, the rotation is to the right. The default is L1 (rotate right one element). rotate(String1[,#ofRotations]) string Returns a copy of String1 rotated right or left by #ofRotations characters. Does not alter String1. If #ofRotations is positive, the rotation is to the left. If #ofRotations is negative, the rotation is to the right. The default is L1 (rotate right one character). round() Catalog > round( Expr1[, digits]) expression Returns the argument rounded to the specified number of digits after the decimal point. digits must be an integer in the range 0–12. If digits is not included, returns the argument rounded to 12 significant digits. Note: Display digits mode may affect how this is displayed. round( List1[, digits]) list Returns a list of the elements rounded to the specified number of digits. round( Matrix1[, digits]) matrix Returns a matrix of the elements rounded to the specified number of digits. 104 TI-Nspire™ CAS Reference Guide rowAdd() Catalog > rowAdd( Matrix1, rIndex1, rIndex2) matrix Returns a copy of Matrix1 with row rIndex2 replaced by the sum of rows rIndex1 and rIndex2. rowDim() rowDim( Matrix) Catalog > expression Returns the number of rows in Matrix. Note: See also colDim(), page 19. rowNorm() rowNorm( Matrix) Catalog > expression Returns the maximum of the sums of the absolute values of the elements in the rows in Matrix. Note: All matrix elements must simplify to numbers. See also colNorm(), page 19. rowSwap() Catalog > rowSwap( Matrix1, rIndex1, rIndex2) matrix Returns Matrix1 with rows rIndex1 and rIndex2 exchanged. rref() rref(Matrix1[, Tol]) Catalog > matrix Returns the reduced row echelon form of Matrix1. TI-Nspire™ CAS Reference Guide 105 rref() Catalog > Optionally, any matrix element is treated as zero if its absolute value is less than Tol. This tolerance is used only if the matrix has floatingpoint entries and does not contain any symbolic variables that have not been assigned a value. Otherwise, Tol is ignored. • • /· or set the Auto or Approximate If you use mode to Approximate, computations are done using floatingpoint arithmetic. If Tol is omitted or not used, the default tolerance is calculated as: 5EL14 ·max(dim(Matrix1)) ·rowNorm(Matrix1) Note: See also ref(), page 100. S μ key sec() sec(Expr1) expression sec(List1) list In Degree angle mode: Returns the secant of Expr1 or returns a list containing the secants of all elements in List1. Note: The argument is interpreted as a degree, gradian or radian angle, according to the current angle mode setting. You can use ¡, G, or R to override the angle mode temporarily. μ key sec /() expression sec/(List1) list sec/(Expr1) Returns the angle whose secant is Expr1 or returns a list containing the inverse secants of each element of List1. In Degree angle mode: In Gradian angle mode: Note: The result is returned as a degree, gradian or radian angle, according to the current angle mode setting. Note: You can insert this function from the keyboard by typing arcsec(...). sech() Catalog > sech(Expr1) expression sech(List1) list Returns the hyperbolic secant of Expr1 or returns a list containing the hyperbolic secants of the List1 elements. 106 In Radian angle mode: TI-Nspire™ CAS Reference Guide sech/() Catalog > expression sech/ (List1) list sech /(Expr1) In Radian angle and Rectangular complex mode: Returns the inverse hyperbolic secant of Expr1 or returns a list containing the inverse hyperbolic secants of each element of List1. Note: You can insert this function from the keyboard by typing arcsech(...). seq() Catalog > seq(Expr, Var, Low, High[, Step]) list Increments Var from Low through High by an increment of Step, evaluates Expr, and returns the results as a list. The original contents of Var are still there after seq() is completed. The default value for Step = 1. Press Ctrl+Enter evaluate: /· (Macintosh®: “+Enter) to TI-Nspire™ CAS Reference Guide 107 seqGen() Catalog > seqGen(Expr, Var, depVar, {Var0, VarMax}[, ListOfInitTerms [, VarStep [, CeilingValue]]]) list Generate the first 5 terms of the sequence u(n) = u(n-1)2/2, with u(1)=2 and VarStep=1. Generates a list of terms for sequence depVar(Var)=Expr as follows: Increments independent variable Var from Var0 through VarMax by VarStep, evaluates depVar(Var) for corresponding values of Var using the Expr formula and ListOfInitTerms, and returns the results as a list. seqGen(ListOrSystemOfExpr, Var, ListOfDepVars, {Var0, VarMax} [, MatrixOfInitTerms [, VarStep [, CeilingValue]]]) matrix Generates a matrix of terms for a system (or list) of sequences Example in which Var0=2: ListOfDepVars(Var)=ListOrSystemOfExpr as follows: Increments independent variable Var from Var0 through VarMax by VarStep, evaluates ListOfDepVars(Var) for corresponding values of Var using ListOrSystemOfExpr formula and MatrixOfInitTerms, and returns the results as a matrix. The original contents of Var are unchanged after seqGen() is completed. The default value for VarStep = 1. Example in which initial term is symbolic: System of two sequences: Note: The Void (_) in the initial term matrix above is used to indicate that the initial term for u1(n) is calculated using the explicit sequence formula u1(n)=1/n. seqn() Catalog > Generate the first 6 terms of the sequence u(n) = u(n-1)/2, with u(1)=2. seqn(Expr(u, n [, ListOfInitTerms[, nMax [, CeilingValue]]]) list Generates a list of terms for a sequence u(n)=Expr(u, n) as follows: Increments n from 1 through nMax by 1, evaluates u(n) for corresponding values of n using the Expr(u, n) formula and ListOfInitTerms, and returns the results as a list. seqn(Expr(n [, nMax [, CeilingValue]]) list Generates a list of terms for a non-recursive sequence u(n)=Expr(n) as follows: Increments n from 1 through nMax by 1, evaluates u(n) for corresponding values of n using the Expr(n) formula, and returns the results as a list. If nMax is missing, nMax is set to 2500 If nMax=0, nMax is set to 2500 Note: seqn() calls seqGen( ) with n0=1 and nstep =1 108 TI-Nspire™ CAS Reference Guide series() Catalog > expression series(Expr1, Var, Order [, Point]) | Var>Point expression series(Expr1, Var, Order [, Point]) | Var<Point expression series(Expr1, Var, Order [, Point]) Returns a generalized truncated power series representation of Expr1 expanded about Point through degree Order. Order can be any rational number. The resulting powers of (Var N Point) can include negative and/or fractional exponents. The coefficients of these powers can include logarithms of (Var N Point) and other functions of Var that are dominated by all powers of (Var N Point) having the same exponent sign. Point defaults to 0. Point can be ˆ or Nˆ, in which cases the expansion is through degree Order in 1/(Var N Point). series(...) returns “series(...)” if it is unable to determine such a representation, such as for essential singularities such as sin(1/z) at z=0, eN1/z at z=0, or ez at z = ˆ or Nˆ. If the series or one of its derivatives has a jump discontinuity at Point, the result is likely to contain sub-expressions of the form sign(…) or abs(…) for a real expansion variable or (-1)floor(…angle(…)…) for a complex expansion variable, which is one ending with “_”. If you intend to use the series only for values on one side of Point, then append the appropriate one of “| Var > Point”, “| Var < Point”, “| “Var | Point”, or “Var { Point” to obtain a simpler result. series() can provide symbolic approximations to indefinite integrals and definite integrals for which symbolic solutions otherwise can't be obtained. series() distributes over 1st-argument lists and matrices. series() is a generalized version of taylor(). As illustrated by the last example to the right, the display routines downstream of the result produced by series(...) might rearrange terms so that the dominant term is not the leftmost one. Note: See also dominantTerm(), page 39. TI-Nspire™ CAS Reference Guide 109 setMode() Catalog > setMode(modeNameInteger, settingInteger) setMode(list) integer list integer Display approximate value of p using the default setting for Display Digits, and then display p with a setting of Fix2. Check to see that the default is restored after the program executes. Valid only within a function or program. setMode(modeNameInteger, settingInteger) temporarily sets mode modeNameInteger to the new setting settingInteger, and returns an integer corresponding to the original setting of that mode. The change is limited to the duration of the program/ function’s execution. modeNameInteger specifies which mode you want to set. It must be one of the mode integers from the table below. settingInteger specifies the new setting for the mode. It must be one of the setting integers listed below for the specific mode you are setting. setMode(list) lets you change multiple settings. list contains pairs of mode integers and setting integers. setMode(list) returns a similar list whose integer pairs represent the original modes and settings. If you have saved all mode settings with getMode(0) & var, you can use setMode(var) to restore those settings until the function or program exits. See getMode(), page 54. Note: The current mode settings are passed to called subroutines. If any subroutine changes a mode setting, the mode change will be lost when control returns to the calling routine. Note for entering the example: In the Calculator application on the handheld, you can enter multi-line definitions @ · instead of at the end of each line. On the by pressing computer keyboard, hold down Alt and press Enter. Mode Name Mode Integer Display Digits 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 Exponential Format 3 1=Normal, 2=Scientific, 3=Engineering Real or Complex 4 1=Real, 2=Rectangular, 3=Polar Auto or Approx. 5 1=Auto, 2=Approximate, 3=Exact Vector Format 6 1=Rectangular, 2=Cylindrical, 3=Spherical Base 7 1=Decimal, 2=Hex, 3=Binary Unit system 8 1=SI, 2=Eng/US 110 Setting Integers TI-Nspire™ CAS Reference Guide shift() Catalog > shift(Integer1[,#ofShifts]) integer In Bin base mode: Shifts the bits in a binary integer. You can enter Integer1 in any number base; it is converted automatically to a signed, 64-bit binary form. If the magnitude of Integer1 is too large for this form, a symmetric modulo operation brings it within the range. For more information, see 4Base2, page 14. If #ofShifts is positive, the shift is to the left. If #ofShifts is negative, the shift is to the right. The default is L1 (shift right one bit). In Hex base mode: In a right shift, the rightmost bit is dropped and 0 or 1 is inserted to match the leftmost bit. In a left shift, the leftmost bit is dropped and 0 is inserted as the rightmost bit. For example, in a right shift: Important: To enter a binary or hexadecimal number, always use the 0b or 0h prefix (zero, not the letter O). Each bit shifts right. 0b0000000000000111101011000011010 Inserts 0 if leftmost bit is 0, or 1 if leftmost bit is 1. produces: 0b00000000000000111101011000011010 The result is displayed according to the Base mode. Leading zeros are not shown. shift(List1 [,#ofShifts]) list In Dec base mode: Returns a copy of List1 shifted right or left by #ofShifts elements. Does not alter List1. If #ofShifts is positive, the shift is to the left. If #ofShifts is negative, the shift is to the right. The default is L1 (shift right one element). Elements introduced at the beginning or end of list by the shift are set to the symbol “undef”. shift(String1 [,#ofShifts]) string Returns a copy of String1 shifted right or left by #ofShifts characters. Does not alter String1. If #ofShifts is positive, the shift is to the left. If #ofShifts is negative, the shift is to the right. The default is L1 (shift right one character). Characters introduced at the beginning or end of string by the shift are set to a space. sign() Catalog > sign(Expr1) expression sign(List1) list sign(Matrix1) matrix For real and complex Expr1, returns Expr1/abs(Expr1) when Expr1ƒ 0. Returns 1 if Expr1 is positive. If complex format mode is Real: Returns L1 if Expr1 is negative. sign(0) returns „1 if the complex format mode is Real; otherwise, it returns itself. sign(0) represents the unit circle in the complex domain. For a list or matrix, returns the signs of all the elements. TI-Nspire™ CAS Reference Guide 111 simult() simult(coeffMatrix, constVector[, Tol]) Catalog > matrix Returns a column vector that contains the solutions to a system of linear equations. Solve for x and y: x + 2y = 1 3x + 4y = L1 Note: See also linSolve(), page 67. coeffMatrix must be a square matrix that contains the coefficients of the equations. The solution is x=L3 and y=2. constVector must have the same number of rows (same dimension) as coeffMatrix and contain the constants. Optionally, any matrix element is treated as zero if its absolute value is less than Tol. This tolerance is used only if the matrix has floatingpoint entries and does not contain any symbolic variables that have not been assigned a value. Otherwise, Tol is ignored. • • Solve: ax + by = 1 cx + dy = 2 If you set the Auto or Approximate mode to Approximate, computations are done using floating-point arithmetic. If Tol is omitted or not used, the default tolerance is calculated as: 5EL14 ·max(dim(coeffMatrix)) ·rowNorm(coeffMatrix) simult(coeffMatrix, constMatrix[, Tol]) matrix Solves multiple systems of linear equations, where each system has the same equation coefficients but different constants. Solve: x + 2y = 1 3x + 4y = L1 Each column in constMatrix must contain the constants for a system x + 2y = 2 3x + 4y = L3 of equations. Each column in the resulting matrix contains the solution for the corresponding system. For the first system, x=L3 and y=2. For the second system, x=L7 and y=9/2. 4sin Catalog > Expr 4sin Note: You can insert this operator from the computer keyboard by typing @>sin. Represents Expr in terms of sine. This is a display conversion operator. It can be used only at the end of the entry line. 4sin reduces all powers of cos(...) modulo 1Nsin(...)^2 so that any remaining powers of sin(...) have exponents in the range (0, 2). Thus, the result will be free of cos(...) if and only if cos(...) occurs in the given expression only to even powers. Note: This conversion operator is not supported in Degree or Gradian Angle modes. Before using it, make sure that the Angle mode is set to Radians and that Expr does not contain explicit references to degree or gradian angles. 112 TI-Nspire™ CAS Reference Guide μ key sin() sin(Expr1) expression sin(List1) list In Degree angle mode: sin(Expr1) returns the sine of the argument as an expression. sin(List1) returns a list of the sines of all elements in List1. Note: The argument is interpreted as a degree, gradian or radian angle, according to the current angle mode. You can use ¡,G, or R to override the angle mode setting temporarily. In Gradian angle mode: In Radian angle mode: sin(squareMatrix1) squareMatrix In Radian angle mode: Returns the matrix sine of squareMatrix1. This is not the same as calculating the sine of each element. For information about the calculation method, refer to cos(). squareMatrix1 must be diagonalizable. The result always contains floating-point numbers. μ key sin/() sin/(Expr1) expression sin/(List1) list In Degree angle mode: sin/(Expr1) returns the angle whose sine is Expr1 as an expression. sin/(List1) returns a list of the inverse sines of each element of List1. In Gradian angle mode: Note: The result is returned as a degree, gradian or radian angle, according to the current angle mode setting. In Radian angle mode: Note: You can insert this function from the keyboard by typing arcsin(...). TI-Nspire™ CAS Reference Guide 113 μ key sin/() sin/(squareMatrix1) squareMatrix In Radian angle mode and Rectangular complex format mode: Returns the matrix inverse sine of squareMatrix1. This is not the same as calculating the inverse sine of each element. For information about the calculation method, refer to cos(). squareMatrix1 must be diagonalizable. The result always contains floating-point numbers. To see the entire result, press move the cursor. sinh() £ and then use ¡ and ¢ to Catalog > sinh(Expr1) expression sinh(List1) list sinh (Expr1) returns the hyperbolic sine of the argument as an expression. sinh (List1) returns a list of the hyperbolic sines of each element of List1. sinh(squareMatrix1) squareMatrix In Radian angle mode: Returns the matrix hyperbolic sine of squareMatrix1. This is not the same as calculating the hyperbolic sine of each element. For information about the calculation method, refer to cos(). squareMatrix1 must be diagonalizable. The result always contains floating-point numbers. sinh /() Catalog > sinh/(Expr1) expression sinh/(List1) list sinh/(Expr1) returns the inverse hyperbolic sine of the argument as an expression. sinh/(List1) returns a list of the inverse hyperbolic sines of each element of List1. Note: You can insert this function from the keyboard by typing arcsinh(...). sinh/(squareMatrix1) squareMatrix Returns the matrix inverse hyperbolic sine of squareMatrix1. This is not the same as calculating the inverse hyperbolic sine of each element. For information about the calculation method, refer to cos(). squareMatrix1 must be diagonalizable. The result always contains floating-point numbers. 114 TI-Nspire™ CAS Reference Guide In Radian angle mode: SinReg Catalog > 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.results variable. (See page 120.) All the lists must have equal dimension except for Include. X and Y are lists of independent and dependent variables. Iterations is a value that specifies the maximum number of times (1 through 16) a solution will be attempted. If omitted, 8 is used. Typically, larger values result in better accuracy but longer execution times, and vice versa. Period specifies an estimated period. If omitted, the difference between values in X should be equal and in sequential order. If you specify Period, the differences between x values can be unequal. Category is a list of category codes for the corresponding X and Y data. Include is a list of one or more of the category codes. Only those data items whose category code is included in this list are included in the calculation. The output of SinReg is always in radians, regardless of the angle mode setting. For information on the effect of empty elements in a list, see “Empty (Void) Elements” on page 162. Output variable Description stat.RegEqn Regression Equation: a·sin(bx+c)+d stat.a, stat.b, stat.c, stat.d Regression coefficients stat.Resid Residuals from the regression stat.XReg List of data points in the modified X List actually used in the regression based on restrictions of Freq, Category List, and Include Categories stat.YReg List of data points in the modified Y List actually used in the regression based on restrictions of Freq, Category List, and Include Categories stat.FreqReg List of frequencies corresponding to stat.XReg and stat.YReg solve() Catalog > solve(Equation, Var) Boolean expression solve(Equation, Var=Guess) Boolean expression solve(Inequality, Var) Boolean expression Returns candidate real solutions of an equation or an inequality for Var. The goal is to return candidates for all solutions. However, there might be equations or inequalities for which the number of solutions is infinite. Solution candidates might not be real finite solutions for some combinations of values for undefined variables. TI-Nspire™ CAS Reference Guide 115 solve() Catalog > For the Auto setting of the Auto or Approximate mode, the goal is to produce exact solutions when they are concise, and supplemented by iterative searches with approximate arithmetic when exact solutions are impractical. Due to default cancellation of the greatest common divisor from the numerator and denominator of ratios, solutions might be solutions only in the limit from one or both sides. For inequalities of types |, {, <, or >, explicit solutions are unlikely unless the inequality is linear and contains only Var. For the Exact mode, portions that cannot be solved are returned as an implicit equation or inequality. Use the constraint (“|”) operator to restrict the solution interval and/ In Radian angle mode: or other variables that occur in the equation or inequality. When you find a solution in one interval, you can use the inequality operators to exclude that interval from subsequent searches. false is returned when no real solutions are found. true is returned if solve() can determine that any finite real value of Var satisfies the equation or inequality. Since solve() always returns a Boolean result, you can use “and,” “or,” and “not” to combine results from solve() with each other or with other Boolean expressions. Solutions might contain a unique new undefined constant of the form In Radian angle mode: nj with j being an integer in the interval 1–255. Such variables designate an arbitrary integer. In Real mode, fractional powers having odd denominators denote only the real branch. Otherwise, multiple branched expressions such as fractional powers, logarithms, and inverse trigonometric functions denote only the principal branch. Consequently, solve() produces only solutions corresponding to that one real or principal branch. Note: See also cSolve(), cZeros(), nSolve(), and zeros(). solve(Eqn1 and Eqn2 [and … ], VarOrGuess1, VarOrGuess2 [, … ]) Boolean expression solve(SystemOfEqns, VarOrGuess1, VarOrGuess2 [, … ]) Boolean expression solve({Eqn1, Eqn2 [,...]} {VarOrGuess1, VarOrGuess2 [, … ]}) Boolean expression Returns candidate real solutions to the simultaneous algebraic equations, where each VarOrGuess specifies a variable that you want to solve for. You can separate the equations with the and operator, or you can enter a SystemOfEqns using a template from the Catalog. The number of VarOrGuess arguments must match the number of equations. Optionally, you can specify an initial guess for a variable. Each VarOrGuess must have the form: variable – or – variable = real or non-real number For example, x is valid and so is x=3. 116 TI-Nspire™ CAS Reference Guide solve() Catalog > If all of the equations are polynomials and if you do NOT specify any initial guesses, solve() uses the lexical Gröbner/Buchberger elimination method to attempt to determine all real solutions. For example, suppose you have a circle of radius r at the origin and another circle of radius r centered where the first circle crosses the positive x-axis. Use solve() to find the intersections. As illustrated by r in the example to the right, simultaneous polynomial equations can have extra variables that have no values, but represent given numeric values that could be substituted later. You can also (or instead) include solution variables that do not appear in the equations. For example, you can include z as a solution variable to extend the previous example to two parallel intersecting cylinders of radius r. The cylinder solutions illustrate how families of solutions might contain arbitrary constants of the form ck, where k is an integer suffix from 1 through 255. To see the entire result, press move the cursor. For polynomial systems, computation time or memory exhaustion may depend strongly on the order in which you list solution variables. If your initial choice exhausts memory or your patience, try rearranging the variables in the equations and/or varOrGuess list. £ and then use ¡ and ¢ to If you do not include any guesses and if any equation is nonpolynomial in any variable but all equations are linear in the solution variables, solve() uses Gaussian elimination to attempt to determine all real solutions. If a system is neither polynomial in all of its variables nor linear in its solution variables, solve() determines at most one solution using an approximate iterative method. To do so, the number of solution variables must equal the number of equations, and all other variables in the equations must simplify to numbers. To see the entire result, press move the cursor. £ and then use ¡ and ¢ to Each solution variable starts at its guessed value if there is one; otherwise, it starts at 0.0. Use guesses to seek additional solutions one by one. For convergence, a guess may have to be rather close to a solution. TI-Nspire™ CAS Reference Guide 117 SortA Catalog > SortA List1[, List2] [, List3] ... SortA Vector1[, Vector2] [, Vector3] ... Sorts the elements of the first argument in ascending order. If you include additional arguments, sorts the elements of each so that their new positions match the new positions of the elements in the first argument. All arguments must be names of lists or vectors. All arguments must have equal dimensions. Empty (void) elements within the first argument move to the bottom. For more information on empty elements, see page 162. SortD Catalog > SortD List1[, List2] [, List3] ... SortD Vector1[,Vector2] [,Vector3] ... Identical to SortA, except SortD sorts the elements in descending order. Empty (void) elements within the first argument move to the bottom. For more information on empty elements, see page 162. 118 TI-Nspire™ CAS Reference Guide 4Sphere Catalog > Vector 4Sphere Note: You can insert this operator from the computer keyboard by Press Ctrl+Enter evaluate: /· (Macintosh®: “+Enter) to Press Ctrl+Enter evaluate: /· (Macintosh®: “+Enter) to typing @>Sphere. Displays the row or column vector in spherical form [r ±q ±f]. Vector must be of dimension 3 and can be either a row or a column vector. Note: 4Sphere is a display-format instruction, not a conversion function. You can use it only at the end of an entry line. Press · Z (ρ,θ,φ) φ ρ Y θ X sqrt() Catalog > sqrt(Expr1) expression sqrt(List1) list Returns the square root of the argument. For a list, returns the square roots of all the elements in List1. Note: See also Square root template, page 1. TI-Nspire™ CAS Reference Guide 119 stat.results Catalog > stat.results Displays results from a statistics calculation. The results are displayed as a set of name-value pairs. The specific names shown are dependent on the most recently evaluated statistics function or command. You can copy a name or value and paste it into other locations. Note: Avoid defining variables that use the same names as those used for statistical analysis. In some cases, an error condition could occur. Variable names used for statistical analysis are listed in the table below. stat.a stat.AdjR² stat.b stat.b0 stat.b1 stat.b2 stat.b3 stat.b4 stat.b5 stat.b6 stat.b7 stat.b8 stat.b9 stat.b10 stat.bList stat.c² stat.c stat.CLower stat.CLowerList stat.CompList stat.CompMatrix stat.CookDist stat.CUpper stat.CUpperList stat.d stat.dfDenom stat.dfBlock stat.dfCol stat.dfError stat.dfInteract stat.dfReg stat.dfNumer stat.dfRow stat.DW stat.e stat.ExpMatrix stat.F stat.FBlock stat.Fcol stat.FInteract stat.FreqReg stat.Frow stat.Leverage stat.LowerPred stat.LowerVal stat.m stat.MaxX stat.MaxY stat.ME stat.MedianX stat.MedianY stat.MEPred stat.MinX stat.MinY stat.MS stat.MSBlock stat.MSCol stat.MSError stat.MSInteract stat.MSReg stat.MSRow stat.n stat.Ç stat.Ç1 stat.Ç2 stat.ÇDiff stat.PList stat.PVal stat.PValBlock stat.PValCol stat.PValInteract stat.PValRow stat.Q1X stat.Q1Y stat.Q3X stat.Q3Y stat.r stat.r² stat.RegEqn stat.Resid stat.ResidTrans stat.sx stat.sy stat.sx1 stat.sx2 stat.Gx stat.Gx² stat.Gxy stat.Gy stat.Gy² stat.s stat.SE stat.SEList stat.SEPred stat.sResid stat.SEslope stat.sp stat.SS stat.SSBlock stat.SSCol stat.SSX stat.SSY stat.SSError stat.SSInteract stat.SSReg stat.SSRow stat.tList stat.UpperPred stat.UpperVal stat.v stat.v1 stat.v2 stat.vDiff stat.vList stat.XReg stat.XVal stat.XValList stat.w y y stat. stat. List stat.YReg Note: Each time the Lists & Spreadsheet application calculates statistical results, it copies the “stat .” group variables to a “stat#.” group, where # is a number that is incremented automatically. This lets you maintain previous results while performing multiple calculations. 120 TI-Nspire™ CAS Reference Guide stat.values Catalog > stat.values See the stat.results example. Displays a matrix of the values calculated for the most recently evaluated statistics function or command. Unlike stat.results, stat.values omits the names associated with the values. You can copy a value and paste it into other locations. stDevPop() stDevPop(List[, freqList]) Catalog > expression In Radian angle and auto modes: Returns the population standard deviation of the elements in List. Each freqList element counts the number of consecutive occurrences of the corresponding element in List. Note: List must have at least two elements. Empty (void) elements are ignored. For more information on empty elements, see page 162. stDevPop(Matrix1[, freqMatrix]) matrix Returns a row vector of the population standard deviations of the columns in Matrix1. Each freqMatrix element counts the number of consecutive occurrences of the corresponding element in Matrix1. Note: Matrix1 must have at least two rows. Empty (void) elements are ignored. For more information on empty elements, see page 162. stDevSamp() stDevSamp(List[, freqList]) Catalog > expression Returns the sample standard deviation of the elements in List. Each freqList element counts the number of consecutive occurrences of the corresponding element in List. Note: List must have at least two elements. Empty (void) elements are ignored. For more information on empty elements, see page 162. TI-Nspire™ CAS Reference Guide 121 stDevSamp() stDevSamp(Matrix1[, freqMatrix]) Catalog > matrix Returns a row vector of the sample standard deviations of the columns in Matrix1. Each freqMatrix element counts the number of consecutive occurrences of the corresponding element in Matrix1. Note: Matrix1 must have at least two rows. Empty (void) elements are ignored. For more information on empty elements, see page 162. Stop Catalog > Stop Programming command: Terminates the program. Stop is not allowed in functions. Note for entering the example: In the Calculator application on the handheld, you can enter multi-line definitions by pressing @ · at the end of each line. On the computer keyboard, instead of hold down Alt and press Enter. See & (store), page 160. Store string() Catalog > string(Expr) string Simplifies Expr and returns the result as a character string. subMat() Catalog > subMat(Matrix1[, startRow] [, startCol] [, endRow] [, endCol]) matrix Returns the specified submatrix of Matrix1. Defaults: startRow=1, startCol=1, endRow=last row, endCol=last column. Sum (Sigma) 122 TI-Nspire™ CAS Reference Guide See G(), page 153. sum() sum(List[, Start[, End]]) Catalog > expression Returns the sum of all elements in List. Start and End are optional. They specify a range of elements. Any void argument produces a void result. Empty (void) elements in List are ignored. For more information on empty elements, see page 162. sum(Matrix1[, Start[, End]]) matrix Returns a row vector containing the sums of all elements in the columns in Matrix1. Start and End are optional. They specify a range of rows. Any void argument produces a void result. Empty (void) elements in Matrix1 are ignored. For more information on empty elements, see page 162. sumIf() sumIf(List,Criteria[, SumList]) Catalog > value Returns the accumulated sum of all elements in List that meet the specified Criteria. Optionally, you can specify an alternate list, sumList, to supply the elements to accumulate. List can be an expression, list, or matrix. SumList, if specified, must have the same dimension(s) as List. Criteria can be: • • A value, expression, or string. For example, 34 accumulates only those elements in List that simplify to the value 34. A Boolean expression containing the symbol ? as a placeholder for each element. For example, ?<10 accumulates only those elements in List that are less than 10. When a List element meets the Criteria, the element is added to the accumulating sum. If you include sumList, the corresponding element from sumList is added to the sum instead. Within the Lists & Spreadsheet application, you can use a range of cells in place of List and sumList. Empty (void) elements are ignored. For more information on empty elements, see page 162. Note: See also countIf(), page 26. sumSeq() system() See G(), page 153. Catalog > system(Eqn1 [, Eqn2 [, Eqn3 [, ...]]]) system(Expr1 [, Expr2 [, Expr3 [, ...]]]) Returns a system of equations, formatted as a list. You can also create a system by using a template. Note: See also System of equations, page 3. TI-Nspire™ CAS Reference Guide 123 T T (transpose) Catalog > Matrix1T matrix Returns the complex conjugate transpose of Matrix1. Note: You can insert this operator from the computer keyboard by typing @t. μ key tan() tan(Expr1) expression tan(List1) list In Degree angle mode: tan(Expr1) returns the tangent of the argument as an expression. tan(List1) returns a list of the tangents of all elements in List1. Note: The argument is interpreted as a degree, gradian or radian angle, according to the current angle mode. You can use ¡, G or R to override the angle mode setting temporarily. In Gradian angle mode: In Radian angle mode: tan(squareMatrix1) squareMatrix Returns the matrix tangent of squareMatrix1. This is not the same as calculating the tangent of each element. For information about the calculation method, refer to cos(). squareMatrix1 must be diagonalizable. The result always contains floating-point numbers. 124 TI-Nspire™ CAS Reference Guide In Radian angle mode: μ key tan/() tan/(Expr1) expression tan/(List1) list In Degree angle mode: tan/(Expr1) returns the angle whose tangent is Expr1 as an expression. In Gradian angle mode: tan/(List1) returns a list of the inverse tangents of each element of List1. Note: The result is returned as a degree, gradian or radian angle, according to the current angle mode setting. In Radian angle mode: Note: You can insert this function from the keyboard by typing arctan(...). tan/(squareMatrix1) squareMatrix In Radian angle mode: Returns the matrix inverse tangent of squareMatrix1. This is not the same as calculating the inverse tangent of each element. For information about the calculation method, refer to cos(). squareMatrix1 must be diagonalizable. The result always contains floating-point numbers. tangentLine() Catalog > expression tangentLine(Expr1,Var=Point) expression tangentLine(Expr1,Var,Point) Returns the tangent line to the curve represented by Expr1 at the point specified in Var=Point. Make sure that the independent variable is not defined. For example, If f1(x):=5 and x:=3, then tangentLine(f1(x),x,2) returns “false.” tanh() Catalog > tanh(Expr1) expression tanh(List1) list tanh(Expr1) returns the hyperbolic tangent of the argument as an expression. tanh(List1) returns a list of the hyperbolic tangents of each element of List1. tanh(squareMatrix1) squareMatrix In Radian angle mode: Returns the matrix hyperbolic tangent of squareMatrix1. This is not the same as calculating the hyperbolic tangent of each element. For information about the calculation method, refer to cos(). squareMatrix1 must be diagonalizable. The result always contains floating-point numbers. TI-Nspire™ CAS Reference Guide 125 tanh /() Catalog > tanh/(Expr1) expression tanh/(List1) list In Rectangular complex format: tanh/(Expr1) returns the inverse hyperbolic tangent of the argument as an expression. tanh/(List1) returns a list of the inverse hyperbolic tangents of each element of List1. Note: You can insert this function from the keyboard by typing arctanh(...). tanh/(squareMatrix1) squareMatrix In Radian angle mode and Rectangular complex format: Returns the matrix inverse hyperbolic tangent of squareMatrix1. This is not the same as calculating the inverse hyperbolic tangent of each element. For information about the calculation method, refer to cos(). squareMatrix1 must be diagonalizable. The result always contains floating-point numbers. To see the entire result, press move the cursor. taylor() £ and then use ¡ and ¢ to Catalog > taylor(Expr1, Var, Order[, Point]) expression Returns the requested Taylor polynomial. The polynomial includes non-zero terms of integer degrees from zero through Order in (Var minus Point). taylor() returns itself if there is no truncated power series of this order, or if it would require negative or fractional exponents. Use substitution and/or temporary multiplication by a power of (Var minus Point) to determine more general power series. Point defaults to zero and is the expansion point. As illustrated by the last example to the right, the display routines downstream of the result produced by taylor(...) might rearrange terms so that the dominant term is not the leftmost one. tCdf() Catalog > tCdf(lowBound,upBound,df) number if lowBound and upBound are numbers, list if lowBound and upBound are lists Computes the Student-t distribution probability between lowBound and upBound for the specified degrees of freedom df. For P(X { upBound), set lowBound = .ˆ. 126 TI-Nspire™ CAS Reference Guide tCollect() tCollect(Expr1) Catalog > expression Returns an expression in which products and integer powers of sines and cosines are converted to a linear combination of sines and cosines of multiple angles, angle sums, and angle differences. The transformation converts trigonometric polynomials into a linear combination of their harmonics. Sometimes tCollect() will accomplish your goals when the default trigonometric simplification does not. tCollect() tends to reverse transformations done by tExpand(). Sometimes applying tExpand() to a result from tCollect(), or vice versa, in two separate steps simplifies an expression. tExpand() tExpand(Expr1) Catalog > expression Returns an expression in which sines and cosines of integer-multiple angles, angle sums, and angle differences are expanded. Because of the identity (sin(x))2+(cos(x))2=1, there are many possible equivalent results. Consequently, a result might differ from a result shown in other publications. Sometimes tExpand() will accomplish your goals when the default trigonometric simplification does not. tExpand() tends to reverse transformations done by tCollect(). Sometimes applying tCollect() to a result from tExpand(), or vice versa, in two separate steps simplifies an expression. Note: Degree-mode scaling by p/180 interferes with the ability of tExpand() to recognize expandable forms. For best results, tExpand() should be used in Radian mode. Text Catalog > Text promptString [, DispFlag] Define a program that pauses to display each of five random numbers in a dialog box. Within the Prgm...EndPrgm template, complete each line by Programming command: Pauses the program and displays the character string promptString in a dialog box. @ · pressing instead of . On the computer keyboard, hold down Alt and press Enter. When the user selects OK, program execution continues. The optional flag argument can be any expression. • • If DispFlag is omitted or evaluates to 1, the text message is added to the Calculator history. If DispFlag evaluates to 0, the text message is not added to the history. Define text_demo()=Prgm For i,1,5 strinfo:=”Random number “ & string(rand(i)) Text strinfo EndFor EndPrgm If the program needs a typed response from the user, refer to Request, page 101, or RequestStr, page 102. Run the program: text_demo() Note: You can use this command within a user-defined program but not within a function. Sample of one dialog box: Then See If, page 57. TI-Nspire™ CAS Reference Guide 127 tInterval Catalog > tInterval List[,Freq[,CLevel]] (Data list input) tInterval v,sx,n[,CLevel] (Summary stats input) Computes a t confidence interval. A summary of results is stored in the stat.results variable. (See page 120.) For information on the effect of empty elements in a list, see “Empty (Void) Elements” on page 162. Output variable Description stat.CLower, stat.CUpper Confidence interval for an unknown population mean stat.x Sample mean of the data sequence from the normal random distribution stat.ME Margin of error stat.df Degrees of freedom stat.sx Sample standard deviation stat.n Length of the data sequence with sample mean tInterval_2Samp Catalog > tInterval_2Samp List1,List2[,Freq1[,Freq2[,CLevel[,Pooled]]]] (Data list input) tInterval_2Samp v1,sx1,n1,v2,sx2,n2[,CLevel[,Pooled]] (Summary stats input) Computes a two-sample t confidence interval. A summary of results is stored in the stat.results variable. (See page 120.) Pooled=1 pools variances; Pooled=0 does not pool variances. For information on the effect of empty elements in a list, see “Empty (Void) Elements” on page 162. Output variable Description stat.CLower, stat.CUpper Confidence interval containing confidence level probability of distribution stat.x1-x2 Sample means of the data sequences from the normal random distribution stat.ME Margin of error stat.df Degrees of freedom stat.x1, stat.x2 Sample means of the data sequences from the normal random distribution stat.sx1, stat.sx2 Sample standard deviations for List 1 and List 2 stat.n1, stat.n2 Number of samples in data sequences stat.sp The pooled standard deviation. Calculated when Pooled = YES 128 TI-Nspire™ CAS Reference Guide tmpCnv() Catalog > tmpCnv(Expr_¡tempUnit, _¡tempUnit2) expression _¡tempUnit2 Converts a temperature value specified by Expr from one unit to another. Valid temperature units are: _¡C _¡F _¡K _¡R Celsius Note: You can use the Catalog to select temperature units. Fahrenheit Kelvin Rankine To type ¡, select it from the Catalog symbols. /_. to type _ , press For example, 100_¡C converts to 212_¡F. To convert a temperature range, use @tmpCnv() instead. @tmpCnv() Catalog > @tmpCnv(Expr_¡tempUnit, _¡tempUnit2) expression _¡tempUnit2 Note: You can insert this function from the keyboard by typing deltaTmpCnv(...). Converts a temperature range (the difference between two temperature values) specified by Expr from one unit to another. Valid temperature units are: Note: You can use the Catalog to select temperature units. _¡C Celsius _¡F Fahrenheit _¡K Kelvin _¡R Rankine To enter ¡, select it from the Symbol Palette or type @d. To type _ , press /_. 1_¡C and 1_¡K have the same magnitude, as do 1_¡F and 1_¡R. However, 1_¡C is 9/5 as large as 1_¡F. For example, a 100_¡C range (from 0_¡C to 100_¡C) is equivalent to a 180_¡F range. To convert a particular temperature value instead of a range, use tmpCnv(). tPdf() tPdf(XVal,df) list Catalog > number if XVal is a number, list if XVal is a Computes the probability density function (pdf) for the Student-t distribution at a specified x value with specified degrees of freedom df. TI-Nspire™ CAS Reference Guide 129 trace() Catalog > trace(squareMatrix) expression Returns the trace (sum of all the elements on the main diagonal) of squareMatrix. Try Catalog > Try block1 Else block2 EndTry Executes block1 unless an error occurs. Program execution transfers to block2 if an error occurs in block1. System variable errCode contains the error code to allow the program to perform error recovery. For a list of error codes, see “Error codes and messages,” page 168. block1 and block2 can be either a single statement or a series of statements separated with the “:” character. Note for entering the example: In the Calculator application on the handheld, you can enter multi-line definitions by pressing @ · instead of at the end of each line. On the computer keyboard, hold down Alt and press Enter. Example 2 To see the commands Try, ClrErr, and PassErr in operation, enter the eigenvals() program shown at the right. Run the program by executing each of the following expressions. Note: See also ClrErr, page 19, and PassErr, page 88. 130 TI-Nspire™ CAS Reference Guide Define eigenvals(a,b)=Prgm © Program eigenvals(A,B) displays eigenvalues 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 a square matrix" ClrErr Else PassErr EndIf EndTry EndPrgm tTest tTest Catalog > m0,List[,Freq[,Hypoth]] (Data list input) tTest m0,x,sx,n,[Hypoth] (Summary stats input) Performs a hypothesis test for a single unknown population mean m when the population standard deviation s is unknown. A summary of results is stored in the stat.results variable. (See page 120.) Test H0: m = m0, against one of the following: For Ha: m < m0, set Hypoth<0 For Ha: m ƒ m0 (default), set Hypoth=0 For Ha: m > m0, set Hypoth>0 For information on the effect of empty elements in a list, see “Empty (Void) Elements” on page 162. Output variable Description stat.t (x N m0) / (stdev / sqrt(n)) stat.PVal Smallest level of significance at which the null hypothesis can be rejected stat.df Degrees of freedom stat.x Sample mean of the data sequence in List stat.sx Sample standard deviation of the data sequence stat.n Size of the sample tTest_2Samp Catalog > tTest_2Samp List1,List2[,Freq1[,Freq2[,Hypoth[,Pooled]]]] (Data list input) tTest_2Samp v1,sx1,n1,v2,sx2,n2[,Hypoth[,Pooled]] (Summary stats input) Computes a two-sample t test. A summary of results is stored in the stat.results variable. (See page 120.) 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 For information on the effect of empty elements in a list, see “Empty (Void) Elements” on page 162. Output variable Description stat.t Standard normal value computed for the difference of means TI-Nspire™ CAS Reference Guide 131 Output variable Description stat.PVal Smallest level of significance at which the null hypothesis can be rejected stat.df Degrees of freedom for the t-statistic stat.x1, stat.x2 Sample means of the data sequences in List 1 and List 2 stat.sx1, stat.sx2 Sample standard deviations of the data sequences in List 1 and List 2 stat.n1, stat.n2 Size of the samples stat.sp The pooled standard deviation. Calculated when Pooled=1. tvmFV() Catalog > tvmFV(N,I,PV,Pmt,[PpY],[CpY],[PmtAt]) value Financial function that calculates the future value of money. Note: Arguments used in the TVM functions are described in the table of TVM arguments, page 132. See also amortTbl(), page 7. tvmI() Catalog > tvmI(N,PV,Pmt,FV,[PpY],[CpY],[PmtAt]) value Financial function that calculates the interest rate per year. Note: Arguments used in the TVM functions are described in the table of TVM arguments, page 132. See also amortTbl(), page 7. tvmN() Catalog > tvmN(I,PV,Pmt,FV,[PpY],[CpY],[PmtAt]) value Financial function that calculates the number of payment periods. Note: Arguments used in the TVM functions are described in the table of TVM arguments, page 132. See also amortTbl(), page 7. tvmPmt() Catalog > tvmPmt(N,I,PV,FV,[PpY],[CpY],[PmtAt]) value Financial function that calculates the amount of each payment. Note: Arguments used in the TVM functions are described in the table of TVM arguments, page 132. See also amortTbl(), page 7. tvmPV() Catalog > tvmPV(N,I,Pmt,FV,[PpY],[CpY],[PmtAt]) value Financial function that calculates the present value. Note: Arguments used in the TVM functions are described in the table of TVM arguments, page 132. See also amortTbl(), page 7. TVM argument* Description Data type N Number of payment periods real number I Annual interest rate real number 132 TI-Nspire™ CAS Reference Guide TVM argument* Description Data type 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 finance solver. Financial functions, however, do not store their argument values or results to the TVM variables. TwoVar Catalog > TwoVar X, Y[, [Freq] [, Category, Include]] Calculates the TwoVar statistics. A summary of results is stored in the stat.results variable. (See page 120.) All the lists must have equal dimension except for Include. X and Y are lists of independent and dependent variables. Freq is an optional list of frequency values. Each element in Freq specifies the frequency of occurrence for each corresponding X and Y data point. The default value is 1. All elements must be integers | 0. Category is a list of numeric category codes for the corresponding X and Y data. Include is a list of one or more of the category codes. Only those data items whose category code is included in this list are included in the calculation. An empty (void) element in any of the lists X, Freq, or Category results in a void for the corresponding element of all those lists. An empty element in any of the lists X1 through X20 results in a void for the corresponding element of all those lists. For more information on empty elements, see page 162. Output variable Description stat.v Mean of x values stat.Gx Sum of x values stat.Gx2 Sum of x2 values stat.sx Sample standard deviation of x stat.sx Population standard deviation of x stat.n Number of data points stat.w Mean of y values stat.Gy Sum of y values stat.Gy2 Sum of y2 values stat.sy Sample standard deviation of y TI-Nspire™ CAS Reference Guide 133 Output variable Description stat.sy Population standard deviation of y stat.Gxy Sum of x·y values stat.r Correlation coefficient stat.MinX Minimum of x values stat.Q1X 1st Quartile of x stat.MedianX Median of x stat.Q3X 3rd Quartile of x stat.MaxX Maximum of x values stat.MinY Minimum of y values stat.Q1Y 1st Quartile of y stat.MedY Median of y stat.Q3Y 3rd Quartile of y stat.MaxY Maximum of y values 2 Sum of squares of deviations from the mean of x 2 Sum of squares of deviations from the mean of y stat.G(x-v) stat.G(y-w) U unitV() Catalog > unitV(Vector1) vector Returns either a row- or column-unit vector, depending on the form of Vector1. Vector1 must be either a single-row matrix or a single-column matrix. To see the entire result, press move the cursor. 134 TI-Nspire™ CAS Reference Guide £ and then use ¡ and ¢ to unLock Catalog > unLock Var1[, Var2] [, Var3] ... unLock Var. Unlocks the specified variables or variable group. Locked variables cannot be modified or deleted. See Lock, page 70, and getLockInfo(), page 53. V varPop() varPop(List[, freqList]) Catalog > expression Returns the population variance of List. Each freqList element counts the number of consecutive occurrences of the corresponding element in List. Note: List must contain at least two elements. If an element in either list is empty (void), that element is ignored, and the corresponding element in the other list is also ignored. For more information on empty elements, see page 162. varSamp() varSamp(List[, freqList]) Catalog > expression Returns the sample variance of List. Each freqList element counts the number of consecutive occurrences of the corresponding element in List. Note: List must contain at least two elements. If an element in either list is empty (void), that element is ignored, and the corresponding element in the other list is also ignored. For more information on empty elements, see page 162. varSamp(Matrix1[, freqMatrix]) matrix Returns a row vector containing the sample variance of each column in Matrix1. Each freqMatrix element counts the number of consecutive occurrences of the corresponding element in Matrix1. If an element in either matrix is empty (void), that element is ignored, and the corresponding element in the other matrix is also ignored. For more information on empty elements, see page 162. Note: Matrix1 must contain at least two rows. TI-Nspire™ CAS Reference Guide 135 W warnCodes() warnCodes(Expr1, StatusVar) Catalog > expression Evaluates expression Expr1, returns the result, and stores the codes of any generated warnings in the StatusVar list variable. If no warnings are generated, this function assigns StatusVar an empty list. Expr1 can be any valid TI-Nspire™ or TI-Nspire™ CAS math expression. You cannot use a command or assignment as Expr1. StatusVar must be a valid variable name. To see the entire result, press move the cursor. £ and then use ¡ and ¢ to For a list of warning codes and associated messages, see page 174. when() Catalog > when(Condition, trueResult [, falseResult][, unknownResult]) expression Returns trueResult, falseResult, or unknownResult, depending on whether Condition is true, false, or unknown. Returns the input if there are too few arguments to specify the appropriate result. Omit both falseResult and unknownResult to make an expression defined only in the region where Condition is true. Use an undef falseResult to define an expression that graphs only on an interval. when() is helpful for defining recursive functions. While Catalog > While Condition Block EndWhile Executes the statements in Block as long as Condition is true. Block can be either a single statement or a sequence of statements separated with the “:” character. Note for entering the example: In the Calculator application on the handheld, you can enter multi-line definitions by pressing @ · instead of at the end of each line. On the computer keyboard, hold down Alt and press Enter. 136 TI-Nspire™ CAS Reference Guide X xor Catalog > BooleanExpr1 xor BooleanExpr2 returns Boolean expression BooleanList1 xor BooleanList2 returns Boolean list BooleanMatrix1 xor BooleanMatrix2 returns Boolean matrix Returns true if BooleanExpr1 is true and BooleanExpr2 is false, or vice versa. Returns false if both arguments are true or if both are false. Returns a simplified Boolean expression if either of the arguments cannot be resolved to true or false. Note: See or, page 87. Integer1 xor Integer2 integer In Hex base mode: Compares two real integers bit-by-bit using an xor operation. Internally, both integers are converted to signed, 64-bit binary numbers. When corresponding bits are compared, the result is 1 if either bit (but not both) is 1; the result is 0 if both bits are 0 or both bits are 1. The returned value represents the bit results, and is displayed according to the Base mode. You can enter the integers in any number base. For a binary or hexadecimal entry, you must use the 0b or 0h prefix, respectively. Without a prefix, integers are treated as decimal (base 10). Important: Zero, not the letter O. In Bin base mode: Note: A binary entry can have up to 64 digits (not counting the 0b prefix). A hexadecimal entry can have up to 16 digits. If you enter a decimal integer that is too large for a signed, 64-bit binary form, a symmetric modulo operation is used to bring the value into the appropriate range. For more information, see 4Base2, page 14. Note: See or, page 87. Z zeros() zeros(Expr, Var) Catalog > list zeros(Expr, Var=Guess) list Returns a list of candidate real values of Var that make Expr=0. zeros() does this by computing exp4list(solve(Expr=0,Var),Var). For some purposes, the result form for zeros() is more convenient than that of solve(). However, the result form of zeros() cannot express implicit solutions, solutions that require inequalities, or solutions that do not involve Var. Note: See also cSolve(), cZeros(), and solve(). TI-Nspire™ CAS Reference Guide 137 zeros() Catalog > zeros({Expr1, Expr2}, {VarOrGuess1, VarOrGuess2 [, … ]}) matrix Returns candidate real zeros of the simultaneous algebraic expressions, where each VarOrGuess specifies an unknown whose value you seek. Optionally, you can specify an initial guess for a variable. Each VarOrGuess must have the form: variable – or – variable = real or non-real number For example, x is valid and so is x=3. If all of the expressions are polynomials and if you do NOT specify any initial guesses, zeros() uses the lexical Gröbner/Buchberger elimination method to attempt to determine all real zeros. For example, suppose you have a circle of radius r at the origin and another circle of radius r centered where the first circle crosses the positive x-axis. Use zeros() to find the intersections. As illustrated by r in the example to the right, simultaneous polynomial expressions can have extra variables that have no values, but represent given numeric values that could be substituted later. Each row of the resulting matrix represents an alternate zero, with the components ordered the same as the varOrGuess list. To extract a row, index the matrix by [row]. Extract row 2: You can also (or instead) include unknowns that do not appear in the expressions. For example, you can include z as an unknown to extend the previous example to two parallel intersecting cylinders of radius r. The cylinder zeros illustrate how families of zeros might contain arbitrary constants in the form ck, where k is an integer suffix from 1 through 255. For polynomial systems, computation time or memory exhaustion may depend strongly on the order in which you list unknowns. If your initial choice exhausts memory or your patience, try rearranging the variables in the expressions and/or varOrGuess list. If you do not include any guesses and if any expression is nonpolynomial in any variable but all expressions are linear in the unknowns, zeros() uses Gaussian elimination to attempt to determine all real zeros. 138 TI-Nspire™ CAS Reference Guide zeros() Catalog > If a system is neither polynomial in all of its variables nor linear in its unknowns, zeros() determines at most one zero using an approximate iterative method. To do so, the number of unknowns must equal the number of expressions, and all other variables in the expressions must simplify to numbers. Each unknown starts at its guessed value if there is one; otherwise, it starts at 0.0. Use guesses to seek additional zeros one by one. For convergence, a guess may have to be rather close to a zero. zInterval zInterval Catalog > s,List[,Freq[,CLevel]] (Data list input) zInterval s,v,n [,CLevel] (Summary stats input) Computes a z confidence interval. A summary of results is stored in the stat.results variable. (See page 120.) For information on the effect of empty elements in a list, see “Empty (Void) Elements” on page 162. Output variable Description stat.CLower, stat.CUpper Confidence interval for an unknown population mean stat.x Sample mean of the data sequence from the normal random distribution stat.ME Margin of error stat.sx Sample standard deviation stat.n Length of the data sequence with sample mean stat.s Known population standard deviation for data sequence List zInterval_1Prop Catalog > zInterval_1Prop x,n [,CLevel] Computes a one-proportion z confidence interval. A summary of results is stored in the stat.results variable. (See page 120.) x is a non-negative integer. For information on the effect of empty elements in a list, see “Empty (Void) Elements” on page 162. Output variable Description stat.CLower, stat.CUpper Confidence interval containing confidence level probability of distribution stat.Ç The calculated proportion of successes stat.ME Margin of error TI-Nspire™ CAS Reference Guide 139 Output variable Description stat.n Number of samples in data sequence zInterval_2Prop Catalog > zInterval_2Prop x1,n1,x2,n2[,CLevel] Computes a two-proportion z confidence interval. A summary of results is stored in the stat.results variable. (See page 120.) x1 and x2 are non-negative integers. For information on the effect of empty elements in a list, see “Empty (Void) Elements” on page 162. Output variable Description stat.CLower, stat.CUpper Confidence interval containing confidence level probability of distribution stat.Ç Diff The calculated difference between proportions stat.ME Margin of error 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 zInterval_2Samp Catalog > s1,s2 ,List1,List2[,Freq1[,Freq2,[CLevel]]] (Data list input) zInterval_2Samp s1,s2,v1,n1,v2,n2[,CLevel] (Summary stats input) Computes a two-sample z confidence interval. A summary of results is stored in the stat.results variable. (See page 120.) For information on the effect of empty elements in a list, see “Empty (Void) Elements” on page 162. Output variable Description stat.CLower, stat.CUpper Confidence interval containing confidence level probability of distribution stat.x1-x2 Sample means of the data sequences from the normal random distribution stat.ME Margin of error stat.x1, stat.x2 Sample means of the data sequences from the normal random distribution stat.sx1, stat.sx2 Sample standard deviations for List 1 and List 2 stat.n1, stat.n2 Number of samples in data sequences stat.r1, stat.r2 Known population standard deviations for data sequence List 1 and List 2 140 TI-Nspire™ CAS Reference Guide zTest zTest Catalog > m0,s,List,[Freq[,Hypoth]] (Data list input) zTest m0,s,v,n[,Hypoth] (Summary stats input) Performs a z test with frequency freqlist. A summary of results is stored in the stat.results variable. (See page 120.) Test H0: m = m0, against one of the following: For Ha: m < m0, set Hypoth<0 For Ha: m ƒ m0 (default), set Hypoth=0 For Ha: m > m0, set Hypoth>0 For information on the effect of empty elements in a list, see “Empty (Void) Elements” on page 162. Output variable Description stat.z (x N m0) / (s / sqrt(n)) stat.P Value Least probability at which the null hypothesis can be rejected stat.x Sample mean of the data sequence in List stat.sx Sample standard deviation of the data sequence. Only returned for Data input. stat.n Size of the sample zTest_1Prop Catalog > zTest_1Prop p0,x,n[,Hypoth] Computes a one-proportion z test. A summary of results is stored in the stat.results variable. (See page 120.) 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 For information on the effect of empty elements in a list, see “Empty (Void) Elements” on page 162. Output variable Description stat.p0 Hypothesized population proportion stat.z Standard normal value computed for the proportion stat.PVal Smallest level of significance at which the null hypothesis can be rejected stat.Ç Estimated sample proportion stat.n Size of the sample TI-Nspire™ CAS Reference Guide 141 zTest_2Prop Catalog > zTest_2Prop x1,n1,x2,n2[,Hypoth] Computes a two-proportion z test. A summary of results is stored in the stat.results variable. (See page 120.) 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 For information on the effect of empty elements in a list, see “Empty (Void) Elements” on page 162. Output variable Description stat.z Standard normal value computed for the difference of proportions stat.PVal Smallest level of significance at which the null hypothesis can be rejected 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 and 2 zTest_2Samp zTest_2Samp Catalog > s1,s2 ,List1,List2[,Freq1[,Freq2[,Hypoth]]] (Data list input) zTest_2Samp s1,s2,v1,n1,v2,n2[,Hypoth] (Summary stats input) Computes a two-sample z test. A summary of results is stored in the stat.results variable. (See page 120.) 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 For information on the effect of empty elements in a list, see “Empty (Void) Elements” on page 162. Output variable Description stat.z Standard normal value computed for the difference of means stat.PVal Smallest level of significance at which the null hypothesis can be rejected stat.x1, stat.x2 Sample means of the data sequences in List1 and List2 stat.sx1, stat.sx2 Sample standard deviations of the data sequences in List1 and List2 stat.n1, stat.n2 Size of the samples 142 TI-Nspire™ CAS Reference Guide Symbols + key + (add) Expr1 + Expr2 expression Returns the sum of the two arguments. List1 + List2 list Matrix1 + Matrix2 matrix Returns a list (or matrix) containing the sums of corresponding elements in List1 and List2 (or Matrix1 and Matrix2). Dimensions of the arguments must be equal. Expr + List1 list List1 + Expr list Returns a list containing the sums of Expr and each element in List1. Expr + Matrix1 matrix Matrix1 + Expr matrix Returns a matrix with Expr added to each element on the diagonal of Matrix1. Matrix1 must be square. Note: Use .+ (dot plus) to add an expression to each element. - key N(subtract) Expr1 N Expr2 expression Returns Expr1 minus Expr2. List1 N List2 list Matrix1 N Matrix2 matrix Subtracts each element in List2 (or Matrix2) from the corresponding element in List1 (or Matrix1), and returns the results. Dimensions of the arguments must be equal. Expr N List1 list List1 N Expr list Subtracts each List1 element from Expr or subtracts Expr from each List1 element, and returns a list of the results. TI-Nspire™ CAS Reference Guide 143 N(subtract) - key Expr N Matrix1 matrix Matrix1 N Expr matrix Expr N Matrix1 returns a matrix of Expr times the identity matrix minus Matrix1. Matrix1 must be square. Matrix1 N Expr returns a matrix of Expr times the identity matrix subtracted from Matrix1. Matrix1 must be square. Note: Use .N (dot minus) to subtract an expression from each element. ·(multiply) r key Expr1 ·Expr2 expression Returns the product of the two arguments. List1·List2 list Returns a list containing the products of the corresponding elements in List1 and List2. Dimensions of the lists must be equal. Matrix1 ·Matrix2 matrix Returns the matrix product of Matrix1 and Matrix2. The number of columns in Matrix1 must equal the number of rows in Matrix2. Expr ·List1 list List1 ·Expr list Returns a list containing the products of Expr and each element in List1. Expr ·Matrix1 matrix Matrix1 ·Expr matrix Returns a matrix containing the products of Expr and each element in Matrix1. Note: Use .·(dot multiply) to multiply an expression by each element. à (divide) Expr1 à Expr2 expression Returns the quotient of Expr1 divided by Expr2. Note: See also Fraction template, page 1. 144 TI-Nspire™ CAS Reference Guide p key p key à (divide) List1 à List2 list Returns a list containing the quotients of List1 divided by List2. Dimensions of the lists must be equal. Expr à List1 list List1 à Expr list Returns a list containing the quotients of Expr divided by List1 or List1 divided by Expr. Matrix1 à Expr matrix Returns a matrix containing the quotients of Matrix1àExpr. Note: Use . / (dot divide) to divide an expression by each element. l key ^ (power) Expr1 ^ Expr2 expression List1 ^ List2 list Returns the first argument raised to the power of the second argument. Note: See also Exponent template, page 1. For a list, returns the elements in List1 raised to the power of the corresponding elements in List2. In the real domain, fractional powers that have reduced exponents with odd denominators use the real branch versus the principal branch for complex mode. Expr ^ List1 list Returns Expr raised to the power of the elements in List1. List1 ^ Expr list Returns the elements in List1 raised to the power of Expr. squareMatrix1 ^ integer matrix Returns squareMatrix1 raised to the integer power. squareMatrix1 must be a square matrix. If integer = L1, computes the inverse matrix. If integer < L1, computes the inverse matrix to an appropriate positive power. TI-Nspire™ CAS Reference Guide 145 x2 (square) q key Expr12 expression Returns the square of the argument. List12 list Returns a list containing the squares of the elements in List1. squareMatrix12 matrix Returns the matrix square of squareMatrix1. This is not the same as calculating the square of each element. Use .^2 to calculate the square of each element. .+ (dot add) ^+ keys Matrix1 .+ Matrix2 matrix Expr .+ Matrix1 matrix Matrix1 .+ Matrix2 returns a matrix that is the sum of each pair of corresponding elements in Matrix1 and Matrix2. Expr .+ Matrix1 returns a matrix that is the sum of Expr and each element in Matrix1. .. (dot subt.) ^- keys Matrix1 .N Matrix2 matrix Expr .NMatrix1 matrix Matrix1 .NMatrix2 returns a matrix that is the difference between each pair of corresponding elements in Matrix1 and Matrix2. Expr .NMatrix1 returns a matrix that is the difference of Expr and each element in Matrix1. .·(dot mult.) Matrix1 .· Matrix2 matrix Expr .·Matrix1 matrix Matrix1 .· Matrix2 returns a matrix that is the product of each pair of corresponding elements in Matrix1 and Matrix2. Expr .· Matrix1 returns a matrix containing the products of Expr and each element in Matrix1. 146 TI-Nspire™ CAS Reference Guide ^r keys ^p keys . / (dot divide) Matrix1 . / Matrix2 matrix Expr . / Matrix1 matrix Matrix1 ./ Matrix2 returns a matrix that is the quotient of each pair of corresponding elements in Matrix1 and Matrix2. Expr ./ Matrix1 returns a matrix that is the quotient of Expr and each element in Matrix1. ^l keys .^ (dot power) Matrix1 .^ Matrix2 matrix Expr . ^ Matrix1 matrix Matrix1 .^ Matrix2 returns a matrix where each element in Matrix2 is the exponent for the corresponding element in Matrix1. Expr .^ Matrix1 returns a matrix where each element in Matrix1 is the exponent for Expr. v key L(negate) LExpr1 expression LLList1 list LMatrix1 matrix Returns the negation of the argument. For a list or matrix, returns all the elements negated. If the argument is a binary or hexadecimal integer, the negation gives In Bin base mode: the two’s complement. Important: Zero, not the letter O To see the entire result, press move the cursor. /k keys % (percent) Expr1 % expression List1 % list Matrix1 % matrix £ and then use ¡ and ¢ to Press Ctrl+Enter evaluate: /· (Macintosh®: “+Enter) to For a list or matrix, returns a list or matrix with each element divided Press Ctrl+Enter by 100. evaluate: /· (Macintosh®: “+Enter) to Returns TI-Nspire™ CAS Reference Guide 147 = key = (equal) Expr1 = Expr2 Boolean expression List1 = List2 Boolean list Example function that uses math test symbols: =, ƒ, <, {, >, | Matrix1 = Matrix2 Boolean matrix Returns true if Expr1 is determined to be equal to Expr2. Returns false if Expr1 is determined to not be equal to Expr2. Anything else returns a simplified form of the equation. For lists and matrices, returns comparisons element by element. Note for entering the example: In the Calculator application on the handheld, you can enter multi-line definitions by pressing @ · instead of at the end of each line. On the computer keyboard, hold down Alt and press Enter. Result of graphing g(x) /= keys ƒ (not equal) Expr1 ƒ Expr2 Boolean expression See “=” (equal) example. List1 ƒ List2 Boolean list Matrix1 ƒ Matrix2 Boolean matrix Returns true if Expr1 is determined to be not equal to Expr2. Returns false if Expr1 is determined to be equal to Expr2. Anything else returns a simplified form of the equation. For lists and matrices, returns comparisons element by element. Note: You can insert this operator from the keyboard by typing /= /= keys < (less than) Expr1 < Expr2 Boolean expression List1 < List2 Boolean list Matrix1 < Matrix2 Boolean matrix Returns true if Expr1 is determined to be less than Expr2. Returns false if Expr1 is determined to be greater than or equal to Expr2. Anything else returns a simplified form of the equation. For lists and matrices, returns comparisons element by element. 148 TI-Nspire™ CAS Reference Guide See “=” (equal) example. /= keys { (less or equal) Expr1 { Expr2 Boolean expression See “=” (equal) example. List1 { List2 Boolean list Matrix1 { Matrix2 Boolean matrix Returns true if Expr1 is determined to be less than or equal to Expr2. Returns false if Expr1 is determined to be greater than Expr2. Anything else returns a simplified form of the equation. For lists and matrices, returns comparisons element by element. Note: You can insert this operator from the keyboard by typing <= /= keys > (greater than) Expr1 > Expr2 Boolean expression See “=” (equal) example. List1 > List2 Boolean list Matrix1 > Matrix2 Boolean matrix Returns true if Expr1 is determined to be greater than Expr2. Returns false if Expr1 is determined to be less than or equal to Expr2. Anything else returns a simplified form of the equation. For lists and matrices, returns comparisons element by element. /= keys | (greater or equal) Expr1 | Expr2 Boolean expression See “=” (equal) example. List1 | List2 Boolean list Matrix1 | Matrix2 Boolean matrix Returns true if Expr1 is determined to be greater than or equal to Expr2. Returns false if Expr1 is determined to be less than Expr2. Anything else returns a simplified form of the equation. For lists and matrices, returns comparisons element by element. Note: You can insert this operator from the keyboard by typing >= (logical implication) /= keys BooleanExpr1 BooleanExpr2 returns Boolean expression BooleanList1 BooleanList2 returns Boolean list BooleanMatrix1 BooleanMatrix2 returns Boolean matrix Integer1 Integer2 returns Integer Evaluates the expression not <argument1> or <argument2> and returns true, false, or a simplified form of the equation. For lists and matrices, returns comparisons element by element. Note: You can insert this operator from the keyboard by typing => TI-Nspire™ CAS Reference Guide 149 ⇔ (logical double implication, XNOR) /= keys BooleanExpr1 ⇔ BooleanExpr2 returns Boolean expression BooleanList1 ⇔ BooleanList2 returns Boolean list BooleanMatrix1 ⇔ BooleanMatrix2 returns Boolean matrix Integer1 ⇔ Integer2 returns Integer Returns the negation of an XOR Boolean operation on the two arguments. Returns true, false, or a simplified form of the equation. For lists and matrices, returns comparisons element by element. Note: You can insert this operator from the keyboard by typing <=> º key ! (factorial) Expr1! expression List1! list Matrix1! matrix Returns the factorial of the argument. For a list or matrix, returns a list or matrix of factorials of the elements. /k keys & (append) String1 & String2 string Returns a text string that is String2 appended to String1. d() (derivative) Catalog > expression d(List1, Var[, Order]) list d(Expr1, Var[, Order]) d(Matrix1,Var[, Order]) matrix Returns the first derivative of the first argument with respect to variable Var. Order, if included, must be an integer. If the order is less than zero, the result will be an anti-derivative. Note: You can insert this function from the keyboard by typing derivative(...). d() does not follow the normal evaluation mechanism of fully simplifying its arguments and then applying the function definition to these fully simplified arguments. Instead, d() performs the following steps: 1. Simplify the second argument only to the extent that it does not lead to a non-variable. 2. Simplify the first argument only to the extent that it does recall any stored value for the variable determined by step 1. 3. Determine the symbolic derivative of the result of step 2 with respect to the variable from step 1. If the variable from step 1 has a stored value or a value specified by the constraint (“|”) operator, substitute that value into the result from step 3. Note: See also First derivative, page 5; Second derivative, page 5; or Nth derivative, page 5. 150 TI-Nspire™ CAS Reference Guide ‰() (integral) Catalog > ‰(Expr1, Var[, Lower, Upper]) expression ‰(Expr1, Var[, Constant]) expression Returns the integral of Expr1 with respect to the variable Var from Lower to Upper. Note: See also Definite or Indefinite integral template, page 5. Note: You can insert this function from the keyboard by typing integral(...). If Lower and Upper are omitted, returns an anti-derivative. A symbolic constant of integration is omitted unless you provide the Constant argument. Equally valid anti-derivatives might differ by a numeric constant. Such a constant might be disguised—particularly when an anti-derivative contains logarithms or inverse trigonometric functions. Moreover, piecewise constant expressions are sometimes added to make an anti-derivative valid over a larger interval than the usual formula. ‰() returns itself for pieces of Expr1 that it cannot determine as an explicit finite combination of its built-in functions and operators. When you provide Lower and Upper, an attempt is made to locate any discontinuities or discontinuous derivatives in the interval Lower < Var < Upper and to subdivide the interval at those places. For the Auto setting of the Auto or Approximate mode, numerical integration is used where applicable when an antiderivative or a limit cannot be determined. For the Approximate setting, numerical integration is tried first, if applicable. Anti-derivatives are sought only where such numerical integration is inapplicable or fails. Press Ctrl+Enter evaluate: /· (Macintosh®: “+Enter) to ‰() can be nested to do multiple integrals. Integration limits can depend on integration variables outside them. Note: See also nInt(), page 82. TI-Nspire™ CAS Reference Guide 151 ‡() (square root) /q keys ‡ (Expr1) expression ‡ (List1) list Returns the square root of the argument. For a list, returns the square roots of all the elements in List1. Note: You can insert this function from the keyboard by typing sqrt(...) Note: See also Square root template, page 1. Π() (prodSeq) Π(Expr1, Var, Low, High) expression Note: You can insert this function from the keyboard by typing prodSeq(...). Evaluates Expr1 for each value of Var from Low to High, and returns the product of the results. Note: See also Product template (Π), page 4. Π(Expr1, Var, Low, LowN1) 1 Π(Expr1, Var, Low, High) 1/Π(Expr1, Var, High+1, LowN1) if High < LowN1 The product formulas used are derived from the following reference: Ronald L. Graham, Donald E. Knuth, and Oren Patashnik. Concrete Mathematics: A Foundation for Computer Science. Reading, Massachusetts: Addison-Wesley, 1994. 152 TI-Nspire™ CAS Reference Guide Catalog > G() (sumSeq) Catalog > G(Expr1, Var, Low, High) expression Note: You can insert this function from the keyboard by typing sumSeq(...). Evaluates Expr1 for each value of Var from Low to High, and returns the sum of the results. Note: See also Sum template, page 4. G(Expr1, Var, Low, LowN1) 0 G(Expr1, Var, Low, High) MG(Expr1, Var, High+1, LowN1) if High < LowN1 The summation formulas used are derived from the following reference: Ronald L. Graham, Donald E. Knuth, and Oren Patashnik. Concrete Mathematics: A Foundation for Computer Science. Reading, Massachusetts: Addison-Wesley, 1994. TI-Nspire™ CAS Reference Guide 153 GInt() Catalog > GInt(NPmt1, NPmt2, N, I, PV ,[Pmt], [FV], [PpY], [CpY], [PmtAt], [roundValue]) value GInt(NPmt1,NPmt2,amortTable) value Amortization function that calculates the sum of the interest during a specified range of payments. NPmt1 and NPmt2 define the start and end boundaries of the payment range. N, I, PV, Pmt, FV, PpY, CpY, and PmtAt are described in the table of TVM arguments, page 132. • • • If you omit Pmt, it defaults to Pmt=tvmPmt(N,I,PV,FV,PpY,CpY,PmtAt). If you omit FV, it defaults to FV=0. The defaults for PpY, CpY, and PmtAt are the same as for the TVM functions. roundValue specifies the number of decimal places for rounding. Default=2. GInt(NPmt1,NPmt2,amortTable) calculates the sum of the interest based on amortization table amortTable. The amortTable argument must be a matrix in the form described under amortTbl(), page 7. Note: See also GPrn(), below, and Bal(), page 13. GPrn() Catalog > GPrn(NPmt1, NPmt2, N, I, PV, [Pmt], [FV], [PpY], [CpY], [PmtAt], [roundValue]) value GPrn(NPmt1,NPmt2,amortTable) value Amortization function that calculates the sum of the principal during a specified range of payments. NPmt1 and NPmt2 define the start and end boundaries of the payment range. N, I, PV, Pmt, FV, PpY, CpY, and PmtAt are described in the table of TVM arguments, page 132. • • • If you omit Pmt, it defaults to Pmt=tvmPmt(N,I,PV,FV,PpY,CpY,PmtAt). If you omit FV, it defaults to FV=0. The defaults for PpY, CpY, and PmtAt are the same as for the TVM functions. roundValue specifies the number of decimal places for rounding. Default=2. GPrn(NPmt1,NPmt2,amortTable) calculates the sum of the principal paid based on amortization table amortTable. The amortTable argument must be a matrix in the form described under amortTbl(), page 7. Note: See also GInt(), above, and Bal(), page 13. 154 TI-Nspire™ CAS Reference Guide /k keys # (indirection) # varNameString Refers to the variable whose name is varNameString. This lets you use strings to create variable names from within a function. Creates or refers to the variable xyz . Returns the value of the variable (r) whose name is stored in variable s1. i key E (scientific notation) mantissaEexponent Enters a number in scientific notation. The number is interpreted as mantissa × 10exponent. Hint: If you want to enter a power of 10 without causing a decimal value result, use 10^integer. Note: You can insert this operator from the computer keyboard by typing @E. for example, type 2.3@E4 to enter 2.3E4. g ¹ key (gradian) Expr1g expression List1g list Matrix1g matrix In Degree, Gradian or Radian mode: This function gives you a way to specify a gradian angle while in the Degree or Radian mode. In Radian angle mode, multiplies Expr1 by p/200. In Degree angle mode, multiplies Expr1 by g/100. In Gradian mode, returns Expr1 unchanged. Note: You can insert this symbol from the computer keyboard by typing @g. ¹ key R(radian) Expr1R expression List1R list Matrix1R matrix In Degree, Gradian or Radian angle mode: This function gives you a way to specify a radian angle while in Degree or Gradian mode. In Degree angle mode, multiplies the argument by 180/p. In Radian angle mode, returns the argument unchanged. In Gradian mode, multiplies the argument by 200/p. Hint: Use R if you want to force radians in a function definition regardless of the mode that prevails when the function is used. Note: You can insert this symbol from the computer keyboard by typing @r. TI-Nspire™ CAS Reference Guide 155 ¹ key ¡ (degree) Expr1¡ expression List1¡ list Matrix1¡ matrix In Degree, Gradian or Radian angle mode: This function gives you a way to specify a degree angle while in Gradian or Radian mode. In Radian angle mode, multiplies the argument by p/180. In Radian angle mode: In Degree angle mode, returns the argument unchanged. Press Ctrl+Enter evaluate: /· (Macintosh®: “+Enter) to In Gradian angle mode, multiplies the argument by 10/9. Note: You can insert this symbol from the computer keyboard by typing @d. /k keys ¡, ', '' (degree/minute/second) dd¡mm'ss.ss'' expression dd In Degree angle mode: A positive or negative number mm A non-negative number ss.ss A non-negative number Returns dd+(mm/60)+(ss.ss/3600). This base-60 entry format lets you: • • Enter an angle in degrees/minutes/seconds without regard to the current angle mode. Enter time as hours/minutes/seconds. Note: Follow ss.ss with two apostrophes (''), not a quote symbol ("). /k keys ± (angle) [Radius,±q_Angle] vector (polar input) In Radian mode and vector format set to: rectangular [Radius,±q_Angle,Z_Coordinate] vector (cylindrical input) [Radius,±q_Angle,±q_Angle] vector (spherical input) cylindrical Returns coordinates as a vector depending on the Vector Format mode setting: rectangular, cylindrical, or spherical. Note: You can insert this symbol from the computer keyboard by typing @<. spherical 156 TI-Nspire™ CAS Reference Guide /k keys ± (angle) (Magnitude ± Angle) complexValue (polar input) In Radian angle mode and Rectangular complex format: Enters a complex value in (r±q) polar form. The Angle is interpreted according to the current Angle mode setting. Press Ctrl+Enter evaluate: /· (Macintosh®: “+Enter) to º key ' (prime) variable ' variable '' Enters a prime symbol in a differential equation. A single prime symbol denotes a 1st-order differential equation, two prime symbols denote a 2nd-order, and so on. _ (underscore as an empty element) See “Empty (Void) Elements” , page 162. /_ keys _ (underscore as unit designator) Expr_Unit Designates the units for an Expr. All unit names must begin with an underscore. Note: You can find the conversion symbol, 4, in the Catalog. You can use pre-defined units or create your own units. For a list of Click pre-defined units, open the Catalog and display the Unit Conversions tab. You can select unit names from the Catalog or type the unit names directly. Variable_ , and then click Math Operators. Assuming z is undefined: When Variable has no value, it is treated as though it represents a complex number. By default, without the _ , the variable is treated as real. If Variable has a value, the _ is ignored and Variable retains its original data type. Note: You can store a complex number to a variable without using _ . However, for best results in calculations such as cSolve() and cZeros(), the _ is recommended. TI-Nspire™ CAS Reference Guide 157 /k keys 4 (convert) Expr_Unit1 4 _Unit2 Expr_Unit2 Converts an expression from one unit to another. The _ underscore character designates the units. The units must be in the same category, such as Length or Area. For a list of pre-defined units, open the Catalog and display the Unit Conversions tab: • • You can select a unit name from the list. You can select the conversion operator, 4, from the top of the list. You can also type unit names manually. To type “_” when typing unit names on the handheld, press /_. Note: To convert temperature units, use tmpCnv() and @tmpCnv(). The 4 conversion operator does not handle temperature units. 10^() Catalog > 10^ (Expr1) expression 10^ (List1) list Returns 10 raised to the power of the argument. For a list, returns 10 raised to the power of the elements in List1. 10^(squareMatrix1) squareMatrix Returns 10 raised to the power of squareMatrix1. This is not the same as calculating 10 raised to the power of each element. For information about the calculation method, refer to cos(). squareMatrix1 must be diagonalizable. The result always contains floating-point numbers. ^/(reciprocal) Expr1 ^/ expression List1 ^/ list Returns the reciprocal of the argument. For a list, returns the reciprocals of the elements in List1. squareMatrix1 ^/ squareMatrix Returns the inverse of squareMatrix1. squareMatrix1 must be a non-singular square matrix. 158 TI-Nspire™ CAS Reference Guide Catalog > /k keys | (constraint operator) Expr | BooleanExpr1 [and BooleanExpr2]... Expr | BooleanExpr1 [or BooleanExpr2]... The constraint (“|”) symbol serves as a binary operator. The operand to the left of | is an expression. The operand to the right of | specifies one or more relations that are intended to affect the simplification of the expression. Multiple relations after | must be joined by logical “and” or “or” operators. The constraint operator provides three basic types of functionality: • • • Substitutions Interval constraints Exclusions Substitutions are in the form of an equality, such as x=3 or y=sin(x). To be most effective, the left side should be a simple variable. Expr | Variable = value will substitute value for every occurrence of Variable in Expr. Interval constraints take the form of one or more inequalities joined by logical “and” or “or” operators. Interval constraints also permit simplification that otherwise might be invalid or not computable. Exclusions use the “not equals” (/= or ƒ) relational operator to exclude a specific value from consideration. They are used primarily to exclude an exact solution when using cSolve(), cZeros(), fMax(), fMin(), solve(), zeros(), and so on. TI-Nspire™ CAS Reference Guide 159 /h key & (store) Expr & Var List & Var Matrix & Var Expr & Function(Param1,...) List & Function(Param1,...) Matrix & Function(Param1,...) If the variable Var does not exist, creates it and initializes it to Expr, List, or Matrix. If the variable Var already exists and is not locked or protected, replaces its contents with Expr, List, or Matrix. Hint: If you plan to do symbolic computations using undefined variables, avoid storing anything into commonly used, one-letter variables such as a, b, c, x, y, z, and so on. Note: You can insert this operator from the keyboard by typing =: as a shortcut. For example, type pi/4 =: myvar. /t keys := (assign) Var := Expr Var := List Var := Matrix Function(Param1,...) := Expr Function(Param1,...) := List Function(Param1,...) := Matrix If variable Var does not exist, creates Var and initializes it to Expr, List, or Matrix. If Var already exists and is not locked or protected, replaces its contents with Expr, List, or Matrix. Hint: If you plan to do symbolic computations using undefined variables, avoid storing anything into commonly used, one-letter variables such as a, b, c, x, y, z, and so on. /k keys © (comment) © [text] © processes text as a comment line, allowing you to annotate functions and programs that you create. © can be at the beginning or anywhere in the line. Everything to the right of ©, to the end of the line, is the comment. Note for entering the example: In the Calculator application on the handheld, you can enter multi-line definitions by pressing @ · instead of at the end of each line. On the computer keyboard, hold down Alt and press Enter. 160 TI-Nspire™ CAS Reference Guide 0B keys, 0H keys 0b, 0h 0b binaryNumber 0h hexadecimalNumber In Dec base mode: Denotes a binary or hexadecimal number, respectively. To enter a binary or hex number, you must enter the 0b or 0h prefix regardless of In Bin base mode: the Base mode. Without a prefix, a number is treated as decimal (base 10). Results are displayed according to the Base mode. In Hex base mode: TI-Nspire™ CAS Reference Guide 161 Empty (Void) Elements When analyzing real-world data, you might not always have a complete data set. TI-Nspire™ CAS Software allows empty, or void, data elements so you can proceed with the nearly 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 & Spreadsheet chapter, 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 35, and isVoid(), page 61. Note: To enter an empty element manually in a math expression, type “_” or the keyword void. The keyword void is automatically converted to a “_” symbol when the expression is evaluated. To type “_” on the handheld, press / _. Calculations involving void elements The majority of calculations involving a void input will produce a void result. See special cases below. List arguments containing void elements The following functions and commands ignore (skip) void elements found in list arguments. count, countIf, cumulativeSum, freqTable4list, frequency, max, mean, median, product, stDevPop, stDevSamp, sum, sumIf, varPop, and varSamp, as well as regression calculations, OneVar, TwoVar, and FiveNumSummary statistics, confidence intervals, and stat tests SortA and SortD move all void elements within the first argument to the bottom. 162 TI-Nspire™ CAS Reference Guide List arguments containing void elements(continued) In regressions, a void in an X or Y list introduces a void for the corresponding element of the residual. An omitted category in regressions introduces a void for the corresponding element of the residual. A frequency of 0 in regressions introduces a void for the corresponding element of the residual. TI-Nspire™ CAS Reference Guide 163 Shortcuts for Entering Math Expressions Shortcuts let you enter elements of math expressions by typing instead of using the Catalog or Symbol Palette. For example, to enter the expression ‡6, you can type sqrt(6) on the entry line. When you press ·, the expression sqrt(6) is changed to ‡6. Some 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) => ⇔ (logical double implication, XNOR) <=> & (store operator) =: | | (absolute value) abs(...) ‡() sqrt(...) d() derivative(...) ‰() integral(...) G() (Sum template) sumSeq(...) Π() (Product template) prodSeq(...) sin/(), cos/(), ... arcsin(...), arccos(...), ... @List() deltaList(...) @tmpCnv() deltaTmpCnv(...) From the Computer Keyboard To enter this: Type this shortcut: c1, c2, @c1, @c2, ... n1, n2, ... (constants) ... (integer constants) i (imaginary constant) 164 @n1, @n2, ... @i TI-Nspire™ CAS Reference Guide To enter this: Type this shortcut: e (natural log base e) @e E (scientific notation) @E T @t (transpose) R (radians) @r ¡ (degrees) @d g @g (gradians) ± (angle) @< 4 (conversion) @> 4Decimal, 4approxFraction(), and so on. @>Decimal, @>approxFraction(), and so on. TI-Nspire™ CAS Reference Guide 165 EOS™ (Equation Operating System) Hierarchy This section describes the Equation Operating System (EOS™) that is used by the TI-Nspire™ CAS math and science learning technology. Numbers, variables, and functions are entered in a simple, straightforward sequence. EOS™ software evaluates expressions and equations using parenthetical grouping and according to the priorities described below. Order of Evaluation Level Operator 1 Parentheses ( ), brackets [ ], braces { } 2 Indirection (#) 3 Function calls 4 Post operators: degrees-minutes-seconds (¡,',"), factorial (!), percentage (%), radian Q ( RS), subscript ([ ]), transpose (T) 5 Exponentiation, power operator (^) 6 Negation ( ) 7 String concatenation (&) 8 Multiplication (†), division (/) L 9 Addition (+), subtraction (-) 10 Equality relations: equal (=), not equal (ƒ or /=), less than (<), less than or equal ({ 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. For example, in the expression 4(1+2), EOS™ software first evaluates the portion of the expression 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 the same 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 ).” 166 TI-Nspire™ CAS Reference Guide Note: Because the TI-Nspire™ CAS software allows you to define your own functions, a variable 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 by b+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. For example, #(“x”&”y”&”z”) creates the variable name xyz. Indirection also allows the creation and modification of variables from inside a program. For example, if 10&r and “r”&s1, then #s1=10. Post Operators Post operators are operators that come directly after an argument, such as 5!, 25%, or 60¡15' 45". Arguments followed by a post operator are evaluated at the fourth priority level. For example, in the expression 4^3!, 3! is evaluated first. The result, 6, then becomes the exponent of 4 to yield 4096. Exponentiation Exponentiation (^) and element-by-element exponentiation (.^) are evaluated from right to left. For example, the expression 2^3^2 is evaluated the same as 2^(3^2) to produce 512. This is different from (2^3)^2, which is 64. Negation To enter a negative number, press v followed by the number. Post operations and exponentiation are performed before negation. For example, the result of Lx2 is a negative 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 that affect the evaluation of the argument preceding the operator. TI-Nspire™ CAS Reference Guide 167 Error Codes and Messages When an error occurs, its code is assigned to variable errCode. User-defined programs and functions can examine errCode to determine the cause of an error. For an example of using errCode, See Example 2 under the Try command, page 130. Note: Some error conditions apply only to TI-Nspire™ CAS products, and some apply only to TI-Nspire™ products. Error code Description 10 A function did 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<b will cause this error if either a or b is undefined when the If statement is executed. 30 Argument cannot be a folder name. 40 Argument error 50 Argument mismatch Two or more arguments must be of the same type. 60 Argument must be a Boolean expression or integer 70 Argument must be a decimal number 90 Argument must be a list 100 Argument must be a matrix 130 Argument must be a string 140 Argument must 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 Argument must be an expression 165 Batteries too low for sending or receiving Install new batteries before sending or receiving. 170 Bound The lower bound must be less than the upper bound to define the search interval. 180 Break The d or c key was pressed during a long calculation or during program execution. 190 Circular definition This message is displayed to avoid running out of memory during infinite replacement of variable values during simplification. For example, a+1->a, where a is an undefined variable, will cause this error. 200 Constraint expression invalid For example, solve(3x^2-4=0,x) | x<0 or x>5 would produce this error message because the constraint is separated by “or” instead of “and.” 210 Invalid Data type An argument is of the wrong data type. 220 Dependent limit 168 TI-Nspire™ CAS Reference Guide Error code Description 230 Dimension A list or matrix index is not valid. For example, if the list {1,2,3,4} is stored in L1, then L1[5] is a dimension error because L1 only contains four elements. 235 Dimension Error. Not enough elements in the lists. 240 Dimension mismatch Two or more arguments must be of the same dimension. For example, [1,2]+[1,2,3] is a dimension mismatch because the matrices contain a different number of elements. 250 Divide by zero 260 Domain error An argument must be in a specified domain. For example, rand(0) is not valid. 270 Duplicate variable name 280 Else and ElseIf invalid outside of If...EndIf block 290 EndTry is missing the matching Else statement 295 Excessive iteration 300 Expected 2 or 3-element list or matrix 310 The first argument of nSolve must be an equation in a single variable. It cannot contain a non-valued variable other than the variable of interest. 320 First argument of solve or cSolve must be an equation or inequality For example, solve(3x^2-4,x) is invalid because the first argument is not an equation. 345 Inconsistent units 350 Index out of range 360 Indirection string is not a valid variable name 380 Undefined Ans Either the previous calculation did not create Ans, or no previous calculation was entered. 390 Invalid assignment 400 Invalid assignment value 410 Invalid command 430 Invalid for the current mode settings 435 Invalid guess 440 Invalid implied multiply For example, x(x+1) is invalid; whereas, x*(x+1) is the correct syntax. This is to avoid confusion between implied multiplication and function calls. 450 Invalid in a function or 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 function or program A number of commands are not valid outside a function or program. For example, Local cannot be used unless it is in a function or program. 560 Invalid outside Loop..EndLoop, For..EndFor, or While..EndWhile blocks For example, the Exit command is valid only inside these loop blocks. 565 Invalid outside program TI-Nspire™ CAS Reference Guide 169 Error code Description 570 Invalid pathname For example, \var is invalid. 575 Invalid polar complex 580 Invalid program reference Programs cannot be referenced within functions or expressions such as 1+p(x) where p is a program. 600 Invalid table 605 Invalid use of units 610 Invalid variable name in a Local statement 620 Invalid variable or function name 630 Invalid variable reference 640 Invalid vector syntax 650 Link transmission A transmission between two units was not completed. Verify that the connecting cable is connected firmly to both ends. 665 Matrix not diagonalizable 670 Low Memory 1. Delete some data in this document 2. Save and close this document If 1 and 2 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 end of block syntax 740 Missing Then in the If..EndIf block 750 Name is not a function or program 765 No functions selected 780 No solution found 800 Non-real result For example, if the software is in the Real setting, ‡(-1) is invalid. To allow complex results, change the “Real or Complex” Mode Setting to RECTANGULAR or POLAR. 830 Overflow 850 Program not found A program reference inside another program could not be found in the provided path during execution. 855 Rand type functions not allowed in graphing 860 Recursion too deep 170 TI-Nspire™ CAS Reference Guide Error code Description 870 Reserved name or system variable 900 Argument error Median-median model could not be applied to data set. 910 Syntax error 920 Text not found 930 Too few arguments The function or command is missing one or more arguments. 940 Too many arguments The expression or equation contains an excessive number of arguments and cannot be 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 Unlicensed OS 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 Window variables domain 1010 Zoom 1020 Internal error 1030 Protected memory violation 1040 Unsupported function. This function requires Computer Algebra System. Try TI-Nspire™ CAS. 1045 Unsupported operator. This operator requires Computer Algebra System. Try TI-Nspire™ CAS. 1050 Unsupported feature. This operator requires Computer Algebra System. Try TI-Nspire™ CAS. 1060 Input argument must be numeric. Only inputs containing numeric values are allowed. 1070 Trig function argument too big for accurate reduction 1080 Unsupported use of Ans.This application does not support Ans. 1090 Function is not defined. Use one of the following commands: • Define • := • sto & to define a function. 1100 Non-real calculation For example, if the software is in the Real setting, ‡(-1) is invalid. To allow complex results, change the “Real or Complex” Mode Setting to RECTANGULAR or POLAR. 1110 Invalid bounds 1120 No sign change TI-Nspire™ CAS Reference Guide 171 Error code Description 1130 Argument cannot be a list or matrix 1140 Argument error The first argument must be a polynomial expression in the second argument. If the second argument is omitted, the software attempts to select a default. 1150 Argument error The first two arguments must be polynomial expressions in the third argument. If the third argument is omitted, the software attempts to select a default. 1160 Invalid library pathname A pathname must be in the form xxx\yyy, where: • The xxx part can have 1 to 16 characters. • The yyy part can have 1 to 15 characters. See the Library section in the documentation for more details. 1170 Invalid use of library pathname • A value cannot be assigned to a pathname using Define, :=, or sto &. • A pathname cannot be declared as a Local variable or be used as a parameter in a function or program definition. 1180 Invalid library variable name. Make sure that the name: • Does not contain a period • Does not begin with an underscore • Does not exceed 15 characters See the Library section in the documentation for more details. 1190 Library document not found: • Verify library is in the MyLib folder. • Refresh Libraries. See the Library section in the documentation for more details. 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. See the Library section in the documentation for more details. 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 See the Library section in the documentation for more details. 1220 Domain error: The tangentLine and normalLine functions support real-valued functions only. 1230 Domain error. Trigonometric conversion operators are not supported in Degree or Gradian angle modes. 1250 Argument Error Use a system of linear equations. Example of a system of two linear equations with variables x and y: 3x+7y=5 2y-5x=-1 1260 Argument Error: The first argument of nfMin or nfMax must be an expression in a single variable. It cannot contain a non-valued variable other than the variable of interest. 1270 Argument Error Order of the derivative must be equal to 1 or 2. 1280 Argument Error Use a polynomial in expanded form in one variable. 172 TI-Nspire™ CAS Reference Guide Error code Description 1290 Argument Error Use a polynomial in one variable. 1300 Argument Error The coefficients of the polynomial must evaluate to numeric values. 1310 Argument error: A function could not be evaluated for one or more of its arguments. 1380 Argument error: Nested calls to domain() function are not allowed. TI-Nspire™ CAS Reference Guide 173 Warning Codes and Messages You can use the warnCodes() function to store the codes of warnings generated by evaluating an expression. This table lists each numeric warning code and its associated message. For an example of storing warning codes, see warnCodes(), page 136. Warning code Message 10000 Operation might introduce false solutions. 10001 Differentiating an equation may produce a false equation. 10002 Questionable solution 10003 Questionable accuracy 10004 Operation might lose solutions. 10005 cSolve might specify more zeros. 10006 Solve may specify more zeros. 10007 More solutions may exist. Try specifying appropriate lower and upper bounds and/or a guess. Examples using solve(): • solve(Equation, Var=Guess)|lowBound<Var<upBound • solve(Equation, Var)|lowBound<Var<upBound • solve(Equation, Var=Guess) 10008 Domain of the result might be smaller than the domain of the input. 10009 Domain of the result might be larger than the domain of the input. 10012 Non-real calculation 10013 ˆ^0 or undef^0 replaced by 1 10014 undef^0 replaced by 1 10015 1^ˆ or 1^undef replaced by 1 10016 1^undef replaced by 1 10017 Overflow replaced by ˆ or Lˆ 10018 Operation requires and returns 64 bit value. 10019 Resource exhaustion, simplification might be incomplete. 10020 Trig function argument too big for accurate reduction. 10021 Input contains an undefined parameter. Result might not be valid for all possible parameter values. 10022 Specifying appropriate lower and upper bounds might produce a solution. 10023 Scalar has been multiplied by the identity matrix. 10024 Result obtained using approximate arithmetic. 10025 Equivalence cannot be verified in EXACT mode. 10026 Constraint might be ignored. Specify constraint in the form "\" 'Variable MathTestSymbol Constant' or a conjunct of these forms, for example 'x<3 and x>-12' 174 TI-Nspire™ CAS Reference Guide Service and Support Texas Instruments Support and Service Home Page: education.ti.com E-mail inquiries: ti-cares@ti.com KnowledgeBase and education.ti.com/support e-mail inquiries: International information: education.ti.com/international Service and Warranty Information For 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 Texas Instruments retailer/distributor. Service and Support 175 176 Service and Support Index Symbols ^, power 145 ^/, reciprocal 158 _, unit designation 157 :=, assign 160 !, factorial 150 .^, dot power 147 .*, dot multiplication 146 .+, dot addition 146 .N, dot subtraction 146 .P, dot division 147 ', minute notation 156 ', prime 157 ", second notation 156 {, less than or equal 149 ©, comment 160 @list( ), list difference 67 -, degree notation 156 -, degrees/minutes/seconds 156 4, convert units 158 â, integral 151 á, square root 152 É, not equal 148 N, subtract 143 P, divide 144 Π, product 152 Σ( ), sum 153 ⇔, logical double implication 150 , logical implication 149, 164 *, multiply 144 &, append 150 &, store 160 #, indirection 155 #, indirection operator 167 %, percent 147 +, add 143 <, less than 148 =, equal 148 >, greater than 149 |, constraint operator 159 |, greater than or equal 149 Numerics 0b, binary indicator 161 0h, hexadecimal indicator 161 10^( ), power of ten 158 2-sample F Test 51 4approxFraction( ) 11 A abs( ), absolute value 7 absolute value template for 3 add, + 143 amortization table, amortTbl( ) 7, 13 amortTbl( ), amortization table 7, 13 and, Boolean operator 7 angle, angle( ) 8 angle( ), angle 8 ANOVA, one-way variance analysis 8 ANOVA2way, two-way variance analysis 9 Ans, last answer 11 answer (last), Ans 11 append, & 150 approx( ), approximate 11, 12 approximate, approx( ) 11, 12 approxRational( ) 11 arc length, arcLen( ) 12 arccos() 11 arccosh() 12 arccosine, cos/( ) 23 arccot() 12 arccoth() 12 arccsc() 12 arccsch() 12 arcLen( ), arc length 12 arcsec() 12 arcsech() 12 arcsin() 12 arcsine, sin/( ) 113 arcsinh() 12 arctan() 12 arctangent, tan/( ) 125 arctanh() 12 arguments in TVM functions 132 augment( ), augment/concatenate 12 177 augment/concatenate, augment( ) 12 average rate of change, avgRC( ) 13 avgRC( ), average rate of change 13 B 4Base10, display as decimal integer 14 4Base16, display as hexadecimal 15 4Base2, display as binary 14 binary display, 4Base2 14 indicator, 0b 161 binomCdf( ) 15 binomPdf( ) 15 Boolean operators and 7 nand 80 nor 83 not 84 or 87 ⇔ 150 xor 137 149, 164 C c22way 17 c2Cdf( ) 17 c2GOF 18 c2Pdf( ) 18 Cdf( ) 47 ceiling, ceiling( ) 15, 16, 26 ceiling( ), ceiling 15 centralDiff( ) 16 cFactor( ), complex factor 16 char( ), character string 17 character string, char( ) 17 characters numeric code, ord( ) 87 string, char( ) 17 charPoly( ) 17 clear error, ClrErr 19 ClearAZ 18 ClrErr, clear error 19 colAugment 19 178 colDim( ), matrix column dimension 19 colNorm( ), matrix column norm 19 combinations, nCr( ) 81 comDenom( ), common denominator 19 comment, © 160 common denominator, comDenom( ) 19 completeSquare( ), complete square 20 complex conjugate, conj( ) 21 factor, cFactor( ) 16 solve, cSolve( ) 28 zeros, cZeros( ) 31 conj( ), complex conjugate 21 constant in solve( ) 116 constants in cSolve( ) 29 in cZeros( ) 32 in deSolve( ) 36 in solve( ) 117 in zeros( ) 138 shortcuts for 164 constraint operator "|" 159 constraint operator, order of evaluation 166 construct matrix, constructMat( ) 21 constructMat( ), construct matrix 21 convert 4Grad 56 4Rad 97 units 158 copy variable or function, CopyVar 21 correlation matrix, corrMat( ) 22 corrMat( ), correlation matrix 22 4cos, display in terms of cosine 22 cos( ), cosine 22 cos/, arccosine 23 cosh( ), hyperbolic cosine 24 cosh/( ), hyperbolic arccosine 24 cosine display expression in terms of 22 cosine, cos( ) 22 cot( ), cotangent 24 cot/( ), arccotangent 25 cotangent, cot( ) 24 coth( ), hyperbolic cotangent 25 coth/( ), hyperbolic arccotangent 25 count days between dates, dbd( ) 33 count items in a list conditionally , countif( ) 26 count items in a list, count( ) 25 count( ), count items in a list 25 countif( ), conditionally count items in a list 26 cPolyRoots() 26 cross product, crossP( ) 26 crossP( ), cross product 26 csc( ), cosecant 27 csc/( ), inverse cosecant 27 csch( ), hyperbolic cosecant 27 csch/( ), inverse hyperbolic cosecant 27 cSolve( ), complex solve 28 cubic regression, CubicReg 30 CubicReg, cubic regression 30 cumulative sum, cumulativeSum( ) 30 cumulativeSum( ), cumulative sum 30 Cycle, cycle 31 cycle, Cycle 31 4Cylind, display as cylindrical vector 31 cylindrical vector display, 4Cylind 31 cZeros( ), complex zeros 31 D d ( ), first derivative 150 days between dates, dbd( ) 33 dbd( ), days between dates 33 4DD, display as decimal angle 33 4Decimal, display result as decimal 33 decimal angle display, 4DD 33 integer display, 4Base10 14 Define 34 Define LibPriv 34 Define LibPub 35 Define, define 34 define, Define 34 defining private function or program 34 public function or program 35 definite integral template for 5 degree notation, - 156 degree/minute/second display, 4DMS 38 degree/minute/second notation 156 delete void elements from list 35 deleting variable, DelVar 35 deltaList() 35 deltaTmpCnv() 35 DelVar, delete variable 35 delVoid( ), remove void elements 35 denominator 19 derivative or nth derivative template for 5 derivative() 35 derivatives first derivative, d ( ) 150 numeric derivative, nDeriv( ) 82 numeric derivative, nDerivative( ) 81 deSolve( ), solution 36 det( ), matrix determinant 37 diag( ), matrix diagonal 37 dim( ), dimension 37 dimension, dim( ) 37 Disp, display data 38 display as binary, 4Base2 14 cylindrical vector, 4Cylind 31 decimal angle, 4DD 33 decimal integer, 4Base10 14 degree/minute/second, 4DMS 38 hexadecimal, 4Base16 15 polar vector, 4Polar 89 rectangular vector, 4Rect 99 spherical vector, 4Sphere 119 display data, Disp 38 distribution functions binomCdf( ) 15 binomPdf( ) 15 c22way( ) 17 179 c2Cdf( ) 17 c2GOF( ) 18 c2Pdf( ) 18 Invc2( ) 60 invNorm( ) 60 invt( ) 60 normCdf( ) 83 normPdf( ) 84 poissCdf( ) 88 poissPdf( ) 88 tCdf( ) 126 tPdf( ) 129 divide, P 144 4DMS, display as degree/minute/ second 38 domain function, domain( ) 38 domain( ), domain function 38 dominant term, dominantTerm( ) 39 dominantTerm( ), dominant term 39 dot addition, .+ 146 division, .P 147 multiplication, .* 146 power, .^ 147 product, dotP( ) 39 subtraction, .N 146 dotP( ), dot product 39 E e exponent template for 2 e to a power, e^( ) 40, 43 e^( ), e to a power 40 e, display expression in terms of 43 E, exponent 155 eff ), convert nominal to effective rate 40 effective rate, eff( ) 40 eigenvalue, eigVl( ) 41 eigenvector, eigVc( ) 40 eigVc( ), eigenvector 40 eigVl( ), eigenvalue 41 else if, ElseIf 41 else, Else 57 ElseIf, else if 41 empty (void) elements 162 end 180 for, EndFor 49 function, EndFunc 52 if, EndIf 57 loop, EndLoop 73 program, EndPrgm 93 try, EndTry 130 while, EndWhile 136 end function, EndFunc 52 end if, EndIf 57 end loop, EndLoop 73 end while, EndWhile 136 EndTry, end try 130 EndWhile, end while 136 EOS (Equation Operating System) 166 equal, = 148 Equation Operating System (EOS) 166 error codes and messages 168 errors and troubleshooting clear error, ClrErr 19 pass error, PassErr 88 euler( ), Euler function 42 evaluate polynomial, polyEval( ) 90 evaluation, order of 166 exact, exact( ) 42 exact( ), exact 42 exclusion with "|" operator 159 Exit, exit 43 exit, Exit 43 4exp, display in terms of e 43 exp( ), e to a power 43 exp4list( ), expression to list 44 expand, expand( ) 44 expand( ), expand 44 exponent, E 155 exponential regession, ExpReg 45 exponents template for 1 expr( ), string to expression 45, 71 ExpReg, exponential regession 45 expressions expression to list, exp4list( ) 44 string to expression, expr( ) 45, 71 F factor, factor( ) 46 factor( ), factor 46 factorial, ! 150 Fill, matrix fill 47 financial functions, tvmFV( ) 132 financial functions, tvmI( ) 132 financial functions, tvmN( ) 132 financial functions, tvmPmt( ) 132 financial functions, tvmPV( ) 132 first derivative template for 5 FiveNumSummary 48 floor, floor( ) 48 floor( ), floor 48 fMax( ), function maximum 48 fMin( ), function minimum 49 For 49 For, for 49 for, For 49 format string, format( ) 50 format( ), format string 50 fpart( ), function part 50 fractions propFrac 94 template for 1 freqTable( ) 50 frequency( ) 51 Frobenius norm, norm( ) 83 Func, function 52 Func, program function 52 functions maximum, fMax( ) 48 minimum, fMin( ) 49 part, fpart( ) 50 program function, Func 52 user-defined 34 functions and variables copying 21 G g, gradians 155 gcd( ), greatest common divisor 52 geomCdf( ) 52 geomPdf( ) 53 get/return denominator, getDenom( ) 53 number, getNum( ) 54 variables injformation, getVarInfo( ) 53, 55 getDenom( ), get/return denominator 53 getLangInfo( ), get/return language information 53 getLockInfo( ), tests lock status of variable or variable group 53 getMode( ), get mode settings 54 getNum( ), get/return number 54 getType( ), get type of variable 55 getVarInfo( ), get/return variables information 55 go to, Goto 56 Goto, go to 56 4, convert to gradian angle 56 gradian notation, g 155 greater than or equal, | 149 greater than, > 149 greatest common divisor, gcd( ) 52 groups, locking and unlocking 70, 135 groups, testing lock status 53 H hexadecimal display, 4Base16 15 indicator, 0h 161 hyperbolic arccosine, cosh/( ) 24 arcsine, sinh/( ) 114 arctangent, tanh/( ) 126 cosine, cosh( ) 24 sine, sinh( ) 114 tangent, tanh( ) 125 I identity matrix, identity( ) 56 identity( ), identity matrix 56 If, if 57 if, If 57 ifFn( ) 58 imag( ), imaginary part 58 imaginary part, imag( ) 58 ImpDif( ), implicit derivative 58 implicit derivative, Impdif( ) 58 181 indefinite integral template for 5 indirection operator (#) 167 indirection, # 155 Input, input 58 input, Input 58 inString( ), within string 59 int( ), integer 59 intDiv( ), integer divide 59 integer divide, intDiv( ) 59 integer part, iPart( ) 61 integer, int( ) 59 integral, â 151 interpolate( ), interpolate 60 Invc2( ) 60 inverse cumulative normal distribution (invNorm( ) 60 inverse, ^/ 158 invF( ) 60 invNorm( ), inverse cumulative normal distribution) 60 invt( ) 60 iPart( ), integer part 61 irr( ), internal rate of return internal rate of return, irr( ) 61 isPrime( ), prime test 61 isVoid( ), test for void 61 L label, Lbl 62 language get language information 53 Lbl, label 62 lcm, least common multiple 62 least common multiple, lcm 62 left, left( ) 62 left( ), left 62 length of string 37 less than or equal, { 149 less than, 148 LibPriv 34 LibPub 35 library create shortcuts to objects 63 libShortcut( ), create shortcuts to library objects 63 limit 182 lim( ) 63 limit( ) 63 template for 6 limit( ) or lim( ), limit 63 linear regression, LinRegAx 64 linear regression, LinRegBx 64, 65 LinRegBx, linear regression 64 LinRegMx, linear regression 64 LinRegtIntervals, linear regression 65 LinRegtTest 66 linSolve() 67 list to matrix, list4mat( ) 68 list, conditionally count items in 26 list, count items in 25 list4mat( ), list to matrix 68 lists augment/concatenate, augment( ) 12 cross product, crossP( ) 26 cumulative sum, cumulativeSum( ) 30 difference, @list( ) 67 differences in a list, @list( ) 67 dot product, dotP( ) 39 empty elements in 162 expression to list, exp4list( ) 44 list to matrix, list4mat( ) 68 matrix to list, mat4list( ) 74 maximum, max( ) 75 mid-string, mid( ) 76 minimum, min( ) 77 new, newList( ) 81 product, product( ) 93 sort ascending, SortA 118 sort descending, SortD 118 summation, sum( ) 123 ln( ), natural logarithm 68 LnReg, logarithmic regression 69 local variable, Local 70 local, Local 70 Local, local variable 70 Lock, lock variable or variable group 70 locking variables and variable groups 70 Log template for 2 logarithmic regression, LnReg 69 logarithms 68 logical double implication, ⇔ 150 logical implication, 149, 164 logistic regression, Logistic 72 logistic regression, LogisticD 72 Logistic, logistic regression 72 LogisticD, logistic regression 72 Loop, loop 73 loop, Loop 73 LU, matrix lower-upper decomposition 74 M mat4list( ), matrix to list 74 matrices augment/concatenate, augment( ) 12 column dimension, colDim( ) 19 column norm, colNorm( ) 19 cumulative sum, cumulativeSum( ) 30 determinant, det( ) 37 diagonal, diag( ) 37 dimension, dim( ) 37 dot addition, .+ 146 dot division, .P 147 dot multiplication, .* 146 dot power, .^ 147 dot subtraction, .N 146 eigenvalue, eigVl( ) 41 eigenvector, eigVc( ) 40 filling, Fill 47 identity, identity( ) 56 list to matrix, list4mat( ) 68 lower-upper decomposition, LU 74 matrix to list, mat4list( ) 74 maximum, max( ) 75 minimum, min( ) 77 new, newMat( ) 81 product, product( ) 93 QR factorization, QR 94 random, randMat( ) 98 reduced row echelon form, rref( ) 105 row addition, rowAdd( ) 105 row dimension, rowDim( ) 105 row echelon form, ref( ) 100 row multiplication and addition, mRowAdd( ) 78 row norm, rowNorm( ) 105 row operation, mRow( ) 78 row swap, rowSwap( ) 105 submatrix, subMat( ) 122, 123 summation, sum( ) 123 transpose, T 124 matrix (1 Q 2) template for 4 matrix (2 Q 1) template for 4 matrix (2 Q 2) template for 3 matrix (m Q n) template for 4 matrix to list, mat4list( ) 74 max( ), maximum 75 maximum, max( ) 75 mean, mean( ) 75 mean( ), mean 75 median, median( ) 75 median( ), median 75 medium-medium line regression, MedMed 76 MedMed, medium-medium line regression 76 mid( ), mid-string 76 mid-string, mid( ) 76 min( ), minimum 77 minimum, min( ) 77 minute notation, ' 156 mirr( ), modified internal rate of return 77 mixed fractions, using propFrac(› with 94 mod( ), modulo 78 mode settings, getMode( ) 54 modes setting, setMode( ) 110 modified internal rate of return, mirr( ) 77 modulo, mod( ) 78 mRow( ), matrix row operation 78 mRowAdd( ), matrix row multiplication and addition 78 183 Multiple linear regression t test 79 multiply, * 144 MultReg 78 MultRegIntervals( ) 79 MultRegTests( ) 79 N nand, Boolean operator 80 natural logarithm, ln( ) 68 nCr( ), combinations 81 nDerivative( ), numeric derivative 81 negation, entering negative numbers 167 net present value, npv( ) 85 new list, newList( ) 81 matrix, newMat( ) 81 newList( ), new list 81 newMat( ), new matrix 81 nfMax( ), numeric function maximum 82 nfMin( ), numeric function minimum 82 nInt( ), numeric integral 82 nom ), convert effective to nominal rate 82 nominal rate, nom( ) 82 nor, Boolean operator 83 norm( ), Frobenius norm 83 normal distribution probability, normCdf( ) 83 normal line, normalLine( ) 83 normalLine( ) 83 normCdf( ) 83 normPdf( ) 84 not equal, É 148 not, Boolean operator 84 nPr( ), permutations 84 npv( ), net present value 85 nSolve( ), numeric solution 85 nth root template for 1 numeric derivative, nDeriv( ) 82 derivative, nDerivative( ) 81 integral, nInt( ) 82 solution, nSolve( ) 85 184 O objects create shortcuts to library 63 OneVar, one-variable statistics 86 one-variable statistics, OneVar 86 operators order of evaluation 166 or (Boolean), or 87 or, Boolean operator 87 ord( ), numeric character code 87 P P4Rx( ), rectangular x coordinate 87 P4Ry( ), rectangular y coordinate 88 pass error, PassErr 88 PassErr, pass error 88 Pdf( ) 50 percent, % 147 permutations, nPr( ) 84 piecewise function (2-piece) template for 2 piecewise function (N-piece) template for 2 piecewise( ) 88 poissCdf( ) 88 poissPdf( ) 88 4Polar, display as polar vector 89 polar coordinate, R4Pq( ) 97 coordinate, R4Pr( ) 97 vector display, 4Polar 89 polyCoef( ) 89 polyDegree( ) 90 polyEval( ), evaluate polynomial 90 polyGcd( ) 90, 91 polynomials evaluate, polyEval( ) 90 random, randPoly( ) 98 PolyRoots() 91 power of ten, 10^( ) 158 power regression, PowerReg 91, 92, 101, 102, 127 power, ^ 145 PowerReg, power regression 92 Prgm, define program 93 prime number test, isPrime( ) 61 prime, ' 157 probability densiy, normPdf( ) 84 prodSeq() 93 product (Π) template for 4 product, Π( ) 152 product, product( ) 93 product( ), product 93 programming define program, Prgm 93 display data, Disp 38 pass error, PassErr 88 programs defining private library 34 defining public library 35 programs and programming clear error, ClrErr 19 display I/O screen, Disp 38 end program, EndPrgm 93 end try, EndTry 130 try, Try 130 proper fraction, propFrac 94 propFrac, proper fraction 94 Q QR factorization, QR 94 QR, QR factorization 94 quadratic regression, QuadReg 95 QuadReg, quadratic regression 95 quartic regression, QuartReg 96 QuartReg, quartic regression 96 R R, radian 155 R4Pq( ), polar coordinate 97 R4Pr( ), polar coordinate 97 4Rad, convert to radian angle 97 radian, R 155 rand( ), random number 97 randBin, random number 98 randInt( ), random integer 98 randMat( ), random matrix 98 randNorm( ), random norm 98 random matrix, randMat( ) 98 norm, randNorm( ) 98 number seed, RandSeed 99 polynomial, randPoly( ) 98 random sample 98 randPoly( ), random polynomial 98 randSamp( ) 98 RandSeed, random number seed 99 real, real( ) 99 real( ), real 99 reciprocal, ^/ 158 4Rect, display as rectangular vector 99 rectangular x coordinate, P4Rx( ) 87 rectangular y coordinate, P4Ry( ) 88 rectangular-vector display, 4Rect 99 reduced row echelon form, rref( ) 105 ref( ), row echelon form 100 regressions cubic, CubicReg 30 exponential, ExpReg 45 linear regression, LinRegAx 64 linear regression, LinRegBx 64, 65 logarithmic, LnReg 69 Logistic 72 logistic, Logistic 72 medium-medium line, MedMed 76 MultReg 78 power regression, PowerReg 91, 92, 101, 102, 127 quadratic, QuadReg 95 quartic, QuartReg 96 sinusoidal, SinReg 115 remain( ), remainder 100 remainder, remain( ) 100 remove void elements from list 35 Request 101 RequestStr 102 result display in terms of cosine 22 display in terms of e 43 display in terms of sine 112 result values, statistics 121 results, statistics 120 Return, return 102 return, Return 102 right, right( ) 20, 42, 60, 102, 103, 136 right( ), right 102 185 rk23( ), Runge Kutta function 103 rotate, rotate( ) 103, 104 rotate( ), rotate 103, 104 round, round( ) 104 round( ), round 104 row echelon form, ref( ) 100 rowAdd( ), matrix row addition 105 rowDim( ), matrix row dimension 105 rowNorm( ), matrix row norm 105 rowSwap( ), matrix row swap 105 rref( ), reduced row echelon form 105 S sec( ), secant 106 sec/( ), inverse secant 106 sech( ), hyperbolic secant 106 sech/( ), inverse hyperbolic secant 107 second derivative template for 5 second notation, " 156 seq( ), sequence 107 seqGen( ) 108 seqn( ) 108 sequence, seq( ) 107, 108 series, series( ) 109 series( ), series 109 set mode, setMode( ) 110 setMode( ), set mode 110 settings, get current 54 shift, shift( ) 111 shift( ), shift 111 sign, sign( ) 111 sign( ), sign 111 simult( ), simultaneous equations 112 simultaneous equations, simult( ) 112 4sin, display in terms of sine 112 sin( ), sine 113 sin/( ), arcsine 113 sine display expression in terms of 112 186 sine, sin( ) 113 sinh( ), hyperbolic sine 114 sinh/( ), hyperbolic arcsine 114 SinReg, sinusoidal regression 115 ΣInt( ) 154 sinusoidal regression, SinReg 115 solution, deSolve( ) 36 solve, solve( ) 115 solve( ), solve 115 SortA, sort ascending 118 SortD, sort descending 118 sorting ascending, SortA 118 descending, SortD 118 4Sphere, display as spherical vector 119 spherical vector display, 4Sphere 119 ΣPrn( ) 154 sqrt( ), square root 119 square root template for 1 square root, ‡( ) 119, 152 standard deviation, stdDev( ) 121, 135 stat.results 120 stat.values 121 statistics combinations, nCr( ) 81 factorial, ! 150 mean, mean( ) 75 median, median( ) 75 one-variable statistics, OneVar 86 permutations, nPr( ) 84 random norm, randNorm( ) 98 random number seed, RandSeed 99 standard deviation, stdDev( ) 121, 135 two-variable results, TwoVar 133 variance, variance( ) 135 stdDevPop( ), population standard deviation 121 stdDevSamp( ), sample standard deviation 121 Stop command 122 storing symbol, & 160 string dimension, dim( ) 37 length 37 string( ), expression to string 122 strings append, & 150 character code, ord( ) 87 character string, char( ) 17 expression to string, string( ) 122 format, format( ) 50 formatting 50 indirection, # 155 left, left( ) 62 mid-string, mid( ) 76 right, right( ) 20, 42, 60, 102, 103, 136 rotate, rotate( ) 103, 104 shift, shift( ) 111 string to expression, expr( ) 45, 71 using to create variable names 167 within, InString 59 student-t distribution probability, tCdf( ) 126 student-t probability density, tPdf( ) 129 subMat( ), submatrix 122, 123 submatrix, subMat( ) 122, 123 substitution with "|" operator 159 subtract, N 143 sum (G) template for 4 sum of interest payments 154 sum of principal payments 154 sum, Σ( ) 153 sum( ), summation 123 sumIf( ) 123 summation, sum( ) 123 sumSeq() 123 system of equations (2-equation) template for 3 system of equations (N-equation) template for 3 T t test, tTest 131 T, transpose 124 tan( ), tangent 124 tan/( ), arctangent 125 tangent line, tangentLine( ) 125 tangent, tan( ) 124 tangentLine( ) 125 tanh( ), hyperbolic tangent 125 tanh/( ), hyperbolic arctangent 126 Taylor polynomial, taylor( ) 126 taylor( ), Taylor polynomial 126 tCdf( ), student-t distribution probability 126 tCollect( ), trigonometric collection 127 templates absolute value 3 definite integral 5 derivative or nth derivative 5 e exponent 2 exponent 1 first derivative 5 fraction 1 indefinite integral 5 limit 6 Log 2 matrix (1 Q 2) 4 matrix (2 Q 1) 4 matrix (2 Q 2) 3 matrix (m Q n) 4 nth root 1 piecewise function (2-piece) 2 piecewise function (N-piece) 2 product (Π) 4 second derivative 5 square root 1 sum (G) 4 system of equations (2-equation) 3 system of equations (Nequation) 3 test for void, isVoid( ) 61 Test_2S, 2-sample F test 51 tExpand( ), trigonometric expansion 127 Text command 127 time value of money, Future Value 132 time value of money, Interest 132 187 time value of money, number of payments 132 time value of money, payment amount 132 time value of money, present value 132 tInterval_2Samp, two-sample t confidence interval 128 tInterval, t confidence interval 128 4tmpCnv() 129 tmpCnv() 129 tPdf( ), student-t probability density 129 trace( ) 130 transpose, T 124 trigonometric collection, tCollect( ) 127 trigonometric expansion, tExpand( ) 127 Try, error handling command 130 tTest_2Samp, two-sample t test 131 tTest, t test 131 TVM arguments 132 tvmFV( ) 132 tvmI( ) 132 tvmN( ) 132 tvmPmt( ) 132 tvmPV( ) 132 TwoVar, two-variable results 133 two-variable results, TwoVar 133 U underscore, _ 157 unit vector, unitV( ) 134 units convert 158 unitV( ), unit vector 134 unLock, unlock variable or variable group 135 unlocking variables and variable groups 135 user-defined functions 34 user-defined functions and programs 34, 35 V variable 188 creating name from a character string 167 variable and functions copying 21 variables clear all single-letter 18 delete, DelVar 35 local, Local 70 variables, locking and unlocking 53, 70, 135 variance, variance( ) 135 varPop( ) 135 varSamp( ), sample variance 135 vectors cross product, crossP( ) 26 cylindrical vector display, 4Cylind 31 dot product, dotP( ) 39 unit, unitV( ) 134 void elements 162 void elements, remove 35 void, test for 61 W warnCodes( ), Warning codes 136 warning codes and messages 174 when, when( ) 136 when( ), when 136 While, while 136 while, While 136 with, | 159 within string, inString( ) 59 X x2, square 146 XNOR 150 xor, Boolean exclusive or 137 Z zeroes, zeroes( ) 137 zeroes( ), zeroes 137 zInterval_1Prop, one-proportion z confidence interval 139 zInterval_2Prop, two-proportion z confidence interval 140 zInterval_2Samp, two-sample z confidence interval 140 zInterval, z confidence interval 139 zTest 141 zTest_1Prop, one-proportion z test 141 zTest_2Prop, two-proportion z test 142 zTest_2Samp, two-sample z test 142 189 190

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