TI-Nspire CAS Reference Guide

Reference GuideThis guidebook applies to TI-Nspire™ software version 2.1. 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 CAS. © 2006 - 2010 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 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 conj() .......................................................... 20 constructMat() ........................................... 20 CopyVar ...................................................... 21 corrMat() .................................................... 21 4cos ............................................................. 21 cos() ............................................................ 22 cosê() .......................................................... 23 cosh() .......................................................... 23 coshê() ........................................................ 23 cot() ............................................................ 24 cotê() .......................................................... 24 coth() .......................................................... 24 cothê() ........................................................ 25 count() ........................................................ 25 countif() ..................................................... 25 cPolyRoots() ............................................... 26 crossP() ....................................................... 26 csc() ............................................................. 26 cscê() ........................................................... 27 csch() ........................................................... 27 cschê() ......................................................... 27 cSolve() ....................................................... 27 CubicReg .................................................... 29 cumulativeSum() ........................................ 30 Cycle ........................................................... 30 4Cylind ........................................................ 30 cZeros() ....................................................... 30 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 D dbd() ........................................................... 32 4DD ............................................................. 32 4Decimal ..................................................... 33 Define ......................................................... 33 Define LibPriv ............................................ 34 Define LibPub ............................................ 34 deltaList() ................................................... 34 deltaTmpCnv() ........................................... 34 DelVar ........................................................ 34 delVoid() .................................................... 35 derivative() ................................................. 35 B bal() ............................................................. 13 4Base2 ......................................................... 14 4Base10 ....................................................... 14 iii ............53 4Grad ......................................................................................41 exact() .................................48 fPart() .............................................................. 63 linSolve() ....................... 57 isPrime() .................. 60 LinRegMx ................................................................................. 55 impDif() .............. 64 ln() .........................................41 Exit .... 69 LU .......................................................................40 EndFor ........................... 72 mid() .......52 getNum() ....51 getLockInfo() ................................................................................38 dotP() ........................................ 56 inString() ............ 66 log() ..................38 E e^() .................................................................................................................................................................. 61 LinRegtIntervals .................53 Goto ................................. 60 LinRegBx ...........42 exp() ............................................................................................................................................................................................................................................................................... 72 min() ...........................................................................................................................................................................46 floor() ..40 EndFunc ...................................................... 70 max() ........................................................ 75 G gcd() ............................................................................................................... 56 intDiv() ....................................................................... 58 L Lbl ........47 For ....44 FCdf() ...............................................................................................................48 freqTable4list() ..........................................................................................................................44 identity() ..... 57 invt() ..............................49 Func ................41 EndTry ............................................... 62 LinRegtTest ...45 Fill ...............................................38 dominantTerm() ............................................................... 64 list4mat() ................................ 57 iPart() ........................................... 67 4logbase .. 59 limit() or lim() ..............................................................................................40 EndIf .............................. 70 F factor() ................................................................................................................................................................................................................................................................................................................................................................48 FPdf() .... 57 invF() ...........50 geomPdf() ......................................47 fMin() ................39 eff() ................36 diag() ......................................................................................... 54 If ........................................51 getMode() ........................................ 58 isVoid() ............................................................................................................ 57 irr() ...............................39 eigVc() ............................... 56 integral ..............................................................................................41 EndPrgm ........... 77 I iv .............................................. 71 median() .51 getDenom() ................................... 65 Local .....................................................................41 EndLoop .. 68 Loop ............................................................................................ 59 libShortcut() .................... 76 nDerivative() .......................51 getLangInfo() ........................................................................................... 74 MultRegIntervals ........... 66 Lock ................................................................................................................37 4DMS ...........................................41 4exp ..................................................................52 getVarInfo() .....................................................................................................................................................................49 FTest_2Samp .......................................... 68 LogisticD .................... 67 Logistic ........................................................................................................................................................... 57 invNorm() .42 expand() .......42 exp4list() .........................37 Disp .................................................................. 56 Indirection ............ 58 lcm() ......................................35 det() .....................................................................46 fMax() ....................................................................... 65 LnReg ........................................................................ 74 mRowAdd() ...... 64 @List() ........................................................................ 59 left() ................ 73 mod() ...................................................................... 74 MultReg ......................43 ExpReg .........................................................................................................45 FiveNumSummary ..................42 expr() ............................deSolve() ....................41 EndWhile ...........................................................................40 Else ....... 54 ifFn() ...............................47 format() ..............50 geomCdf() .................................................................................................54 N nCr() ....... 55 imag() ................................................... 71 MedMed ........................................40 eigVl() .................... 64 4ln .......................................................................................................................... 73 mirr() ....37 dim() ................................ 74 mRow() .............................................................................................................................................................. 75 MultRegTests ...................................................................................................................48 frequency() ....................... 71 mean() ............................... 56 invc2() ......................................................... 56 int() .........................................................................................................................................................................................................................................................................40 ElseIf .................................................................................................50 M mat4list() ......................................................................................................................... ... 90 QuartReg ............. 94 4Rect ........................................................... 97 right() ..................... 81 or ... 103 simult() ............... 78 normalLine() .................................................... 117 tanh() ..................................................................................................... 93 RandSeed ..................................................................................................................................................................... 115 sumSeq() .......... 94 ref() ............................................................................................................................................ 86 polyRemainder() ................................ 111 stat.... 112 stat.. 92 randBin() ..................... 118 tCdf() ............................................................................................. 97 rotate() ................................................................................................................. 99 S sec() ................................................................................................ 84 polyCoeffs() .................... 115 O OneVar ................................................................................. 119 Text .......................................... 103 sign() ...... 89 Q QR ............ 93 randNorm() .. 93 randSamp() ................................... 87 PowerReg ................ 89 QuadReg .................................... 79 normCdf() .......................................... 83 P4Ry() .......................... 119 tExpand() ........... 91 R R4Pq() ................................................ 116 tanê() ......................................................................................................................... 105 sinh() ....................................................................... 117 tangentLine() .................... 114 string() .............................. 120 v .... 78 norm() ................................................................................. 85 polyDegree() ....................................................... 79 not ........... 77 nInt() ................................ 86 polyRoots() ........... 82 P P4Rx() ............................................................................................................................. 104 sin() ........................................................... 98 rowDim() ................................................................................................................ 82 ord() ...................................................... 100 series() . 116 tan() ........................................................................................... 97 round() .......................... 114 subMat() ....... 77 nfMin() .......................................................................................................................................... 94 real() ....................................................................................................... 101 setMode() .................................................... 84 poissPdf() ................ 119 Then .. 92 rand() ................................................................................................................ 98 rowNorm() ........ 86 polyQuotient() ..... 110 4Sphere .............. 77 nfMax() ................................................................................... 88 Product (PI) ......................................................... 85 polyEval() ................................................................................................................................................................................................................................................................... 99 sec/() ............... 115 system() ............................................................ 85 polyGcd() ................. 100 sech() .................................................. 88 propFrac() ............................................................................................ 113 stDevSamp() .............................................................................................................................................................. 83 poissCdf() ............................................................ 95 T T (transpose) ....................................................................... 96 Return ...................................................................................................................................................................................................................... 77 newMat() .............................................................................................................................. 87 Prgm ... 114 sum() ........ 115 sumIf() ................................ 104 4sin ............................................... 93 randPoly() ....................values ...................................................................... 78 nom() ............................................................................................ 84 4Polar ............................................................. 80 npv() .................................................................................................................................................................................................................................................................................. 96 RequestStr ..................................................................... 88 product() .................................................................... 110 SortD . 105 sinê() ....................... 118 taylor() ................................................................................... 107 solve() . 106 SinReg ........................................................... 83 piecewise() .................newList() . 83 PassErr ............................................................. 106 sinhê() ......................................... 97 root() ...................................................................................................... 79 nPr() ............................. 100 sechê() ........................... 98 rowAdd() .............. 119 tInterval .......... 113 Stop ....................................................................................................... 99 rowSwap() .................................................. 111 sqrt() .............................. 107 SortA ............................. 114 Sum (Sigma) ........................................ 80 Request ..................... 93 randInt() ............................................................................................................................ 100 seq() ...................................................................................... 80 nSolve() .......................................... 117 tanhê() ................................................. 99 rref() .............................. 114 Store .................................. 93 randMat() ........results ...... 88 prodSeq() ............................................................................................ 102 shift() ............................................................................................. 118 tCollect() ......... 113 stDevPop() ..... 92 4Rad ............................................................................................................ 92 R4Pr() ........ 79 normPdf() .............. 95 remain() ............................ ...........127 varSamp() .132 zTest .....................................................128 X xor ..................................................139 ...132 zInterval_2Samp ................... 151 Empty (void) elements Calculations involving void elements ..^ (dot power) ................... 141 | (greater or equal) .......................................................................·(dot mult................... 144 GInt() ................... 141 & (append) .........139 ë(negate) ........................................136 ^ (power) ............. 149 ^ê (reciprocal) .......... 140 ƒ (not equal) ..............................122 Try ......... / (dot divide) .................................................................................................127 V varPop() ............................................................................. 139 = (equal) ........................... 141 > (greater than) ...................................................... 146 ô(radian) ............) .........................................................................................138 ....... 140 { (less or equal) .................................................................................. 148 4 (convert) ......................................................................................................124 TwoVar ................................................................................ 152 List arguments containing void elements ...................................................... 150 & (store) ............122 tTest ................................+ (dot add) .............. 152 Symbols + (add) ............................................................ 143 G() (sumSeq) .................134 zTest_2Samp .. 0h .............................129 zInterval ...................................... 140 < (less than) .............................................................................................. 146 g (gradian) ................................................... '' (degree/minute/second) ......................................................... 145 # (indirection) ........................................................... 151 © (comment) ....................................................................................................................... 147 ' (prime) ................... 141 d() (derivative) .........................................................................................................................................129 Z zeros() ...........................133 zTest_2Prop ...............135 ·(multiply) ........................................................ 142 ‰() (integral) .. 142 ‡() (square root) .....133 zTest_1Prop ........................................................................128 While ..................................138 .................................138 .............................................138 ..................tInterval_2Samp .......139 Shortcuts for entering math expressions EOS™ (Equation Operating System) hierarchy Error codes and messages Texas Instruments Support and Service vi .......................................................................................123 tTest_2Samp .................................................136 à (divide) ............................................................................................................................124 tvmPmt() ....................................................................................................... '...................131 zInterval_2Prop .............131 zInterval_1Prop .....121 @tmpCnv() ................................................................................................................................................. 146 ¡ (degree) .............................................. 151 0b...................................123 tvmFV() ..................121 tPdf() ...........................121 trace() .......................................... 146 í (scientific notation) ................... 141 ! (factorial) ...................... 147 ¡.........................137 x2 (square) ................................. 148 _ (underscore as unit designator) ...............125 U unitV() ............ 149 | (“with”) .....................120 tmpCnv() .... 143 Π() (prodSeq) .... 148 _ (underscore as an empty element) ..............................128 “With” ...................................................................................124 tvmPV() ..... 147  (angle) ..................................................................... 150 := (assign) ...............................................................................................................................127 W when() ....................................135 N(subtract) ...............................................) ...............................124 tvmN() ..................... 145 GPrn() ............................................................................... (dot subt............................................................... 149 10^() ....................................................................................................................124 tvmI() ......126 unLock ...........................134 % (percent) .................... functions. When you insert a template. press To return the cursor to the baseline. l. and then type the exponent. and type a value or expression for the element. page 97. Note: See also ^ (power). Use the arrow keys or press e to move the cursor to each element’s position. Nth root template Example: /l keys Note: See also root(). Expression templates Expression templates give you an easy way to enter math expressions in standard mathematical notation. it appears on the entry line with small blocks at positions where you can enter elements. press right arrow ( ). TI-Nspire™ CAS Reference Guide 1 .TI-Nspire™ CAS Reference Guide This guide lists the templates. commands. Exponent template Example: l key Note: Type the first value. A cursor shows which element you can enter. Press · or /· to evaluate the expression. page 136. ¢ /q keys Example: Square root template Note: See also ‡() (square root). and operators available for evaluating math expressions. page 143. page 137. Fraction template Example: /p keys Note: See also / (divide). e exponent template Example: u keys Natural exponential e raised to a power Note: See also e^(). Piecewise template (2-piece) Example: Catalog > Lets you create expressions and conditions for a two-piece piecewise function. To add a piece. omit the base. Note: See also piecewise(). page 83. Catalog > Example: See the example for Piecewise template (2-piece). 2 TI-Nspire™ CAS Reference Guide . Prompts for N. click in the template and repeat the template. page 67. Log template Example: /s key Calculates log to a specified base. page 83. For a default of base 10. Note: See also piecewise(). Piecewise template (N-piece) Lets you create expressions and conditions for an N-piece piecewise function. Note: See also log(). page 39. Note: See also system(). TI-Nspire™ CAS Reference Guide 3 .ss’’ format. page 115. Prompts for N.System of 2 equations template Example: Catalog > Creates a system of two equations. Catalog > Example: See the example for System of equations template (2-equation). System of N equations template Lets you create a system of N equations.ss is the number of seconds. Note: See also system(). mm is the number of minutes. page 7. To add a row to an existing system. click in the template and repeat the template. page 115.ss’’ template Example: Lets you enter angles in dd°mm’ss. and ss. where dd is the number of decimal degrees. Matrix template (2 x 2) Example: Catalog > Catalog > Creates a 2 x 2 matrix. Absolute value template Example: Note: See also abs(). Catalog > dd°mm’ss. it may take a few moments to appear. page 143. Example: Catalog > Note: If you create a matrix with a large number of rows and columns. Product template (Π) Example: Catalog > Note: See also Π() (prodSeq). Catalog > Matrix template (2 x 1) Example: Catalog > Matrix template (m x n) The template appears after you are prompted to specify the number of rows and columns. page 144.Matrix template (1 x 2) Example: . 4 TI-Nspire™ CAS Reference Guide . Sum template (G) Example: Catalog > Note: See also G() (sumSeq). page 142. page 142. Note: See also d() (derivative). page 1. Note: See also d() (derivative). Definite integral template Example: Catalog > Note: See also ‰() integral(). Nth derivative template Example: Catalog > The nth derivative template can be used to calculate the nth derivative. Second derivative template Example: Catalog > The second derivative template can also be used to calculate second derivative at a point. page 1. Note: See also d() (derivative). Indefinite integral template Example: Catalog > Note: See also ‰() integral().First derivative template Example: Catalog > The first derivative template can also be used to calculate first derivative at a point. page 142. TI-Nspire™ CAS Reference Guide 5 . Note: See also limit(). 6 TI-Nspire™ CAS Reference Guide . page 60.Limit template Example: Catalog > Use N or (N) for left hand limit. Use + for right hand limit. PpY. Catalog > TI-Nspire™ CAS Reference Guide 7 .PmtAt). starting on page 135. and >) are listed at the end of this section. [PmtAt]. Default=2. CpY. all examples in this section were performed in the default reset mode. and PmtAt are described in the table of TVM arguments. CpY. and bal(). [roundValue]) ⇒ matrix Catalog > Amortization function that returns a matrix as an amortization table for a set of TVM arguments. N. it defaults to FV=0. Note: All undefined variables are treated as real variables. PV.I. and balance. • • • If you omit Pmt.I. A abs() abs(Expr1) ⇒ expression abs(List1) ⇒ list abs(Matrix1) ⇒ matrix Catalog > Returns the absolute value of the argument. roundValue specifies the number of decimal places for rounding. amortTbl() amortTbl(NPmt. NPmt is the number of payments to be included in the table. !. [CpY]. I. The columns in the result matrix are in this order: Payment number.Alphabetical listing Items whose names are not alphabetic (such as +. [Pmt]. FV.PV.PpY. The balance displayed in row n is the balance after payment n. page 13. and PmtAt are the same as for the TVM functions. Note: See also Absolute value template. Unless otherwise specified. it defaults to Pmt=tvmPmt(N. amount paid to interest. If the argument is a complex number. amount paid to principal. Pmt. page 145.FV. You can use the output matrix as input for the other amortization functions GInt() and GPrn(). If you omit FV. and all variables are assumed to be undefined.CpY. The table starts with the first payment. [FV]. page 124. page 3. and BooleanExpr1 and BooleanExpr2 ⇒ Boolean expression BooleanList1 and BooleanList2 ⇒ Boolean list BooleanMatrix1 and BooleanMatrix2 ⇒ Boolean matrix Returns true or false or a simplified form of the original entry. returns the number’s modulus.PV.N. [PpY]. The defaults for PpY. interpreting each element as a complex number that represents a two-dimensional rectangular coordinate point. Internally. the result is 0.PVal stat.F stat. A hexadecimal entry can have up to 16 digits. angle() angle(Expr1) Catalog > ⇒ expression In Degree angle mode: Returns the angle of the argument.df stat. you must use the 0b or 0h prefix. For a binary or hexadecimal entry.List2[. the result is 1 if both bits are 1. The returned value represents the bit results. integers are treated as decimal (base 10). ANOVA ANOVA List1. respectively. A summary of results is stored in the stat. interpreting the argument as a complex number. otherwise. 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.. not the letter O. Without a prefix. both integers are converted to signed.SS Description Value of the F statistic Smallest level of significance at which the null hypothesis can be rejected Degrees of freedom of the groups Sum of squares of the groups 8 TI-Nspire™ CAS Reference Guide .and Integer1 and Integer2 ⇒ integer Compares two real integers bit-by-bit using an and operation.. When corresponding bits are compared. In Hex base mode: Catalog > Important: Zero.. 64-bit binary numbers..) Flag=0 for Data. In Bin base mode: In Dec base mode: Note: A binary entry can have up to 64 digits (not counting the 0b prefix). Note: All undefined variables are treated as real variables.List20][. (See page 112. Flag=1 for Stats Output variable stat. and is displayed according to the Base mode. You can enter the integers in any number base.Flag] Catalog > Performs a one-way analysis of variance for comparing the means of two to 20 populations.results variable.List3. levRow] Catalog > Computes a two-way analysis of variance for comparing the means of two to 10 populations.) LevRow=0 for Block LevRow=2.MSBlock stat. for Two Factor.3...s Description F statistic of the column factor Smallest level of significance at which the null hypothesis can be rejected Degrees of freedom of the column factor Sum of squares of the column factor Mean squares for column factor F statistic for factor Least probability at which the null hypothesis can be rejected Degrees of freedom for factor Sum of squares for factor Mean squares for factor Degrees of freedom of the errors Sum of squares of the errors Mean squares for the errors Standard deviation of the error TI-Nspire™ CAS Reference Guide 9 . A summary of results is stored in the stat.Len-1. (See page 112.dfError stat.CUpperList Description Mean squares for the groups Degrees of freedom of the errors Sum of squares of the errors Mean square for the errors Pooled standard deviation Mean of the input of the lists 95% confidence intervals for the mean of each input list 95% confidence intervals for the mean of each input list ANOVA2way ANOVA2way List1..results variable.List3.…} Outputs: Block Design Output variable stat. where Len=length(List1)=length(List2) = … = length(List10) and Len / LevRow ∈ {2.MSError stat.dfError stat.List10][.FBlock stat.MS stat.sp stat.PVal stat..PValBlock stat.Output variable stat.SSError stat.F stat.CLowerList stat.SSError stat.….MS stat.MSError stat.List2[.df stat.dfBlock stat.SS stat.xbarlist stat.3.SSBlock stat. SSError stat.dfInteract stat.SSInteract stat.COLUMN FACTOR Outputs Output variable stat.dfError stat.Fcol stat.FRow stat.dfRow stat.FInteract stat.MSInteract Description F statistic of the interaction Probability value of the interaction Degrees of freedom of the interaction Sum of squares of the interaction Mean squares for interaction ERROR Outputs Output variable stat.PValInteract stat.SSRow stat.MSError s Description Degrees of freedom of the errors Sum of squares of the errors Mean squares for the errors Standard deviation of the error 10 TI-Nspire™ CAS Reference Guide .PValRow stat.PValCol stat.MSRow Description F statistic of the row factor Probability value of the row factor Degrees of freedom of the row factor Sum of squares of the row factor Mean squares for row factor INTERACTION Outputs Output variable stat.dfCol stat.SSCol stat.MSCol Description F statistic of the column factor Probability value of the column factor Degrees of freedom of the column factor Sum of squares of the column factor Mean squares for column factor ROW FACTOR Outputs Output variable stat. when possible. TI-Nspire™ CAS Reference Guide 11 . using a tolerance of Tol. regardless of the current Auto or Approximate mode. approxRational() Catalog > ⇒ expression approxRational(List[. Tol]) Returns the argument as a fraction using a tolerance of Tol. 4approxFraction() Expr 4approxFraction([Tol]) ⇒ expression List 4approxFraction([Tol]) ⇒ list Matrix 4approxFraction([Tol]) ⇒ matrix Returns the input as a fraction. a tolerance of 5.E-14 is used. a tolerance of 5. If Tol is omitted. when possible. Note: You can insert this function from the computer keyboard by Catalog > typing @>approxFraction(.Ans Ans /v keys ⇒ value Returns the result of the most recently evaluated expression.). Tol]) ⇒ list approxRational(Matrix[. approx(List1) ⇒ list approx(Matrix1) ⇒ matrix Returns a list or matrix where each element has been evaluated to a decimal value. This is equivalent to entering the argument and pressing /·. Tol]) ⇒ matrix approxRational(Expr[. page 23.. arccos() See cosê(). approx() approx(Expr1) Catalog > ⇒ expression Returns the evaluation of the argument as an expression containing decimal values.. If Tol is omitted.E-14 is used. arccoth() See cothê(). arccot() See cotê(). page 24. page 100. 12 TI-Nspire™ CAS Reference Guide . page 100. arcsinh() See sinhê(). page 25. List2) Catalog > ⇒ list Returns a new list that is List2 appended to the end of List1. Arc length is calculated as an integral assuming a function mode definition.End) Catalog > ⇒ expression Returns the arc length of Expr1 from Start to End with respect to variable Var.Var. page 23. page 106. arctan() See tanê(). arcLen() arcLen(Expr1.End) ⇒ list Returns a list of the arc lengths of each element of List1 from Start to End with respect to Var.Var. page 105.arccosh() See coshê(). arcsin() See sinê(). arccsch() See cschê(). page 27.Start. augment() augment(List1. arctanh() See tanhê().Start. page 117. arcLen(List1. arccsc() See cscê(). arcsech() See sechê(). page 118. arcsec() See secê(). page 27. N. it defaults to 0. CpY. [CpY]. [PpY].[Pmt]. The amortTable argument must be a matrix in the form described under amortTbl().” character is used. the matrices must have equal row dimensions. B bal() bal(NPmt. PV. TI-Nspire™ CAS Reference Guide 13 . [FV]. List1]) ⇒ list avgRC(List1. CpY. Step]) ⇒ matrix avgRC(Expr1. Var [=Value] [. page 124. and PmtAt are described in the table of TVM arguments. • • • If you omit Pmt. it defaults to FV=0. FV.001. NPmt specifies the payment number after which you want the data calculated.PpY. it overrides any prior variable assignment or any current “with” substitution for the variable. When Value is specified. based on amortization table amortTable. N. and PmtAt are described in the table of TVM arguments. CpY.I. roundValue specifies the number of decimal places for rounding. PpY. FV.PV . page 124. Var [=Value] [. N. Step is the step value.FV.PmtAt). Matrix2) Catalog > ⇒ matrix Returns a new matrix that is Matrix2 appended to Matrix1. and Matrix2 is appended to Matrix1 as new columns. bal(NPmt. PpY.amortTable) calculates the balance after payment number NPmt. Var [=Value] [. The defaults for PpY. and PmtAt are the same as for the TVM functions. I. If you omit FV. page 7. Step]) Returns the forward-difference quotient (average rate of change). page 145. [roundValue]) ⇒ value bal(NPmt. If Step is omitted. Note that the similar function centralDiff() uses the centraldifference quotient. Default=2.amortTable) Catalog > ⇒ value Amortization function that calculates schedule balance after a specified payment. I. Pmt. PV. Step]) ⇒ list avgRC(Matrix1. it defaults to Pmt=tvmPmt(N.augment() augment(Matrix1. avgRC() Catalog > ⇒ expression avgRC(Expr1. Note: See also GInt() and GPrn(). Pmt.PV. When the “. Var [=Value] [.I. [PmtAt]. Does not alter Matrix1 or Matrix2.CpY. Expr1 can be a user-defined function name (see Func). 4Base2 Integer1 4Base2 ⇒ integer Note: You can insert this operator from the computer keyboard by typing @>Base2. Catalog > 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. Catalog > 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 4Base16 Integer1 4Base16 ⇒ integer Note: You can insert this operator from the computer keyboard by Catalog > 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 > binomPdf(n,p,XVal) XVal is a list ⇒ number ⇒ number if XVal is a number, list if 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 “with” 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() cFactor(Expr1[,Var]) ⇒ expression cFactor(List1[,Var]) ⇒ list cFactor(Matrix1[,Var]) ⇒ matrix Catalog > 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. £ and then use ¡ and ¢ to 16 TI-Nspire™ CAS Reference Guide For P(X  upBound). list if lowBound and upBound are lists Catalog > Computes the c2 distribution probability between lowBound and upBound for the specified degrees of freedom df. TI-Nspire™ CAS Reference Guide 17 . The characteristic polynomial of n×n matrix A.Matrix2) ⇒ polynomial expression charPoly(squareMatrix.df) ⇒ number if lowBound and upBound are numbers. list if lowBound and upBound are lists chi2Cdf(lowBound.results variable. 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.) For information on the effect of empty elements in a matrix. The valid range for Integer is 0– 65535. A summary of results is stored in the stat.ExpMat stat.PVal stat. (See page 112.CompMat Description Chi square stat: sum (observed .char() char(Integer) Catalog > ⇒ character Returns a character string containing the character numbered Integer from the handheld character set.upBound.df stat. squareMatrix1 and squareMatrix2 must have the equal dimensions. see “Empty (void) elements” on page 152. see “Empty (void) elements” on page 152.upBound.c2 stat. assuming null hypothesis Matrix of elemental chi square statistic contributions c2Cdf() c2Cdf(lowBound.Var) Returns the characteristic polynomial of squareMatrix.df) ⇒ number if lowBound and upBound are numbers. For information on the effect of empty elements in a list. set lowBound = 0. denoted by pA(l). Output variable stat.expected)2/expected Smallest level of significance at which the null hypothesis can be rejected Degrees of freedom for the chi square statistics Matrix of expected elemental count table. charPoly() Catalog > ⇒ polynomial expression charPoly(squareMatrix.Expr) ⇒ polynomial expression charPoly(squareMatrix1. is the polynomial defined by pA(l) = det(l• I NA) where I denotes the n×n identity matrix. A summary of results is stored in the stat.results variable.df Performs a test to confirm that sample data is from a population that conforms to a specified distribution.df stat.CompList Description Chi square stat: sum((observed . obsList is a list of counts and must contain integers.expList.PVal stat. see “Empty (void) elements” on page 152. 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. this command displays an error message and deletes only the unlocked variables. For information on the effect of empty elements in a list.) For information on the effect of empty elements in a list.expected)2/expected Smallest level of significance at which the null hypothesis can be rejected Degrees of freedom for the chi square statistics Elemental chi square statistic contributions c2Pdf() c2Pdf(XVal. Output variable stat.df chi2GOF obsList.c2 stat.df) ⇒ number if XVal is a number. See unLock. (See page 112.c2GOF c 2 Catalog > GOF obsList. If one or more of the variables are locked. page 127.expList.df) a list Catalog > ⇒ number if XVal is a number. list if XVal is a list chi2Pdf(XVal. ClearAZ ClearAZ Catalog > Clears all single-character variables in the current problem space. see “Empty (void) elements” on page 152. 18 TI-Nspire™ CAS Reference Guide . the error dialog box will be displayed as normal. Note: See also PassErr. and Matrix2 is appended to Matrix1 as new rows. comDenom() comDenom(Expr1[. colNorm() colNorm(Matrix) Catalog > ⇒ expression Returns the maximum of the sums of the absolute values of the elements in the columns in Matrix. The matrices must have equal column dimensions. See Example 2 under the Try command. The Else clause of the Try. If the error is to be processed or ignored. Note: See also rowDim().. Does not alter Matrix1 or Matrix2. use PassErr to send it to the next error handler. page 122. page 122.. and Try...EndTry error handlers. Matrix2) · Catalog > ⇒ matrix Returns a new matrix that is Matrix2 appended to Matrix1.Else. If what to do with the error is not known. On the computer keyboard.. colAugment() colAugment(Matrix1.EndTry block should use ClrErr or PassErr. Clears the error status and sets system variable errCode to zero..Var]) ⇒ expression comDenom(List1[. you can enter multi-line definitions by pressing @ instead of at the end of each line. hold down Alt and press Enter. See also rowNorm().. Note for entering the example: In the Calculator application on the handheld. use ClrErr. If there are no more pending Try.ClrErr ClrErr Catalog > For an example of ClrErr. page 83.Var]) ⇒ list comDenom(Matrix1[.Else.Var]) ⇒ matrix Catalog > comDenom(Expr1) returns a reduced ratio of a fully expanded numerator over a fully expanded denominator. colDim() colDim(Matrix) Catalog > ⇒ expression Returns the number of columns contained in Matrix. TI-Nspire™ CAS Reference Guide 19 . Note: Undefined matrix elements are not allowed.. Note: All undefined variables are treated as real variables. conj() conj(Expr1) ⇒ expression conj(List1) ⇒ list conj(Matrix1) ⇒ matrix Catalog > Returns the complex conjugate of the argument. There might be some incidental factoring of the collected coefficients. Such results usually save even more time.Var2.Var) returns a reduced ratio of numerator and denominator expanded with respect to Var. and screen space. Expr is an expression in variables Var1 and Var2. Var2 is incremented from 1 through numCols. Var1 is automatically incremented from 1 through numRows. It also makes subsequent operations on the result faster and less likely to exhaust memory. Such partially factored results also make subsequent operations on the result much faster and much less likely to exhaust memory. memory. comDenom(Expr1. Catalog > If Var does not occur in Expr1. Elements in the resulting matrix are formed by evaluating Expr for each incremented value of Var1 and Var2.Var1. Within each row. Compared to omitting Var. memory.numRows. while making the expression more comprehensible. Similar powers of Var are collected. The terms and their factors are sorted with Var as the main variable. constructMat() constructMat(Expr.Var) returns a reduced ratio of an unexpanded numerator over an unexpanded denominator. and screen space. this often saves time.numCols) Catalog > ⇒ matrix Returns a matrix based on the arguments.comDenom() comDenom(Expr1. 20 TI-Nspire™ CAS Reference Guide . the comden function is often a fast way to achieve partial factorization if factor() is too slow or if it exhausts memory. Even when there is no denominator. Hint: Enter this comden() function definition and routinely try it as an alternative to comDenom() and factor(). CopyVar CopyVar Var1, Var2 CopyVar Var1. , Var2. Catalog > 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. corrMat() corrMat(List1,List2[,…[,List20]]) Catalog > Computes the correlation matrix for the augmented matrix [List1, List2, ..., List20]. 4cos Expr 4cos Note: You can insert this operator from the computer keyboard by Catalog > 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. TI-Nspire™ CAS Reference Guide 21 cos() μ key In Degree angle mode: ⇒ expression cos(List1) ⇒ list cos(Expr1) 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 ó, G, or ôto override the angle mode temporarily. In Gradian angle mode: In Radian angle mode: 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 Xêand f(A) = X f(B) Xê. For example, cos(A) = X cos(B) Xê where: cos(B) = All computations are performed using floating-point arithmetic. 22 TI-Nspire™ CAS Reference Guide cos ê() cosê(Expr1) ⇒ expression cosê(List1) ⇒ list μ key In Degree angle mode: cosê(Expr1) returns the angle whose cosine is Expr1 as an expression. cosê(List1) returns a list of the inverse cosines of each element of List1. Note: The result is returned as a degree, gradian or radian angle, In Gradian angle mode: In Radian angle mode: according to the current angle mode setting. Note: You can insert this function from the keyboard by typing arccos(...). cosê(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. cosh() cosh(Expr1) ⇒ expression cosh(List1) ⇒ list £ and then use ¡ and ¢ to Catalog > 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 Returns the matrix hyperbolic cosine of squareMatrix1. This is not the same as calculating the hyperbolic cosine of each element. For information about the calculation method, refer to cos(). squareMatrix1 must be diagonalizable. The result always contains floating-point numbers. In Radian angle mode: cosh ê() coshê(Expr1) ⇒ expression coshê(List1) ⇒ list Catalog > coshê(Expr1) returns the inverse hyperbolic cosine of the argument as an expression. coshê(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(...). TI-Nspire™ CAS Reference Guide 23 gradian or radian angle. The result always contains floating-point numbers. Note: You can insert this function from the keyboard by typing arccot(. Note: The argument is interpreted as a degree. according to the current angle mode setting. gradian or radian In Gradian angle mode: angle..cosh ê() coshê(squareMatrix1) Catalog > ⇒ squareMatrix In Radian angle mode and In Rectangular Complex Format: Returns the matrix inverse hyperbolic cosine of squareMatrix1. For information about the calculation method. To see the entire result. Note: The result is returned as a degree. This is not the same as calculating the inverse hyperbolic cosine of each element. refer to cos(). You can use ó. In Radian angle mode: cot ê() cotê(Expr1) ⇒ expression cotê(List1) ⇒ list μ key In Degree angle mode: Returns the angle whose cotangent is Expr1 or returns a list containing the inverse cotangents of each element of List1.. squareMatrix1 must be diagonalizable. G. In Gradian angle mode: according to the current angle mode setting. press move the cursor. orôto override the angle mode temporarily. 24 TI-Nspire™ CAS Reference Guide . cot() cot(Expr1) ⇒ expression cot(List1) ⇒ list £ and then use ¡ and ¢ to μ key In Degree angle mode: Returns the cotangent of Expr1 or returns a list of the cotangents of all elements in List1.). In Radian angle mode: coth() coth(Expr1) ⇒ expression coth(List1) ⇒ list Catalog > Returns the hyperbolic cotangent of Expr1 or returns a list of the hyperbolic cotangents of all elements of List1. Returns the accumulated count of all elements in List that meet the specified Criteria. Counts the number of elements equal to “def.. Counts 1 and 3.cothê() cothê(Expr1) ⇒ expression cothê(List1) ⇒ list Catalog > Returns the inverse hyperbolic cotangent of Expr1 or returns a list containing the inverse hyperbolic cotangents of each element of List1. list. and 7. only 1/2 and 3+4*i are counted.. you can use a range of cells in place of any argument.. Note: See also sumIf().Criteria) Catalog > ⇒ value Counts the number of elements equal to 3. or string.Value2orList2 [. You can mix data types and use arguments of various dimensions. page 115. Criteria can be: • • A value.]]) Catalog > ⇒ value Returns the accumulated count of all elements in the arguments that evaluate to numeric values. In the last example. Counts 1. For more information on empty elements.. each element is evaluated to determine if it should be included in the count. or range of cells. Counts the number of elements equal to x. TI-Nspire™ CAS Reference Guide 25 . countif() countif(List. Counts 3. For example. 7. The remaining arguments. Within the Lists & Spreadsheet application. Empty (void) elements in the list are ignored.. see page 152. Each argument can be an expression. Empty (void) elements are ignored.” Within the Lists & Spreadsheet application. this example assumes the variable x is undefined. 5. matrix. A Boolean expression containing the symbol ? as a placeholder for each element.). Note: You can insert this function from the keyboard by typing arccoth(. do not evaluate to numeric values. you can use a range of cells in place of List. value. For a list. 3 counts only those elements in List that simplify to the value 3. 3. page 49. and frequency(). or matrix. For more information on empty elements. expression. count() count(Value1orList1 [. assuming x is undefined. see page 152. ?<5 counts only those elements in List that are less than 5. For example. and 9. and the dimension must be either 2 or 3. or both must be column vectors. returns a list of complex roots of polynomial Poly with respect to variable Var. cPolyRoots(ListOfCoeffs).Var). and the dimension must be either 2 or 3. crossP(Vector1. Both vectors must have equal dimension. crossP() crossP(List1. cPolyRoots(Poly.cPolyRoots() Catalog > ⇒ list cPolyRoots(ListOfCoeffs) ⇒ list cPolyRoots(Poly. Note: See also polyRoots(). csc() csc(Expr1) ⇒ expression csc(List1) ⇒ list μ key In Degree angle mode: Returns the cosecant of Expr1 or returns a list containing the cosecants of all elements in List1. List2) Catalog > ⇒ list Returns the cross product of List1 and List2 as a list. The second syntax. page 87.Var) The first syntax. returns a list of complex roots for the coefficients in ListOfCoeffs. Both Vector1 and Vector2 must be row vectors. Poly must be a polynomial in one variable. In Gradian angle mode: In Radian angle mode: 26 TI-Nspire™ CAS Reference Guide . Vector2) ⇒ vector Returns a row or column vector (depending on the arguments) that is the cross product of Vector1 and Vector2. List1 and List2 must have equal dimension. cSolve() temporarily sets the domain to complex during the solution even if the current domain is real.. cSolve() Catalog > ⇒ Boolean expression cSolve(Equation.cscê() csc ê(Expr1) ⇒ expression csc ê(List1) ⇒ list μ key In Degree angle mode: Returns the angle whose cosecant is Expr1 or returns a list containing the inverse cosecants of each element of List1. TI-Nspire™ CAS Reference Guide 27 ..).). Note: You can insert this function from the keyboard by typing arccsc(. The goal is to produce candidates for all real and non-real solutions. Even if Equation is real. Although all undefined variables that do not end with an underscore (_) are processed as if they were real. Consequently. Note: The result is returned as a degree. cSolve() allows non-real results in Real result Complex Format. Var) ⇒ Boolean expression cSolve(Equation. solutions from solve() to equations involving such fractional powers are not necessarily a subset of those from cSolve(). Var) Returns candidate complex solutions of an equation or inequality for Var. cSolve() can solve polynomial equations for complex solutions. cschê() cschê(Expr1) ⇒ expression cschê(List1) ⇒ list Catalog > Returns the inverse hyperbolic cosecant of Expr1 or returns a list containing the inverse hyperbolic cosecants of each element of List1. Var=Guess) ⇒ Boolean expression cSolve(Inequality. In Gradian angle mode: according to the current angle mode setting. Note: You can insert this function from the keyboard by typing arccsch(.. In Radian angle mode: csch() Catalog > ⇒ expression csch(List1) ⇒ list csch(Expr1) Returns the hyperbolic cosecant of Expr1 or returns a list of the hyperbolic cosecants of all elements of List1. gradian or radian angle.. fractional powers having odd denominators use the principal rather than the real branch. In the complex domain. VarOrGuess2 [. These solutions show how families of solutions might contain arbitrary constants of the form ck. you can specify an initial guess for a variable. VarOrGuess1. press If your initial choice exhausts memory or your patience. press the cursor. you may receive unexpected results. By default. x is valid and so is x=3+i. … ]) ⇒ Boolean expression cSolve(SystemOfEqns. …]) ⇒ Boolean expression Returns candidate complex solutions to the simultaneous algebraic equations. and zeros(). computation time or memory exhaustion may depend strongly on the order in which you list solution variables. but represent given numeric values that could be substituted later. you should place an underscore Catalog > In Display Digits mode of Fix 2: (press ) at the end of Var. Optionally. try the cursor. where each varOrGuess specifies a variable that you want to solve for. If you use var_ . VarOrGuess2 [.cSolve() cSolve() starts with exact symbolic methods. real(). If all of the equations are polynomials and if you do NOT specify any initial guesses. Complex solutions can include both real and non-real solutions. angle(). as in the example to the right. Note: See also cZeros(). rearranging the variables in the equations and/or varOrGuess list. the variable is treated as complex. a variable is treated as a real value. if necessary. cSolve() uses the lexical Gröbner/Buchberger elimination method to attempt to determine all complex solutions. £ and then use ¡ and ¢ to move £ and then use ¡ and ¢ to move 28 TI-Nspire™ CAS Reference Guide . Simultaneous polynomial equations can have extra variables that have no values. VarOrGuess1. press the cursor. Note: The following examples use an underscore (press / _) so that the variables will be treated as complex. To see the entire result. conj(). Otherwise. cSolve() also uses iterative approximate complex polynomial factoring. z_ is treated as complex: z is treated as real: /_ £ and then use ¡ and ¢ to move cSolve(Eqn1 and Eqn2 [and …]. To see the entire result. You can also include solution variables that do not appear in the equations. Note: If Equation is non-polynomial with functions such as abs(). or imag(). solve(). £ and then use ¡ and ¢ to move To see the entire result. To see the entire result. You should also use var_ for any other variables in Equation that might have unreal values. press the cursor. Each varOrGuess must have the form: variable – or – variable = real or non-real number For example. For polynomial systems. where k is an integer suffix from 1 through 255. stat.XReg Description Regression equation: a·x3+b·x2+c·x+d Regression coefficients Coefficient of determination Residuals from the regression List of data points in the modified X List actually used in the regression based on restrictions of Freq. and all other variables in the equations must simplify to numbers. [Freq] [.Resid stat. stat. Output variable stat. the number of solution variables must equal the number of equations. and Include Categories List of frequencies corresponding to stat.cSolve() 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. To see the entire result. Only those data items whose category code is included in this list are included in the calculation. see “Empty (void) elements” on page 152. Category List.R2 stat. A non-real guess is often necessary to determine a non-real solution.XReg and stat. Each element in Freq specifies the frequency of occurrence for each corresponding X and Y data point. Category is a list of category codes for the corresponding X and Y data. All elements must be integers | 0.c.YReg stat.b. A summary of results is stored in the stat.FreqReg TI-Nspire™ CAS Reference Guide 29 .RegEqn stat.a. stat. Category List. Catalog > If a system is neither polynomial in all of its variables nor linear in its solution variables. Freq is an optional list of frequency values. CubicReg CubicReg X.d stat. (See page 112. X and Y are lists of independent and dependent variables. cSolve() uses Gaussian elimination to attempt to determine all solutions. For information on the effect of empty elements in a list. Include]] £ and then use ¡ and ¢ to move Catalog > Computes the cubic polynomial regression y = a·x3+b· x2+c·x+d on lists X and Y with frequency Freq.results variable. For convergence. a guess might have to be rather close to a solution. The default value is 1. Include is a list of one or more of the category codes. To do so. Category. and Include Categories List of data points in the modified Y List actually used in the regression based on restrictions of Freq.) All the lists must have equal dimension except for Include. Y[. press the cursor.YReg stat. cSolve() determines at most one solution using an approximate iterative method. cumulativeSum() cumulativeSum(List1) Catalog > ⇒ list Returns a list of the cumulative sums of the elements in List1. and zeros(). Vector must have exactly three elements. While. hold down Alt and press Enter. While. cZeros() is similar to zeros().Var). you can enter multi-line definitions by pressing @ instead of at the end of each line. £ and then use ¡ and ¢ to 30 TI-Nspire™ CAS Reference Guide . press move the cursor. · 4Cylind Vector 4Cylind Note: You can insert this operator from the computer keyboard by typing @>Cylind. Transfers control immediately to the next iteration of the current loop (For. Each element is the cumulative sum of the column from top to bottom. or Loop). or Loop). An empty (void) element in List1 or Matrix1 produces a void element in the resulting list or matrix. cZeros() cZeros(Expr.q. For more information on empty elements. Otherwise. z]. 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. Note for entering the example: In the Calculator application on the handheld. Note: See also cSolve(). Cycle is not allowed outside the three looping structures (For. solve(). On the computer keyboard.Var). Catalog > Displays the row or column vector in cylindrical form [r. see page 152. starting at element 1. cumulativeSum(Matrix1) ⇒ matrix Returns a matrix of the cumulative sums of the elements in Matrix1. It can be either a row or a column. Cycle Cycle Catalog > Function listing that sums the integers from 1 to 100 skipping 50. To see the entire result. cZeros() does this by computing exp4list(cSolve(Expr=0. cZeros() uses the lexical Gröbner/Buchberger elimination method to attempt to determine all complex zeros. If all of the expressions are polynomials and you do NOT specify any initial guesses. a variable is treated (press as a real value. index the matrix by [row]. you can specify an initial guess for a variable. Each row of the resulting matrix represents an alternate zero. By default. Complex zeros can include both real and non-real zeros. … ] }. Each VarOrGuess must have the form: variable – or – variable = real or non-real number For example. If your initial choice exhausts memory or your patience. where k is an integer suffix from 1 through 255. or imag(). To extract a row. cZeros({Expr1.cZeros() Note: If Expr is non-polynomial with functions such as abs(). TI-Nspire™ CAS Reference Guide 31 . Expr2 [. You should also use var_ for any other variables in Expr that might have unreal values.VarOrGuess2 [. with the components ordered the same as the VarOrGuess list. Extract row 2: Simultaneous polynomials can have extra variables that have no values. … ] }) /_ z_ is treated as complex: ⇒ matrix Returns candidate positions where the expressions are zero simultaneously. Note: The following examples use an underscore _ (press / _) so that the variables will be treated as complex. Otherwise. try rearranging the variables in the expressions and/or VarOrGuess list. as in the example to the right. conj(). If you use var_ . real(). For polynomial systems. x is valid and so is x=3+i. These zeros show how families of zeros might contain arbitrary constants of the form ck. computation time or memory exhaustion may depend strongly on the order in which you list unknowns. Each VarOrGuess specifies an unknown whose value you seek. you should place an underscore ) at the end of Var. you may receive unexpected results. {VarOrGuess1. You can also include unknown variables that do not appear in the expressions. Optionally. but represent given numeric values that could be substituted later. Catalog > z is treated as real: angle(). the variable is treated as complex. Catalog > If a system is neither polynomial in all of its variables nor linear in its unknowns. list. The argument is a number. For convergence. date1 and date2 must be between the years 1950 through 2049. A non-real guess is often necessary to determine a non-real zero. MM. radians or degrees.YY (format use commonly in Europe) 4DD Expr1 4DD ⇒ value List1 4DD ⇒ list Matrix1 4DD ⇒ matrix Note: You can insert this operator from the computer keyboard by typing @>DD. and all other variables in the expressions must simplify to numbers. In Gradian angle mode: In Radian angle mode: 32 TI-Nspire™ CAS Reference Guide . The decimal placement differentiates between the date formats. they must be the same length. cZeros() determines at most one zero using an approximate iterative method. a guess might have to be rather close to a zero. If both date1 and date2 are lists.date2) Catalog > ⇒ value Returns the number of days between date1 and date2 using the actual-day-count method. or matrix that is interpreted by the Angle mode setting in gradians. You can enter the dates in either of two formats. Catalog > In Degree angle mode: Returns the decimal equivalent of the argument expressed in degrees.cZeros() If you do not include any guesses and if any expression is nonpolynomial in any variable but all expressions are linear in all unknowns. the number of unknowns must equal the number of expressions. date1 and date2 can be numbers or lists of numbers within the range of the dates on the standard calendar. To do so. D dbd() dbd(date1. cZeros() uses Gaussian elimination to attempt to determine all zeros.DDYY (format used commonly in the United States) DDMM. 4Decimal Expression1 4Decimal ⇒ expression List1 4Decimal ⇒ expression Matrix1 4Decimal ⇒ expression Note: You can insert this operator from the computer keyboard by Catalog > typing @>Decimal. Displays the argument in decimal form. This operator can be used only at the end of the entry line. Define Define Var = Expression Define Function(Param1, Param2, ...) = Expression Catalog > 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 34. TI-Nspire™ CAS Reference Guide 33 Define LibPriv Define LibPriv Var = Expression Define LibPriv Function(Param1, Param2, ...) = Expression Define LibPriv Function(Param1, Param2, ...) = Func Catalog > 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 33, and Define LibPub, page 34. Define LibPub Define LibPub Var = Expression Define LibPub Function(Param1, Param2, ...) = Expression Define LibPub Function(Param1, Param2, ...) = Func Catalog > 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 33, and Define LibPriv, page 34. deltaList() See @List(), page 64. deltaTmpCnv() See @tmpCnv(), page 121. DelVar DelVar Var1[, Var2] [, Var3] ... DelVar Var. Deletes the specified variable or variable group from memory. Catalog > If one or more of the variables are locked, this command displays an error message and deletes only the unlocked variables. See unLock, page 127. 34 TI-Nspire™ CAS Reference Guide DelVar DelVar Var. deletes all members of the Var. variable group (such as Catalog > 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 152. derivative() See d(), page 142. deSolve() deSolve(1stOr2ndOrderODE, Var, depVar) Catalog > ⇒ 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: • • 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. º 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. TI-Nspire™ CAS Reference Guide 35 computations are done using floatingpoint arithmetic. depVar) ⇒ a particular solution Returns a particular solution that satisfies 2ndOrderODE and has specified values at two different points. any matrix element is treated as zero if its absolute value is less than Tolerance. det() det(squareMatrix[.deSolve() deSolve(1stOrderODE and initCond. substituting initial values. Var. solving for the arbitrary constant. 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. Var. the default tolerance is calculated as: 5EM14 ·max(dim(squareMatrix))· rowNorm(squareMatrix) /· • 36 TI-Nspire™ CAS Reference Guide . use the form: depVar (initialIndependentValue) = initialDependentValue For initCond2. 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. Implicit differentiation can help verify implicit solutions. Var. deSolve(2ndOrderODE and initCond1 and initCond2. For initCond1. Otherwise. and then substituting that value into the general solution. This is usually easier than determining a general solution. use the form: depVar (initialIndependentValue) = initial1stDerivativeValue deSolve(2ndOrderODE and bndCond1 and bndCond2. 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. If Tolerance is omitted or not used. depVar) Catalog > ⇒ a particular solution Returns a particular solution that satisfies 1stOrderODE and initCond. • If you use or set the Auto or Approximate mode to Approximate. Tolerance is ignored. Tolerance]) Catalog > ⇒ expression Returns the determinant of squareMatrix. Optionally. Useful mainly in programs and functions to ensure the display of intermediate calculations. The arguments are displayed in succession. Disp Disp [exprOrString1] [. On the computer keyboard. dim(String) ⇒ integer Returns the number of characters contained in character string String. exprOrString2] .. squareMatrix must be square. with thin spaces as separators.. · TI-Nspire™ CAS Reference Guide 37 . hold down Alt and press Enter. Catalog > Displays the arguments in the Calculator history. Note for entering the example: In the Calculator application on the handheld. diag(squareMatrix) ⇒ rowMatrix Returns a row matrix containing the elements from the main diagonal of squareMatrix. you can enter multi-line definitions by pressing @ instead of at the end of each line. columns}. dim() dim(List) Catalog > ⇒ integer ⇒ list Returns the dimension of List. dim(Matrix) Returns the dimensions of matrix as a two-element list {rows.diag() diag(List) ⇒ matrix diag(rowMatrix) ⇒ matrix diag(columnMatrix) ⇒ matrix Catalog > Returns a matrix with the values in the argument list or matrix in its main diagonal. eN1/z at z=0. Point]) | Var>Point ⇒ expression dominantTerm(Expr1. or “Var  Point” to obtain a simpler result. dominantTerm() is also useful when it isn’t obvious what the degree of the first non-zero term of a series will be. dominantTerm(…) returns “dominantTerm(…)” if it is unable to determine such a representation. You can use 4DMS only at the end of an entry line. minutes.) the appropriate one of “| Var > 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. Var [.ss'') number. '' on page 147 for DMS (degree. '. “| “Var ‚ Point”. page 101. Var [. Catalog > In Degree angle mode: Interprets the argument as an angle and displays the equivalent DMS (DDDDDD¡MM'SS. dominantTerm() is useful when you want to know the simplest possible expression that is asymptotic to another expression as Var " Point. seconds) format. and you don’t want to iteratively guess either interactively or by a program loop. If you intend to use the dominant term only for values on one side of Point. Point can be ˆ or Nˆ. which is one ending with “_”. “| Var < Point”. 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. 38 TI-Nspire™ CAS Reference Guide ... dotP() dotP(List1. Note: 4DMS will convert from radians to degrees when used in radian mode. If the series or one of its derivatives has a jump discontinuity at Point. See ¡. then append to dominantTerm(. Point defaults to 0. or ez at z = ˆ or Nˆ. Point]) | Var<Point ⇒ expression Returns the dominant term of a power series representation of Expr1 expanded about Point. List2) Catalog > ⇒ expression Returns the “dot” product of two lists.4DMS Expr 4DMS List 4DMS Matrix 4DMS Note: You can insert this operator from the computer keyboard by typing @>DMS. The resulting power of (Var N Point) can have a negative and/or fractional exponent. Var [. such as for essential singularities such as sin(1/z) at z=0. dominantTerm() dominantTerm(Expr1. no conversion will occur. in which cases the dominant term will be the term having the largest exponent of Var rather than the smallest exponent of Var. dominantTerm() distributes over 1st-argument lists and matrices. Note: See also series(). If the input is followed by a degree symbol ¡ . Point]) Catalog > ⇒ expression dominantTerm(Expr1. The dominant term is the one whose magnitude grows most rapidly near Var = Point. TI-Nspire™ CAS Reference Guide 39 . given CpY as the number of compounding periods per year. However. e^(List1) ⇒ list Returns e raised to the power of each element in List1. page 2. Note: See also nom().dotP() dotP(Vector1. or both must be column vectors. and CpY must be a real number > 0. You can enter a complex number in rei q polar form. page 78. E e^() e^(Expr1) u key ⇒ expression Returns e raised to the Expr1 power. eff() eff(nominalRate. This is not the same as calculating e raised to the power of each element. it causes a Domain error in Degree or Gradian angle mode. For information about the calculation method.CpY) Catalog > ⇒ value Financial function that converts the nominal interest rate nominalRate to an annual effective rate. Both must be row vectors. nominalRate must be a real number. Note: Pressing character u to display e^( is different from pressing the E on the keyboard. refer to cos(). e^(squareMatrix1) ⇒ squareMatrix Returns the matrix exponential of squareMatrix1. squareMatrix1 must be diagonalizable. Vector2) Catalog > ⇒ expression Returns the “dot” product of two vectors. The result always contains floating-point numbers. Note: See also e exponent template. use this form in Radian angle mode only. … . · EndFor See For. The squareMatrix is then reduced to upper Hessenberg form and the eigenvalues are computed from the upper Hessenberg matrix. On the computer keyboard. x n]. hold down Alt and press Enter. Note that an eigenvector is not unique. 40 TI-Nspire™ CAS Reference Guide . The eigenvectors are normalized. page 47. x 2. press move the cursor. To see the entire result. it may be scaled by any constant factor. The squareMatrix is then reduced to upper Hessenberg form and the eigenvectors are computed via a Schur factorization. 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. Else £ and then use ¡ and ¢ to See If. page 50. EndFunc See Func. squareMatrix is first balanced with similarity transformations until the row and column norms are as close to the same value as possible. To see the entire result. you can enter multi-line definitions by pressing @ instead of at the end of each line. meaning that if V = [x 1. eigVl() eigVl(squareMatrix) £ and then use ¡ and ¢ to Catalog > ⇒ list In Rectangular complex format mode: Returns a list of the eigenvalues of a real or complex squareMatrix. where each column in the result corresponds to an eigenvalue. page 54. ElseIf If BooleanExpr1 Then Block1 ElseIf BooleanExpr2 Then Block2 Catalog > © ElseIf BooleanExprN Then BlockN EndIf © Note for entering the example: In the Calculator application on the handheld. press move the cursor.eigVc() eigVc(squareMatrix) Catalog > ⇒ matrix In Rectangular Complex Format: Returns a matrix containing the eigenvectors for a real or complex squareMatrix. While. page 69. page 88. or Loop). Note for entering the example: In the Calculator application on the handheld. or Loop block. the default is 0 (zero). page 128. Tolerance]) ⇒ matrix Catalog > Uses Exact mode arithmetic to return. While. Exit is not allowed outside the three looping structures (For. page 122. EndTry See Try. EndLoop See Loop. page 54. EndPrgm See Prgm. Tolerance]) ⇒ expression exact( List1 [. · TI-Nspire™ CAS Reference Guide 41 . On the computer keyboard. the rationalnumber equivalent of the argument. exact() exact( Expr1 [. Exit Exit Catalog > Function listing: Exits the current For.EndIf See If. hold down Alt and press Enter. Tolerance]) ⇒ list exact( Matrix1 [. Tolerance specifies the tolerance for the conversion. EndWhile See While. you can enter multi-line definitions by pressing @ instead of at the end of each line. when possible. The expansion is polynomial expansion for polynomials and partial fraction expansion for rational expressions. exp4list() exp4list(Expr.Var]) ⇒ list expand(Matrix1 [. use this form in Radian angle mode only.. In contrast. Note: You can insert this operator from the computer keyboard by typing @>exp. exp(List1) ⇒ list Returns e raised to the power of each element in List1. fMin(). Catalog > exp() exp(Expr1) u key ⇒ expression Returns e raised to the Expr1 power. This is a display conversion operator. You can enter a complex number in rei q polar form. Note: See also e exponent template. However. 42 TI-Nspire™ CAS Reference Guide .4exp Expr 4exp Represents Expr in terms of the natural exponential e. page 2. and fMax() functions. The result always contains floating-point numbers. It can be used only at the end of the entry line. the goal of factor() is to transform Expr1 into a product and/or quotient of simple factors.Var]) ⇒ matrix expand(Expr1 [. squareMatrix1 must be diagonalizable.Var) Catalog > ⇒ list Examines Expr for equations that are separated by the word “or. You can insert this function from the keyboard by typing exp@>list(.). exp(squareMatrix1) ⇒ squareMatrix Returns the matrix exponential of squareMatrix1. This is not the same as calculating e raised to the power of each element. refer to cos(). Var]) expand(Expr1) returns Expr1 expanded with respect to all its variables. expand() Catalog > ⇒ expression expand(List1 [. This gives you an easy way to extract some solution values embedded in the results of the solve(). cSolve(). it causes a Domain error in Degree or Gradian angle mode. Note: exp4list() is not necessary with the zeros and cZeros() functions because they return a list of solution values directly. The goal of expand() is to transform Expr1 into a sum and/or difference of simple terms..” and returns a list containing the right-hand sides of the equations of the form Var=Expr. For information about the calculation method. expand(Expr1. regardless of Var. sign(). Similar powers of Var are collected. while making the expression more comprehensible. this often saves time. expr() expr(String) Catalog > ⇒ expression Returns the character string contained in String as an expression and immediately executes it. and exponentials.expand() expand(Expr1. propFrac() is a faster but less extreme alternative to expand(). For increased distribution of logarithms and fractional powers. Note: See also comDenom() for an expanded numerator over an expanded denominator. TI-Nspire™ CAS Reference Guide 43 . Compared to omitting Var. Catalog > Even when there is only one variable.Var) returns Expr1 expanded with respect to Var. The terms and their factors are sorted with Var as the main variable. [Var]) also distributes absolute values. memory. Note: See also tExpand() for trigonometric angle-sum and multiple-angle expansion. inequality constraints might be necessary to guarantee that some factors are nonnegative. expand(Expr1.[Var]) also distributes logarithms and fractional powers regardless of Var. There might be some incidental factoring or expansion of the collected coefficients. Hint: For rational expressions. and screen space. using Var might make the denominator factorization used for partial fraction expansion more complete. The default value is 1. A summary of results is stored in the stat. Include]] Catalog > Computes the exponential regression y = a·(b)x on lists X and Y with frequency Freq. X and Y are lists of independent and dependent variables. Only those data items whose category code is included in this list are included in the calculation. Expr1 is factored as much as possible toward linear rational factors without introducing new non-real subexpressions. Include is a list of one or more of the category codes.Resid stat. This alternative is appropriate if you want factorization with respect to more than one variable. Category List. ln(y)) Residuals associated with the exponential model Residuals associated with linear fit of transformed data List of data points in the modified X List actually used in the regression based on restrictions of Freq.YReg stat.) All the lists must have equal dimension except for Include. Var]) factor(List1[. Y [.Var]) ⇒ matrix factor(Expr1[.b stat. stat. Category is a list of category codes for the corresponding X and Y data.XReg 2 Description Regression equation: a·(b)x Regression coefficients Coefficient of linear determination for transformed data Correlation coefficient for transformed data (x. 44 TI-Nspire™ CAS Reference Guide . Category List. [Freq] [.r stat. see “Empty (void) elements” on page 152.XReg and stat.Var]) factor(Expr1) returns Expr1 factored with respect to all of its variables over a common denominator. Output variable stat. (See page 112.FreqReg F factor() Catalog > ⇒ expression ⇒ list factor(Matrix1[.r stat.a. Freq is an optional list of frequency values. For information on the effect of empty elements in a list.ResidTrans stat. and Include Categories List of data points in the modified Y List actually used in the regression based on restrictions of Freq. All elements must be integers | 0.ExpReg ExpReg X.RegEqn stat.YReg stat. Each element in Freq specifies the frequency of occurrence for each corresponding X and Y data point. and Include Categories List of frequencies corresponding to stat. Category.results variable. Even when there is only one variable.upBound. matrixVar must already exist.Var) returns Expr1 factored with respect to variable Var. For P(X  upBound). matrixVar Catalog > Catalog > ⇒ matrix Replaces each element in variable matrixVar with Expr. 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. set lowBound = 0. Fill Fill Expr. 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. the computing time grows exponentially with the number of digits in the second-largest factor. Note: See also comDenom() for a fast way to achieve partial Catalog > factoring when factor() is not fast enough or if it exhausts memory. list if lowBound and upBound are lists FCdf(lowBound. The factors and their terms are sorted with Var as the main variable. including Var might yield more complete factorization. TI-Nspire™ CAS Reference Guide 45 . factoring a 30-digit integer could take more than a day. Similar powers of Var are collected in each factor. Note: See also cFactor() for factoring all the way to complex coefficients in pursuit of linear factors. For composite numbers.dfNumer. For example. It is much faster. For the Auto setting of the Auto or Approximate mode. factor(rationalNumber) returns the rational number factored into primes. Expr1 is factored as much as possible toward real factors that are linear in Var. If you merely want to determine if a number is prime. particularly if rationalNumber is not prime and if the second-largest factor has more than five digits. There might be some incidental factoring with respect to other variables.dfDenom) ⇒ number if lowBound and upBound are numbers. use isPrime() instead.upBound. Note: To interrupt a computation. FCdf() FCdf(lowBound. and factoring a 100-digit number could take more than a century. even if it introduces irrational constants or subexpressions that are irrational in other variables.dfNumer.factor() factor(Expr1. press and hold d or c. including Var permits approximation with floating-point coefficients where irrational coefficients cannot be explicitly expressed concisely in terms of the built-in functions.dfDenom) ⇒ number if lowBound and upBound are numbers. Note: See also ceiling() and int().) X represents a list containing the data. Maximum of x values. Each element in Freq specifies the frequency of occurrence for each corresponding X and Y data point. 46 TI-Nspire™ CAS Reference Guide . Catalog > Output variable stat. Median of x.MinX stat. An empty (void) element in any of the lists X. Only those data items whose category code is included in this list are included in the calculation. floor(List1) ⇒ list floor(Matrix1) ⇒ matrix Returns a list or matrix of the floor of each element. Category is a list of numeric category codes for the corresponding X data.MaxX Description Minimum of x values. Freq. Include is a list of one or more of the category codes.Fill Fill Expr. The default value is 1.MedianX stat.Q3X stat. 1st Quartile of x. listVar must already exist. Freq is an optional list of frequency values. see page 152. or Category results in a void for the corresponding element of all those lists. 3rd Quartile of x.Q1X stat.results variable. listVar Catalog > ⇒ list Replaces each element in variable listVar with Expr.[Freq][. For more information on empty elements. (See page 112.Include]] Provides an abbreviated version of the 1-variable statistics on list X. floor() floor(Expr1) Catalog > ⇒ integer Returns the greatest integer that is { the argument. This function is identical to int(). FiveNumSummary FiveNumSummary X[. The argument can be a real or a complex number. A summary of results is stored in the stat.Category. fMax() iteratively searches for one approximate local maximum. · TI-Nspire™ CAS Reference Guide 47 .lowBound. The default value is 1. Var must not be a system variable. For the Approximate setting of the Auto or Approximate mode. you can enter multi-line definitions by pressing @ instead of at the end of each line.lowBound) fMin(Expr.lowBound) fMax(Expr. Step can be positive or negative. in increments of Step. fMin() fMin(Expr. hold down Alt and press Enter. Note for entering the example: In the Calculator application on the handheld. Var) | lowBound<Var<upBound Catalog > Returns a Boolean expression specifying candidate values of Var that maximize Expr or locate its least upper bound. Step] Catalog > Block EndFor Executes the statements in Block iteratively for each value of Var. Var. Var. Var) ⇒ Boolean expression fMax(Expr.lowBound.upBound) fMin(Expr. On the computer keyboard. Note: See also fMin() and max(). Var.fMax() fMax(Expr. fMin() iteratively searches for one approximate local minimum. Var) Catalog > ⇒ Boolean expression fMin(Expr.upBound) fMax(Expr. Var) | lowBound<Var<upBound Returns a Boolean expression specifying candidate values of Var that minimize Expr or locate its greatest lower bound. particularly if you use the “|” operator to constrain the search to a relatively small interval that contains exactly one local minimum. Block can be either a single statement or a series of statements separated with the “:” character. This is often faster. High [. Low. You can use the “|” operator to restrict the solution interval and/or specify other constraints. Note: See also fMax() and min(). particularly if you use the “|” operator to constrain the search to a relatively small interval that contains exactly one local maximum. You can use the “|” operator to restrict the solution interval and/or specify other constraints. For the Approximate setting of the Auto or Approximate mode. For For Var. Var. from Low to High. This is often faster. fPart() fPart(Expr1) ⇒ expression fPart(List1) ⇒ list fPart(Matrix1) ⇒ matrix Catalog > Returns the fractional part of the argument. and the decimal point is moved to the right by zero. The argument can be a real or a complex number. If c is a period. For a list or matrix. 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. n is the number of digits after the first significant digit. Empty (void) elements are ignored. 48 TI-Nspire™ CAS Reference Guide . the radix will be shown as a comma... returns the fractional parts of the elements. A value of zero excludes the corresponding List1 element. Each element specifies the number of times the corresponding List1 element will be repeated in the result list. FPdf() FPdf(XVal. Note: You can insert this function from the computer keyboard by typing freqTable@>list(. S[n]: Scientific format. The exponent is adjusted to a multiple of three. For more information on empty elements. see page 152. n is the number of digits to display after the decimal point. List1 can be any valid list. This function can be used for building a frequency table for the Data & Statistics application. “E[n]”.dfDenom) ⇒ number if XVal is a number.format() format(Expr[. freqIntegerList) Catalog > Catalog > ⇒ list Returns a list containing the elements from List1 expanded according to the frequencies in freqIntegerList. where [ ] indicate optional portions. c specifies the group separator character and defaults to a comma. formatString is a string and must be in the form: “F[n]”. one.). [Rc]: Any of the above specifiers may be suffixed with the Rc radix flag. G[n][c]: Same as fixed format but also separates digits to the left of the radix into groups of three. Expr must simplify to a number. “S[n]”. freqIntegerList must have the same dimension as List1 and must contain non-negative integer elements only. F[n]: Fixed format. n is the number of digits to display after the decimal point. “G[n][c]”. E[n]: Engineering format.dfNumer. where c is a single character that specifies what to substitute for the radix point. or two digits. formatString]) Catalog > ⇒ string Returns Expr as a character string based on the format template. If binsList is {b(1).Freq1[.) For Ha: s1 > s2. The counts are based on ranges (bins) that you define in binsList. …. you can use a range of cells in place of both arguments.dfNumer stat. the specified ranges are {?{b(1).List2[. Expressed in terms of the countIf() function.Hypoth]]] Catalog > (Data list input) FTest_2Samp sx1.n2[. stat.F stat.Hypoth] (Summary stats input) Performs a two-sample F test.…. …. Explanation of result: 2 elements from Datalist are {2.Hypoth]]] FTest_2Samp List1. b(n)>?}.Hypoth] FTest_2Samp sx1.sx2 stat.n2 Description Calculated ó statistic for the data sequence Smallest level of significance at which the null hypothesis can be rejected numerator degrees of freedom = n1-1 denominator degrees of freedom = n2-1 Sample standard deviations of the data sequences in List 1 and List 2 Sample means of the data sequences in List 1 and List 2 Size of the samples TI-Nspire™ CAS Reference Guide 49 .5 and {4. For more information on empty elements. countIf(list. b(n)>?)}. set Hypoth<0 For information on the effect of empty elements in a list. the result is { countIf(list.x2_bar stat.b(n-1)<?{b(n).Freq2[. b(n-1)<?{b(n)).5 3 elements from Datalist are >4.x1_bar stat.n2[. countIf(list. Within the Lists & Spreadsheet application.n1. b(1)<?{b(2)). set Hypoth =0 For Ha: s1 < s2.PVal stat. page 25. see “Empty (void) elements” on page 152. b(2).binsList) Catalog > ⇒ list Returns a list containing counts of the elements in List1.Freq2[.sx2. countIf(list. FTest_2Samp FTest_2Samp List1. stat. The resulting list is one element longer than binsList. see page 152. Empty (void) elements are also ignored. Output variable stat. b(1)<?{b(2).frequency() frequency(List1. ?{b(1)). Note: See also countIf(). set Hypoth>0 For Ha: s1 ƒ s2 (default). b(n)}.sx1.n1.sx2. A summary of results is stored in the stat.List2[. Each element of the result corresponds to the number of elements from List1 that are in the range of that bin.5 4 elements from Datalist are >2. (See page 112. Elements of List1 that cannot be “placed in a bin” are ignored.Freq1[.results variable.5 The element “hello” is a string and cannot be placed in any of the defined bins.n1.dfDenom stat. 0. List2) ⇒ list Returns the greatest common divisors of the corresponding elements in List1 and List2. the gcd of fractional floating-point numbers is 1.lowBound. you can enter multi-line definitions by pressing @ Result of graphing g(x) instead of at the end of each line. hold down Alt and press Enter. Block can be a single statement. · G gcd() gcd(Number1. or a series of statements on separate lines. The gcd of two fractions is the gcd of their numerators divided by the lcm of their denominators. On the computer keyboard. gcd(Matrix1. set lowBound = 1. Matrix2) ⇒ matrix Returns the greatest common divisors of the corresponding elements in Matrix1 and Matrix2. In Auto or Approximate mode. Number2) Catalog > ⇒ expression Returns the greatest common divisor of the two arguments. a series of statements separated with the “:” character. 50 TI-Nspire™ CAS Reference Guide . geomCdf() geomCdf(p. For P(X  upBound). Note for entering the example: In the Calculator application on the handheld. list if upBound is a list Catalog > ⇒ number if Computes a cumulative geometric probability from lowBound to upBound with the specified probability of success p. The function can use the Return instruction to return a specific result.Func Func Catalog > Define a piecewise function: Block EndFunc Template for creating a user-defined function. gcd(List1. list if lowBound and upBound are lists geomCdf(p.upBound) ⇒ number if lowBound and upBound are numbers.upBound) for P(1XupBound) upBound is a number. See Lock. for the discrete geometric distribution with the specified probability of success p.geomPdf() geomPdf(p. value =0: Var is unlocked or does not exist. page 127. TI-Nspire™ CAS Reference Guide 51 .XVal) is a list Catalog > ⇒ number if XVal is a number. and unLock. the number of the trial on which the first success occurs. getLangInfo() getLangInfo() Catalog > ⇒ string Returns a string that corresponds to the short name of the currently active language. for example. and then returns its denominator. 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. page 66. You can. list if XVal Computes a probability at XVal. getDenom() getDenom(Expr1) Catalog > ⇒ expression Transforms the argument into an expression having a reduced common denominator. value =1: Var is locked and cannot be modified or deleted. 52 TI-Nspire™ CAS Reference Guide . 8=Float7. 16=Fix2. 3=Gradian 1=Normal. 11=Float10. 25=Fix11. 26=Fix12 1=Radian. 2=Approximate. 20=Fix6. 2=Scientific. 2=Cylindrical. 3=Polar 1=Auto. getMode(0) returns a list containing number pairs. 18=Fix4. 5=Float4. 24=Fix10. 4=Float3. 13=Float12.getMode() getMode(ModeNameInteger) getMode(0) Catalog > ⇒ value ⇒ list getMode(ModeNameInteger) returns a value representing the current setting of the ModeNameInteger mode. 2=Eng/US Angle Exponential Format Real or Complex Auto or Approx. If you save the settings with getMode(0) & var. 19=Fix5. 12=Float11. 17=Fix3. 2=Rectangular. you can use setMode(var) in a function or program to temporarily restore the settings within the execution of the function or program only. Each pair consists of a mode integer and a setting integer. Mode Name Display Digits Mode Integer 1 Setting Integers 1=Float. refer to the table below. and then returns its numerator. 10=Float9. 23=Fix9. 21=Fix7. 14=Fix0. 3=Binary 1=SI. 3=Spherical 1=Decimal. 3=Float2. For a listing of the modes and their settings. 15=Fix1. 22=Fix8. 2=Hex. Vector Format Base Unit system 2 3 4 5 6 7 8 getNum() getNum(Expr1) Catalog > ⇒ expression Transforms the argument into an expression having a reduced common denominator. 3=Engineering 1=Real. See setMode(). 2=Degree. 2=Float1. 6=Float5. 3=Exact 1=Rectangular. 9=Float8. 7=Float6. page 102. On the computer keyboard. labelName must be defined in the same function using a Lbl instruction. for example) revaluates to a matrix. If no variables are defined. hold down Alt and press Enter. and locked/unlocked state) for all variables and library objects defined in the current problem. an error occurs. Note the example to the left. · TI-Nspire™ CAS Reference Guide 53 . in which the result of getVarInfo() is assigned to variable vs. type. library accessibility.getVarInfo() Catalog > ⇒ matrix or string getVarInfo(LibNameString) ⇒ matrix or string getVarInfo() getVarInfo() returns a matrix of information (variable name. getVarInfo() returns the string "NONE". getVarInfo(LibNameString) returns a matrix of information for all library objects defined in library LibNameString. Note for entering the example: In the Calculator application on the handheld. 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. This error could also occur when using Ans to reevaluate a getVarInfo() result. LibNameString must be a string (text enclosed in quotation marks) or a string variable. If the library LibNameString does not exist. you can enter multi-line definitions by pressing @ instead of at the end of each line. 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. Goto Goto labelName Catalog > Transfers control to the label labelName. executes the single statement Statement or the block of statements Block before continuing execution. continues execution without executing the statement or block of statements. If If BooleanExpr Catalog > Statement If BooleanExpr Then Block EndIf If BooleanExpr evaluates to true. If BooleanExpr evaluates to false. Integer must be a positive integer. 54 TI-Nspire™ CAS Reference Guide . If BooleanExpr Then · Block1 Else Block2 EndIf If BooleanExpr evaluates to true.4Grad Expr1 4 Grad ⇒ expression Converts Expr1 to gradian angle measure. skips Block1 but executes Block2. Catalog > In Degree angle mode: In Radian angle mode: I identity() identity(Integer) Catalog > ⇒ matrix Returns the identity matrix with a dimension of Integer. Note for entering the example: In the Calculator application on the handheld. Block1 and Block2 can be a single statement. On the computer keyboard. executes Block1 and then skips Block2. hold down Alt and press Enter. Block can be either a single statement or a sequence of statements separated with the “:” character. Note: You can insert this operator from the computer keyboard by typing @>Grad. If BooleanExpr evaluates to false. you can enter multi-line definitions by pressing @ instead of at the end of each line. Value_If_true [.5. Test value of 3 is not less than 2. If the second. a list. Test value of 1 is less than 2. One element selected from Value_If_true. Note: All undefined variables are treated as real variables.Value_If_false [. returns undef. If you omit Value_If_unknown. the Boolean test is applied to every position in BooleanExpr. If BooleanExpr1 evaluates to true. and so on. or matrix Catalog > 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. 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. imag() imag(Expr1) Catalog > ⇒ expression Returns the imaginary part of the argument. TI-Nspire™ CAS Reference Guide 55 . If an element of BooleanExpr evaluates to true. returns the corresponding element from Value_If_true. ifFn() ifFn(BooleanExpr. evaluates BooleanExpr2. or a matrix.Value_If_unknown]]) ⇒ expression. See also real(). returns the corresponding element Value_If_unknown. and the result will have the same dimension(s). list.5. One element selected from Value_If_unknown. or fourth argument of the ifFn() function is a single expression. so its corresponding Value_If_True element of 6 is copied to the result list. returns undef. so its corresponding Value_If_True element of 5 is copied to the result list. If BooleanExpr1 evaluates to false. If an element of BooleanExpr evaluates to false.If If BooleanExpr1 Then Catalog > Block1 ElseIf BooleanExpr2 Then Block2 © ElseIf BooleanExprN Then BlockN EndIf Allows for branching.5. Test value of 2 is less than 2. Value_If_false is not specified. page 94 imag(List1) ⇒ list Returns a list of the imaginary parts of the elements. If an element of BooleanExpr is neither true nor false. third. If you omit Value_If_false. all other list or matrix arguments must have the same dimension(s). Note: If the simplified BooleanExpr statement involves a list or matrix. executes Block1. returns the corresponding element from Value_If_false. Undef is used. integral See ‰(). Var. returns zero. For lists and matrices. The argument can be a real or a complex number. page 146. Computes the implicit derivative for equations in which one variable is defined implicitly in terms of another. Start. if included. Matrix2) ⇒ matrix Catalog > Returns the signed integer part of (Number1 ÷ Number2).imag() imag(Matrix1) Catalog > ⇒ matrix Returns a matrix of the imaginary parts of the elements. returns the greatest integer of each of the elements. Default = 1 (the first character of srcString).Ord]) Catalog > ⇒ expression where the order Ord defaults to 1. impDif() impDif(Equation. int() int(Expr) ⇒ integer int(List1) ⇒ list int(Matrix1) ⇒ matrix Catalog > Returns the greatest integer that is less than or equal to the argument. Number2) ⇒ integer intDiv(List1. returns the signed integer part of (argument 1 ÷ argument 2) for each element pair. List2) ⇒ list intDiv(Matrix1. Indirection See #(). intDiv() intDiv(Number1. This function is identical to floor(). If srcString does not contain subString or Start is > the length of srcString. subString[. For a list or matrix. dependVar[. inString() inString(srcString. Start]) Catalog > ⇒ integer Returns the character position in string srcString at which the first occurrence of string subString begins. specifies the character position within srcString where the search begins. 56 TI-Nspire™ CAS Reference Guide . page 1. invF() invF(Area.CFList [.dfNumer. if you enter values. iPart() iPart(Number) ⇒ integer iPart(List1) ⇒ list iPart(Matrix1) ⇒ matrix Catalog > Returns the integer part of the argument.dfDenom) Catalog > computes the Inverse cumulative F distribution function specified by dfNumer and dfDenom for a given Area under the curve. page 73.m[. Note: See also mirr().df) invChi2(Area.dfDenom) invF(Area.df) Catalog > Computes the inverse cumulative student-t probability function specified by degree of freedom. CF0 is the initial cash flow at time 0. they must be positive integers < 10.dfNumer. df for a given Area under the curve.df) 2 Catalog > Computes the Inverse cumulative c2 (chi-square) probability function specified by degree of freedom. The default is 1. CFFreq is an optional list in which each element specifies the frequency of occurrence for a grouped (consecutive) cash flow amount.invc2() invc (Area. it must be a real number. invNorm() invNorm(Area[. TI-Nspire™ CAS Reference Guide 57 . irr() irr(CF0.CFFreq]) Catalog > ⇒ value Financial function that calculates internal rate of return of an investment. For lists and matrices. CFList is a list of cash flow amounts after the initial cash flow CF0. The argument can be a real or a complex number. which is the corresponding element of CFList.s]]) Catalog > Computes the inverse cumulative normal distribution function for a given Area under the normal distribution curve specified by m and s. df for a given Area under the curve.000. invt() invt(Area. returns the integer part of each element. If Number exceeds about 306 digits and has no factors {1021. you can enter multi-line definitions by pressing @ instead of at the end of each line. · isVoid() isVoid(Var) ⇒ Boolean constant expression isVoid(Expr) ⇒ Boolean constant expression isVoid(List) ⇒ list of Boolean constant expressions Catalog > Returns true or false to indicate if the argument is a void data type. If you merely want to determine if Number is prime. L Lbl Lbl labelName Catalog > Defines a label with the name labelName within a function.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. For more information on void elements. hold down Alt and press Enter. use isPrime() instead of factor(). Note for entering the example: In the Calculator application Function to find the next prime after a specified number: on the handheld. particularly if Number is not prime and has a second-largest factor that exceeds about five digits. see page 152. you can enter multi-line definitions by pressing @ instead of at the end of each line. You can use a Goto labelName instruction to transfer control to the instruction immediately following the label. isPrime(Number) displays an error message. hold down Alt and press Enter. It is much faster. labelName must meet the same naming requirements as a variable name. Note for entering the example: In the Calculator application on the handheld. · 58 TI-Nspire™ CAS Reference Guide . On the computer keyboard. On the computer keyboard. The lcm of fractional floating-point numbers is their product. see DelVar on page 34. TI-Nspire™ CAS Reference Guide 59 . Matrix2) ⇒ matrix Catalog > Returns the least common multiple of the two arguments. Num]) ⇒ list Returns the leftmost Num elements contained in List1. ShortcutNameString [. left(Comparison) ⇒ expression Returns the left-hand side of an equation or inequality. For two lists or matrices. To delete a variable group. Set LibPrivFlag=0 to exclude private library objects (default) Set LibPrivFlag=1 to include private library objects To copy a variable group. Num]) Catalog > ⇒ string Returns the leftmost Num characters contained in character string sourceString. The lcm of two fractions is the lcm of their numerators divided by the gcd of their denominators. Creates a variable group in the current problem that contains references to all the objects in the specified library document libNameString. returns all of List1. see CopyVar on page 21. libShortcut() libShortcut(LibNameString. left(List1[. You can then refer to each object using its ShortcutNameString. Number2) ⇒ expression lcm(List1. If you omit Num. Also adds the group members to the Variables menu. returns all of sourceString. List2) ⇒ list lcm(Matrix1. If you omit Num. LibPrivFlag]) ⇒ list of variables Catalog > This example assumes a properly stored and refreshed library document named linalg2 that contains objects defined as clearmat. gauss1. and gauss2. returns the least common multiples of the corresponding elements.lcm() lcm(Number1. left() left(sourceString[. Only those data items whose category code is included in this list are included in the calculation. Point [. (If omitted.Direction]) ⇒ expression limit(List1. page 6. limits that should be zero or have infinite magnitude probably will not.) Limits at positive ˆ and at negative ˆ are always converted to onesided limits from the finite side.[Freq][. Point [.Category. Direction]) ⇒ matrix Catalog > Returns the limit requested. avoid the Approximate setting of the Auto or Approximate mode and approximate numbers when computing limits. undef means that the result is either an unknown number with finite or infinite magnitude. Point [. Limits can be very sensitive to rounding error. Var. X and Y are lists of independent and dependent variables. For information on the effect of empty elements in a list.RegEqn Description Regression Equation: a+b·x 60 TI-Nspire™ CAS Reference Guide . Category is a list of category codes for the corresponding X and Y data.Y[.limit() or lim() limit(Expr1. and limits that should have finite non-zero magnitude might not. When possible. All elements must be integers | 0. If Expr1 contains undefined variables other than Var. Depending on the circumstances. Each element in Freq specifies the frequency of occurrence for each corresponding X and Y data point.results variable. limit() returns itself or undef when it cannot determine a unique limit. positive=from right. you might have to constrain them to obtain a more concise result. so there are unique limits that it cannot determine. Var.) All the lists must have equal dimension except for Include. The default value is 1. Direction defaults to both. Note: See also Limit template. (See page 112. Otherwise. Include is a list of one or more of the category codes. LinRegBx LinRegBx X. limit() uses methods such as L’Hopital’s rule. Direction: negative=from left. Freq is an optional list of frequency values. or it is the entire set of such numbers.Include]] Computes the linear regression y = a+b·x on lists X and Y with frequency Freq. otherwise=both. This does not necessarily mean that a unique limit does not exist. see “Empty (void) elements” on page 152. Catalog > Output variable stat. Direction]) ⇒ list limit(Matrix1. A summary of results is stored in the stat. Var. Only those data items whose category code is included in this list are included in the calculation.r2 stat. Each element in Freq specifies the frequency of occurrence for each corresponding X and Y data point. and Include Categories List of data points in the modified Y List actually used in the regression based on restrictions of Freq. Include is a list of one or more of the category codes.YReg stat.a. Category List.m.Include]] Computes the linear regression y = m·x+b on lists X and Y with frequency Freq. Catalog > Output variable stat. All elements must be integers | 0.YReg stat.b stat.r2 stat. The default value is 1.YReg stat.) All the lists must have equal dimension except for Include.XReg Description Regression Equation: y = m·x+b Regression coefficients Coefficient of determination Correlation coefficient Residuals from the regression List of data points in the modified X List actually used in the regression based on restrictions of Freq. For information on the effect of empty elements in a list.Category.RegEqn stat.b stat. A summary of results is stored in the stat. and Include Categories List of data points in the modified Y List actually used in the regression based on restrictions of Freq.XReg and stat. Category List. and Include Categories List of frequencies corresponding to stat.Resid stat. Category List. stat.[Freq][.YReg stat.Y[.XReg and stat. and Include Categories List of frequencies corresponding to stat.r stat.XReg Description Regression coefficients Coefficient of determination Correlation coefficient Residuals from the regression List of data points in the modified X List actually used in the regression based on restrictions of Freq.FreqReg LinRegMx LinRegMx X.Output variable stat.r stat. (See page 112.FreqReg TI-Nspire™ CAS Reference Guide 61 . Freq is an optional list of frequency values.results variable. Category is a list of category codes for the corresponding X and Y data. stat. X and Y are lists of independent and dependent variables. see “Empty (void) elements” on page 152.Resid stat. Category List. CLev]]] For Response.a. Each element in F specifies the frequency of occurrence for each corresponding X and Y data point.CLower. a level C prediction interval for a single observation. For information on the effect of empty elements in a list.F[. LinRegtIntervals X.SESlope stat. Output variable stat.Y[. All elements must be integers | 0. see “Empty (void) elements” on page 152. The default value is 1.CUpper] stat.SE [stat. and a level C confidence interval for the mean response. X and Y are lists of independent and dependent variables. A summary of results is stored in the stat. stat. (See page 112. Computes a predicted y-value.df stat. Computes a level C confidence interval for the slope.s Description Confidence interval for the slope Confidence interval margin of error Standard error of slope Standard error about the line For Response type only Output variable [stat.Xval[.LowerPred.Y[.0[.ME stat.UpperPred] Description Confidence interval for the mean response Confidence interval margin of error Standard error of mean response Prediction interval for a single observation 62 TI-Nspire™ CAS Reference Guide .b stat.LinRegtIntervals LinRegtIntervals X.r stat.1. stat.CUpper] stat.Resid 2 Description Regression Equation: a+b·x Regression coefficients Degrees of freedom Coefficient of determination Correlation coefficient Residuals from the regression For Slope type only Output variable [stat.CLower. stat.) All the lists must have equal dimension. stat.results variable. F is an optional list of frequency values.RegEqn stat.ME stat.r stat.F[.CLev]]] Catalog > For Slope. a. r=0) against one of three alternative hypotheses. Output variable stat. see “Empty (void) elements” on page 152.Output variable stat.Y[. set Hypoth<0 For Ha: b>0 and r>0. Hypoth is an optional value specifying one of three alternative hypotheses against which the null hypothesis (H0:b=r=0) will be tested.SEPred stat. stat. set Hypoth>0 A summary of results is stored in the stat.t stat.RegEqn stat.SESlope stat. Description Prediction interval margin of error Standard error for prediction a + b·XVal y LinRegtTest LinRegtTest X. It tests the null hypothesis H0:b=0 (equivalently.r stat. X and Y are lists of independent and dependent variables.df stat.b stat. Freq is an optional list of frequency values.Hypoth]] Catalog > 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.) For information on the effect of empty elements in a list. The default value is 1.MEPred stat.PVal stat. Each element in Freq specifies the frequency of occurrence for each corresponding X and Y data point.results variable.r2 stat. set Hypoth=0 For Ha: b<0 and r<0. All elements must be integers | 0.Freq[.Resid Description Regression equation: a + b·x t-Statistic for significance test Smallest level of significance at which the null hypothesis can be rejected Degrees of freedom Regression coefficients Standard error about the line Standard error of slope Coefficient of determination Correlation coefficient Residuals from the regression TI-Nspire™ CAS Reference Guide 63 . (See page 112. All the lists must have equal dimension.s stat. For Ha: bƒ0 and rƒ0 (default). Var2. . Note: You can insert this function from the computer keyboard by typing list@>mat(. elementsPerRow. an argument error occurs... {Var1. if included.linSolve() linSolve( SystemOfLinearEqns. The resulting list is always one element shorter than the original List1... . . list4mat() list4mat( List [.. {Var1.....)..}) ⇒ list linSolve({LinearEqn1.. Var2.}) linSolve(LinearEqn1 and LinearEqn2 and . Catalog > 64 TI-Nspire™ CAS Reference Guide .}. Var1. Var2.).) Catalog > ⇒ list ⇒ list ⇒ list linSolve(SystemOfLinearEqns. Default is the number of elements in List (one row).. Var2. . . Note: You can insert this operator from the computer keyboard by typing @>ln. . LinearEgn2..}...) ⇒ list linSolve({LinearEqn1..) linSolve(LinearEqn1 and LinearEqn2 and . Each element of List1 is subtracted from the next element of List1. zeros are added..}) ⇒ list Returns a list of solutions for the variables Var1. For example. Var2. Otherwise. Var1. Catalog > Returns a list containing the differences between consecutive elements in List1... . Var1.. Var2. The first argument must evaluate to a system of linear equations or a single linear equation. . @List() @List(List1) ⇒ list Note: You can insert this function from the keyboard by typing deltaList(.. If List does not fill the resulting matrix. elementsPerRow]) Catalog > ⇒ matrix Returns a matrix filled row-by-row with the elements from List.. specifies the number of elements per row. 4ln Expr 4ln ⇒ expression Causes the input Expr to be converted to an expression containing only natural logs (ln).x) produces an “Argument Error” result... Var2. LinearEqn2.. .. evaluating linSolve(x=1 and x=2... {Var1. ) All the lists must have equal dimension except for Include. X and Y are lists of independent and dependent variables. LnReg LnReg X.r2 stat. [Freq] [.ln() ln(Expr1) ⇒ expression ln(List1) ⇒ list /u keys Returns the natural logarithm of the argument. press move the cursor. Category. (See page 112. For information about the calculation method. This is not the same as calculating the natural logarithm of each element. refer to cos() on. Only those data items whose category code is included in this list are included in the calculation. Include is a list of one or more of the category codes.a. If complex format mode is Real: If complex format mode is Rectangular: ln(squareMatrix1) ⇒ squareMatrix In Radian angle mode and Rectangular complex format: Returns the matrix natural logarithm of squareMatrix1. The result always contains floating-point numbers. All elements must be integers | 0. Output variable stat. For a list. The default value is 1. Freq is an optional list of frequency values. y) Residuals associated with the logarithmic model TI-Nspire™ CAS Reference Guide 65 . returns the natural logarithms of the elements. Y[.results variable.r stat.RegEqn stat. To see the entire result. squareMatrix1 must be diagonalizable. For information on the effect of empty elements in a list.Resid Description Regression equation: a+b·ln(x) Regression coefficients Coefficient of linear determination for transformed data Correlation coefficient for transformed data (ln(x).b stat. see “Empty (void) elements” on page 152. Include]] £ and then use ¡ and ¢ to Catalog > Computes the logarithmic regression y = a+b·ln(x) on lists X and Y with frequency Freq. Each element in Freq specifies the frequency of occurrence for each corresponding X and Y data point. Category is a list of category codes for the corresponding X and Y data. stat. A summary of results is stored in the stat. . Var3] . Note: Local variables save memory because they only exist temporarily. Lock Var.. Also. Category List. Catalog > Declares the specified vars as local variables. and you cannot lock the system variable groups stat.YReg stat.Output variable stat.FreqReg Local Local Var1[. On the computer keyboard. Var2] [. Note: The Lock command clears the Undo/Redo history when applied to unlocked variables. page 51. instead of hold down Alt and press Enter.. · Lock Lock Var1[. Var3] . page 127. and Include Categories List of frequencies corresponding to stat. and Include Categories List of data points in the modified Y List actually used in the regression based on restrictions of Freq.XReg and stat. You cannot lock or unlock the system variable Ans.XReg Description Residuals associated with linear fit of transformed data List of data points in the modified X List actually used in the regression based on restrictions of Freq.. they do not disturb any existing global variable values.YReg stat. Note for entering the example: In the Calculator application on the handheld. Catalog > Locks the specified variables or variable group. 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. 66 TI-Nspire™ CAS Reference Guide . or tvm. you can enter multi-line definitions by pressing @ at the end of each line.ResidTrans stat. Locked variables cannot be modified or deleted. Those variables exist only during evaluation of a function and are deleted when the function finishes execution. Category List. See unLock. Var2] [. and getLockInfo(). log() log(Expr1[. The result always contains floating-point numbers. TI-Nspire™ CAS Reference Guide 67 . 10 is used as the base. press move the cursor. If complex format mode is Real: If complex format mode is Rectangular: log(squareMatrix1[. Note: See also Log template. /s keys For a list. £ and then use ¡ and ¢ to Catalog > 4logbase Expr 4logbase(Expr1) ⇒ expression Causes the input Expression to be simplified to an expression using base Expr1. In Radian angle mode and Rectangular complex format: To see the entire result. 10 is used as base. For information about the calculation method. This is not the same as calculating the base-Expr logarithm of each element.Expr]) ⇒ squareMatrix Returns the matrix base-Expr logarithm of squareMatrix1. If the second argument is omitted. If the base argument is omitted. returns the base-Expr2 logarithm of the elements.). refer to cos().. page 2. squareMatrix1 must be diagonalizable.Expr2]) ⇒ expression log(List1[.Expr2]) ⇒ list Returns the base-Expr2 logarithm of the first argument. Note: You can insert this operator from the computer keyboard by typing @>logbase(.. [Freq] [. Category is a list of category codes for the corresponding X and Y data. Freq is an optional list of frequency values. A summary of results is stored in the stat. A summary of results is stored in the stat. Freq is an optional list of frequency values. see “Empty (void) elements” on page 152. Each element in Freq specifies the frequency of occurrence for each corresponding X and Y data point. Only those data items whose category code is included in this list are included in the calculation. Only those data items whose category code is included in this list are included in the calculation.results variable. 68 TI-Nspire™ CAS Reference Guide . Category. using a specified number of Iterations.YReg stat.results variable. Include is a list of one or more of the category codes. All elements must be integers | 0.Resid stat. stat. For information on the effect of empty elements in a list. and Include Categories List of data points in the modified Y List actually used in the regression based on restrictions of Freq.XReg and stat. see “Empty (void) elements” on page 152. The default value is 1. Y[.b.Logistic Logistic X.RegEqn stat. Include]] Catalog > Computes the logistic regression y = (c/(1+a·e-bx)) on lists X and Y with frequency Freq. For information on the effect of empty elements in a list. Y [ . Category List. Each element in Freq specifies the frequency of occurrence for each corresponding X and Y data point. X and Y are lists of independent and dependent variables.YReg stat.) All the lists must have equal dimension except for Include. (See page 112. [Iterations] . [Freq] [. Include is a list of one or more of the category codes. Include] ] Catalog > Computes the logistic regression y = (c/(1+a·e-bx)+d) on lists X and Y with frequency Freq. All elements must be integers | 0.c stat.a. Category is a list of category codes for the corresponding X and Y data. X and Y are lists of independent and dependent variables.FreqReg LogisticD LogisticD X.) All the lists must have equal dimension except for Include. Output variable stat. Category List. stat. and Include Categories List of frequencies corresponding to stat. Category.XReg Description Regression equation: c/(1+a·e-bx) Regression coefficients Residuals from the regression List of data points in the modified X List actually used in the regression based on restrictions of Freq. The default value is 1. (See page 112. RegEqn stat.XReg Description Regression equation: c/(1+a·e-bx)+d) Regression coefficients Residuals from the regression List of data points in the modified X List actually used in the regression based on restrictions of Freq.Output variable stat. stat. instead of hold down Alt and press Enter. Note for entering the example: In the Calculator application on the handheld.d stat. · TI-Nspire™ CAS Reference Guide 69 .YReg stat. On the computer keyboard. Note that the loop will be executed endlessly. Category List. and Include Categories List of data points in the modified Y List actually used in the regression based on restrictions of Freq. Category List. stat. you can enter multi-line definitions by pressing @ at the end of each line.FreqReg Loop Loop Catalog > Block EndLoop Repeatedly executes the statements in Block.b. and Include Categories List of frequencies corresponding to stat. Block is a sequence of statements separated with the “:” character.XReg and stat.c. unless a Goto or Exit instruction is executed within Block.a.Resid stat. stat.YReg stat. Note: You can insert this function from the computer keyboard by typing mat@>list(. Tol is ignored. lMatrix · uMatrix = pMatrix · matrix Optionally. lMatrix. Otherwise. the upper triangular matrix in uMatrix. and the permutation matrix (which describes the row swaps done during the calculation) in pMatrix. M mat4list() mat4list(Matrix) Catalog > ⇒ list Returns a list filled with the elements in Matrix..). The elements are copied from Matrix row by row. computations are done using floatingpoint arithmetic.Tol] Catalog > Calculates the Doolittle LU (lower-upper) decomposition of a real or complex matrix. the default tolerance is calculated as: 5EM14 ·max(dim(Matrix)) ·rowNorm(Matrix) /· • The LU factorization algorithm uses partial pivoting with row interchanges. If Tol is omitted or not used.. The lower triangular matrix is stored in lMatrix. 70 TI-Nspire™ CAS Reference Guide . • or set the Auto or Approximate If you use mode to Approximate. any matrix element is treated as zero if its absolute value is less than Tol.LU LU Matrix. 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. pMatrix[. uMatrix. Each freqList element counts the number of consecutive occurrences of the corresponding element in List. Matrix2) ⇒ matrix Catalog > Returns the maximum of the two arguments. freqMatrix]) ⇒ matrix In Rectangular vector format: Returns a row vector of the means of all the columns in Matrix1. returns a list or matrix containing the maximum value of each pair of corresponding elements. max(List) ⇒ expression ⇒ matrix Returns the maximum element in list. see page 152. mean() mean(List[. freqList]) Catalog > ⇒ expression Returns the median of the elements in List. Note: See also fMax() and min().max() max(Expr1. List2) ⇒ list max(Matrix1. mean(Matrix1[. Expr2) ⇒ expression max(List1. see page 152. TI-Nspire™ CAS Reference Guide 71 . For more information on empty elements. freqList]) Catalog > ⇒ expression Returns the mean of the elements in List. max(Matrix1) Returns a row vector containing the maximum element of each column in Matrix1. Each freqMatrix element counts the number of consecutive occurrences of the corresponding element in Matrix1. If the arguments are two lists or matrices. Empty (void) elements are ignored. median() median(List[. For more information on empty elements. Each freqList element counts the number of consecutive occurrences of the corresponding element in List. Empty (void) elements are ignored. Notes: • • All entries in the list or matrix must simplify to numbers. and Include Categories List of frequencies corresponding to stat. see “Empty (void) elements” on page 152. beginning with character number Start. X and Y are lists of independent and dependent variables. Count must be ‚ 0. If Count is omitted or is greater than the dimension of sourceString. returns an empty string.results variable. Freq is an optional list of frequency values. (See page 112.YReg stat.XReg Description Median-median line equation: m·x+b Model coefficients Residuals from the median-median line List of data points in the modified X List actually used in the regression based on restrictions of Freq. If Count = 0. returns all characters from sourceString. Category List. 72 TI-Nspire™ CAS Reference Guide . Empty (void) elements in the list or matrix are ignored. Start[. beginning with character number Start. Freq] [. Include]] Catalog > Computes the median-median line y = (m·x+b) on lists X and Y with frequency Freq.Y [. Each freqMatrix element counts the number of consecutive occurrences of the corresponding element in Matrix1.YReg stat. All elements must be integers | 0. A summary of results is stored in the stat.median() median(Matrix1[.FreqReg mid() mid(sourceString. Count]) Catalog > ⇒ string Returns Count characters from character string sourceString. Include is a list of one or more of the category codes.) All the lists must have equal dimension except for Include.b stat. stat. freqMatrix]) Catalog > ⇒ matrix Returns a row vector containing the medians of the columns in Matrix1. For more information on empty elements. Output variable stat. see page 152. Only those data items whose category code is included in this list are included in the calculation.Resid stat. MedMed MedMed X. For information on the effect of empty elements in a list.RegEqn stat. Category is a list of category codes for the corresponding X and Y data.XReg and stat. Category List. Category. The default value is 1.m. and Include Categories List of data points in the modified Y List actually used in the regression based on restrictions of Freq. Each element in Freq specifies the frequency of occurrence for each corresponding X and Y data point. Expr2) ⇒ expression min(List1. min(List) ⇒ expression ⇒ matrix Returns the minimum element of List. If the arguments are two lists or matrices. it must be a real number. If Count is omitted or is greater than the dimension of sourceList. beginning with element number Start. Count]) ⇒ list Returns Count strings from the list of strings sourceStringList. returns an empty list. TI-Nspire™ CAS Reference Guide 73 .CFFreq]) Catalog > Financial function that returns the modified internal rate of return of an investment. which is the corresponding element of CFList. if you enter values. financeRate is the interest rate that you pay on the cash flow amounts. Start[. min() min(Expr1. Count must be ‚ 0.CF0. they must be positive integers < 10. Count]) Catalog > ⇒ list Returns Count elements from sourceList. CF0 is the initial cash flow at time 0. The default is 1. If Count = 0. mirr() mirr(financeRate. CFFreq is an optional list in which each element specifies the frequency of occurrence for a grouped (consecutive) cash flow amount. returns a list or matrix containing the minimum value of each pair of corresponding elements. page 57. reinvestRate is the interest rate at which the cash flows are reinvested. returns all elements from sourceList. beginning with element number Start. Note: See also fMin() and max(). CFList is a list of cash flow amounts after the initial cash flow CF0. Note: See also irr().000. List2) ⇒ list min(Matrix1.mid() mid(sourceList. min(Matrix1) Returns a row vector containing the minimum element of each column in Matrix1. mid(sourceStringList. Matrix2) ⇒ matrix Catalog > Returns the minimum of the two arguments.reinvestRate. beginning with element number Start. Start [.CFList[. X2. For information on the effect of empty elements in a list.y) = x ... . stat. page 95 mRow() mRow(Expr. Expr2) ⇒ expression mod(List1. Index2) Catalog > ⇒ matrix Returns a copy of Matrix1 with each element in row Index2 of Matrix1 replaced with: Expr · row Index1 + row Index2 MultReg MultReg Y. Index) Catalog > ⇒ matrix Returns a copy of Matrix1 with each element in row Index of Matrix1 multiplied by Expr. Matrix1. Matrix2) ⇒ matrix Catalog > Returns the first argument modulo the second argument as defined by the identities: mod(x. Note: See also remain(). Matrix1.results variable.b1.mod() mod(Expr1.b0. returns a list or matrix containing the modulo of each pair of corresponding elements. List stat.y floor(x/y) When the second argument is non-zero. List2) ⇒ list mod(Matrix1.X2[...RegEqn stat. The result is either zero or has the same sign as the second argument. see “Empty (void) elements” on page 152..R2 stat. X1[.X3. the result is periodic in that argument. Regression coefficients Coefficient of multiple determination y yList = b0+b1·x1+ .…[. Residuals from the regression 74 TI-Nspire™ CAS Reference Guide . A summary of results is stored in the stat.0) = x mod(x. stat. If the arguments are two lists or two matrices. …. X10. mRowAdd() mRowAdd(Expr.) All the lists must have equal dimension.Resid Description Regression Equation: b0+b1·x1+b2·x2+ . Output variable stat. Index1.X10]]] Catalog > Calculates multiple linear regression of list Y on lists X1. (See page 112.. } Residuals from the regression MultRegTests MultRegTests Y. {b0.X3. Outputs Output variable stat.. (See page 112.RegEqn stat.X2[.b1. for XValList stat. and a level C confidence interval for the mean response.Resid Error degrees of freedom Confidence interval for a mean response Confidence interval margin of error Standard error of mean response Prediction interval for a single observation Prediction interval margin of error Standard error for prediction List of regression coefficients.b2. see “Empty (void) elements” on page 152. Output variable stat. For information on the effect of empty elements in a list.…[. X1[.F stat. Description Regression Equation: b0+b1·x1+b2·x2+ .…[.X10]]] Catalog > 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.X3.. (See page 112.UpperrPred stat.MEPred stat.) For information on the effect of empty elements in a list.X2[.dfError stat. a level C prediction interval for a single observation.results variable.results variable.. A summary of results is stored in the stat.X10]]]..CLower.. stat. A point estimate: y y = b0 + b1 · xl + . stat. A summary of results is stored in the stat.RegEqn stat.CUpper stat. see “Empty (void) elements” on page 152.LowerPred.bList stat..SEPred stat.) All the lists must have equal dimension.PVal stat..SE stat...XValList[.MultRegIntervals MultRegIntervals Y.R2 Description Regression Equation: b0+b1·x1+b2·x2+ .ME stat. X1[.CLevel] Catalog > Computes a predicted y-value. Global F test statistic P-value associated with global F statistic Coefficient of multiple determination TI-Nspire™ CAS Reference Guide 75 . ) Both arguments can be integers or symbolic expressions.Leverage Description Adjusted coefficient of multiple determination Standard deviation of the error Durbin-Watson statistic. 76 TI-Nspire™ CAS Reference Guide .dfError stat. List2) ⇒ list Returns a list of combinations based on the corresponding element pairs in the two lists. one for each coefficient in the bList List P-values for each t statistic List of standard errors for coefficients in bList y yList = b0+b1·x1+ .b1.s stat. The arguments must be the same size list.CookDist stat. nonInteger) ⇒ 0 ⇒ Expr·(ExprN1). .tList stat.MSReg stat. negInteger) nCr(Expr.Resid stat..PList stat. ⇒ expression!/ (ExprNposInteger+1)/ posInteger! ((ExprNnonInteger)!·nonInteger!) nCr(List1.Output variable stat.} List of coefficients List of t statistics.dfReg stat..DW stat. measure of the influence of an observation based on the residual and leverage Measure of how far the values of the independent variable are from their mean values N nCr() nCr(Expr1. obtained by dividing a residual by its standard deviation Cook’s distance. used to determine whether first-order auto correlation is present in the model Regression degrees of freedom Regression sum of squares Regression mean square Error degrees of freedom Error sum of squares Error mean square {b0. . List stat.sResid stat. (This is also known as a binomial coefficient.SEList stat. posInteger) nCr(Expr. 0) ⇒ 1 nCr(Expr. nCr(Expr.SSError stat. Expr2) Catalog > ⇒ expression For integer Expr1 and Expr2 with Expr1 ‚ Expr2 ‚ 0.SSReg stat.MSError stat. Residuals from the regression Standardized residuals..AdjR2 stat... nCr() is the number of combinations of Expr1 things taken Expr2 at a time.bList stat. Order of the derivative must be 1 or 2. TI-Nspire™ CAS Reference Guide 77 . If you supply lowBound and upBound. newMat() newMat(numRows. If you supply lowBound and upBound. nDerivative() Catalog > ⇒ value nDerivative(Expr1. Note: See also fMin() and d(). newList() newList(numElements) Catalog > ⇒ list Returns a list with a dimension of numElements. upBound) nfMin(Expr. the function looks between those values for the local minimum. Matrix2) Catalog > ⇒ matrix Returns a matrix of combinations based on the corresponding element pairs in the two matrices. When Value is specified. Each element is zero. lowBound) Catalog > ⇒ value ⇒ value ⇒ value nfMin(Expr. Var) ⇒ value nfMin(Expr.Var=Value[. numColumns) Catalog > ⇒ matrix Returns a matrix of zeros with the dimension numRows by numColumns. Note: See also fMax() and d().Var [. Var) | lowBound<Var<upBound Returns a candidate numerical value of variable Var where the local maximum of Expr occurs. Var. The arguments must be the same size matrix. Var. lowBound. Var. the function looks between those values for the local maximum. Var) | lowBound<Var<upBound Returns a candidate numerical value of variable Var where the local minimum of Expr occurs. Var) ⇒ value nfMax(Expr. lowBound) Catalog > ⇒ value ⇒ value ⇒ value nfMax(Expr. Var. upBound) nfMax(Expr.nCr() nCr(Matrix1. nfMax() nfMax(Expr. it overrides any prior variable assignment or any current “with” substitution for the variable. lowBound. nfMin() nfMin(Expr.Order]) | Var=Value ⇒ value nDerivative(Expr1.Order]) Returns the numerical derivative calculated using auto differentiation methods. Note: See also ‰(). or when it seems unlikely that additional samples will yield a worthwhile improvement. and CpY must be a real number > 0. This approximation is a weighted average of some sample values of the integrand in the interval Lower<Var<Upper. 78 TI-Nspire™ CAS Reference Guide . Var. or negative ˆ. page 1.nInt() nInt(Expr1. then nInt() returns an approximation of ‰(Expr1. The adaptive algorithm terminates when it seems likely that the goal has been achieved. A warning is displayed (“Questionable accuracy”) when it seems that the goal has not been achieved. Note: See also eff(). and if Lower and Upper are constants. norm() norm(Matrix) norm(Vector) Catalog > ⇒ expression ⇒ expression Returns the Frobenius norm. Upper). given CpY as the number of compounding periods per year. effectiveRate must be a real number.CpY) Catalog > ⇒ value Financial function that converts the annual effective interest rate effectiveRate to a nominal rate. The goal is six significant digits. Lower. Lower. Upper) Catalog > ⇒ expression If the integrand Expr1 contains no variable other than Var. nom() nom(effectiveRate. Nest nInt() to do multiple numeric integration. Integration limits can depend on integration variables outside them. positive ˆ. page 39. Var. You can enter the integer in any number base. page 14. set lowBound = .upBound[. For more information. Make sure that the independent variable is not defined. 64-bit binary number.2) returns “false.s]]) ⇒ number if lowBound and upBound are numbers. If you enter a decimal integer that is too large for a signed. For a binary or hexadecimal entry. then normalLine(f1(x).m[. not Integer1 ⇒ integer In Hex base mode: Important: Zero. £ ¡ ¢ TI-Nspire™ CAS Reference Guide 79 .x.” normCdf() normCdf(lowBound. and vice versa) for the one’s complement. a symmetric modulo operation is used to bring the value into the appropriate range. If f1(x):=5 and x:=3. For example. see 4Base2. Returns the one’s complement of a real integer. Results are displayed according to the Base mode. list if Computes the probability density function for the normal distribution at a specified XVal value for the specified m and s. or a simplified form of the argument. Note: A binary entry can have up to 64 digits (not counting the 0b prefix). The value of each bit is flipped (0 becomes 1.ˆ. normPdf() normPdf(XVal[. Internally. 64-bit binary form. the integer is treated as decimal (base 10).s]]) XVal is a list Catalog > ⇒ number if XVal is a number.Var=Point) ⇒ expression normalLine(Expr1.normalLine() Catalog > ⇒ expression normalLine(Expr1. A hexadecimal entry can have up to 16 digits. list if lowBound and upBound are lists Catalog > Computes the normal distribution probability between lowBound and upBound for the specified m (default=0) and s (default=1). you must use the 0b or 0h prefix. respectively.m[. not not BooleanExpr Catalog > ⇒ Boolean expression Returns true. Without a prefix. Integer1 is converted to a signed.Var.Point) Returns the normal line to the curve represented by Expr1 at the point specified in Var=Point. press move the cursor. For P(X  upBound). not the letter O. false. In Bin base mode: and then use and to To see the entire result. Specify the variable as: variable – or – variable = real number For example.Var[=Guess].. nPr(Matrix1. which is the corresponding element of CFList..CFList[. if you enter values. negInteger) ⇒ 1/((Expr+1)·(Expr+2).. nPr(Expr..lowBound) ⇒ number or error_string ⇒ number or error_string ⇒ number or error_string nSolve(Equation.nPr() nPr(Expr1. 80 TI-Nspire™ CAS Reference Guide .lowBound. InterestRate is the rate by which to discount the cash flows (the cost of money) over one period.Var[=Guess]) | lowBound<Var<upBound Note: If there are multiple solutions. The default is 1. A positive result for npv indicates a profitable investment. Matrix2) ⇒ matrix Returns a matrix of permutations based on the corresponding element pairs in the two matrices. Expr2) Catalog > ⇒ expression For integer Expr1 and Expr2 with Expr1 ‚ Expr2 ‚ 0.CFFreq]) Catalog > Financial function that calculates net present value. you can use a guess to Iteratively searches for one approximate real numeric solution to Equation for its one variable. (ExprNposInteger+1) nPr(Expr. x is valid and so is x=3. they must be positive integers < 10.Var[=Guess]) Catalog > ⇒ number or error_string nSolve(Equation.CFO. nSolve() nSolve(Equation. CF0 is the initial cash flow at time 0.000. it must be a real number. CFList is a list of cash flow amounts after the initial cash flow CF0. The arguments must be the same size list. 0) ⇒ 1 nPr(Expr. npv() npv(InterestRate. List2) ⇒ Expr! / (ExprNnonInteger)! ⇒ list Returns a list of permutations based on the corresponding element pairs in the two lists. (expressionNnegInteger)) nPr(Expr. the sum of the present values for the cash inflows and outflows. nonInteger) nPr(List1. posInteger) ⇒ Expr·(ExprN1). help find a particular solution. Both arguments can be integers or symbolic expressions.Var[=Guess].upBound) nSolve(Equation. CFFreq is a list in which each element specifies the frequency of occurrence for a grouped (consecutive) cash flow amount. nPr() is the number of permutations of Expr1 things taken Expr2 at a time. The arguments must be the same size matrix. Each element in Freq specifies the frequency of occurrence for each corresponding X and Y data point.X20]]] Catalog > Calculates 1-variable statistics on up to 20 lists.sx s stat.MinX stat. or Category results in a void for the corresponding element of all those lists. (See page 112.[Freq][. Output variable stat.]X[. For more information on empty elements.Gx2 stat.…[. and zeros().Q3X stat.MedianX stat.]X1. Catalog > O OneVar OneVar [1.sx stat.Category. solve().” Note: See also cSolve(). Only those data items whose category code is included in this list are included in the calculation.Q1X stat. Freq.) All the lists must have equal dimension except for Include. The default value is 1.v stat.nSolve() nSolve() is often much faster than solve() or zeros(). it returns the string “no solution found. All elements must be integers | 0. particularly if the “|” operator is used to constrain the search to a small interval containing exactly one simple solution. An empty element in any of the lists X1 through X20 results in a void for the corresponding element of all those lists. If it cannot achieve this using a modest number of sample points. 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. An empty (void) element in any of the lists X. see page 152. Include is a list of one or more of the category codes. Category is a list of numeric category codes for the corresponding X values. A summary of results is stored in the stat.results variable.X2[X3[.n stat. Freq is an optional list of frequency values. cZeros().Include]] OneVar [n.Gx stat.MaxX Description Mean of x values Sum of x values Sum of x2 values Sample standard deviation of x Population standard deviation of x Number of data points Minimum of x values 1st Quartile of x Median of x 3rd Quartile of x Maximum of x values TI-Nspire™ CAS Reference Guide 81 . Note: A binary entry can have up to 64 digits (not counting the 0b prefix). A hexadecimal entry can have up to 16 digits. Note: See xor. · Integer1 or Integer2 ⇒ integer In Hex base mode: Compares two real integers bit-by-bit using an or operation. Returns true if either or both expressions simplify to true. Note: See xor. Without a prefix. Internally. On the computer keyboard. you must use the 0b or 0h prefix. the result is 1 if either bit is 1. the result is 0 only if both bits are 0. Note for entering the example: In the Calculator application Catalog > on the handheld. ord() ord(String) ⇒ integer ord(List1) ⇒ list Catalog > Returns the numeric code of the first character in character string String. not the letter O. 64-bit binary Important: Zero. hold down Alt and press Enter. or a list of the first characters of each list element. For more information. and is displayed according to the Base mode. You can enter the integers in any number base. see 4Base2. both integers are converted to signed. For a binary or hexadecimal entry. 64-bit binary form. integers are treated as decimal (base 10). The returned value In Bin base mode: represents the bit results. respectively. If you enter a decimal integer that is too large for a signed. 82 TI-Nspire™ CAS Reference Guide .SSX Description Sum of squares of deviations from the mean of x or BooleanExpr1 or BooleanExpr2 ⇒ Boolean expression Returns true or false or a simplified form of the original entry. a symmetric modulo operation is used to bring the value into the appropriate range. Returns false only if both expressions evaluate to false. you can enter multi-line definitions by pressing @ instead of at the end of each line.Output variable stat. page 14. When corresponding bits are compared. numbers. page 19. Note: The q argument is interpreted as either a degree. G or ôto override the angle mode setting temporarily. according to the current angle mode... Cond2 [. and Try.. You can also create piecewise definitions by using a template. P4Ry() P4Ry(rExpr. radian or gradian angle.. you can enter multi-line definitions by pressing @ instead of at the end of each line. Note for entering the example: In the Calculator application on the handheld. according to the current angle mode. piecewise() piecewise(Expr1 [.EndTry error handlers. you can use ó.. Note: You can insert this function from the computer keyboard by typing P@>Rx(. If the argument is an expression. Note: You can insert this function from the computer keyboard by typing P@>Ry(. If the argument is an expression. G or ôto override the angle mode setting temporarily. gradian or radian angle. On the computer keyboard. TI-Nspire™ CAS Reference Guide 83 .).Else.. … ]]]]) · Catalog > Returns definitions for a piecewise function in the form of a list.. qExpr) ⇒ expression P4Rx(rList.. Cond1 [. q) pair. If there are no more pending Try. use ClrErr. Note: See also Piecewise template. If system variable errCode is zero.Else. use PassErr to send it to the next error handler.. PassErr PassErr Catalog > For an example of PassErr. Note: The q argument is interpreted as either a degree. See Example 2 under the Try command.P P4Rx() P4Rx(rExpr. qMatrix) ⇒ matrix Catalog > In Radian angle mode: Returns the equivalent y-coordinate of the (r. If what to do with the error is not known. hold down Alt and press Enter. Passes an error to the next level. qList) ⇒ list P4Ry(rMatrix. Expr2 [. you can use ó. qExpr) ⇒ expression P4Ry(rList..EndTry block should use ClrErr or PassErr. qList) ⇒ list P4Rx(rMatrix. page 2. page 122. the error dialog box will be displayed as normal.. page 122. qMatrix) ⇒ matrix Catalog > In Radian angle mode: Returns the equivalent x-coordinate of the (r.. q) pair. Note: See also ClrErr. PassErr does not do anything.). The Else clause of the Try. If the error is to be processed or ignored. You can use it only at the end of an entry line. • • Degree angle mode returns (rq). The vector must be of dimension 2 and can be a row or a column.upBound) for P(0XupBound) upBound is a number. In Gradian angle mode: In Degree angle mode: 84 TI-Nspire™ CAS Reference Guide . In Radian angle mode: complexValue can have any complex form.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. Radian angle mode returns reiq. complexValue 4Polar Displays complexVector in polar form. Note: You must use the parentheses for an (rq) polar entry. and it does not update ans. list if upBound is a list Catalog > ⇒ number if Computes a cumulative probability for the discrete Poisson distribution with specified mean l. Note: 4Polar is a display-format instruction. list if lowBound and upBound are lists poissCdf(l. For P(X  upBound).lowBound.poissCdf() poissCdf(l.upBound) ⇒ number if lowBound and upBound are numbers. However. page 94. 4Polar Vector 4Polar Note: You can insert this operator from the computer keyboard by typing @>Polar. an reiq entry causes an error in Degree angle mode. set lowBound=0 poissPdf() poissPdf(l. not a conversion function. Note: See also 4Rect. Catalog > Displays vector in polar form [r q]. the polyDegree() function selects a default from the variables contained in the polynomial Poly. Poly must be a polynomial expression in Var.Var]) Catalog > ⇒ value Returns the degree of polynomial expression Poly with respect to variable Var.polyCoeffs() polyCoeffs(Poly [. Expands the polynomial and selects x for the omitted Var. Expr1) ⇒ expression polyEval(List1. We recommend that you do not omit Var unless Poly is an expression in a single variable. and returns the polynomial evaluated for the value of the second argument.Var]) Catalog > ⇒ list Returns a list of the coefficients of polynomial Poly with respect to variable Var. We recommend that you do not omit Var unless Poly is an expression in a single variable. List2) ⇒ expression Catalog > Interprets the first argument as the coefficient of a descending-degree polynomial. polyDegree() polyDegree(Poly [. Poly must be a polynomial expression in Var. TI-Nspire™ CAS Reference Guide 85 . polyEval() polyEval(List1. This is because the degree can be extracted without expanding the polynomial. If you omit Var. Constant polynomials The degree can be extracted even though the coefficients cannot. matrix.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.polyGcd() polyGcd(Expr1. polyRemainder() polyRemainder(Poly1. polyQuotient() polyQuotient(Poly1. We recommend that you do not omit Var unless Poly1 and Poly2 are expressions in the same single variable. Poly1 and Poly2 must be polynomial expressions in Var. 86 TI-Nspire™ CAS Reference Guide . Expr1 and Expr2 must be polynomial expressions. and Boolean arguments are not allowed.Expr2) Catalog > ⇒ expression Returns greatest common divisor of the two arguments. List.Var]) Catalog > ⇒ expression Returns the quotient of polynomial Poly1 divided by polynomial Poly2 with respect to the specified variable Var. We recommend that you do not omit Var unless Poly1 and Poly2 are expressions in the same single variable.Poly2 [.Poly2 [. returns a list of real roots of polynomial Poly with respect to variable Var. returns a list of real roots for the coefficients in ListOfCoeffs. Category List. Note: See also cPolyRoots(). A summary of results is stored in the stat.) All the lists must have equal dimension except for Include. PowerReg PowerReg X. Each element in Freq specifies the frequency of occurrence for each corresponding X and Y data point. polyRoots(Poly. The default value is 1. see “Empty (void) elements” on page 152. All elements must be integers | 0.polyRoots() Catalog > ⇒ list polyRoots(ListOfCoeffs) ⇒ list polyRoots(Poly. Only those data items whose category code is included in this list are included in the calculation. returns an empty list: { }.b stat. Include]] Catalog > Computes the power regression y = (a·(x)b) on lists X and Y with frequency Freq.r stat.a. Freq] [.Var).Resid stat. If no real roots exist.results variable. Category is a list of category codes for the corresponding X and Y data.RegEqn stat.r2 stat. Category List. and Include Categories List of frequencies corresponding to stat. Category. (See page 112. Poly must be a polynomial in one variable.Var) The first syntax.YReg stat.FreqReg TI-Nspire™ CAS Reference Guide 87 . and Include Categories List of data points in the modified Y List actually used in the regression based on restrictions of Freq.ResidTrans stat. For information on the effect of empty elements in a list. The second syntax. Output variable stat.YReg stat. Freq is an optional list of frequency values. page 26.XReg Description Regression equation: a·(x)b Regression coefficients Coefficient of linear determination for transformed data Correlation coefficient for transformed data (ln(x). polyRoots(ListOfCoeffs). Include is a list of one or more of the category codes. stat.Y [. X and Y are lists of independent and dependent variables. ln(y)) Residuals associated with the power model Residuals associated with linear fit of transformed data List of data points in the modified X List actually used in the regression based on restrictions of Freq.XReg and stat. · prodSeq() See Π( ). Block can be a single statement. Block EndPrgm Template for creating a user-defined program. Note for entering the example: In the Calculator application on the handheld. They specify a range of elements. page 143. Start and End are optional. see page 152. or Define LibPriv command. Start[. Empty (void) elements are ignored. product(Matrix1[. Must be used with the Define. End]]) ⇒ matrix Returns a row vector containing the products of the elements in the columns of Matrix1. They specify a range of rows. hold down Alt and press Enter. On the computer keyboard. product() product(List[. End]]) Catalog > ⇒ expression Returns the product of the elements contained in List. For more information on empty elements. 88 TI-Nspire™ CAS Reference Guide .Prgm Prgm Catalog > Calculate GCD and display intermediate results. you can enter multi-line definitions by pressing @ instead of at the end of each line. Start and end are optional. Product (PI) See Π( ). or a series of statements on separate lines. Define LibPub. Start[. page 143. a series of statements separated with the “:” character. computations are done using floatingpoint arithmetic. qMatrix. Calculates the Householder QR factorization of a real or complex matrix. propFrac() is a faster but less extreme alternative to expand(). • If you use or set the Auto or Approximate mode to Approximate.Var) returns the sum of proper ratios and a polynomial with respect to Var. For rational expressions. rMatrix[. The degree of Var in the denominator exceeds the degree of Var in the numerator in each proper ratio. 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. Var]) Catalog > ⇒ 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. Optionally. The R matrix is upper triangular.propFrac() propFrac(Expr1[. You can use the propFrac() function to represent mixed fractions and demonstrate addition and subtraction of mixed fractions. any matrix element is treated as zero if its absolute value is less than Tol. The resulting Q and R matrices are stored to the specified Matrix. The Q matrix is unitary. Tol is ignored. propFrac(rational_expression. If Var is omitted. Similar powers of Var are collected. Otherwise. Q QR QR Matrix. Tol] Catalog > The floating-point number (9. The terms and their factors are sorted with Var as the main variable. The coefficients of the polynomial part are then made proper with respect to their most main variable first and so on. the default tolerance is calculated as: 5Eë14 ·max(dim(Matrix)) ·rowNorm(Matrix) /· • TI-Nspire™ CAS Reference Guide 89 . a proper fraction expansion is done with respect to the most main variable.) in m1 causes results to be calculated in floating-point form. If Tol is omitted or not used. Each element in Freq specifies the frequency of occurrence for each corresponding X and Y data point. Category is a list of category codes for the corresponding X and Y data.R2 stat. All elements must be integers | 0. The columns in qMatName are the orthonormal basis vectors that span the space defined by matrix.results variable.) All the lists must have equal dimension except for Include.a. The symbolic solution is computed using GramSchmidt. Category List. Include]] Catalog > Computes the quadratic polynomial regression y = a·x2+b·x+c on lists X and Y with frequency Freq. stat.XReg Description Regression equation: a·x2+b·x+c Regression coefficients Coefficient of determination Residuals from the regression List of data points in the modified X List actually used in the regression based on restrictions of Freq.RegEqn stat. Only those data items whose category code is included in this list are included in the calculation.XReg and stat.Resid stat. A summary of results is stored in the stat.QR The QR factorization is computed numerically using Householder transformations. Freq] [. Category. stat. For information on the effect of empty elements in a list.c stat.Y [. Catalog > QuadReg QuadReg X.FreqReg 90 TI-Nspire™ CAS Reference Guide . X and Y are lists of independent and dependent variables. and Include Categories List of data points in the modified Y List actually used in the regression based on restrictions of Freq.YReg stat. The default value is 1. Include is a list of one or more of the category codes. and Include Categories List of frequencies corresponding to stat. (See page 112. Category List. Output variable stat. see “Empty (void) elements” on page 152. Freq is an optional list of frequency values.b.YReg stat. Category is a list of category codes for the corresponding X and Y data. Category List. All elements must be integers | 0.FreqReg TI-Nspire™ CAS Reference Guide 91 .Y [. For information on the effect of empty elements in a list.XReg and stat.QuartReg QuartReg X.e stat. and Include Categories List of data points in the modified Y List actually used in the regression based on restrictions of Freq.RegEqn stat.b. Category. and Include Categories List of frequencies corresponding to stat. stat.) All the lists must have equal dimension except for Include. Only those data items whose category code is included in this list are included in the calculation.a. Output variable stat. (See page 112.d. Each element in Freq specifies the frequency of occurrence for each corresponding X and Y data point.XReg Description Regression equation: a·x4+b·x3+c· x2+d·x+e Regression coefficients Coefficient of determination Residuals from the regression List of data points in the modified X List actually used in the regression based on restrictions of Freq. stat. The default value is 1. stat. Include is a list of one or more of the category codes.YReg stat. stat. see “Empty (void) elements” on page 152.results variable. X and Y are lists of independent and dependent variables. Freq is an optional list of frequency values.YReg stat. A summary of results is stored in the stat. Include]] Catalog > Computes the quartic polynomial regression y = a·x4+b·x3+c· x2+d·x+e on lists X and Y with frequency Freq.c. Freq] [.R2 stat.Resid stat. Category List. . 4Rad Expr14Rad ⇒ expression Converts the argument to radian angle measure. Note: You can insert this function from the computer keyboard by typing R@>Pr(.y) pair arguments. Note: The result is returned as a degree. 92 TI-Nspire™ CAS Reference Guide .). In Gradian angle mode: In Radian angle mode: R4Pr() R4Pr (xExpr.y) pair arguments. yExpr) ⇒ expression R4Pq (xList.. rand(#Trials) returns a list containing #Trials random values between 0 and 1. Note: You can insert this function from the computer keyboard by typing R@>Ptheta(. gradian or radian angle. according to the current angle mode setting.R R4Pq() R4Pq (xExpr. Catalog > In Degree angle mode: In Gradian angle mode: rand() rand() ⇒ expression rand(#Trials) ⇒ list Catalog > Sets the random-number seed. yList) ⇒ list R4Pq (xMatrix.). yMatrix) ⇒ matrix Catalog > In Degree angle mode: Returns the equivalent q-coordinate of the (x. rand() returns a random value between 0 and 1.. yMatrix) ⇒ matrix Catalog > In Radian angle mode: Returns the equivalent r-coordinate of the (x. Note: You can insert this operator from the computer keyboard by typing @>Rad.. yList) ⇒ list R4Pr (xMatrix. yExpr) ⇒ expression R4Pr (xList. s. numColumns) Catalog > ⇒ matrix Returns a matrix of integers between -9 and 9 of the specified dimension. randNorm(m.#Trials) returns a list containing Catalog > #Trials random integers within the specified range. Both arguments must simplify to integers. or no sample replacement (noRepl=1). p. p. Catalog > s) ⇒ expression s. #Trials) returns a list containing #Trials random real numbers from a specified Binomial distribution. #Trials) returns a list containing #Trials decimal numbers from the specified normal distribution. The leading coefficient will not be zero. randInt(lowBound. TI-Nspire™ CAS Reference Guide 93 .noRepl]) Catalog > ⇒ list Returns a list containing a random sample of #Trials trials from List with an option for sample replacement (noRepl=0).upBound . randMat() randMat(numRows. It could be any real number but will be heavily concentrated in the interval [mN3·s. p) ⇒ expression randBin(n. randNorm(m. randInt() randInt(lowBound.#Trials) ⇒ list randInt(lowBound. The coefficients are random integers in the range ë9 through 9. #Trials) ⇒ list randNorm(m. #Trials) ⇒ list randBin(n.randBin() randBin(n. Order must be 0–99. s) returns a decimal number from the specified normal distribution.#Trials[. p) returns a random real number from a specified Catalog > Binomial distribution. m+3·s].upBound . The default is with sample replacement. randSamp() randSamp(List. randBin(n. randNorm() randNorm(m. Note: The values in this matrix will change each time you press ·. randPoly() randPoly(Var.upBound) returns a random integer within the range specified by lowBound and upBound integer bounds. Order) Catalog > ⇒ expression Returns a polynomial in Var of the specified Order.upBound) ⇒ expression randInt(lowBound. sets the seeds to the factory defaults for the randomnumber generator. page 84. See also imag(). real( List1) ⇒ list Returns the real parts of all elements. real() real( Expr1) Catalog > ⇒ expression Returns the real part of the argument. The vector must be of dimension 2 or 3 and can be a row or a column. However. The complexValue can have any complex form. Note: 4Rect is a display-format instruction. real( Matrix1) ⇒ matrix Returns the real parts of all elements. and it does not update ans. If Number ƒ 0. In Radian angle mode: In Gradian angle mode: In Degree angle mode: Note: To type . z].RandSeed RandSeed Number Catalog > If Number = 0. 4Rect Vector 4Rect Note: You can insert this operator from the computer keyboard by typing @>Rect. which are stored in system variables seed1 and seed2. not a conversion function. select it from the symbol list in the Catalog. y. 94 TI-Nspire™ CAS Reference Guide . You can use it only at the end of an entry line. complexValue 4Rect Displays complexValue in rectangular form a+bi. Note: See also 4Polar. Catalog > Displays Vector in rectangular form [x. Note: All undefined variables are treated as real variables. Note: You must use parentheses for an (rq) polar entry. page 55. it is used to generate two seeds. an reiq entry causes an error in Degree angle mode. Note: See also rref(). If Tol is omitted or not used. computations are done using floatingpoint arithmetic. Tol is ignored. Otherwise. TI-Nspire™ CAS Reference Guide 95 . 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. 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. Tol]) Catalog > ⇒ matrix Returns the row echelon form of Matrix1. Expr2) ⇒ expression remain(List1. page 99. List2) ⇒ list remain(Matrix1. note that remain(Nx. Note: See also mod(). They can lead to unexpected results.0)  x remain(x. as shown in the following example. remain() remain(Expr1. if a is undefined in the following expression. Optionally. the default tolerance is calculated as: 5Eë14 ·max(dim(Matrix1)) ·rowNorm(Matrix1) /· • Avoid undefined elements in Matrix1. Matrix2) ⇒ matrix Catalog > Returns the remainder of the first argument with respect to the second argument as defined by the identities: remain(x.ref() ref( Matrix1[.y). any matrix element is treated as zero if its absolute value is less than Tol.y)  Nremain(x. You can avoid this by storing a value to a beforehand or by using the “|” substitution mechanism. For example.y)  xNy·iPart(x/y) As a consequence. page 74. The result is either zero or it has the same sign as the first argument. • or set the Auto or Approximate If you use mode to Approximate. DispFlag] Catalog > Define a program: Define requestStr_demo()=Prgm Programming command: Operates identically to the first syntax of the RequestStr “Your name:”. By contrast.argn) = user’s response EndPrgm The program can then use the defined function func().r Disp “Area = “. requestStr_demo() Note: You can use the RequestStr command within a userdefined program but not within a function.. Note: You can use the Request command within a user-defined program but not within a function.Request Request promptString.322185} RequestStr RequestStr promptString. The optional DispFlag argument can be any expression. 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 (““). This syntax operates as if the user executed the Define polynomial()=Prgm Request "Enter a polynomial in x:".” characters. If DispFlag evaluates to 0.polyRoots(p(x). DispFlag] Catalog > Define a program: Define request_demo()=Prgm Request “Radius: ”. When the user types a response and clicks OK. • • If DispFlag is omitted or evaluates to 1. page 96.. Result after selecting OK: Radius: 6/2 Area= 28. var [. the prompt and response are not displayed in the history. the contents of the input box are assigned to variable var. func ( arg1. . The promptString should guide the user to enter an appropriate user’s response that completes the function definition.dim(name).x) Define func(arg1. the prompt message and user’s response are displayed in the Calculator history. . Run the program and type a response: polynomial() Result after selecting OK: Enter a polynomial in x: x^3+3x+1 Real roots are: {-0.” interpreted as a string. Note: See also Request. Note: See also RequestStr. 96 TI-Nspire™ CAS Reference Guide . DispFlag] Request promptString.p(x) command: Disp "Real roots are:".0 Request command. The program uses the previous value of var if var was already defined.2743 The func() argument allows a program to store the user’s response as Define a program: a function definition. page 96. the program proceeds without accepting any input.. If the user clicks Cancel.pi*r2 EndPrgm Run the program and type a response: request_demo() Programming command: Pauses the program and displays a dialog box containing the message promptString and an input box for the user’s response. 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. except that the user’s response is always Disp “Response has “.name..argn ) [. var [. the rotation is to the left. If #ofRotations In Hex base mode: is negative. Use within a Func.#ofRotations]) Catalog > ⇒ integer In Bin base mode: Rotates the bits in a binary integer. or a general symbolic expression. right(Comparison) ⇒ expression Returns the right side of an equation or inequality. an integer or complex rational constant. a symmetric modulo operation brings it within the range. If you omit Num. Note for entering the example: In the Calculator application on the handheld. Note: Use Return without an argument within a Prgm. right(sourceString[. 64-bit binary form. If you omit Num. Expr2) returns the Expr2 root of Expr1. the rotation is to the right. Expr1 can be a real or complex floating point constant. You can enter Integer1 in any number base. If the magnitude of Integer1 is too large for this form. you can enter multi-line definitions by pressing @ at the end of each line.EndFunc block. For more information. in a right rotation: £ and then use ¡ and ¢ to TI-Nspire™ CAS Reference Guide 97 . Num]) Catalog > ⇒ list Returns the rightmost Num elements contained in List1... For example. page 14. root(Expr1. Expr2) ⇒ root ⇒ root root(Expr) returns the square root of Expr. On the computer keyboard.EndPrgm block to exit a program. it is converted automatically to a signed.. press move the cursor. returns all of List1. returns all of sourceString. Note: See also Nth root template. The default is ë1 (rotate right one bit).. To see the entire result. instead of hold down Alt and press Enter.Return Return [Expr] Catalog > Returns Expr as the result of the function. rotate() rotate(Integer1[. If #ofRotations is positive. page 1. · right() right(List1[. see 4Base2. root() root(Expr) Catalog > root(Expr1. Num]) ⇒ string Returns the rightmost Num characters contained in character string sourceString. ⇒ list In Dec base mode: Returns a copy of List1 rotated right or left by #of Rotations elements. If #of Rotations is negative. rIndex2) Catalog > ⇒ matrix Returns a copy of Matrix1 with row rIndex2 replaced by the sum of rows rIndex1 and rIndex2. page 19. digits]) ⇒ list Returns a list of the elements rounded to the specified number of digits. always use the 0b or 0h prefix (zero. If #ofRotations is negative. returns the argument rounded to 12 significant digits. 98 TI-Nspire™ CAS Reference Guide . the rotation is to the left. the rotation is to the right.rotate() Each bit rotates right. not the letter O). rowAdd() rowAdd( Matrix1. digits must be an integer in the range 0–12. If #ofRotations is positive. If #ofRotations is positive. If digits is not included. round() round( Expr1[. rIndex1. round( Matrix1[. Note: See also colDim(). round( List1[. the rotation is to the left. The default is ë1 (rotate right one element). digits]) Catalog > ⇒ expression Returns the argument rounded to the specified number of digits after the decimal point. rotate(List1[. The default is ë1 (rotate right one character). digits]) ⇒ matrix Returns a matrix of the elements rounded to the specified number of digits. Does not alter String1. rowDim() rowDim( Matrix) Catalog > ⇒ expression Returns the number of rows in Matrix. the rotation is to the right. produces: 0b10000000000000111101011000011010 The result is displayed according to the Base mode. Does not alter List1. Note: Display digits mode may affect how this is displayed.#ofRotations]) ⇒ string Returns a copy of String1 rotated right or left by #ofRotations characters.#ofRotations]) Catalog > Important: To enter a binary or hexadecimal number. 0b00000000000001111010110000110101 Rightmost bit rotates to leftmost. rotate(String1[. Note: The argument is interpreted as a degree. rowSwap() rowSwap( Matrix1. any matrix element is treated as zero if its absolute value is less than Tol. See also colNorm(). rIndex2) Catalog > ⇒ matrix Returns Matrix1 with rows rIndex1 and rIndex2 exchanged. computations are done using floatingpoint arithmetic. 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. G. page 95. Otherwise. according to the current angle mode setting. Note: All matrix elements must simplify to numbers. TI-Nspire™ CAS Reference Guide 99 . You can use ó. • If you use or set the Auto or Approximate mode to Approximate. rIndex1. rref() rref(Matrix1[. S sec() sec(Expr1) ⇒ expression sec(List1) ⇒ list μ key In Degree angle mode: Returns the secant of Expr1 or returns a list containing the secants of all elements in List1. If Tol is omitted or not used. Tol is ignored.rowNorm() rowNorm( Matrix) Catalog > ⇒ expression Returns the maximum of the sums of the absolute values of the elements in the rows in Matrix. gradian or radian angle. page 19. Tol]) Catalog > ⇒ matrix Returns the reduced row echelon form of Matrix1. orôto override the angle mode temporarily. the default tolerance is calculated as: 5Eë14 ·max(dim(Matrix1)) ·rowNorm(Matrix1) /· • Note: See also ref(). Optionally. . sechê() Catalog > In Radian angle and Rectangular complex mode: ⇒ expression sechê (List1) ⇒ list sech ê(Expr1) Returns the inverse hyperbolic secant of Expr1 or returns a list containing the inverse hyperbolic secants of each element of List1.. In Radian angle mode: sech() sech(Expr1) ⇒ expression sech(List1) ⇒ list Catalog > Returns the hyperbolic secant of Expr1 or returns a list containing the hyperbolic secants of the List1 elements. Note: You can insert this function from the keyboard by typing arcsech(. seq() seq(Expr. Low. High[. In Gradian angle mode: according to the current angle mode setting.).).. and returns the results as a list. Step]) Catalog > ⇒ list Increments Var from Low through High by an increment of Step.sec /() sec/(Expr1) ⇒ expression sec/(List1) ⇒ list μ key In Degree angle mode: Returns the angle whose secant is Expr1 or returns a list containing the inverse secants of each element of List1. The default value for Step = 1. The original contents of Var are still there after seq() is completed. evaluates Expr. Note: You can insert this function from the keyboard by typing arcsec(. Var. gradian or radian angle. Press Ctrl+Enter evaluate: /· (Macintosh®: “+Enter) to 100 TI-Nspire™ CAS Reference Guide .. Note: The result is returned as a degree. Var cannot be a system variable. 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. Var. series(. Point]) | Var>Point ⇒ expression series(Expr1.. Order can be any rational number. then append the appropriate one of “| Var > Point”. which is one ending with “_”. “| “Var ‚ Point”. such as for essential singularities such as sin(1/z) at z=0. Var. series() distributes over 1st-argument lists and matrices.. Point can be ˆ or Nˆ. 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.) might rearrange terms so that the dominant term is not the leftmost one. Order [.. or ez at z = ˆ or Nˆ. Var. Order [.)” if it is unable to determine such a representation. in which cases the expansion is through degree Order in 1/(Var N Point). Order [. page 38.) returns “series(. Point]) | Var<Point ⇒ expression series(Expr1. The resulting powers of (Var N Point) can include negative and/or fractional exponents. If you intend to use the series only for values on one side of Point.. eN1/z at z=0. Point defaults to 0. If the series or one of its derivatives has a jump discontinuity at Point. TI-Nspire™ CAS Reference Guide 101 . or “Var  Point” to obtain a simpler result. Note: See also dominantTerm().series() Catalog > ⇒ expression series(Expr1. series() can provide symbolic approximations to indefinite integrals and definite integrals for which symbolic solutions otherwise can't be obtained. Point]) Returns a generalized truncated power series representation of Expr1 expanded about Point through degree Order. “| Var < Point”.. 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(. 20=Fix6. 2=Approximate. 24=Fix10. The change is limited to the duration of the program/ function’s execution. 17=Fix3. modeNameInteger specifies which mode you want to set. settingInteger specifies the new setting for the mode. Vector Format Base Unit system 2 3 4 5 6 7 8 102 TI-Nspire™ CAS Reference Guide . 2=Rectangular. settingInteger) temporarily sets mode modeNameInteger to the new setting settingInteger. If any subroutine changes a mode setting. 18=Fix4. 25=Fix11. 2=Hex. 10=Float9. setMode(list) returns a similar list whose integer pairs represent the original modes and settings.setMode() setMode(modeNameInteger. 5=Float4. 22=Fix8. It must be one of the setting integers listed below for the specific mode you are setting. 4=Float3. 3=Exact 1=Rectangular. 3=Gradian 1=Normal. 14=Fix0. setMode(list) lets you change multiple settings. 26=Fix12 1=Radian. Note for entering the example: In the Calculator application on the handheld. 13=Float12. 6=Float5. Note: The current mode settings are passed to called subroutines. 15=Fix1. list contains pairs of mode integers and setting integers. 16=Fix2. and returns an integer corresponding to the original setting of that mode. 11=Float10. setMode(modeNameInteger. 7=Float6. 2=Float1. See getMode(). Valid only within a function or program. 3=Spherical 1=Decimal. @ · Mode Name Display Digits Mode Integer 1 Setting Integers 1=Float. It must be one of the mode integers from the table below. 2=Degree. 8=Float7. 3=Float2. If you have saved all mode settings with getMode(0) & var. page 52. On the by pressing computer keyboard. and then display p with a setting of Fix2. 3=Engineering 1=Real. 12=Float11. 3=Binary 1=SI. 3=Polar 1=Auto. 19=Fix5. 23=Fix9. you can use setMode(var) to restore those settings until the function or program exits. 2=Eng/US Angle Exponential Format Real or Complex Auto or Approx. Check to see that the default is restored after the program executes. 9=Float8. settingInteger) setMode(list) ⇒ integer list Catalog > ⇒ integer Display approximate value of p using the default setting for Display Digits. you can enter multi-line definitions instead of at the end of each line. hold down Alt and press Enter. the mode change will be lost when control returns to the calling routine. 2=Cylindrical. 2=Scientific. 21=Fix7. Does not alter List1. the shift is to the right. otherwise. the rightmost bit is dropped and 0 or 1 is inserted to match the leftmost bit. in a right shift: Each bit shifts right. see 4Base2. Leading zeros are not shown. Elements introduced at the beginning or end of list by the shift are set to the symbol “undef”. the leftmost bit is dropped and 0 is inserted as the rightmost bit. the shift is to the left. In a left shift. If #ofShifts is negative. not the letter O). 64-bit binary form. returns Expr1/abs(Expr1) when Expr1ƒ 0. shift(String1 [. If the magnitude of Integer1 is too large for this form. The default is ë1 (shift right one element). If complex format mode is Real: TI-Nspire™ CAS Reference Guide 103 . The default is ë1 (shift right one character). a symmetric modulo operation brings it within the range. In a right shift. the shift is to the right. If #ofShifts is negative. the shift is to the left. shift(List1 [.#ofShifts]) Important: To enter a binary or hexadecimal number. sign(0) returns „1 if the complex format mode is Real. If #ofShifts is positive. sign() sign(Expr1) ⇒ expression sign(List1) ⇒ list sign(Matrix1) ⇒ matrix Catalog > For real and complex Expr1. Does not alter String1. Returns 1 if Expr1 is positive.#ofShifts]) Catalog > ⇒ integer In Bin base mode: Shifts the bits in a binary integer. returns the signs of all the elements. the shift is to the right. ⇒ list In Dec base mode: Returns a copy of List1 shifted right or left by #ofShifts elements. always In Hex base mode: use the 0b or 0h prefix (zero. it is converted automatically to a signed.shift() shift(Integer1[. or 1 if leftmost bit is 1. For example.#ofShifts]) ⇒ string Returns a copy of String1 shifted right or left by #ofShifts characters. produces: 0b00000000000000111101011000011010 The result is displayed according to the Base mode. For a list or matrix. page 14. sign(0) represents the unit circle in the complex domain. If #ofShifts is negative. The default is ë1 (shift right one bit). You can enter Integer1 in any number base. Characters introduced at the beginning or end of string by the shift are set to a space. For more information. the shift is to the left. If #ofShifts is positive. Returns ë1 if Expr1 is negative. If #ofShifts is positive. it returns itself. 0b0000000000000111101011000011010 Inserts 0 if leftmost bit is 0. . where each system has the same equation coefficients but different constants. This is a display conversion operator. Otherwise. constVector must have the same number of rows (same dimension) as coeffMatrix and contain the constants. x=ë7 and y=9/2.) occurs in the given expression only to even powers. x=ë3 and y=2. Note: See also linSolve().)^2 so that any remaining powers of sin(. Note: This conversion operator is not supported in Degree or Gradian Angle modes. Solve for x and y: x + 2y = 1 3x + 4y = ë1 coeffMatrix must be a square matrix that contains the coefficients of the equations. Solve: x + 2y = 1 3x + 4y = ë1 Each column in constMatrix must contain the constants for a system x + 2y = 2 3x + 4y = ë3 of equations. For the second system.. Before using it. Thus.. 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.. Optionally.. the default tolerance is calculated as: 5Eë14 ·max(dim(coeffMatrix)) ·rowNorm(coeffMatrix) Solve: ax + by = 1 cx + dy = 2 simult(coeffMatrix. 4sin Expr 4sin Note: You can insert this operator from the computer keyboard by Catalog > typing @>sin. make sure that the Angle mode is set to Radians and that Expr does not contain explicit references to degree or gradian angles. 4sin reduces all powers of cos(. the result will be free of cos(. 104 TI-Nspire™ CAS Reference Guide . 2). Tol]) Catalog > ⇒ matrix Returns a column vector that contains the solutions to a system of linear equations.) have exponents in the range (0. • • If you set the Auto or Approximate mode to Approximate.. It can be used only at the end of the entry line.) if and only if cos(. constMatrix[. any matrix element is treated as zero if its absolute value is less than Tol. If Tol is omitted or not used.. Represents Expr in terms of sine. For the first system.) modulo 1Nsin(.simult() simult(coeffMatrix. constVector[. Each column in the resulting matrix contains the solution for the corresponding system.. Tol]) ⇒ matrix Solves multiple systems of linear equations.. Tol is ignored. The solution is x=ë3 and y=2.. page 64. computations are done using floating-point arithmetic. In Gradian angle mode: according to the current angle mode setting. gradian or radian angle.sin() sin(Expr1) ⇒ expression sin(List1) ⇒ list μ key In Degree angle mode: sin(Expr1) returns the sine of the argument as an expression. sinê(List1) returns a list of the inverse sines of each element of List1. Note: You can insert this function from the keyboard by typing In Radian angle mode: arcsin(. sinê() sinê(Expr1) ⇒ expression sinê(List1) ⇒ list μ key In Degree angle mode: sinê(Expr1) returns the angle whose sine is Expr1 as an expression. The result always contains floating-point numbers. squareMatrix1 must be diagonalizable.. gradian or radian angle. Note: The result is returned as a degree. For information about the calculation method. sin(List1) returns a list of the sines of all elements in List1.G. TI-Nspire™ CAS Reference Guide 105 .. refer to cos().). This is not the same as calculating the sine of each element. Note: The argument is interpreted as a degree. You can use ó. In Gradian angle mode: In Radian angle mode: sin(squareMatrix1) ⇒ squareMatrix In Radian angle mode: Returns the matrix sine of squareMatrix1. or ô to override the angle mode setting temporarily. according to the current angle mode. squareMatrix1 must be diagonalizable. For information about the calculation method. sinhê(squareMatrix1) ⇒ squareMatrix In Radian angle mode: Returns the matrix inverse hyperbolic sine of squareMatrix1. refer to cos(). The result always contains floating-point numbers. Note: You can insert this function from the keyboard by typing arcsinh(. sinh(squareMatrix1) ⇒ squareMatrix In Radian angle mode: Returns the matrix hyperbolic sine of squareMatrix1. press move the cursor. For information about the calculation method. This is not the same as calculating the inverse hyperbolic sine of each element. squareMatrix1 must be diagonalizable. sinh() sinh(Expr1) ⇒ expression sinh(List1) ⇒ list £ and then use ¡ and ¢ to Catalog > sinh (Expr1) returns the hyperbolic sine of the argument as an expression. 106 TI-Nspire™ CAS Reference Guide . squareMatrix1 must be diagonalizable. sinh ê() sinhê(Expr1) ⇒ expression sinhê(List1) ⇒ list Catalog > sinhê(Expr1) returns the inverse hyperbolic sine of the argument as an expression. The result always contains floating-point numbers.sinê() sinê(squareMatrix1) μ key ⇒ squareMatrix In Radian angle mode and Rectangular complex format mode: Returns the matrix inverse sine of squareMatrix1. To see the entire result. sinh (List1) returns a list of the hyperbolic sines of each element of List1. refer to cos(). refer to cos().). This is not the same as calculating the inverse sine of each element.. The result always contains floating-point numbers. sinhê(List1) returns a list of the inverse hyperbolic sines of each element of List1. For information about the calculation method.. This is not the same as calculating the hyperbolic sine of each element. the differences between x values can be unequal. larger values result in better accuracy but longer execution times. A summary of results is stored in the stat. If you specify Period. If omitted.a. For information on the effect of empty elements in a list. Iterations is a value that specifies the maximum number of times (1 through 16) a solution will be attempted. regardless of the angle mode setting. stat. Category is a list of category codes for the corresponding X and Y data. Category List. Typically. Category List. TI-Nspire™ CAS Reference Guide 107 . If omitted. Var) ⇒ Boolean expression Catalog > Returns candidate real solutions of an equation or an inequality for Var.[ Period] [.XReg Description Regression Equation: a·sin(bx+c)+d Regression coefficients Residuals from the regression List of data points in the modified X List actually used in the regression based on restrictions of Freq.b. and Include Categories List of data points in the modified Y List actually used in the regression based on restrictions of Freq. the difference between values in X should be equal and in sequential order. Include] ] Catalog > Computes the sinusoidal regression on lists X and Y.YReg stat.c. see “Empty (void) elements” on page 152. Y [ .Resid stat. (See page 112. stat.YReg stat. X and Y are lists of independent and dependent variables. [Iterations] . Var=Guess) ⇒ Boolean expression solve(Inequality. The output of SinReg is always in radians.XReg and stat. there might be equations or inequalities for which the number of solutions is infinite. However. Solution candidates might not be real finite solutions for some combinations of values for undefined variables. Output variable stat. 8 is used. Only those data items whose category code is included in this list are included in the calculation.RegEqn stat. Include is a list of one or more of the category codes.d stat.) All the lists must have equal dimension except for Include. The goal is to return candidates for all solutions. Period specifies an estimated period. Var) ⇒ Boolean expression solve(Equation. and vice versa.FreqReg solve() solve(Equation. and Include Categories List of frequencies corresponding to stat.SinReg SinReg X. stat.results variable. Category. ” and “not” to combine results from solve() with each other or with other Boolean expressions. the goal is to produce exact solutions when they are concise. 108 TI-Nspire™ CAS Reference Guide . . Catalog > For the Exact mode. Such variables designate an arbitrary integer. … ]) ⇒ Boolean expression solve({Eqn1. VarOrGuess2 [. Otherwise.” “or. solutions might be solutions only in the limit from one or both sides. 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. VarOrGuess2 [. you can use “and. logarithms. In Real mode.. and zeros(). multiple branched expressions such as fractional powers. portions that cannot be solved are returned as an implicit equation or inequality. solve() produces only solutions corresponding to that one real or principal branch. where each VarOrGuess specifies a variable that you want to solve for. or >. For inequalities of types ‚. In Radian angle mode: false is returned when no real solutions are found. Since solve() always returns a Boolean result. VarOrGuess1. or you can enter a SystemOfEqns using a template from the Catalog. Each VarOrGuess must have the form: variable – or – variable = real or non-real number For example. fractional powers having odd denominators denote only the real branch. When you find a solution in one interval. Due to default cancellation of the greatest common divisor from the numerator and denominator of ratios. and supplemented by iterative searches with approximate arithmetic when exact solutions are impractical.]} {VarOrGuess1. nSolve(). Note: See also cSolve(). you can use the inequality operators to exclude that interval from subsequent searches.solve() For the Auto setting of the Auto or Approximate mode. true is returned if solve() can determine that any finite real value of Var satisfies the equation or inequality. VarOrGuess1. you can specify an initial guess for a variable.. … ]}) ⇒ Boolean expression Returns candidate real solutions to the simultaneous algebraic equations. cZeros(). You can separate the equations with the and operator. solve(Eqn1 and Eqn2 [and … ]. x is valid and so is x=3. explicit solutions are unlikely unless the inequality is linear and contains only Var. Eqn2 [. Consequently.. <. … ]) ⇒ Boolean expression solve(SystemOfEqns. The number of VarOrGuess arguments must match the number of equations. and inverse trigonometric functions denote only the principal branch. VarOrGuess2 [. Use the “|” operator to restrict the solution interval and/or other variables that occur in the equation or inequality. Optionally. simultaneous polynomial equations can have extra variables that have no values. press move the cursor. solve() determines at most one solution using an approximate iterative method. solve() uses Gaussian elimination to attempt to determine all real solutions. You can also (or instead) include solution variables that do not appear in the equations. 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. you can include z as a solution variable to extend the previous example to two parallel intersecting cylinders of radius r. try rearranging the variables in the equations and/or varOrGuess list. otherwise. it starts at 0. Use guesses to seek additional solutions one by one. but represent given numeric values that could be substituted later.0. the number of solution variables must equal the number of equations. where k is an integer suffix from 1 through 255. To do so. 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. For example. £ and then use ¡ and ¢ to TI-Nspire™ CAS Reference Guide 109 . For convergence. To see the entire result. £ and then use ¡ and ¢ to If a system is neither polynomial in all of its variables nor linear in its solution variables. and all other variables in the equations must simplify to numbers. solve() uses the lexical Gröbner/Buchberger elimination method to attempt to determine all real solutions. a guess may have to be rather close to a solution. Each solution variable starts at its guessed value if there is one.solve() If all of the equations are polynomials and if you do NOT specify any initial guesses. To see the entire result. The cylinder solutions illustrate how families of solutions might contain arbitrary constants of the form ck. For example. Catalog > As illustrated by r in the example to the right. press move the cursor. For polynomial systems. Use solve() to find the intersections. 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. All arguments must be names of lists or vectors. Catalog > Identical to SortA. SortA Vector1[.. For more information on empty elements..Vector2] [. 110 TI-Nspire™ CAS Reference Guide . Vector3] . SortD Vector1[. Empty (void) elements within the first argument move to the bottom..SortA SortA List1[. Vector2] [. see page 152.. Catalog > Sorts the elements of the first argument in ascending order. Empty (void) elements within the first argument move to the bottom. see page 152. All arguments must have equal dimensions... For more information on empty elements... sorts the elements of each so that their new positions match the new positions of the elements in the first argument. List2] [. except SortD sorts the elements in descending order. If you include additional arguments. List2] [. List3] . List3] .Vector3] . SortD SortD List1[. page 1. TI-Nspire™ CAS Reference Guide 111 . Note: 4Sphere is a display-format instruction.φ) ρ Y θ X φ sqrt() sqrt(Expr1) ⇒ expression sqrt(List1) ⇒ list Catalog > Returns the square root of the argument. You can use it only at the end of an entry line. For a list. Displays the row or column vector in spherical form [r q f]. Press Ctrl+Enter evaluate: /· (Macintosh®: “+Enter) to Press · Z (ρ. not a conversion function. returns the square roots of all the elements in List1. Note: See also Square root template.θ.4Sphere Vector 4Sphere Note: You can insert this operator from the computer keyboard by Catalog > Press Ctrl+Enter evaluate: /· (Macintosh®: “+Enter) to typing @>Sphere. Vector must be of dimension 3 and can be either a row or a column vector. SEslope stat.r stat.dfInteract stat. The results are displayed as a set of name-value pairs.SEPred stat.PValCol stat.MS stat.MSRow stat.v2 stat. stat.b1 stat.YReg y y Note: Each time the Lists & Spreadsheet application calculates statistical results.ExpMatrix stat.dfCol stat.CLowerList stat.s stat. where # is a number that is incremented automatically.Gy² stat.b8 stat.sx2 stat.b4 stat.UpperVal stat.r² stat.PList stat.UpperPred stat.dfBlock stat.SE stat.MSCol stat.vDiff stat.CLower stat. In some cases.CUpperList stat.MinX stat.results Displays results from a statistics calculation.SSRow stat.XValList stat.sp stat.a stat.CUpper stat.PVal stat.v stat.Gxy stat.sy stat.CompMatrix stat.c stat.dfReg stat.Leverage stat.MedianY stat.dfDenom stat.dfNumer stat.results stat. You can copy a name or value and paste it into other locations.m stat.CompList stat.MaxY stat.e stat. List stat.dfRow stat.XVal stat.ÇDiff stat.” group variables to a “stat#.dfError stat.AdjR² stat.FBlock stat.F stat.Frow stat.Ç stat.b7 stat.d stat.b2 stat.PValInteract stat.b9 stat.b3 stat.Gx² stat.MSError stat.Q3X stat.tList stat.PValRow stat.bList stat.sx1 stat.ResidTrans stat.RegEqn stat.MaxX stat.Q1Y stat.SSBlock stat.SSY stat.FInteract stat.sResid stat.SSCol stat.Fcol stat. Catalog > Note: Avoid defining variables that use the same names as those used for statistical analysis.LowerPred stat.MEPred stat.XReg stat. it copies the “stat .c² stat. an error condition could occur.b6 stat.CookDist stat.ME stat. stat.DW stat.b0 stat.b stat.w stat.LowerVal stat.Ç1 stat.MSReg stat.b5 stat.Ç2 stat.MSBlock stat.sx stat.SEList stat.” group.SSInteract stat.n stat.MedianX stat.SSReg stat. Variable names used for statistical analysis are listed in the table below.MSInteract stat. 112 TI-Nspire™ CAS Reference Guide .SS stat. The specific names shown are dependent on the most recently evaluated statistics function or command.Gy stat.SSX stat.vList stat.Q1X stat.MinY stat.SSError stat.v1 stat.b10 stat.Gx stat.Q3Y stat.stat.Resid stat.PValBlock stat.FreqReg stat. This lets you maintain previous results while performing multiple calculations. Empty (void) elements are ignored.results. Unlike stat. Note: List must have at least two elements.values stat. For more information on empty elements.values omits the names associated with the values. TI-Nspire™ CAS Reference Guide 113 . Empty (void) elements are ignored. For more information on empty elements. stDevSamp() stDevSamp(List[. Note: List must have at least two elements. see page 152. see page 152. freqMatrix]) ⇒ matrix Returns a row vector of the population standard deviations of the columns in Matrix1. For more information on empty elements. stat. stDevPop(Matrix1[. Empty (void) elements are ignored. see page 152. freqList]) Catalog > ⇒ expression Returns the sample standard deviation of the elements in List. stDevPop() stDevPop(List[. Each freqList element counts the number of consecutive occurrences of the corresponding element in List. Each freqList element counts the number of consecutive occurrences of the corresponding element in List. freqList]) Catalog > See the stat.values Displays a matrix of the values calculated for the most recently evaluated statistics function or command. Each freqMatrix element counts the number of consecutive occurrences of the corresponding element in Matrix1. Note: Matrix1 must have at least two rows. Catalog > ⇒ expression In Radian angle and auto modes: Returns the population standard deviation of the elements in List.stat.results example. You can copy a value and paste it into other locations. freqMatrix]) Catalog > ⇒ matrix Returns a row vector of the sample standard deviations of the columns in Matrix1. see page 152. startCol] [. Empty (void) elements are ignored. Note for entering the example: In the Calculator application on the handheld. instead of hold down Alt and press Enter. · Store See & (store). Each freqMatrix element counts the number of consecutive occurrences of the corresponding element in Matrix1. startCol=1. startRow] [. page 150.stDevSamp() stDevSamp(Matrix1[. you can enter multi-line definitions by pressing @ at the end of each line. subMat() subMat(Matrix1[. For more information on empty elements. endRow=last row. string() string(Expr) Catalog > ⇒ string Simplifies Expr and returns the result as a character string. On the computer keyboard. Note: Matrix1 must have at least two rows. Stop is not allowed in functions. Sum (Sigma) See G(). page 144. 114 TI-Nspire™ CAS Reference Guide . Defaults: startRow=1. Stop Stop Catalog > Programming command: Terminates the program. endRow] [. endCol]) Catalog > ⇒ matrix Returns the specified submatrix of Matrix1. endCol=last column. For more information on empty elements. . Within the Lists & Spreadsheet application. Empty (void) elements in Matrix1 are ignored. Any void argument produces a void result. SumList. A Boolean expression containing the symbol ? as a placeholder for each element. 34 accumulates only those elements in List that simplify to the value 34. Start[. List can be an expression. Expr2 [.]]]) system(Expr1 [. Optionally. End]]) ⇒ matrix Returns a row vector containing the sums of all elements in the columns in Matrix1. . You can also create a system by using a template. or string. sum(Matrix1[. the element is added to the accumulating sum. For more information on empty elements. list.]]]) Catalog > Returns a system of equations. When a List element meets the Criteria. They specify a range of elements.. Note: See also countIf(). sumIf() sumIf(List. ?<10 accumulates only those elements in List that are less than 10. Any void argument produces a void result. see page 152. SumList]) Catalog > ⇒ value Returns the accumulated sum of all elements in List that meet the specified Criteria. system() system(Eqn1 [. or matrix.Criteria[. Criteria can be: • • A value. For more information on empty elements. If you include sumList. formatted as a list. Eqn3 [. Start and End are optional.. expression. the corresponding element from sumList is added to the sum instead. For example. page 3. if specified. sumSeq() See G(). page 25. you can use a range of cells in place of List and sumList. Start[. End]]) Catalog > ⇒ expression Returns the sum of all elements in List. to supply the elements to accumulate. Empty (void) elements are ignored. Empty (void) elements in List are ignored.. see page 152. Expr3 [. must have the same dimension(s) as List. see page 152. They specify a range of rows. sumList. Start and End are optional.. Note: See also System of equations. For example. TI-Nspire™ CAS Reference Guide 115 . Eqn2 [. you can specify an alternate list.sum() sum(List[. page 144. Catalog > tan() tan(Expr1) ⇒ expression tan(List1) ⇒ list μ key In Degree angle mode: tan(Expr1) returns the tangent of the argument as an expression. 116 TI-Nspire™ CAS Reference Guide . This is not the same as calculating the tangent of each element. gradian or radian angle. refer to cos(). The result always contains floating-point numbers. G orôto override the angle mode setting temporarily. Note: The argument is interpreted as a degree. In Gradian angle mode: In Radian angle mode: tan(squareMatrix1) ⇒ squareMatrix In Radian angle mode: Returns the matrix tangent of squareMatrix1.T T (transpose) Matrix1T ⇒ matrix Returns the complex conjugate transpose of Matrix1. according to the current angle mode. tan(List1) returns a list of the tangents of all elements in List1. For information about the calculation method. squareMatrix1 must be diagonalizable. Note: You can insert this operator from the computer keyboard by typing @t. You can use ó. tanê() tanê(Expr1) ⇒ expression tanê(List1) ⇒ list μ key In Degree angle mode: tanê(Expr1) returns the angle whose tangent is Expr1 as an expression..2) returns “false. Make sure that the independent variable is not defined. Note: You can insert this function from the keyboard by typing In Radian angle mode: arctan(. The result always contains floating-point numbers.Var. TI-Nspire™ CAS Reference Guide 117 . For information about the calculation method. For example. Note: The result is returned as a degree.Point) Returns the tangent line to the curve represented by Expr1 at the point specified in Var=Point. tanê(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. tanê(List1) returns a list of the inverse tangents of each element of List1. tanh(List1) returns a list of the hyperbolic tangents of each element of List1. refer to cos(). In Gradian angle mode: according to the current angle mode setting. refer to cos().” tanh() tanh(Expr1) ⇒ expression tanh(List1) ⇒ list Catalog > tanh(Expr1) returns the hyperbolic tangent of the argument as an expression. tanh(squareMatrix1) ⇒ squareMatrix In Radian angle mode: Returns the matrix hyperbolic tangent of squareMatrix1. The result always contains floating-point numbers. squareMatrix1 must be diagonalizable. then tangentLine(f1(x).x.. tangentLine() Catalog > ⇒ expression tangentLine(Expr1.Var=Point) ⇒ expression tangentLine(Expr1. If f1(x):=5 and x:=3. gradian or radian angle. This is not the same as calculating the hyperbolic tangent of each element.). squareMatrix1 must be diagonalizable. For information about the calculation method. tanh ê() tanhê(Expr1) ⇒ expression tanhê(List1) ⇒ list Catalog > In Rectangular complex format: tanhê(Expr1) returns the inverse hyperbolic tangent of the argument as an expression.) might rearrange terms so that the dominant term is not the leftmost one. taylor() returns itself if there is no truncated power series of this order. refer to cos(). Var. Order[. or if it would require negative or fractional exponents. This is not the same as calculating the inverse hyperbolic tangent of each element. tanhê(List1) returns a list of the inverse hyperbolic tangents of each element of List1..ˆ..upBound. set lowBound = . list if lowBound and upBound are lists Catalog > Computes the Student-t distribution probability between lowBound and upBound for the specified degrees of freedom df.. The polynomial includes non-zero terms of integer degrees from zero through Order in (Var minus Point).. For information about the calculation method. the display routines downstream of the result produced by taylor(. press move the cursor. Use substitution and/or temporary multiplication by a power of (Var minus Point) to determine more general power series.df) ⇒ number if lowBound and upBound are numbers. taylor() taylor(Expr1. Point]) £ and then use ¡ and ¢ to Catalog > ⇒ expression Returns the requested Taylor polynomial.). For P(X  upBound). As illustrated by the last example to the right. Point defaults to zero and is the expansion point. To see the entire result. 118 TI-Nspire™ CAS Reference Guide . Note: You can insert this function from the keyboard by typing arctanh(. tanhê(squareMatrix1) ⇒ squareMatrix In Radian angle mode and Rectangular complex format: Returns the matrix inverse hyperbolic tangent of squareMatrix1. The result always contains floating-point numbers. tCdf() tCdf(lowBound. squareMatrix1 must be diagonalizable. DispFlag] Catalog > Define a program that pauses to display each of five random numbers in a dialog box. angle sums. Note: Degree-mode scaling by p/180 interferes with the ability of tExpand() to recognize expandable forms. page 96. tCollect() tends to reverse transformations done by tExpand(). For best results.. tExpand() tExpand(Expr1) Catalog > ⇒ expression Returns an expression in which sines and cosines of integer-multiple angles. When the user selects OK.1. refer to Request. On the computer keyboard. Because of the identity (sin(x))2+(cos(x))2=1. page 54. • • If DispFlag is omitted or evaluates to 1. @ · If the program needs a typed response from the user. or vice versa. Text Text promptString [. The transformation converts trigonometric polynomials into a linear combination of their harmonics. a result might differ from a result shown in other publications. Within the Prgm. in two separate steps simplifies an expression. the text message is not added to the history. Run the program: text_demo() Note: You can use this command within a user-defined program but not within a function. and angle differences. Consequently. TI-Nspire™ CAS Reference Guide 119 . If DispFlag evaluates to 0. The optional flag argument can be any expression. page 96. Define text_demo()=Prgm For i. Sometimes tExpand() will accomplish your goals when the default trigonometric simplification does not. angle sums. hold down Alt and press Enter.. in two separate steps simplifies an expression. Sometimes tCollect() will accomplish your goals when the default trigonometric simplification does not. the text message is added to the Calculator history. Sometimes applying tExpand() to a result from tCollect(). Sometimes applying tCollect() to a result from tExpand(). tExpand() should be used in Radian mode. program execution continues. or vice versa. or RequestStr.5 strinfo:=”Random number “ & string(rand(i)) Text strinfo Next EndPrgm Programming command: Pauses the program and displays the character string promptString in a dialog box. tExpand() tends to reverse transformations done by tCollect(). complete each line by pressing instead of .EndPrgm template.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. and angle differences are expanded. there are many possible equivalent results. Sample of one dialog box: Then See If. CLevel[.CUpper stat.CLower.n1. Pooled=0 does not pool variances. see “Empty (void) elements” on page 152.) For information on the effect of empty elements in a list.sx1.Pooled]]]] Catalog > (Data list input) tInterval_2Samp v1.List2[.df stat.Freq2[.sx2 stat.n Description Confidence interval for an unknown population mean Sample mean of the data sequence from the normal random distribution Margin of error Degrees of freedom Sample standard deviation Length of the data sequence with sample mean tInterval_2Samp tInterval_2Samp List1.x2 stat. For information on the effect of empty elements in a list. A summary of results is stored in the stat.results variable. stat.) Pooled=1 pools variances.tInterval tInterval List[. stat. stat.CLower.v2.results variable.sx stat.Freq1[. Output variable stat. (See page 112. see “Empty (void) elements” on page 152.n2[.ME stat.sx2. stat.Pooled]] (Summary stats input) Computes a two-sample t confidence interval.ME stat.n2 stat.x1.n1. (See page 112.CLevel] (Summary stats input) Computes a t confidence interval.x1-x2 stat.x stat. stat.CUpper stat.df stat.sx1. A summary of results is stored in the stat.CLevel]] Catalog > (Data list input) tInterval v.CLevel[.n[.sx. Calculated when Pooled = YES 120 TI-Nspire™ CAS Reference Guide .sp Description Confidence interval containing confidence level probability of distribution Sample means of the data sequences from the normal random distribution Margin of error Degrees of freedom Sample means of the data sequences from the normal random distribution Sample standard deviations for List 1 and List 2 Number of samples in data sequences The pooled standard deviation. Output variable stat.Freq[. . tPdf() tPdf(XVal. use @tmpCnv() instead. 1_¡C is 9/5 as large as 1_¡F. To type ¡. Valid temperature units are: _¡C _¡F _¡K _¡R Celsius Fahrenheit Kelvin Rankine Note: You can use the Catalog to select temperature units. Converts a temperature range (the difference between two temperature values) specified by Expr from one unit to another. Catalog > ⇒ expression _¡tempUnit2 _¡tempUnit2) Converts a temperature value specified by Expr from one unit to another. For example. To type _ . To convert a particular temperature value instead of a range. Valid temperature units are: _¡C Celsius _¡F Fahrenheit _¡K Kelvin _¡R Rankine To enter ¡. as do 1_¡F and 1_¡R. a 100_¡C range (from 0_¡C to 100_¡C) is equivalent to a 180_¡F range.tmpCnv() tmpCnv(Expr_¡tempUnit. @tmpCnv() @tmpCnv(Expr_¡tempUnit.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. /_. However. For example. press /_. _¡tempUnit2) ⇒ expression _¡tempUnit2 Note: You can insert this function from the keyboard by typing Catalog > deltaTmpCnv(. 1_¡C and 1_¡K have the same magnitude. TI-Nspire™ CAS Reference Guide 121 . 100_¡C converts to 212_¡F.). To convert a temperature range. to type _ . use tmpCnv(). select it from the Catalog symbols.. press Note: You can use the Catalog to select temperature units. select it from the Symbol Palette or type @d. Try Try Catalog > block1 Else block2 EndTry Executes block1 unless an error occurs. Note for entering the example: In the Calculator application on the handheld.trace() trace(squareMatrix) Catalog > ⇒ expression Returns the trace (sum of all the elements on the main diagonal) of squareMatrix. and PassErr. hold down Alt and press Enter. page 83. you can enter multi-line definitions by pressing @ instead of at the end of each line. and PassErr in operation.B) displays eigenvalues of A·B Try Disp "A= ". see “Error codes and messages. 122 TI-Nspire™ CAS Reference Guide . · Example 2 To see the commands Try.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 Note: See also ClrErr. Define eigenvals(a.a Disp "B= ". Run the program by executing each of the following expressions.” page 158. block1 and block2 can be either a single statement or a series of statements separated with the “:” character.b Disp " " Disp "Eigenvalues of A·B are:". page 19. For a list of error codes. ClrErr.b)=Prgm © Program eigenvals(A. Program execution transfers to block2 if an error occurs in block1. enter the eigenvals() program shown at the right. System variable errCode contains the error code to allow the program to perform error recovery. On the computer keyboard. List2[.n2[.t Description Standard normal value computed for the difference of means TI-Nspire™ CAS Reference Guide 123 . (See page 112. A summary of results is stored in the stat. Output variable stat.Hypoth]] m0.n.results variable. see “Empty (void) elements” on page 152. set Hypoth<0 For Ha: m1ƒ m2 (default).n Description (x N m0) / (stdev / sqrt(n)) Smallest level of significance at which the null hypothesis can be rejected Degrees of freedom Sample mean of the data sequence in List Sample standard deviation of the data sequence Size of the sample tTest_2Samp tTest_2Samp List1. (See page 112.v2. set Hypoth=0 For Ha: m > m0.) Test H0: m1 = m2. against one of the following: For Ha: m1< m2.[Hypoth] (Data list input) tTest (Summary stats input) Performs a hypothesis test for a single unknown population mean m when the population standard deviation s is unknown.sx1.n1. Output variable stat.t stat.df stat.sx2. set Hypoth>0 Pooled=1 pools variances Pooled=0 does not pool variances For information on the effect of empty elements in a list.x stat. against one of the following: For Ha: m < m0. set Hypoth>0 For information on the effect of empty elements in a list. see “Empty (void) elements” on page 152.Freq1[.sx.tTest tTest Catalog > m0.Pooled]] (Summary stats input) Computes a two-sample t test.) Test H0: m = m0.Freq[. set Hypoth<0 For Ha: m ƒ m0 (default).Freq2[. set Hypoth=0 For Ha: m1> m2.PVal stat.sx stat.Hypoth[.Hypoth[.List[.Pooled]]]] Catalog > (Data list input) tTest_2Samp v1.results variable. A summary of results is stored in the stat.x. Output variable stat.PV.sx2 stat.[PmtAt]) Catalog > ⇒ 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.[CpY].[PpY].FV.FV.[PpY]. tvmFV() tvmFV(N. page 7.n1. Note: Arguments used in the TVM functions are described in the table of TVM arguments.[PmtAt]) Catalog > ⇒ value Financial function that calculates the number of payment periods.[PpY].df stat.[PmtAt]) Catalog > ⇒ value Financial function that calculates the future value of money.[PmtAt]) Catalog > ⇒ value Financial function that calculates the amount of each payment.I. TVM argument* N I Description Data type Number of payment periods Annual interest rate real number real number 124 TI-Nspire™ CAS Reference Guide . page 7.PV. page 124. page 124.Pmt.sx1.PVal stat. tvmI() tvmI(N.Pmt. tvmPV() tvmPV(N. stat. Note: Arguments used in the TVM functions are described in the table of TVM arguments. stat. stat. Note: Arguments used in the TVM functions are described in the table of TVM arguments.I. Note: Arguments used in the TVM functions are described in the table of TVM arguments.[CpY]. page 7.PV. tvmPmt() tvmPmt(N. See also amortTbl(). page 124. tvmN() tvmN(I.I.[CpY]. page 124.n2 stat.x2 stat.Pmt.Pmt. page 7. See also amortTbl(). Calculated when Pooled=1. See also amortTbl().FV.x1.PV. page 7.FV.[PpY].[PmtAt]) Catalog > ⇒ value Financial function that calculates the present value.[PpY].[CpY]. See also amortTbl(). page 124. See also amortTbl().[CpY].sp Description Smallest level of significance at which the null hypothesis can be rejected Degrees of freedom for the t-statistic Sample means of the data sequences in List 1 and List 2 Sample standard deviations of the data sequences in List 1 and List 2 Size of the samples The pooled standard deviation. TVM argument* PV Pmt FV PpY CpY PmtAt Description Data type Present value Payment amount Future value Payments per year. (See page 112. [Freq] [. Freq. Financial functions.pmt) that are used by the Calculator application’s finance solver.sy Description Mean of x values Sum of x values Sum of x2 values Sample standard deviation of x Population standard deviation of x Number of data points Mean of y values Sum of y values Sum of y2 values Sample standard deviation of y TI-Nspire™ CAS Reference Guide 125 . do not store their argument values or results to the TVM variables.Gy G stat. A summary of results is stored in the stat. Freq is an optional list of frequency values. Include is a list of one or more of the category codes. TwoVar TwoVar X.Gx G stat. Category. or Category results in a void for the corresponding element of all those lists. Output variable stat.pv and tvm. For more information on empty elements. see page 152. Include]] Catalog > Calculates the TwoVar statistics. An empty (void) element in any of the lists X.v stat. All elements must be integers | 0.Gx2 G stat.sx s stat. X and Y are lists of independent and dependent variables. default=1 Payment due at the end or beginning of each period. The default value is 1. Only those data items whose category code is included in this list are included in the calculation. An empty element in any of the lists X1 through X20 results in a void for the corresponding element of all those lists. Category is a list of numeric category codes for the corresponding X and Y data.Gy2 G stat.) All the lists must have equal dimension except for Include. default=1 Compounding periods per year. however. 1=beginning) * These time-value-of-money argument names are similar to the TVM variable names (such as tvm. default=end real number real number real number integer > 0 integer > 0 integer (0=end.n stat.sx stat. Y[.w stat. Each element in Freq specifies the frequency of occurrence for each corresponding X and Y data point.results variable. Gxy G stat.MinX stat.Output variable stat.G(x-v) G v stat. £ and then use ¡ and ¢ to 126 TI-Nspire™ CAS Reference Guide .MedY stat.MaxX stat.MinY stat.Q3X stat. depending on the form of Vector1.Q1X stat.sy s stat.G(y-w) G w 2 Description Population standard deviation of y Sum of x·y values Correlation coefficient Minimum of x values 1st Quartile of x Median of x 3rd Quartile of x Maximum of x values Minimum of y values 1st Quartile of y Median of y 3rd Quartile of y Maximum of y values Sum of squares of deviations from the mean of x Sum of squares of deviations from the mean of y 2 U unitV() unitV(Vector1) Catalog > ⇒ vector Returns either a row. To see the entire result.r stat.or column-unit vector. Vector1 must be either a single-row matrix or a single-column matrix.Q3Y stat.Q1Y stat.MedianX stat.MaxY stat. press move the cursor. Locked variables cannot be modified or deleted. Each freqList element counts the number of consecutive occurrences of the corresponding element in List. Catalog > Unlocks the specified variables or variable group. Var3] . that element is ignored. page 51. For more information on empty elements. see page 152. see page 152. Note: List must contain at least two elements. Note: List must contain at least two elements.unLock unLock Var1[. Var2] [. If an element in either list is empty (void). page 66. See Lock. unLock Var. see page 152. and getLockInfo(). freqMatrix]) ⇒ matrix Returns a row vector containing the sample variance of each column in Matrix1. Note: Matrix1 must contain at least two rows. Each freqMatrix element counts the number of consecutive occurrences of the corresponding element in Matrix1. V varPop() varPop(List[. freqList]) Catalog > ⇒ expression Returns the population variance of List. and the corresponding element in the other list is also ignored. freqList]) Catalog > ⇒ expression Returns the sample variance of List. that element is ignored. varSamp(Matrix1[. If an element in either matrix is empty (void). that element is ignored. If an element in either list is empty (void). and the corresponding element in the other matrix is also ignored. varSamp() varSamp(List[. Each freqList element counts the number of consecutive occurrences of the corresponding element in List. TI-Nspire™ CAS Reference Guide 127 .. For more information on empty elements. and the corresponding element in the other list is also ignored.. For more information on empty elements. hold down Alt and press Enter. depending on whether Condition is true. or unknownResult. While While Condition Catalog > Block EndWhile Executes the statements in Block as long as Condition is true. · “With” See (“with”). falseResult. you can enter multi-line definitions by pressing @ instead of at the end of each line. page 150. false. when() is helpful for defining recursive functions. Returns the input if there are too few arguments to specify the appropriate result. or unknown. | 128 TI-Nspire™ CAS Reference Guide . Omit both falseResult and unknownResult to make an expression defined only in the region where Condition is true. falseResult][. Note for entering the example: In the Calculator application on the handheld. Block can be either a single statement or a sequence of statements separated with the “:” character. trueResult [.W when() when(Condition. On the computer keyboard. unknownResult]) Catalog > ⇒ expression Returns trueResult. Use an undef falseResult to define an expression that graphs only on an interval. solutions that require inequalities. Var) Catalog > ⇒ list ⇒ list zeros(Expr. 64-bit binary numbers.X xor BooleanExpr1 xor BooleanExpr2 ⇒ Boolean expression Returns true if BooleanExpr1 is true and BooleanExpr2 is false. a symmetric modulo operation is used to bring the value into the appropriate range. Z zeros() zeros(Expr. For a binary or hexadecimal entry. the result form of zeros() cannot express implicit solutions. or solutions that do not involve Var. the result form for zeros() is more convenient than that of solve(). page 82. Var=Guess) Returns a list of candidate real values of Var that make Expr=0. For some purposes. Note: See or. If you enter a decimal integer that is too large for a signed. A hexadecimal entry can have up to 16 digits. When corresponding bits are compared. The returned value represents the bit results. Catalog > Integer1 xor Integer2 ⇒ integer Compares two real integers bit-by-bit using an xor operation. Note: See also cSolve(). page 82. the result is 1 if either bit (but not both) is 1. and solve(). zeros() does this by computing exp4list(solve(Expr=0. and is displayed according to the Base mode. However. integers are treated as decimal (base 10). Internally. Note: See or. Returns a simplified Boolean expression if either of the arguments cannot be resolved to true or false.Var). not the letter O. Returns false if both arguments are true or if both are false. You can enter the integers in any number base. the result is 0 if both bits are 0 or both bits are 1. or vice versa. Without a prefix. In Hex base mode: Important: Zero. you must use the 0b or 0h prefix. respectively. For more information. cZeros(). 64-bit binary form. page 14. see 4Base2. In Bin base mode: Note: A binary entry can have up to 64 digits (not counting the 0b prefix). both integers are converted to signed. TI-Nspire™ CAS Reference Guide 129 .Var). To extract a row. 130 TI-Nspire™ CAS Reference Guide . Optionally. Each row of the resulting matrix represents an alternate zero. where k is an integer suffix from 1 through 255. Expr2}. Extract row 2: You can also (or instead) include unknowns that do not appear in the expressions. For example. zeros() uses the lexical Gröbner/Buchberger elimination method to attempt to determine all real zeros. you can include z as an unknown to extend the previous example to two parallel intersecting cylinders of radius r. {VarOrGuess1. For example. index the matrix by [row]. Use zeros() to find the intersections. you can specify an initial guess for a variable. … ]}) Catalog > ⇒ matrix Returns candidate real zeros of the simultaneous algebraic expressions. 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. If all of the expressions are polynomials and if you do NOT specify any initial guesses. If you do not include any guesses and if any expression is nonpolynomial in any variable but all expressions are linear in the unknowns. but represent given numeric values that could be substituted later. simultaneous polynomial expressions can have extra variables that have no values. The cylinder zeros illustrate how families of zeros might contain arbitrary constants in the form ck.zeros() zeros({Expr1. Each VarOrGuess must have the form: variable – or – variable = real or non-real number For example. where each VarOrGuess specifies an unknown whose value you seek. try rearranging the variables in the expressions and/or varOrGuess list. with the components ordered the same as the varOrGuess list. zeros() uses Gaussian elimination to attempt to determine all real zeros. As illustrated by r in the example to the right. If your initial choice exhausts memory or your patience. x is valid and so is x=3. computation time or memory exhaustion may depend strongly on the order in which you list unknowns. VarOrGuess2 [. For polynomial systems. a guess may have to be rather close to a zero. Catalog > zInterval zInterval s.n [.0.results variable.List[. Output variable stat. stat. Output variable stat.CUpper stat. see “Empty (void) elements” on page 152. For information on the effect of empty elements in a list.n stat. A summary of results is stored in the stat. (See page 112.CLower.x stat. stat.CLevel] Catalog > Computes a one-proportion z confidence interval.Ç stat. Use guesses to seek additional zeros one by one. it starts at 0.s Description Confidence interval for an unknown population mean Sample mean of the data sequence from the normal random distribution Margin of error Sample standard deviation Length of the data sequence with sample mean Known population standard deviation for data sequence List zInterval_1Prop zInterval_1Prop x. and all other variables in the expressions must simplify to numbers. For convergence. the number of unknowns must equal the number of expressions. (See page 112.CLevel]] Catalog > (Data list input) zInterval s.n [. zeros() determines at most one zero using an approximate iterative method.zeros() If a system is neither polynomial in all of its variables nor linear in its unknowns. A summary of results is stored in the stat.CLower. otherwise.ME stat.CLevel] (Summary stats input) Computes a z confidence interval.) x is a non-negative integer. To do so. see “Empty (void) elements” on page 152.sx stat.ME Description Confidence interval containing confidence level probability of distribution The calculated proportion of successes Margin of error TI-Nspire™ CAS Reference Guide 131 .v.Freq[.results variable. Each unknown starts at its guessed value if there is one.) For information on the effect of empty elements in a list.CUpper stat. n2[.) x1 and x2 are non-negative integers. see “Empty (void) elements” on page 152.[CLevel]]] s1.Ç2 stat.n2 Description Confidence interval containing confidence level probability of distribution The calculated difference between proportions Margin of error First sample proportion estimate Second sample proportion estimate Sample size in data sequence one Sample size in data sequence two zInterval_2Samp zInterval_2Samp Catalog > s1.x2 stat.s2 .n1. stat. A summary of results is stored in the stat. A summary of results is stored in the stat.r1.n1. see “Empty (void) elements” on page 152.results variable.List1. stat.results variable.n2 stat.n1.List2[. stat.n1 stat.Freq1[. Output variable stat. (See page 112.CLower.ME stat.CLevel] (Data list input) zInterval_2Samp (Summary stats input) Computes a two-sample z confidence interval.s2.n2[.CUpper stat.) For information on the effect of empty elements in a list. stat.x1-x2 stat.sx1.x2.n Description Number of samples in data sequence zInterval_2Prop zInterval_2Prop x1. Output variable stat.CLower.x1.CUpper stat.v2.r2 Description Confidence interval containing confidence level probability of distribution Sample means of the data sequences from the normal random distribution Margin of error Sample means of the data sequences from the normal random distribution Sample standard deviations for List 1 and List 2 Number of samples in data sequences Known population standard deviations for data sequence List 1 and List 2 132 TI-Nspire™ CAS Reference Guide . (See page 112. stat. For information on the effect of empty elements in a list.Freq2. stat.sx2 stat.v1.ME stat.CLevel] Catalog > Computes a two-proportion z confidence interval.Ç1 stat.ÇDiff stat.Output variable stat. p0 stat.zTest zTest Catalog > m0. Test H0: p = p0 against one of the following: For Ha: p > p0.z stat.v. (See page 112.n Description Hypothesized population proportion Standard normal value computed for the proportion Smallest level of significance at which the null hypothesis can be rejected Estimated sample proportion Size of the sample TI-Nspire™ CAS Reference Guide 133 . Only returned for Data input. see “Empty (void) elements” on page 152.n[. set Hypoth>0 For Ha: p ƒ p0 (default).[Freq[. A summary of results is stored in the stat. set Hypoth<0 For Ha: m ƒ m0 (default).sx stat.z stat. set Hypoth=0 For Ha: m > m0. set Hypoth>0 For information on the effect of empty elements in a list.) x is a non-negative integer.Ç stat.s.List.) Test H0: m = m0. set Hypoth<0 For information on the effect of empty elements in a list.Hypoth]] m0. Output variable stat.Hypoth] Catalog > Computes a one-proportion z test.results variable.s. set Hypoth=0 For Ha: p < p0.n Description (x N m0) / (s / sqrt(n)) Least probability at which the null hypothesis can be rejected Sample mean of the data sequence in List Sample standard deviation of the data sequence. Output variable stat. see “Empty (void) elements” on page 152.P Value stat.n[. A summary of results is stored in the stat.Hypoth] (Data list input) zTest (Summary stats input) Performs a z test with frequency freqlist. against one of the following: For Ha: m < m0.x stat. (See page 112.PVal stat.results variable.x. Size of the sample zTest_1Prop zTest_1Prop p0. against one of the following: For Ha: m1 < m2.List2[.) x1 and x2 are non-negative integers. (See page 112.x2.sx2 stat.s2 . Test H0: p1 = p2.n1.Freq2[. set Hypoth<0 For information on the effect of empty elements in a list. stat. stat. stat.n2 Description Standard normal value computed for the difference of proportions Smallest level of significance at which the null hypothesis can be rejected First sample proportion estimate Second sample proportion estimate Pooled sample proportion estimate Number of samples taken in trials 1 and 2 zTest_2Samp zTest_2Samp Catalog > s1. A summary of results is stored in the stat.Hypoth] Catalog > Computes a two-proportion z test.n1. Hypoth>0 For information on the effect of empty elements in a list. set Hypoth<0 For Ha: m1 ƒ m2 (default). Output variable stat.Hypoth]]] s1.Hypoth] (Data list input) zTest_2Samp (Summary stats input) Computes a two-sample z test. Output variable stat.z stat.PVal stat.Ç stat.n2 Description Standard normal value computed for the difference of means Smallest level of significance at which the null hypothesis can be rejected Sample means of the data sequences in List1 and List2 Sample standard deviations of the data sequences in List1 and List2 Size of the samples 134 TI-Nspire™ CAS Reference Guide .results variable.List1.Ç2 stat.v1. (See page 112. against one of the following: For Ha: p1 > p2. set Hypoth=0 For Ha: p < p0.n2[.z stat.Ç1 stat.sx1. stat. set Hypoth>0 For Ha: p1 ƒ p2 (default).results variable. set Hypoth=0 For Ha: m1 > m2.x2 stat. A summary of results is stored in the stat.Freq1[.zTest_2Prop zTest_2Prop x1.n1.v2.) Test H0: m1 = m2.n1. see “Empty (void) elements” on page 152.PVal stat.s2.x1.n2[. see “Empty (void) elements” on page 152. Expr + Matrix1 ⇒ matrix Matrix1 + Expr ⇒ matrix Returns a matrix with Expr added to each element on the diagonal of Matrix1. Dimensions of the arguments must be equal. 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. N(subtract) Expr1 N Expr2 ⇒ expression Returns Expr1 minus Expr2. TI-Nspire™ CAS Reference Guide 135 .key List1 N List2 ⇒ list Matrix1 N Matrix2 ⇒ matrix Subtracts each element in List2 (or Matrix2) from the corresponding element in List1 (or Matrix1). Expr + List1 ⇒ list List1 + Expr ⇒ list Returns a list containing the sums of Expr and each element in List1. Matrix1 must be square. .+ (dot plus) to add an expression to each element.Symbols + (add) Expr1 + Expr2 ⇒ expression Returns the sum of the two arguments. and returns a list of the results. and returns the results. + key 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). Note: Use . Dimensions of the lists must be equal. p key 136 TI-Nspire™ CAS Reference Guide . Matrix1 N Expr returns a matrix of Expr times the identity matrix subtracted from Matrix1. Matrix1 must be square. Note: See also Fraction template. Matrix1 ·Matrix2 ⇒ matrix Returns the matrix product of Matrix1 and Matrix2.key ·(multiply) Expr1 ·Expr2 ⇒ expression Returns the product of the two arguments. r key List1·List2 ⇒ list Returns a list containing the products of the corresponding elements in List1 and List2. Expr ·Matrix1 ⇒ matrix Matrix1 ·Expr ⇒ matrix Returns a matrix containing the products of Expr and each element in Matrix1. The number of columns in Matrix1 must equal the number of rows in Matrix2. Note: Use .N (dot minus) to subtract an expression from each element. à (divide) Expr1 à Expr2 ⇒ expression Returns the quotient of Expr1 divided by Expr2. page 1. .N(subtract) Expr N Matrix1 ⇒ matrix Matrix1 N Expr ⇒ matrix Expr N Matrix1 returns a matrix of Expr times the identity matrix minus Matrix1. Note: Use . Expr ·List1 ⇒ list List1 ·Expr ⇒ list Returns a list containing the products of Expr and each element in List1.·(dot multiply) to multiply an expression by each element. Matrix1 must be square. Expr à List1 ⇒ list List1 à Expr ⇒ list Returns a list containing the quotients of Expr divided by List1 or List1 divided by Expr.à (divide) List1 à List2 ⇒ list Returns a list containing the quotients of List1 divided by List2. If integer = ë1. / (dot divide) to divide an expression by each element. fractional powers that have reduced exponents with odd denominators use the real branch versus the principal branch for complex mode. TI-Nspire™ CAS Reference Guide 137 . Note: See also Exponent template. Expr ^ List1 ⇒ list Returns Expr raised to the power of the elements in List1. computes the inverse matrix. If integer < ë1. Dimensions of the lists must be equal. Note: Use . returns the elements in List1 raised to the power of the corresponding elements in List2. computes the inverse matrix to an appropriate positive power. List1 ^ Expr ⇒ list Returns the elements in List1 raised to the power of Expr. ^ (power) Expr1 ^ Expr2 ⇒ expression List1 ^ List2 ⇒ list Returns the first argument raised to the power of the second argument. squareMatrix1 must be a square matrix. p key Matrix1 à Expr ⇒ matrix Returns a matrix containing the quotients of Matrix1àExpr. In the real domain. l key For a list. page 1. squareMatrix1 ^ integer ⇒ matrix Returns squareMatrix1 raised to the integer power. Expr .+ Matrix1 returns a matrix that is the sum of Expr and each element in Matrix1. Expr . squareMatrix12 ⇒ matrix Returns the matrix square of squareMatrix1.+ (dot add) Matrix1 . ^r keys 138 TI-Nspire™ CAS Reference Guide . q key .) Matrix1 .· Matrix2 ⇒ matrix Expr . Expr .·(dot mult. ^+ keys . List12 ⇒ list Returns a list containing the squares of the elements in List1.+ Matrix2 ⇒ matrix Expr .^2 to calculate the square of each element. This is not the same as calculating the square of each element.·Matrix1 ⇒ matrix Matrix1 . ^.NMatrix1 returns a matrix that is the difference of Expr and each element in Matrix1.NMatrix1 ⇒ matrix Matrix1 .· Matrix1 returns a matrix containing the products of Expr and each element in Matrix1.· Matrix2 returns a matrix that is the product of each pair of corresponding elements in Matrix1 and Matrix2.+ Matrix2 returns a matrix that is the sum of each pair of corresponding elements in Matrix1 and Matrix2.NMatrix2 returns a matrix that is the difference between each pair of corresponding elements in Matrix1 and Matrix2.+ Matrix1 ⇒ matrix Matrix1 . Use .N Matrix2 ⇒ matrix Expr .x2 (square) Expr12 ⇒ expression Returns the square of the argument.. (dot subt.keys .) Matrix1 . ^ Matrix1 returns a matrix where each element in Matrix1 is the exponent for Expr. returns all the elements negated./ Matrix2 returns a matrix that is the quotient of each pair of corresponding elements in Matrix1 and Matrix2.^ Matrix2 returns a matrix where each element in Matrix2 is the exponent for the corresponding element in Matrix1. / Matrix2 ⇒ matrix Expr .. Expr . returns a list or matrix with each element divided Press Ctrl+Enter by 100. Expr . If the argument is a binary or hexadecimal integer.^ (dot power) Matrix1 ./ Matrix1 returns a matrix that is the quotient of Expr and each element in Matrix1. ^ Matrix1 ⇒ matrix Matrix1 . the negation gives In Bin base mode: the two’s complement. £ and then use ¡ and ¢ to /k keys % (percent) Expr1 % ⇒ expression List1 % ⇒ list Matrix1 % ⇒ matrix Returns For a list or matrix. For a list or matrix. Important: Zero. ^l keys ë(negate) ëExpr1 ⇒ expression ëList1 ⇒ list ëMatrix1 ⇒ matrix Returns the negation of the argument. not the letter O v key To see the entire result. ^p keys .^ Matrix2 ⇒ matrix Expr . / (dot divide) Matrix1 . / Matrix1 ⇒ matrix Matrix1 . evaluate: Press Ctrl+Enter evaluate: /· (Macintosh®: “+Enter) to /· (Macintosh®: “+Enter) to TI-Nspire™ CAS Reference Guide 139 . press move the cursor. Anything else returns a simplified form of the equation. For lists and matrices.= (equal) Expr1 = Expr2 ⇒ Boolean expression List1 = List2 ⇒ Boolean list Matrix1 = Matrix2 ⇒ Boolean matrix Returns true if Expr1 is determined to be equal to Expr2. returns comparisons element by element. {. Note: You can insert this operator from the keyboard by typing /= /= keys See “=” (equal) example. hold down Alt and press Enter. · Result of graphing g(x) ƒ (not equal) Expr1 ƒ Expr2 ⇒ Boolean expression List1 ƒ List2 ⇒ Boolean list Matrix1 ƒ Matrix2 ⇒ Boolean matrix Returns true if Expr1 is determined to be not equal to Expr2. See “=” (equal) example. >. you can enter multi-line definitions by pressing @ instead of at the end of each line. returns comparisons element by element. Returns false if Expr1 is determined to not be equal to Expr2. ‚ on the handheld. returns comparisons element by element. Returns false if Expr1 is determined to be greater than or equal to Expr2. Anything else returns a simplified form of the equation. Anything else returns a simplified form of the equation. <. Returns false if Expr1 is determined to be equal to Expr2. For lists and matrices. /= keys 140 TI-Nspire™ CAS Reference Guide . ƒ. < (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. Note for entering the example: In the Calculator application = key Example function that uses math test symbols: =. On the computer keyboard. For lists and matrices. º key /k keys TI-Nspire™ CAS Reference Guide 141 . > (greater than) Expr1 > Expr2 ⇒ Boolean expression List1 > List2 ⇒ Boolean list Matrix1 > Matrix2 ⇒ Boolean matrix Returns true if Expr1 is determined to be greater than Expr2. Note: You can insert this operator from the keyboard by typing <= /= keys See “=” (equal) example. Returns false if Expr1 is determined to be less than Expr2. returns comparisons element by element. See “=” (equal) example. & (append) String1 & String2 ⇒ string Returns a text string that is String2 appended to String1. Anything else returns a simplified form of the equation. For a list or matrix. returns comparisons element by element. /= keys | (greater or equal) Expr1 | Expr2 ⇒ Boolean expression 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 or equal to Expr2. For lists and matrices. Note: You can insert this operator from the keyboard by typing >= /= keys See “=” (equal) example. Returns false if Expr1 is determined to be greater than Expr2. returns a list or matrix of factorials of the elements. For lists and matrices. Anything else returns a simplified form of the equation. For lists and matrices.{ (less or equal) Expr1 { Expr2 ⇒ Boolean expression List1 { List2 ⇒ Boolean list Matrix1 { Matrix2 ⇒ Boolean matrix Returns true if Expr1 is determined to be less than or equal to Expr2. ! (factorial) Expr1! ⇒ expression List1! ⇒ list Matrix1! ⇒ matrix Returns the factorial of the argument. Anything else returns a simplified form of the equation. returns comparisons element by element. Order]) Catalog > ⇒ expression ⇒ matrix ⇒ list d(Matrix1. Equally valid anti-derivatives might differ by a numeric constant.). If the order is less than zero. Moreover. Instead. Determine the symbolic derivative of the result of step 2 with respect to the variable from step 1. Note: See also First derivative. 3. Constant]) ⇒ expression Returns the integral of Expr1 with respect to the variable Var from Lower to Upper. Order. ‰() returns itself for pieces of Expr1 that it cannot determine as an explicit finite combination of its built-in functions and operators. Lower.). Note: See also Definite or Indefinite integral template. 2.Var [.d() (derivative) d(Expr1.Order]) Returns the first derivative of the first argument with respect to variable Var. Such a constant might be disguised—particularly when an anti-derivative contains logarithms or inverse trigonometric functions. page 5. Var [. Simplify the second argument only to the extent that it does not lead to a non-variable. Upper]) ⇒ expression ‰(Expr1. returns an anti-derivative. When you provide Lower and Upper.. Var[. must be an integer. Simplify the first argument only to the extent that it does recall any stored value for the variable determined by step 1.Order]) d(List1.. or Nth 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.. substitute that value into the result from step 3. Var[. d() performs the following steps: 1. If Lower and Upper are omitted. if included. page Catalog > 5. Second derivative. 142 TI-Nspire™ CAS Reference Guide .Var [. Note: You can insert this function from the keyboard by typing derivative(.. A symbolic constant of integration is omitted unless you provide the Constant argument. page 5. ‰() (integral) ‰(Expr1. piecewise constant expressions are sometimes added to make an anti-derivative valid over a larger interval than the usual formula. 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. the result will be an anti-derivative. page 5. Note: You can insert this function from the keyboard by typing integral(. If the variable from step 1 has a stored value or a value specified by a “with” (|) operator. . returns the square roots of all the elements in List1. numerical integration is used where applicable when an antiderivative or a limit cannot be determined. and returns the product of the results. if applicable.) Note: See also Square root template.‰() (integral) For the Auto setting of the Auto or Approximate mode. For the Approximate setting. Note: See also Product template (Π). numerical integration is tried first. page 1. Low. Note: You can insert this function from the keyboard by typing /q keys sqrt(.. Var. High) ⇒ expression Note: You can insert this function from the keyboard by typing Catalog > prodSeq(. Integration limits can depend on integration variables outside them. Evaluates Expr1 for each value of Var from Low to High. Press Ctrl+Enter evaluate: Catalog > /· (Macintosh®: “+Enter) to ‰() can be nested to do multiple integrals... Anti-derivatives are sought only where such numerical integration is inapplicable or fails. Π() (prodSeq) Π(Expr1. TI-Nspire™ CAS Reference Guide 143 . ‡() (square root) ‡ (Expr1) ⇒ expression ‡ (List1) ⇒ list Returns the square root of the argument. page 4. For a list. Note: See also nInt(). page 78.). Var. 1994. Low. Catalog > Evaluates Expr1 for each value of Var from Low to High. High) ⇒ expression Note: You can insert this function from the keyboard by typing sumSeq(. Concrete Mathematics: A Foundation for Computer Science. Massachusetts: Addison-Wesley. and returns the sum of the results. Var. High+1. Var. Knuth. LowN1) ⇒ 1 Π(Expr1.Π() (prodSeq) Π(Expr1. Concrete Mathematics: A Foundation for Computer Science. Low. 1994. Donald E. Var. Low. High+1. Note: See also Sum template. LowN1) if High < LowN1 The product formulas used are derived from the following reference: Ronald L. page 4. Var. Reading. Var. LowN1) if High < LowN1 The summation formulas used are derived from the following reference: Ronald L. High) ⇒ ëG(Expr1. and Oren Patashnik. and Oren Patashnik. Massachusetts: Addison-Wesley. Graham. Knuth. Reading. Donald E. Graham. Var.). 144 TI-Nspire™ CAS Reference Guide ... G(Expr1. High) ⇒ 1/Π(Expr1. Low. Low. LowN1) ⇒ 0 G(Expr1. Catalog > G() (sumSeq) G(Expr1. CpY.FV. N.PV. and Bal(). [roundValue]) ⇒ value GPrn(NPmt1. NPmt2.I. • • • If you omit Pmt. below. and PmtAt are the same as for the TVM functions. I. The amortTable argument must be a matrix in the form described under amortTbl().FV. PV . If you omit FV. PpY. and PmtAt are the same as for the TVM functions.[Pmt]. I. it defaults to Pmt=tvmPmt(N.NPmt2. page 13. GInt(NPmt1.amortTable) ⇒ value Amortization function that calculates the sum of the interest during a specified range of payments. Default=2. PV. it defaults to FV=0.PmtAt). PpY.PV. [CpY]. PV.NPmt2. page 124. and PmtAt are described in the table of TVM arguments. page 124.PpY.amortTable) ⇒ value Amortization function that calculates the sum of the principal during a specified range of payments. NPmt2. CpY. Catalog > roundValue specifies the number of decimal places for rounding. N. PV. CpY. [PpY]. FV. I. [CpY]. [PmtAt]. [roundValue]) ⇒ value GInt(NPmt1. Pmt. Pmt.PpY. [PmtAt].NPmt2.CpY.GInt() GInt(NPmt1. CpY. page 7.PmtAt). GPrn(NPmt1. NPmt1 and NPmt2 define the start and end boundaries of the payment range. N. Note: See also GInt(). The amortTable argument must be a matrix in the form described under amortTbl(). • • • If you omit Pmt.amortTable) calculates the sum of the interest based on amortization table amortTable. The defaults for PpY. [PpY]. The defaults for PpY. page 13. FV. Catalog > roundValue specifies the number of decimal places for rounding. If you omit FV. TI-Nspire™ CAS Reference Guide 145 .amortTable) calculates the sum of the principal paid based on amortization table amortTable. [FV]. NPmt1 and NPmt2 define the start and end boundaries of the payment range.I. page 7. N.NPmt2. [Pmt]. and PmtAt are described in the table of TVM arguments. it defaults to Pmt=tvmPmt(N. Default=2. it defaults to FV=0. I. [FV].CpY. Note: See also GPrn(). GPrn() GPrn(NPmt1. above. and Bal(). type 2. returns the argument unchanged. Note: You can insert this operator from the computer keyboard by typing @E. In Radian angle mode. Returns the value of the variable (r) whose name is stored in variable s1. Gradian or Radian mode: ¹ key Expr1g ⇒ expression List1g ⇒ list Matrix1g ⇒ matrix This function gives you a way to specify a gradian angle while in the Degree or Radian mode. multiplies the argument by 200/p. This lets you use strings to create variable names from within a function. Refers to the variable whose name is varNameString. ¹ key In Degree. Gradian or Radian angle mode: 146 TI-Nspire™ CAS Reference Guide . use 10^integer. In Degree angle mode.3@E4 to enter 2. Note: You can insert this symbol from the computer keyboard by typing @g. multiplies Expr1 by p/200.3E4. ô(radian) Expr1ô ⇒ expression List1ô ⇒ list Matrix1ô ⇒ matrix This function gives you a way to specify a radian angle while in Degree or Gradian mode. Note: You can insert this symbol from the computer keyboard by typing @r. í (scientific notation) mantissaEexponent Enters a number in scientific notation. multiplies the argument by 180/p. In Gradian mode. Hint: Use ôif you want to force radians in a function definition regardless of the mode that prevails when the function is used. In Radian angle mode. returns Expr1 unchanged. g i key (gradian) In Degree.# (indirection) # varNameString /k keys Creates or refers to the variable xyz . Hint: If you want to enter a power of 10 without causing a decimal value result. In Degree angle mode. multiplies Expr1 by g/100. for example. The number is interpreted as mantissa × 10exponent. In Gradian mode.  (angle) [Radius. multiplies the argument by p/180.¡ (degree) Expr1¡ ⇒ expression List1¡ ⇒ list Matrix1¡ ⇒ matrix This function gives you a way to specify a degree angle while in Gradian or Radian mode. Note: You can insert this symbol from the computer keyboard by ¹ key In Degree.q_Angle. In Gradian angle mode. not a quote symbol (").q_Angle] ⇒ vector (spherical input) Returns coordinates as a vector depending on the Vector Format mode setting: rectangular.ss with two apostrophes (''). returns the argument unchanged. '. multiplies the argument by 10/9. '' (degree/minute/second) dd¡mm'ss. Note: Follow ss. ¡. or spherical.q_Angle] ⇒ vector (polar input) [Radius.q_Angle.ss'' ⇒ expression dd A positive or negative number In Degree angle mode: /k keys mm A non-negative number ss.ss A non-negative number Returns dd+(mm/60)+(ss. 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. In Degree angle mode. Gradian or Radian angle mode: In Radian angle mode: Press Ctrl+Enter evaluate: /· (Macintosh®: “+Enter) to typing @d. spherical TI-Nspire™ CAS Reference Guide 147 . cylindrical. Note: You can insert this symbol from the computer keyboard by /k keys In Radian mode and vector format set to: rectangular cylindrical typing @<. In Radian angle mode.ss/3600).Z_Coordinate] ⇒ vector (cylindrical input) [Radius. If Variable has a value. without the _ . All unit names must begin with an underscore. Variable_ When Variable has no value. You can select unit names from the Catalog or type the unit names directly. For a list of Click pre-defined units. By default. it is treated as though it represents a complex number. the _ is ignored and Variable retains its original data type. /_ keys Note: You can find the conversion symbol. in the Catalog. the _ is recommended. However. _ (underscore as unit designator) Expr_Unit Designates the units for an Expr. º key _ (underscore as an empty element) See “Empty (void) elements” . and so on. and then click Math Operators. for best results in calculations such as cSolve() and cZeros(). Note: You can store a complex number to a variable without using _ . Press Ctrl+Enter evaluate: /k keys In Radian angle mode and Rectangular complex format: /· (Macintosh®: “+Enter) to ' (prime) variable ' variable '' Enters a prime symbol in a differential equation. Assuming z is undefined: 148 TI-Nspire™ CAS Reference Guide . (angle) (Magnitude  Angle) ⇒ complexValue (polar input) Enters a complex value in (rq) polar form. two prime symbols denote a 2nd-order. open the Catalog and display the Unit Conversions tab. The Angle is interpreted according to the current Angle mode setting. 4. the variable is treated as real. You can use pre-defined units or create your own units. . A single prime symbol denotes a 1st-order differential equation. page 152. Note: To convert temperature units. TI-Nspire™ CAS Reference Guide 149 . ^ê (reciprocal) Expr1 ^ê ⇒ expression List1 ^ê ⇒ list Returns the reciprocal of the argument. such as Length or Area. returns the reciprocals of the elements in List1. For information about the calculation method. /k keys You can also type unit names manually. For a list of pre-defined units. The 4 conversion operator does not handle temperature units. Catalog > squareMatrix1 ^ê ⇒ squareMatrix Returns the inverse of squareMatrix1. press /_. from the top of the list. To type “_” when typing unit names on the handheld. squareMatrix1 must be diagonalizable. squareMatrix1 must be a non-singular square matrix. The _ underscore character designates the units. The result always contains floating-point numbers. 10^(squareMatrix1) ⇒ squareMatrix Returns 10 raised to the power of squareMatrix1.4 (convert) Expr_Unit1 4 _Unit2 ⇒ Expr_Unit2 Converts an expression from one unit to another. 4. open the Catalog and display the Unit Conversions tab: • • You can select a unit name from the list. You can select the conversion operator. For a list. 10^() 10^ (Expr1) ⇒ expression 10^ (List1) ⇒ list Catalog > Returns 10 raised to the power of the argument. returns 10 raised to the power of the elements in List1. This is not the same as calculating 10 raised to the power of each element. use tmpCnv() and @tmpCnv(). The units must be in the same category. For a list. refer to cos(). The “with” (|) symbol serves as a binary operator.. b. zeros(). If the variable Var already exists and is not locked or protected. z. y. creates it and initializes it to Expr. Hint: If you plan to do symbolic computations using undefined variables. solve(). /h key 150 TI-Nspire™ CAS Reference Guide .) List & Function(Param1. List.) If the variable Var does not exist..| (“with”) Expr | BooleanExpr1 [and BooleanExpr2]. They are used primarily to exclude an exact solution when using cSolve(). To be most effective. and exclusions. Multiple relations after | must be joined by a logical “and”. fMax().. The operand to the right of | specifies one or more relations that are intended to affect the simplification of the expression..) Matrix & Function(Param1. Substitutions are in the form of an equality.. The “with” operator provides three basic types of functionality: substitutions. Expr | Variable = value will substitute value for every occurrence of Variable in Expr. or Matrix. and so on. the left side should be a simple variable.. replaces its contents with Expr.. For example... avoid storing anything into commonly used.. Exclusions use the “not equals” (/= or ƒ) relational operator to exclude a specific value from consideration. The operand to the left of | is an expression. and so on. List. one-letter variables such as a. /k keys Interval constraints take the form of one or more inequalities joined by logical “and” operators. & (store) Expr & Var List & Var Matrix & Var Expr & Function(Param1. such as x=3 or y=sin(x). Note: You can insert this operator from the keyboard by typing =: as a shortcut.. c. fMin(). or Matrix. Interval constraints also permit simplification that otherwise might be invalid or not computable. type pi/4 =: myvar. interval constraints. cZeros(). x. . · 0b. you must enter the 0b or 0h prefix regardless of In Bin base mode: the Base mode. to the end of the line. To enter a binary or hex number. replaces its contents with Expr. b.:= (assign) Var := Expr Var := List Var := Matrix Function(Param1.. creates Var and initializes it to Expr. In Hex base mode: TI-Nspire™ CAS Reference Guide 151 . is the comment. one-letter variables such as a. 0H keys In Dec base mode: Denotes a binary or hexadecimal number. allowing you to annotate /t keys /k keys functions and programs that you create.) := List Function(Param1. you can enter multi-line definitions by pressing @ at the end of each line.) := Matrix If variable Var does not exist. a number is treated as decimal (base 10). If Var already exists and is not locked or protected. © (comment) © [text] © processes text as a comment line. or Matrix. Everything to the right of ©. avoid storing anything into commonly used. z... List. List. © can be at the beginning or anywhere in the line. c. and so on. x. or Matrix. Hint: If you plan to do symbolic computations using undefined variables.. instead of hold down Alt and press Enter. Results are displayed according to the Base mode... Without a prefix... 0h 0b binaryNumber 0h hexadecimalNumber 0B keys. respectively. Note for entering the example: In the Calculator application on the handheld.) := Expr Function(Param1. y. On the computer keyboard. median. See special cases below. you might not always have a complete data set. page 58. sum. under “Graphing spreadsheet data. stDevSamp. product. confidence intervals. mean. press / _. The keyword void is automatically converted to a “_” symbol when the expression is evaluated. OneVar. You can find an example of data involving empty elements in the Lists & Spreadsheet chapter. 152 TI-Nspire™ CAS Reference Guide . or void.Empty (void) elements When analyzing real-world data. Note: To enter an empty element manually in a math expression. and varSamp. The isVoid() function lets you test for an empty element. List arguments containing void elements The following functions and commands ignore (skip) void elements found in list arguments. max. For details.” The delVoid() function lets you remove empty elements from a list. and stat tests SortA and SortD move all void elements within the first argument to the bottom. countIf. data elements so you can proceed with the nearly complete data rather than having to start over or discard the incomplete cases. as well as regression calculations. count. type “_” or the keyword void. freqTable4list. stDevPop. page 35. cumulativeSum. sumIf. and FiveNumSummary statistics. and isVoid(). To type “_” on the handheld. TwoVar. Calculations involving void elements The majority of calculations involving a void input will produce a void result. see delVoid(). varPop. frequency. TI-Nspire™ CAS Software allows empty. An omitted category in regressions introduces a void for the corresponding element of the residual.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. A frequency of 0 in regressions introduces a void for the corresponding element of the residual. TI-Nspire™ CAS Reference Guide 153 . n1... @n1..) arcsin(. @c2...... Type this shortcut: @c1. @i @e @E . c2.. @List() @tmpCnv() From the computer keyboard To enter this: c1...) p q ˆ  ‚ ƒ & (store operator) | | (absolute value) ‡() d() ‰() G() (Sum template) Π() (Product template) sinê(). (integer constants) i (imaginary constant) e (natural log base e) í (scientific notation) 154 TI-Nspire™ CAS Reference Guide . When you press ·. the expression sqrt(6) is changed to ‡6.. From the handheld or computer keyboard To enter this: Type this shortcut: pi theta infinity <= >= /= =: abs(.. .) derivative(..) sqrt(. deltaList(.... (constants) .) prodSeq(..) sumSeq(..). Some shortrcuts are useful from both the handheld and the computer keyboard....) deltaTmpCnv(. to enter the expression ‡6.. .. cosê().. n2. For example...) integral(. arccos(.. @n2.. you can type sqrt(6) on the entry line.). .. ...Shortcuts for entering math expressions Shortcuts let you enter elements of math expressions by typing instead of using the Catalog or Symbol Palette. Others are useful primarily from the computer keyboard. TI-Nspire™ CAS Reference Guide 155 . and so on. @>approxFraction(). and so on.To enter this: T Type this shortcut: @t @r @d @g @< @> @>Decimal. (transpose) ô (radians) ¡ (degrees) g (gradians)  (angle) 4 (conversion) 4Decimal. 4approxFraction(). greater than (>). use explicit multiplication: a∗(b+c).” Note: Because the TI-Nspire™ CAS software allows you to define your own functions.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. 3. subscript ([ ]). division (/) Addition (+). For example a(b+c) is the function a evaluated by b+c. brackets."). and braces must be the same within an expression or equation. by 4. in the expression 4(1+2). 156 TI-Nspire™ CAS Reference Guide . less than (<). Order of evaluation Level Operator 1 2 3 4 Parentheses ( ). factorial (!). and functions are entered in a simple. transpose (T) Q 5 6 7 8 9 10 Exponentiation. radian ( RS). and braces All calculations inside a pair of parentheses. (1+2)/(3+4 will display the error message “Missing ). The number of opening and closing parentheses. brackets. an error message is displayed that indicates the missing element. less than or equal ( or <=). brackets [ ]. braces { } Indirection (#) Function calls Post operators: degrees-minutes-seconds (-. subtraction (-) Equality relations: equal (=). For example. EOS™ software first evaluates the portion of the expression inside the parentheses. not equal (ƒ or /=). brackets. Numbers. For example. 1+2. and then multiplies the result. If not. straightforward sequence. a variable name followed by an expression in parentheses is considered a “function call” instead of implied multiplication. greater than or equal (‚ or >=) Logical not Logical and Logical or. exclusive logical xor Constraint “with” operator (|) Store (") L 11 12 13 14 15 Parentheses. variables. To multiply the expression b+c by the variable a. power operator (^) Negation ( ) String concatenation (&) Multiplication (†).'. percentage (%). EOS™ software evaluates expressions and equations using parenthetical grouping and according to the priorities described below. or braces are evaluated first. in the expression 4^3!. For example. Indirection also allows the creation and modification of variables from inside a program. Use parentheses to square a negative number such as (L9)2 to produce 81. For example. the expression 2^3^2 is evaluated the same as 2^(3^2) to produce 512. then #s1=10. the result of Lx2 is a negative number. 6. 25%. Arguments followed by a post operator are evaluated at the fourth priority level. which is 64. For example. Post operators Post operators are operators that come directly after an argument. Exponentiation Exponentiation (^) and element-by-element exponentiation (. Constraint (|) The argument following the “with” (|) operator provides a set of constraints that affect the evaluation of the argument preceding the “with” operator. then becomes the exponent of 4 to yield 4096.Indirection The indirection operator (#) converts a string to a variable or function name. For example. For example.^) are evaluated from right to left. The result. 3! is evaluated first. or 60¡15' 45". TI-Nspire™ CAS Reference Guide 157 . such as 5!. Negation To enter a negative number. Post operations and exponentiation are performed before negation. press v followed by the number. This is different from (2^3)^2. if 10"r and “r”"s1. and L92 = L81. #(“x”&”y”&”z”) creates the variable name xyz. Bound The lower bound must be less than the upper bound to define the search interval. where a is an undefined variable. For an example of using errCode. Error code 10 20 Description A function did not return a value A test did not resolve to TRUE or FALSE. page 122. Generally.Error codes and messages When an error occurs. Circular definition This message is displayed to avoid running out of memory during infinite replacement of variable values during simplification. will cause this error. Break The 190 30 40 50 60 70 90 100 130 140 160 165 170 180 d or c key was pressed during a long calculation or during program execution. solve(3x^2-4=0. Note: Some error conditions apply only to TI-Nspire™ CAS products. Argument must be an expression Batteries too low for sending or receiving Install new batteries before sending or receiving. Dependent limit 200 210 220 158 TI-Nspire™ CAS Reference Guide . its code is assigned to variable errCode. and some apply only to TI-Nspire™ products. Argument error Argument mismatch Two or more arguments must be of the same type. Argument must be a Boolean expression or integer Argument must be a decimal number Argument must be a list Argument must be a matrix Argument must be a string Argument must be a variable name. the test If a<b will cause this error if either a or b is undefined when the If statement is executed. User-defined programs and functions can examine errCode to determine the cause of an error. undefined variables cannot be compared.x) | x<0 or x>5 would produce this error message because the constraint is separated by “or” instead of “and. For example. 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. a+1->a. Argument cannot be a folder name. For example.” Invalid Data type An argument is of the wrong data type. Constraint expression invalid For example. See Example 2 under the Try command. Inconsistent units Index out of range Indirection string is not a valid variable name Undefined Ans Either the previous calculation did not create Ans. For example.2. Local cannot be used unless it is in a function or program. For example.EndLoop.4} is stored in L1. x*(x+1) is the correct syntax..3. if the list {1. solve(3x^2-4.EndTry block Invalid list or matrix Invalid outside function or program A number of commands are not valid outside a function or program. then L1[5] is a dimension error because L1 only contains four elements. rand(0) is not valid..EndIf block EndTry is missing the matching Else statement Excessive iteration Expected 2 or 3-element list or matrix The first argument of nSolve must be an equation in a single variable. Not enough elements in the lists.EndWhile blocks For example. [1.x) is invalid because the first argument is not an equation. Invalid assignment Invalid assignment value Invalid command Invalid for the current mode settings Invalid guess Invalid implied multiply For example. whereas. This is to avoid confusion between implied multiplication and function calls.EndFor. Duplicate variable name Else and ElseIf invalid outside of If. First argument of solve or cSolve must be an equation or inequality For example. Invalid in Try. Invalid outside program 235 240 250 260 270 280 290 295 300 310 320 345 350 360 380 390 400 410 430 435 440 450 490 510 550 560 565 TI-Nspire™ CAS Reference Guide 159 . Dimension Error.2]+[1. Invalid in a function or current expression Only certain commands are valid in a user-defined function. x(x+1) is invalid. Dimension mismatch Two or more arguments must be of the same dimension... For example.2.Error code 230 Description Dimension A list or matrix index is not valid.. It cannot contain a non-valued variable other than the variable of interest.. the Exit command is valid only inside these loop blocks. Invalid outside Loop.3] is a dimension mismatch because the matrices contain a different number of elements. or no previous calculation was entered. For example. Divide by zero Domain error An argument must be in a specified domain. For. or While. Invalid polar complex Invalid program reference Programs cannot be referenced within functions or expressions such as 1+p(x) where p is a program. To allow complex results. Overflow Program not found A program reference inside another program could not be found in the provided path during execution. Rand type functions not allowed in graphing Recursion too deep Reserved name or system variable Argument error Median-median model could not be applied to data set. Matrix not diagonalizable Low Memory 1. Verify that the connecting cable is connected firmly to both ends. ‡(-1) is invalid. if the software is in the Real setting. Delete some data in this document 2.. Save and close this document If 1 and 2 fail. 575 580 600 605 610 620 630 640 650 665 670 680 690 700 710 720 730 740 750 765 780 800 830 850 855 860 870 900 160 TI-Nspire™ CAS Reference Guide . change the “Real or Complex” Mode Setting to RECTANGULAR or POLAR. Invalid table Invalid use of units Invalid variable name in a Local statement Invalid variable or function name Invalid variable reference Invalid vector syntax Link transmission A transmission between two units was not completed. pull out and re-insert batteries Missing ( Missing ) Missing “ Missing ] Missing } Missing start or end of block syntax Missing Then in the If.Error code 570 Description Invalid pathname For example. \var is invalid.EndIf block Name is not a function or program No functions selected No solution found Non-real result For example. Try TI-Nspire™ CAS. Too many arguments The expression or equation contains an excessive number of arguments and cannot be evaluated. 1110 1120 1130 1140 TI-Nspire™ CAS Reference Guide 161 . Use one of the following commands: • sto & • := • Define 940 950 955 960 to assign values to variables.Error code 920 930 Description Text not found Too few arguments The function or command is missing one or more arguments. To allow complex results. Use one of the following commands: • Define 1000 1010 1020 1030 1040 1045 1050 1060 1070 1080 1090 • := • sto & to define a function. if the software is in the Real setting. Try TI-Nspire™ CAS. Only inputs containing numeric values are allowed. change the “Real or Complex” Mode Setting to RECTANGULAR or POLAR. Trig function argument too big for accurate reduction Unsupported use of Ans. Unsupported operator. Unsupported feature. This function requires Computer Algebra System. Invalid bounds No sign change Argument cannot be a list or matrix Argument error The first argument must be a polynomial expression in the second argument. 965 970 980 990 Unlicensed OS Variable in use so references or changes are not allowed Variable is protected Invalid variable name Make sure that the name does not exceed the length limitations Window variables domain Zoom Internal error Protected memory violation Unsupported function. This operator requires Computer Algebra System. 1100 Non-real calculation For example. Too many subscripts Too many undefined variables Variable is not defined No value is assigned to variable. If the second argument is omitted. ‡(-1) is invalid. This operator requires Computer Algebra System. Input argument must be numeric. Try TI-Nspire™ CAS. the software attempts to select a default. Function is not defined.This application does not support Ans. Invalid library pathname A pathname must be in the form xxx\yyy. • The yyy part can have 1 to 15 characters.Error code 1150 Description Argument error The first two arguments must be polynomial expressions in the third argument. the software attempts to select a default. Example of a system of two linear equations with variables x and y: 3x+7y=5 2y-5x=-1 Argument Error: The first argument of nfMin or nfMax must be an expression in a single variable. Domain error. Argument Error Use a system of linear equations. Argument Error Use a polynomial in expanded form in one variable. 1160 1170 1180 1190 1200 1210 1220 1230 1250 1260 1270 1280 1290 1300 162 TI-Nspire™ CAS Reference Guide . or sto &. • A pathname cannot be declared as a Local variable or be used as a parameter in a function or program definition. Invalid use of library pathname • A value cannot be assigned to a pathname using Define. It cannot contain a non-valued variable other than the variable of interest. Argument Error Use a polynomial in one variable. See the Library section in the documentation for more details. • Make sure library variable has been defined as LibPub or LibPriv. 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. • Refresh Libraries. Library document not found: • Verify library is in the MyLib folder. Argument Error Order of the derivative must be equal to 1 or 2. Library variable not found: • Verify library variable exists in the first problem in the library. Domain error: The tangentLine and normalLine functions support real-valued functions only. where: • The xxx part can have 1 to 16 characters. If the third argument is omitted. See the Library section in the documentation for more details. :=. Trigonometric conversion operators are not supported in Degree or Gradian angle modes. See the Library section in the documentation for more details. 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. Argument Error The coefficients of the polynomial must evaluate to numeric values. Invalid library variable name. • Refresh Libraries. Invalid library shortcut name. Error code 1310 Description Argument error: A function could not be evaluated for one or more of its arguments. 163 . 164 . Service and Support Texas Instruments Support and Service For general information For more information about TI products and services.ti. E-mail inquiries: Home Page: [email protected] education. Service and Support 165 .com 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. contact TI by e-mail or visit the TI Internet address. 166 Service and Support . hexadecimal indicator 151 10^( ). 13 and. with 150 ©. indirection 146 #. not equal 140 N. augment( ) 12 Numerics 0b. sin/( ) 105 arcsinh() 12 arctan() 12 arctangent. reciprocal 149 _. product 143 Σ( ).P. tan/( ) 117 arctanh() 12 arguments in TVM functions 124 augment( ). power 137 ^/. absolute value 7 absolute value template for 3 add. angle 8 angle. divide 136 Π. add 135 . arc length 12 arcsec() 12 arcsech() 12 arcsin() 12 arcsine. cos/( ) 23 arccot() 12 arccoth() 12 arccsc() 12 arccsch() 12 arcLen( ). & 141 approx( ). Ans 11 append. amortTbl( ) 7. dot multiplication 138 . factorial 141 ". integral 142 ‡. greater than 141 @list( ). unit designation 148 {. approx( ) 11. prime 148 -. approximate 11. binary indicator 151 0h.+. list difference 64 ^. equal 140 >. dot addition 138 . less than 140 =. dot subtraction 138 . comment 151 2-sample F Test 49 4approxFraction( ) 11 A abs( ). append 141 &. square root 143 ƒ. 13 amortTbl( ). 12 approximate. arcLen( ) 12 arccos() 11 arccosh() 12 arccosine. multiply 136 +.Index Symbols !.^. less than or equal 141 |. convert units 149 ‰. assign 151 <. degree notation 147 -. minute notation 147 '.*. second notation 147 #. sum 144 *. Boolean and 7 angle( ). percent 139 &. dot power 139 . angle( ) 8 ANOVA. augment/concatenate 12 augment/concatenate. two-way variance analysis 9 Ans. indirection operator 157 %. 12 approxRational( ) 11 arc length.N. dot division 139 :=. greater than or equal 141 |. one-way variance analysis 8 ANOVA2way. store 150 '. + 135 amortization table. amortization table 7. degrees/minutes/seconds 147 4. power of ten 149 167 . subtract 135 P. last answer 11 answer (last). not 79 or. count items in a list 25 . average rate of change 13 B 4Base10. comDenom( ) 19 complex conjugate. hyperbolic cotangent 24 coth/( ). complex factor 16 char( ).average rate of change. xor 129 not. cos( ) 22 cot( ). count( ) 25 count( ). cotangent 24 cot/( ). corrMat( ) 21 corrMat( ). character string 17 character string. countif( ) 25 count items in a list. and 7 exclusive or. char( ) 17 characters numeric code. avgRC( ) 13 avgRC( ). 26 centralDiff( ) 16 cFactor( ). arccosine 23 cosh( ). display as decimal integer 14 4Base16. 16. conj( ) 20 factor. hyperbolic arccotangent 24 cotangent. matrix column dimension 19 colNorm( ). nCr( ) 76 comDenom( ). © 151 168 common denominator. char( ) 17 charPoly( ) 17 clear error. 4Base2 14 indicator. correlation matrix 21 4cos. cot( ) 24 coth( ). constructMat( ) 20 constructMat( ). cFactor( ) 16 solve. or 82 C c22way 17 c2Cdf( ) 17 c2GOF 18 c2Pdf( ) 18 Cdf( ) 45 ceiling( ). hyperbolic cosine 23 cosh/( ). dbd( ) 32 count items in a list conditionally . hyperbolic arccotangent 25 count days between dates. ceiling 15 ceiling. display in terms of cosine 21 cos( ). common denominator 19 comment. ord( ) 82 string. display as hexadecimal 15 4Base2. clear error 19 colAugment 19 colDim( ). construct matrix 20 contact information 165 convert 4Grad 54 4Rad 92 units 149 copy variable or function. complex conjugate 20 constant in solve( ) 108 constants in cSolve( ) 28 in cZeros( ) 31 in deSolve( ) 35 in solve( ) 109 in zeros( ) 130 shortcuts for 154 construct matrix. cosine 22 cos/. cSolve( ) 27 zeros. matrix column norm 19 combinations. 0b 151 binomCdf( ) 15 binomPdf( ) 15 Boolean and. hyperbolic arccosine 23 cosine display expression in terms of 21 cosine. cZeros( ) 30 conj( ). display as binary 14 binary display. ceiling( ) 15. CopyVar 21 copyright statement ii correlation matrix. ClrErr 19 ClearAZ 18 ClrErr. cumulativeSum( ) 30 cumulativeSum( ). first derivative 142 days between dates. 4Base10 14 Define 33 Define LibPriv 34 Define LibPub 34 Define. cross product 26 csc( ). complex zeros 30 D d ( ). cycle 30 cycle. . 4Base10 14 degree/minute/second. 4DD 32 decimal integer. 4Sphere 111 display data. display as decimal angle 32 4Decimal. display result as decimal 33 decimal angle display. 4Cylind 30 cZeros( ). inverse cosecant 27 csch( ). conditionally count items in a list 25 cPolyRoots() 26 cross product. cubic regression 29 cumulative sum. inverse hyperbolic cosecant 27 cSolve( ). dim( ) 37 Disp. 4Polar 84 rectangular vector. 4DMS 38 hexadecimal. 4Rect 94 spherical vector. matrix diagonal 37 dim( ). remove void elements 35 denominator 19 derivative or nth derivative template for 5 derivative() 35 derivatives first derivative. 4DD 32 integer display.147 degree/minute/second display.countif( ). CubicReg 29 CubicReg. nDerivative( ) 77 deSolve( ). solution 35 det( ). 4Base2 14 cylindrical vector. crossP( ) 26 crossP( ). 4DMS 38 degree/minute/second notation 147 delete void elements from list 35 deleting variable. Define 33 defining private function or program 34 public function or program 34 definite integral template for 5 degree notation. display data 37 display as binary. dimension 37 dimension. display as cylindrical vector 30 cylindrical vector display. cosecant 26 csc/( ). dbd( ) 32 dbd( ). 4Cylind 30 decimal angle. Disp 37 distribution functions binomCdf( ) 15 binomPdf( ) 15 c22way( ) 17 c2Cdf( ) 17 c2GOF( ) 18 c2Pdf( ) 18 Invc2( ) 57 invNorm( ) 57 invt( ) 57 normCdf( ) 79 169 . nDeriv( ) 77 numeric derivative. complex solve 27 cubic regression. matrix determinant 36 diag( ). cumulative sum 30 customer support and service 165 Cycle. d ( ) 142 numeric derivative. hyperbolic cosecant 27 csch/( ). days between dates 32 4DD. delete variable 34 delVoid( ). DelVar 34 deltaList() 34 deltaTmpCnv() 34 DelVar. define 33 define. 4Base16 15 polar vector. Cycle 30 4Cylind. exponent 146 e^( ). EndIf 54 loop. .P 139 multiplication. end try 122 EndWhile. exact 41 exact. 42 e. 67 F factor( ). xor 129 Exit. EndWhile 128 EndTry. matrix fill 45 financial functions. EndLoop 69 end while. exponential regession 44 expressions expression to list. eff( ) 39 eigenvalue. factor 44 factor. convert nominal to effective rate 39 effective rate. else if 40 empty (void) elements 152 end for. Else 54 ElseIf. tvmN( ) 124 financial functions. e^( ) 39. display expression in terms of 42 E. eigVl( ) 40 eigenvector. e to a power 39 eff ). ! 141 Fill. E 146 exponential regession. eigenvector 40 eigVl( ). e to a power 42 exp4list( ). dot product 38 E e exponent template for 2 e to a power. eigVc( ) 40 eigVc( ). tvmI( ) 124 financial functions. display in terms of e 42 exp( ). . EndLoop 69 program. order of 156 exact( ). dominant term 38 dot addition. eigenvalue 40 else if. tvmPmt( ) 124 financial functions. Exit 41 4exp. expr( ) 43. expand( ) 42 exponent. . dotP( ) 38 subtraction. polyEval( ) 85 evaluation. EndTry 122 while. exact( ) 41 exclusive or (Boolean).N 138 dotP( ). EndFunc 50 if. PassErr 83 evaluate polynomial.+ 138 division. tvmFV( ) 124 financial functions. ClrErr 19 pass error. string to expression 43. ElseIf 40 else. . exp4list( ) 42 string to expression. EndFor 47 function. EndIf 54 end loop. = 140 Equation Operating System (EOS) 156 error codes and messages 158 errors and troubleshooting clear error.* 138 power. 67 ExpReg. EndFunc 50 end if.normPdf( ) 79 poissCdf( ) 84 poissPdf( ) 84 tCdf( ) 118 tPdf( ) 121 divide. expand 42 expand.^ 139 product. end while 128 EOS (Equation Operating System) 156 equal. display as degree/minute/ second 38 dominant term. P 136 4DMS. tvmPV( ) 124 first derivative 170 . factor( ) 44 factorial. expression to list 42 expand( ). dominantTerm( ) 38 dominantTerm( ). ExpReg 44 exponents template for 1 expr( ). . EndWhile 128 end function. EndPrgm 88 try. exit 41 exit. Input 56 inString( ). 53 getDenom( ). iPart( ) 57 integer. Goto 53 Goto. identity( ) 54 identity( ). get/return language information 51 getLockInfo( ). tanh/( ) 118 cosine. function maximum 47 fMin( ). input 56 input. getDenom( ) 51 number. implicit derivative 56 implicit derivative. format string 48 fpart( ). intDiv( ) 56 integer part. gradians 146 gcd( ). norm( ) 78 Func. get mode settings 52 getNum( ). sinh( ) 106 tangent. gcd( ) 50 groups. tests lock status of variable or variable group 51 getMode( ). cosh( ) 23 sine. sinh/( ) 106 arctangent. get/return denominator 51 getLangInfo( ). # 146 Input. 127 groups. integer divide 56 integer divide. program function 50 functions maximum. integer 56 intDiv( ). get/return variables information 53 go to. g 146 greater than or equal. for 47 for. int( ) 56 171 G g. cosh/( ) 23 arcsine. if 54 if. > 141 greatest common divisor. convert to gradian angle 54 gradian notation.template for 5 FiveNumSummary 46 floor( ). Impdif( ) 56 indefinite integral template for 5 indirection operator (#) 157 indirection. For 47 format string. floor( ) 46 fMax( ). getNum( ) 52 variables injformation. fpart( ) 48 program function. floor 46 floor. fMin( ) 47 part. fMax( ) 47 minimum. greatest common divisor 50 geomCdf( ) 50 geomPdf( ) 51 get/return denominator. within string 56 int( ). format( ) 48 format( ). function minimum 47 For 47 For. function 50 Func. testing lock status 51 H hexadecimal display. | 141 greater than. 0h 151 hyperbolic arccosine. locking and unlocking 66. identity matrix 54 If. Func 50 user-defined 33 functions and variables copying 21 getVarInfo( ). tanh( ) 117 I identity matrix. imag( ) 55 ImpDif( ). If 54 ifFn( ) 55 imag( ). go to 53 4. getVarInfo( ) 51. 4Base16 15 indicator. imaginary part 55 imaginary part. get/return number 52 . function part 48 fractions propFrac 89 template for 1 freqTable( ) 48 frequency( ) 49 Frobenius norm. integral, ‰ 142 Invc2( ) 57 inverse cumulative normal distribution (invNorm( ) 57 inverse, ^/ 149 invF( ) 57 invNorm( ), inverse cumulative normal distribution) 57 invt( ) 57 iPart( ), integer part 57 irr( ), internal rate of return internal rate of return, irr( ) 57 isPrime( ), prime test 58 isVoid( ), test for void 58 L label, Lbl 58 language get language information 51 Lbl, label 58 lcm, least common multiple 59 least common multiple, lcm 59 left( ), left 59 left, left( ) 59 length of string 37 less than or equal, { 141 less than, 140 LibPriv 34 LibPub 34 library create shortcuts to objects 59 libShortcut( ), create shortcuts to library objects 59 limit lim( ) 60 limit( ) 60 template for 6 limit( ) or lim( ), limit 60 linear regression, LinRegAx 61 linear regression, LinRegBx 60, 62 LinRegBx, linear regression 60 LinRegMx, linear regression 61 LinRegtIntervals, linear regression 62 LinRegtTest 63 linSolve() 64 list to matrix, list4mat( ) 64 172 list, conditionally count items in 25 list, count items in 25 list4mat( ), list to matrix 64 lists augment/concatenate, augment( ) 12 cross product, crossP( ) 26 cumulative sum, cumulativeSum( ) 30 difference, @list( ) 64 differences in a list, @list( ) 64 dot product, dotP( ) 38 empty elements in 152 expression to list, exp4list( ) 42 list to matrix, list4mat( ) 64 matrix to list, mat4list( ) 70 maximum, max( ) 71 mid-string, mid( ) 72 minimum, min( ) 73 new, newList( ) 77 product, product( ) 88 sort ascending, SortA 110 sort descending, SortD 110 summation, sum( ) 115 ln( ), natural logarithm 65 LnReg, logarithmic regression 65 local variable, Local 66 local, Local 66 Local, local variable 66 Lock, lock variable or variable group 66 locking variables and variable groups 66 Log template for 2 logarithmic regression, LnReg 65 logarithms 65 logistic regression, Logistic 68 logistic regression, LogisticD 68 Logistic, logistic regression 68 LogisticD, logistic regression 68 Loop, loop 69 loop, Loop 69 LU, matrix lower-upper decomposition 70 M mat4list( ), matrix to list 70 matrices augment/concatenate, augment( ) 12 column dimension, colDim( ) 19 column norm, colNorm( ) 19 cumulative sum, cumulativeSum( ) 30 determinant, det( ) 36 diagonal, diag( ) 37 dimension, dim( ) 37 dot addition, .+ 138 dot division, .P 139 dot multiplication, .* 138 dot power, .^ 139 dot subtraction, .N 138 eigenvalue, eigVl( ) 40 eigenvector, eigVc( ) 40 filling, Fill 45 identity, identity( ) 54 list to matrix, list4mat( ) 64 lower-upper decomposition, LU 70 matrix to list, mat4list( ) 70 maximum, max( ) 71 minimum, min( ) 73 new, newMat( ) 77 product, product( ) 88 QR factorization, QR 89 random, randMat( ) 93 reduced row echelon form, rref( ) 99 row addition, rowAdd( ) 98 row dimension, rowDim( ) 98 row echelon form, ref( ) 95 row multiplication and addition, mRowAdd( ) 74 row norm, rowNorm( ) 99 row operation, mRow( ) 74 row swap, rowSwap( ) 99 submatrix, subMat( ) 114, 115 summation, sum( ) 115 transpose, T 116 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( ) 70 max( ), maximum 71 maximum, max( ) 71 mean( ), mean 71 mean, mean( ) 71 median( ), median 71 median, median( ) 71 medium-medium line regression, MedMed 72 MedMed, medium-medium line regression 72 mid( ), mid-string 72 mid-string, mid( ) 72 min( ), minimum 73 minimum, min( ) 73 minute notation, ' 147 mirr( ), modified internal rate of return 73 mixed fractions, using propFrac(› with 89 mod( ), modulo 74 mode settings, getMode( ) 52 modes setting, setMode( ) 102 modified internal rate of return, mirr( ) 73 modulo, mod( ) 74 mRow( ), matrix row operation 74 mRowAdd( ), matrix row multiplication and addition 74 Multiple linear regression <Equation Variables>t test 75 multiply, * 136 MultReg 74 MultRegIntervals( ) 75 MultRegTests( ) 75 N natural logarithm, ln( ) 65 nCr( ), combinations 76 nDerivative( ), numeric derivative 77 173 negation, entering negative numbers 157 net present value, npv( ) 80 new list, newList( ) 77 matrix, newMat( ) 77 newList( ), new list 77 newMat( ), new matrix 77 nfMax( ), numeric function maximum 77 nfMin( ), numeric function minimum 77 nInt( ), numeric integral 78 nom ), convert effective to nominal rate 78 nominal rate, nom( ) 78 norm( ), Frobenius norm 78 normal distribution probability, normCdf( ) 79 normal line, normalLine( ) 79 normalLine( ) 79 normCdf( ) 79 normPdf( ) 79 not (Boolean), not 79 not equal, ƒ 140 not, Boolean not 79 nPr( ), permutations 80 npv( ), net present value 80 nSolve( ), numeric solution 80 nth root template for 1 numeric derivative, nDeriv( ) 77 derivative, nDerivative( ) 77 integral, nInt( ) 78 solution, nSolve( ) 80 P P4Rx( ), rectangular x coordinate 83 P4Ry( ), rectangular y coordinate 83 pass error, PassErr 83 PassErr, pass error 83 Pdf( ) 48 percent, % 139 permutations, nPr( ) 80 piecewise function (2-piece) template for 2 piecewise function (N-piece) template for 2 piecewise( ) 83 poissCdf( ) 84 poissPdf( ) 84 4Polar, display as polar vector 84 polar coordinate, R4Pq( ) 92 coordinate, R4Pr( ) 92 vector display, 4Polar 84 polyCoef( ) 85 polyDegree( ) 85 polyEval( ), evaluate polynomial 85 polyGcd( ) 86 polynomials evaluate, polyEval( ) 85 random, randPoly( ) 93 PolyRoots() 87 power of ten, 10^( ) 149 power regression, PowerReg 87, 96, 119 power, ^ 137 PowerReg, power regression 87 Prgm, define program 88 prime number test, isPrime( ) 58 prime, ' 148 probability densiy, normPdf( ) 79 prodSeq() 88 product (Π) template for 4 product( ), product 88 product, Π( ) 143 product, product( ) 88 programming define program, Prgm 88 display data, Disp 37 pass error, PassErr 83 O objects create shortcuts to library 59 OneVar, one-variable statistics 81 one-variable statistics, OneVar 81 operators order of evaluation 156 or (Boolean), or 82 or, Boolean or 82 ord( ), numeric character code 82 174 real( ) 94 reciprocal. PowerReg 87. 62 logarithmic. Logistic 68 medium-medium line. matrix row swap 99 rref( ). QuadReg 90 QuadReg. matrix row norm 99 rowSwap( ). 96. QuartReg 91 sinusoidal. rotate( ) 97 round( ). row echelon form 95 regressions cubic. polar coordinate 92 R4Pr( ). rref( ) 99 ref( ). EndTry 122 try. LinRegBx 60. right( ) 97 rotate( ). SinReg 107 remain( ). random polynomial 93 randSamp( ) 93 RandSeed. right 97 right. statistics 112 Return.programs defining private library 34 defining public library 34 programs and programming clear error. 4Rect 94 reduced row echelon form. CubicReg 29 exponential. R 146 rand( ). RandSeed 94 polynomial. remainder 95 remainder. convert to radian angle 92 radian. randMat( ) 93 norm. proper fraction 89 Q QR factorization. polar coordinate 92 4Rad. matrix row dimension 98 rowNorm( ). QuadReg 90 quartic. QuartReg 91 QuartReg. propFrac 89 propFrac. Try 122 proper fraction. random integer 93 randMat( ). randPoly( ) 93 random sample 93 randPoly( ). randNorm( ) 93 number seed. ExpReg 44 linear regression. quadratic regression 90 quartic regression. display as rectangular vector 94 rectangular x coordinate. statistics 113 results. LinRegAx 61 linear regression. random number seed 94 real( ). remain( ) 95 remove void elements from list 35 Request 96 RequestStr 96 result display in terms of cosine 21 display in terms of e 42 display in terms of sine 104 result values. Return 97 right( ). EndPrgm 88 end try. P4Ry( ) 83 rectangular-vector display. reduced row echelon form 99 175 . random matrix 93 randNorm( ). quartic regression 91 R R. round( ) 98 row echelon form. ClrErr 19 display I/O screen. random number 92 randBin. return 97 return. round 98 round. random number 93 randInt( ). ^/ 149 4Rect. radian 146 R4Pq( ). matrix row addition 98 rowDim( ). QR factorization 89 quadratic regression. MedMed 72 MultReg 74 power regression. QR 89 QR. real 94 real. ref( ) 95 rowAdd( ). rotate 97 rotate. LnReg 65 Logistic 68 logistic. random norm 93 random matrix. P4Rx( ) 83 rectangular y coordinate. Disp 37 end program. 119 quadratic. mean( ) 71 median. dim( ) 37 length 37 string( ).results 112 stat. 127 stat. ! 141 mean. TwoVar 125 variance. mid( ) 72 176 . 4Sphere 111 ΣPrn( ) 145 sqrt( ). # 146 left. stdDev( ) 113. OneVar 81 permutations. solve 107 solve. display as spherical vector 111 spherical vector display. ord( ) 82 character string. set mode 102 settings. variance( ) 127 stdDevPop( ). simultaneous equations 104 simultaneous equations. series( ) 101 service and support 165 set mode. inverse secant 100 sech( ). 151 string dimension. & 150. setMode( ) 102 setMode( ). get current 52 shift( ). shift 103 shift. SortA 110 descending. simult( ) 104 4sin. left( ) 59 mid-string. arcsine 105 sine display expression in terms of 104 sine. seq( ) 100 series( ). format( ) 48 formatting 48 indirection. secant 99 sec/( ). nPr( ) 80 random norm. string( ) 114 format. & 141 character code. " 147 seq( ). display in terms of sine 104 sin( ). hyperbolic arcsine 106 SinReg. hyperbolic secant 100 sech/( ). SinReg 107 solution. square root 111 square root template for 1 square root. median( ) 71 one-variable statistics. nCr( ) 76 factorial. RandSeed 94 standard deviation. sample standard deviation 113 Stop command 114 storing symbol. 143 standard deviation. shift( ) 103 sign( ). sin( ) 105 sinh( ). à( ) 111. sign 103 sign. sort ascending 110 SortD. sinusoidal regression 107 ΣInt( ) 145 sinusoidal regression. sign( ) 103 simult( ). SortD 110 4Sphere. sequence 100 sequence. hyperbolic sine 106 sinh/( ). inverse hyperbolic secant 100 second derivative template for 5 second notation.values 113 statistics combinations. stdDev( ) 113. series 101 series. deSolve( ) 35 solve( ). population standard deviation 113 stdDevSamp( ). char( ) 17 expression to string. expression to string 114 strings append. solve( ) 107 SortA.S sec( ). sort descending 110 sorting ascending. 127 two-variable results. randNorm( ) 93 random number seed. sine 105 sin/( ). right. expr( ) 43. shift( ) 103 string to expression. summation 115 sum. hyperbolic tangent 117 tanh/( ). right( ) 97 rotate. sum( ) 115 sumSeq() 115 support and service 165 system of equations (2-equation) template for 3 system of equations (N-equation) template for 3 T t test. payment amount 124 time value of money. transpose 116 tan( ). 115 subtract. number of payments 124 time value of money. N 135 sum (G) template for 4 sum of interest payments 145 sum of principal payments 145 sum( ). hyperbolic arctangent 118 Taylor polynomial. rotate( ) 97 shift. tPdf( ) 121 subMat( ). student-t probability density 121 trace( ) 122 transpose. subMat( ) 114. arctangent 117 tangent line. submatrix 114. InString 56 student-t distribution probability. Taylor polynomial 118 tCdf( ). 2-sample F test 49 tExpand( ). tan( ) 116 tangentLine( ) 117 tanh( ). Σ( ) 144 sumIf( ) 115 summation. tTest 123 T. Future Value 124 time value of money. trigonometric collection 119 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. tCdf( ) 118 student-t probability density. student-t distribution probability 118 tCollect( ). two-sample t confidence interval 120 4tmpCnv() 121 tmpCnv() 121 tPdf( ). trigonometric expansion 119 Text command 119 time value of money. tangent 116 tan/( ). 115 submatrix. tangentLine( ) 117 tangent. 67 using to create variable names 157 within. T 116 177 . taylor( ) 118 taylor( ). t confidence interval 120 tInterval_2Samp. present value 124 tInterval. Interest 124 time value of money. isVoid( ) 58 Test_2S. two-proportion z test 134 zTest_2Samp. square 138 xor. unlock variable or variable group 127 unlocking variables and variable groups 127 user-defined functions 33 user-defined functions and programs 34 X x2. inString( ) 56 U underscore. zeroes 129 zeroes. Local 66 variables.trigonometric collection. one-proportion z test 133 zTest_2Prop. when 128 when. one-proportion z confidence interval 131 zInterval_2Prop. unitV( ) 126 void elements 152 void elements. variance( ) 127 varPop( ) 127 varSamp( ). While 128 with. 127 variance. zeroes( ) 129 zInterval. tExpand( ) 119 Try. two-proportion z confidence interval 132 zInterval_2Samp. two-variable results 125 two-variable results. unit vector 126 unLock. z confidence interval 131 zInterval_1Prop. while 128 while. crossP( ) 26 178 . _ 148 unit vector. unitV( ) 126 units convert 149 unitV( ). when( ) 128 While. sample variance 127 vectors cross product. t test 123 tTest_2Samp. two-sample z confidence interval 132 zTest 133 zTest_1Prop. Boolean exclusive or 129 Z zeroes( ). | 150 within string. 66. test for 58 W when( ). TwoVar 125 cylindrical vector display. two-sample t test 123 TVM arguments 124 tvmFV( ) 124 tvmI( ) 124 tvmN( ) 124 tvmPmt( ) 124 tvmPV( ) 124 TwoVar. locking and unlocking 51. 4Cylind 30 dot product. tCollect( ) 119 trigonometric expansion. remove 35 void. dotP( ) 38 unit. error handling command 122 tTest. two-sample z test 134 V variable creating name from a character string 157 variable and functions copying 21 variables clear all single-letter 18 delete. DelVar 34 local.