Texas Instruments TI-Nspire Reference Manual

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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 Definite integral template ..........................5 Alphabetical listing A abs() ..............................................................6 amortTbl() ....................................................6 and ................................................................6 angle() ..........................................................7 ANOVA .........................................................7 ANOVA2way ................................................8 Ans ................................................................9 approx() ......................................................10 4approxFraction() .......................................10 approxRational() ........................................10 arccos() ........................................................10 arccosh() .....................................................10 arccot() ........................................................10 arccoth() .....................................................11 arccsc() ........................................................11 arccsch() ......................................................11 arcsec() ........................................................11 arcsech() ......................................................11 arcsin() ........................................................11 arcsinh() ......................................................11 arctan() .......................................................11 arctanh() .....................................................11 augment() ...................................................11 avgRC() .......................................................12 B bal() .............................................................12 4Base2 .........................................................12 4Base10 .......................................................13 4Base16 .......................................................14 binomCdf() .................................................14 binomPdf() .................................................14 C ceiling() ...................................................... 14 centralDiff() ............................................... 15 char() .......................................................... 15 c22way ........................................................ 15 c2Cdf() ........................................................ 16 c2GOF ......................................................... 16 c2Pdf() ........................................................ 16 ClearAZ ....................................................... 16 ClrErr .......................................................... 17 colAugment() ............................................. 17 colDim() ...................................................... 17 colNorm() ................................................... 17 completeSquare() ...................................... 18 conj() .......................................................... 18 constructMat() ........................................... 18 CopyVar ...................................................... 18 corrMat() .................................................... 19 cos() ............................................................ 19 cos/() .......................................................... 20 cosh() .......................................................... 21 cosh/() ........................................................ 21 cot() ............................................................ 21 cot/() .......................................................... 22 coth() .......................................................... 22 coth/() ........................................................ 22 count() ........................................................ 22 countif() ..................................................... 23 cPolyRoots() ............................................... 23 crossP() ....................................................... 23 csc() ............................................................. 24 csc/() ........................................................... 24 csch() ........................................................... 24 csch/() ......................................................... 24 CubicReg .................................................... 25 cumulativeSum() ........................................ 25 Cycle ........................................................... 26 4Cylind ........................................................ 26 D dbd() ........................................................... 26 4DD ............................................................. 27 4Decimal ..................................................... 27 Define ......................................................... 27 Define LibPriv ............................................ 28 Define LibPub ............................................ 28 deltaList() ................................................... 29 DelVar ........................................................ 29 delVoid() .................................................... 29 det() ............................................................ 29 diag() .......................................................... 30 dim() ........................................................... 30 Disp ............................................................. 30 4DMS ........................................................... 31 dotP() .......................................................... 31 E e^() ............................................................. 31 eff() ............................................................. 32

L Lbl ............................................................... 50 lcm() ............................................................ 50 left() ............................................................ 50 libShortcut() ............................................... 51 LinRegBx ..................................................... 51 LinRegMx ................................................... 52 LinRegtIntervals ......................................... 52 LinRegtTest ................................................ 54 linSolve() ..................................................... 55 @List() .......................................................... 55 list4mat() ..................................................... 55 ln() .............................................................. 55 LnReg .......................................................... 56 Local ........................................................... 57 Lock ............................................................ 57 log() ............................................................ 58 Logistic ....................................................... 58 LogisticD ..................................................... 59 Loop ............................................................ 60 LU ................................................................ 60 M mat4list() ..................................................... 60 max() ........................................................... 61 mean() ........................................................ 61 median() ..................................................... 61 MedMed ..................................................... 62 mid() ........................................................... 62 min() ........................................................... 63 mirr() ........................................................... 63 mod() .......................................................... 64 mRow() ....................................................... 64 mRowAdd() ................................................ 64 MultReg ...................................................... 64 MultRegIntervals ....................................... 65 MultRegTests ............................................. 65 N nCr() ............................................................ 66 nDerivative() .............................................. 67 newList() ..................................................... 67 newMat() .................................................... 67 nfMax() ....................................................... 67 nfMin() ....................................................... 68 nInt() ........................................................... 68 nom() .......................................................... 68 norm() ......................................................... 68 normCdf() ................................................... 69 normPdf() ................................................... 69 not .............................................................. 69 nPr() ............................................................ 69 npv() ........................................................... 70 nSolve() ....................................................... 70 O OneVar ....................................................... 71 or ................................................................ 72 ord() ............................................................ 72 P

product() .....................................................76 propFrac() ...................................................77 Q QR ...............................................................77 QuadReg .....................................................78 QuartReg ....................................................78 R R4Pq() ..........................................................79 R4Pr() ...........................................................79 4Rad .............................................................80 rand() ..........................................................80 randBin() .....................................................80 randInt() .....................................................80 randMat() ...................................................80 randNorm() .................................................80 randPoly() ...................................................81 randSamp() .................................................81 RandSeed ....................................................81 real() ...........................................................81 4Rect ............................................................81 ref() .............................................................82 remain() ......................................................83 Request .......................................................83 RequestStr ..................................................84 Return .........................................................84 right() ..........................................................84 rk23() ..........................................................85 root() ...........................................................85 rotate() .......................................................85 round() ........................................................86 rowAdd() ....................................................86 rowDim() ....................................................87 rowNorm() ..................................................87 rowSwap() ..................................................87 rref() ............................................................87 S sec() .............................................................88 sec/() ...........................................................88 sech() ...........................................................88 sech/() .........................................................88 seq() ............................................................89 seqGen() .....................................................89 seqn() ..........................................................90 setMode() ...................................................90 shift() ..........................................................91 sign() ...........................................................92 simult() ........................................................92 sin() ............................................................. 93 sin/() ........................................................... 93 sinh() ........................................................... 94 sinh/() ......................................................... 94 SinReg ........................................................ 95 SortA .......................................................... 95 SortD .......................................................... 96 4Sphere ....................................................... 96 sqrt() ........................................................... 96 stat.results .................................................. 97 stat.values .................................................. 98 stDevPop() .................................................. 98 stDevSamp() ............................................... 98 Stop ............................................................ 99 Store ........................................................... 99 string() ........................................................ 99 subMat() ..................................................... 99 Sum (Sigma) ............................................... 99 sum() ........................................................... 99 sumIf() ...................................................... 100 sumSeq() ................................................... 100 system() .................................................... 100 T T (transpose) ............................................ 100 tan() .......................................................... 101 tan/() ........................................................ 101 tanh() ........................................................ 102 tanh/() ...................................................... 102 tCdf() ........................................................ 103 Text ........................................................... 103 Then ......................................................... 103 tInterval .................................................... 103 tInterval_2Samp ....................................... 104 tPdf() ........................................................ 104 trace() ....................................................... 104 Try ............................................................. 105 tTest .......................................................... 105 tTest_2Samp ............................................. 106 tvmFV() ..................................................... 106 tvmI() ........................................................ 107 tvmN() ...................................................... 107 tvmPmt() .................................................. 107 tvmPV() ..................................................... 107 TwoVar ..................................................... 108 U unitV() ...................................................... 109 unLock ...................................................... 109 V varPop() .................................................... 109 varSamp() ................................................. 110 W warnCodes() ............................................. 110 when() ...................................................... 110 While ........................................................ 111 “With” ...................................................... 111 X xor ............................................................ 111

N(subtract) ................................................116 ·(multiply) ...............................................117 à (divide) ...................................................117 ^ (power) ..................................................118 x2 (square) ................................................118 .+ (dot add) ...............................................119 .. (dot subt.) ..............................................119 .·(dot mult.) .............................................119 . / (dot divide) ...........................................119 .^ (dot power) ..........................................119 L(negate) ...................................................120 % (percent) ...............................................120 = (equal) ....................................................121 ƒ (not equal) .............................................121 < (less than) ..............................................121 { (less or equal) ........................................122 > (greater than) ........................................122 | (greater or equal) ..................................122 ! (factorial) ................................................122 & (append) ................................................122 d() (derivative) ..........................................123 ‰() (integral) ..............................................123 ‡() (square root) .......................................123 Π() (prodSeq) ............................................124 G() (sumSeq) ..............................................124 GInt() .........................................................125 GPrn() ........................................................ 125 # (indirection) .......................................... 126 E (scientific notation) ............................... 126 g (gradian) ............................................... 126 R(radian) .................................................... 126 ¡ (degree) ................................................. 127 ¡, ', '' (degree/minute/second) ................. 127 ± (angle) .................................................. 127 _ (underscore as an empty element) ...... 127 10^() .......................................................... 128 ^/(reciprocal) ........................................... 128 | (“with”) .................................................. 128 & (store) ................................................... 129 := (assign) ................................................. 129 © (comment) ............................................ 129 0b, 0h ........................................................ 130 Empty (void) elements Calculations involving void elements ................................................... 131 List arguments containing void elements ................................................... 131 Shortcuts for entering math expressions EOS™ (Equation Operating System) hierarchy Error codes and messages Warning codes and messages Texas Instruments Support and Service

1 TI-Nspire™ Reference Guide This guide lists the templates, functions, commands, and operators available for evaluating math expressions. Expression templates Expression templates give you an easy way to enter math expressions in standard mathematical notation. When you insert a template, it appears on the entry line with small blocks at positions where you can enter elements. A cursor shows which element you can enter. Use the arrow keys or press e to move the cursor to each element’s position, and type a value or expression for the element. Press · or /· to evaluate the expression. Fraction template /p keys Note: See also / (divide), page 117. Example: Exponent template l key Note: Type the first value, press l, and then type the exponent. To return the cursor to the baseline, press right arrow (¢). Note: See also ^ (power), page 118. Example: Square root template /q keys Note: See also ‡() (square root), page 123. Example: Nth root template /l keys Note: See also root(), page 85. Example:

e exponent template u keys Natural exponential e raised to a power Note: See also e^(), page 31. Example: Log template /s key Calculates log to a specified base. For a default of base 10, omit the base. Note: See also log(), page 58. Example: Piecewise template (2-piece) Catalog > Lets you create expressions and conditions for a two-piece piecewise function. To add a piece, click in the template and repeat the template. Note: See also piecewise(), page 73. Example: Piecewise template (N-piece) Catalog > Lets you create expressions and conditions for an N-piece piecewise function. Prompts for N. Note: See also piecewise(), page 73. Example: See the example for Piecewise template (2-piece).

3 System of 2 equations template Catalog > Creates a system of two linear equations. To add a row to an existing system, click in the template and repeat the template. Note: See also system(), page 100. Example: System of N equations template Catalog > Lets you create a system of N linear equations. Prompts for N. Note: See also system(), page 100. Example: See the example for System of equations template (2-equation). Absolute value template Catalog > Note: See also abs(), page 6. Example: dd°mm’ss.ss’’ template Catalog > Lets you enter angles in dd°mm’ss.ss’’ format, where dd is the number of decimal degrees, mm is the number of minutes, and ss.ss is the number of seconds. Example: Matrix template (2 x 2) Catalog > Creates a 2 x 2 matrix. Example:

Matrix template (1 x 2) Catalog > . Example: Matrix template (2 x 1) Catalog > Example: Matrix template (m x n) Catalog > The template appears after you are prompted to specify the number of rows and columns. Note: If you create a matrix with a large number of rows and columns, it may take a few moments to appear. Example: Sum template (G) Catalog > Note: See also G() (sumSeq), page 124. Example: Product template (Π) Catalog > Note: See also Π() (prodSeq), page 124. Example:

5 First derivative template Catalog > The first derivative template can be used to calculate first derivative at a point numerically, using auto differentiation methods. Note: See also d() (derivative), page 123. Example: Second derivative template Catalog > The second derivative template can be used to calculate second derivative at a point numerically, using auto differentiation methods. Note: See also d() (derivative), page 123. Example: Definite integral template Catalog > The definite integral template can be used to calculate the definite integral numerically, using the same method as nInt(). 183Note: See also nInt(), page 68. Example:

Alphabetical listing Items whose names are not alphabetic (such as +, !, and >) are listed at the end of this section, starting on page 116. Unless otherwise specified, all examples in this section were performed in the default reset mode, and all variables are assumed to be undefined. A abs() Catalog > abs(Value1) ⇒value abs(List1) ⇒list abs(Matrix1) ⇒matrix Returns the absolute value of the argument. Note: See also Absolute value template, page 3. If the argument is a complex number, returns the number’s modulus. amortTbl() Catalog > amortTbl(NPmt,N,I,PV, [Pmt], [FV], [PpY], [CpY], [PmtAt], [roundValue]) ⇒matrix Amortization function that returns a matrix as an amortization table for a set of TVM arguments. NPmt is the number of payments to be included in the table. The table starts with the first payment. N, I, PV, Pmt, FV, PpY, CpY, and PmtAt are described in the table of TVM arguments, page 107. • If you omit Pmt, it defaults to Pmt=tvmPmt(N,I,PV,FV,PpY,CpY,PmtAt). • If you omit FV, it defaults to FV=0. • The defaults for PpY, CpY, and PmtAt are the same as for the TVM functions. roundValue specifies the number of decimal places for rounding. Default=2. The columns in the result matrix are in this order: Payment number, amount paid to interest, amount paid to principal, and balance. The balance displayed in row n is the balance after payment n. You can use the output matrix as input for the other amortization functions GInt() and GPrn(), page 125, and bal(), page 12. and Catalog > BooleanExpr1 and BooleanExpr2 ⇒Boolean expression BooleanList1 and BooleanList2 ⇒ Boolean list BooleanMatrix1 and BooleanMatrix2 ⇒ Boolean matrix Returns true or false or a simplified form of the original entry.

7 Integer1 and Integer2 ⇒integer Compares two real integers bit-by-bit using an and operation. Internally, both integers are converted to signed, 64-bit binary numbers. When corresponding bits are compared, the result is 1 if both bits are 1; otherwise, the result is 0. The returned value represents the bit results, and is displayed according to the Base mode. You can enter the integers in any number base. For a binary or hexadecimal entry, you must use the 0b or 0h prefix, respectively. Without a prefix, integers are treated as decimal (base 10). In Hex base mode: Important: Zero, not the letter O. In Bin base mode: In Dec base mode: Note: A binary entry can have up to 64 digits (not counting the 0b prefix). A hexadecimal entry can have up to 16 digits. angle() Catalog > angle(Value1) ⇒value Returns the angle of the argument, interpreting the argument as a complex number. In Degree angle mode: In Gradian angle mode: In Radian angle mode: angle(List1) ⇒list angle(Matrix1) ⇒matrix Returns a list or matrix of angles of the elements in List1 or Matrix1, interpreting each element as a complex number that represents a two-dimensional rectangular coordinate point. ANOVA Catalog > ANOVA List1,List2[,List3,...,List20][,Flag] Performs a one-way analysis of variance for comparing the means of two to 20 populations. A summary of results is stored in the stat.results variable. (See page 97.) Flag=0 for Data, Flag=1 for Stats Output variable Description stat.F Value of the F statistic stat.PVal Smallest level of significance at which the null hypothesis can be rejected stat.df Degrees of freedom of the groups stat.SS Sum of squares of the groups stat.MS Mean squares for the groups stat.dfError Degrees of freedom of the errors and Catalog >

Outputs: Block Design COLUMN FACTOR Outputs stat.SSError Sum of squares of the errors stat.MSError Mean square for the errors stat.sp Pooled standard deviation stat.xbarlist Mean of the input of the lists stat.CLowerList 95% confidence intervals for the mean of each input list stat.CUpperList 95% confidence intervals for the mean of each input list ANOVA2way Catalog > ANOVA2way List1,List2[,List3,…,List10][,levRow] Computes a two-way analysis of variance for comparing the means of two to 10 populations. A summary of results is stored in the stat.results variable. (See page 97.) LevRow=0 for Block LevRow=2,3,...,Len-1, for Two Factor, where Len=length(List1)=length(List2) = … = length(List10) and Len / LevRow ∈ {2,3,…} Output variable Description stat.F F statistic of the column factor stat.PVal Smallest level of significance at which the null hypothesis can be rejected stat.df Degrees of freedom of the column factor stat.SS Sum of squares of the column factor stat.MS Mean squares for column factor stat.FBlock F statistic for factor stat.PValBlock Least probability at which the null hypothesis can be rejected stat.dfBlock Degrees of freedom for factor stat.SSBlock Sum of squares for factor stat.MSBlock Mean squares for factor stat.dfError Degrees of freedom of the errors stat.SSError Sum of squares of the errors stat.MSError Mean squares for the errors stat.s Standard deviation of the error Output variable Description stat.Fcol F statistic of the column factor Output variable Description

9 ROW FACTOR Outputs INTERACTION Outputs ERROR Outputs stat.PValCol Probability value of the column factor stat.dfCol Degrees of freedom of the column factor stat.SSCol Sum of squares of the column factor stat.MSCol Mean squares for column factor Output variable Description stat.FRow F statistic of the row factor stat.PValRow Probability value of the row factor stat.dfRow Degrees of freedom of the row factor stat.SSRow Sum of squares of the row factor stat.MSRow Mean squares for row factor Output variable Description stat.FInteract F statistic of the interaction stat.PValInteract Probability value of the interaction stat.dfInteract Degrees of freedom of the interaction stat.SSInteract Sum of squares of the interaction stat.MSInteract Mean squares for interaction Output variable Description stat.dfError Degrees of freedom of the errors stat.SSError Sum of squares of the errors stat.MSError Mean squares for the errors s Standard deviation of the error Ans /v keys Ans ⇒value Returns the result of the most recently evaluated expression. Output variable Description

approx() Catalog > approx(Value1) ⇒number Returns the evaluation of the argument as an expression containing decimal values, when possible, regardless of the current Auto or Approximate mode. This is equivalent to entering the argument and pressing / ·. approx(List1) ⇒list approx(Matrix1) ⇒matrix Returns a list or matrix where each element has been evaluated to a decimal value, when possible. 4approxFraction() Catalog > Value 4approxFraction([Tol]) ⇒value List 4approxFraction([Tol]) ⇒list Matrix 4approxFraction([Tol]) ⇒matrix Returns the input as a fraction, using a tolerance of Tol. If Tol is omitted, a tolerance of 5.E-14 is used. Note: You can insert this function from the computer keyboard by typing @>approxFraction(...). approxRational() Catalog > approxRational(Value[, Tol]) ⇒value approxRational(List[, Tol]) ⇒list approxRational(Matrix[, Tol]) ⇒matrix Returns the argument as a fraction using a tolerance of Tol. If Tol is omitted, a tolerance of 5.E-14 is used. arccos() See cos/(), page 20. arccosh() See cosh/(), page 21. arccot() See cot/(), page 22.

11 arccoth() See coth/(), page 22. arccsc() See csc/(), page 24. arccsch() See csch/(), page 24. arcsec() See sec/(), page 88. arcsech() See sech/(), page 88. arcsin() See sin/(), page 93. arcsinh() See sinh/(), page 94. arctan() See tan/(), page 101. arctanh() See tanh/(), page 102. augment() Catalog > augment(List1, List2) ⇒list Returns a new list that is List2 appended to the end of List1. augment(Matrix1, Matrix2) ⇒matrix Returns a new matrix that is Matrix2 appended to Matrix1. When the “,” character is used, the matrices must have equal row dimensions, and Matrix2 is appended to Matrix1 as new columns. Does not alter Matrix1 or Matrix2.

B avgRC() Catalog > avgRC(Expr1, Var [=Value] [, Step]) ⇒expression avgRC(Expr1, Var [=Value] [, List1]) ⇒list avgRC(List1, Var [=Value] [, Step]) ⇒list avgRC(Matrix1, Var [=Value] [, Step]) ⇒matrix Returns the forward-difference quotient (average rate of change). Expr1 can be a user-defined function name (see Func). When Value is specified, it overrides any prior variable assignment or any current “with” substitution for the variable. Step is the step value. If Step is omitted, it defaults to 0.001. Note that the similar function centralDiff() uses the central- difference quotient. bal() Catalog > bal(NPmt,N,I,PV ,[Pmt], [FV], [PpY], [CpY], [PmtAt], [roundValue]) ⇒value bal(NPmt,amortTable) ⇒value Amortization function that calculates schedule balance after a specified payment. N, I, PV, Pmt, FV, PpY, CpY, and PmtAt are described in the table of TVM arguments, page 107. NPmt specifies the payment number after which you want the data calculated. N, I, PV, Pmt, FV, PpY, CpY, and PmtAt are described in the table of TVM arguments, page 107. • If you omit Pmt, it defaults to Pmt=tvmPmt(N,I,PV,FV,PpY,CpY,PmtAt). • If you omit FV, it defaults to FV=0. • The defaults for PpY, CpY, and PmtAt are the same as for the TVM functions. roundValue specifies the number of decimal places for rounding. Default=2. bal(NPmt,amortTable) calculates the balance after payment number NPmt, based on amortization table amortTable. The amortTable argument must be a matrix in the form described under amortTbl(), page 6. Note: See also GInt() and GPrn(), page 125. 4Base2 Catalog > Integer1 4Base2 ⇒integer Note: You can insert this operator from the computer keyboard by typing @>Base2. Converts Integer1 to a binary number. Binary or hexadecimal numbers always have a 0b or 0h prefix, respectively.

13 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 Catalog > Integer1 4Base10 ⇒integer Note: You can insert this operator from the computer keyboard by typing @>Base10. Converts Integer1 to a decimal (base 10) number. A binary or hexadecimal entry must always have a 0b or 0h prefix, respectively. 0b binaryNumber 0h hexadecimalNumber Zero, not the letter O, followed by b or h. A binary number can have up to 64 digits. A hexadecimal number can have up to 16. Without a prefix, Integer1 is treated as decimal. The result is displayed in decimal, regardless of the Base mode. 4Base2 Catalog > 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. 0b binaryNumber 0h hexadecimalNumber

C 4Base16 Catalog > Integer1 4Base16 ⇒integer Note: You can insert this operator from the computer keyboard by typing @>Base16. Converts Integer1 to a hexadecimal number. Binary or hexadecimal numbers always have a 0b or 0h prefix, respectively. 0b binaryNumber 0h hexadecimalNumber Zero, not the letter O, followed by b or h. A binary number can have up to 64 digits. A hexadecimal number can have up to 16. Without a prefix, Integer1 is treated as decimal (base 10). The result is displayed in hexadecimal, regardless of the Base mode. If you enter a decimal integer that is too large for a signed, 64-bit binary form, a symmetric modulo operation is used to bring the value into the appropriate range. For more information, see 4Base2, page 12. binomCdf() Catalog > binomCdf(n,p) ⇒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() Catalog > binomPdf(n,p) ⇒number binomPdf(n,p,XVal) ⇒number if XVal is a number, list if XVal is a list Computes a probability for the discrete binomial distribution with n number of trials and probability p of success on each trial. ceiling() Catalog > ceiling(Value1) ⇒value Returns the nearest integer that is | the argument. The argument can be a real or a complex number. Note: See also floor(). ceiling(List1) ⇒list ceiling(Matrix1) ⇒matrix Returns a list or matrix of the ceiling of each element.

15 centralDiff() Catalog > centralDiff(Expr1,Var [=Value][,Step]) ⇒expression centralDiff(Expr1,Var [,Step])|Var=Value ⇒expression centralDiff(Expr1,Var [=Value][,List]) ⇒list centralDiff(List1,Var [=Value][,Step]) ⇒list centralDiff(Matrix1,Var [=Value][,Step]) ⇒matrix Returns the numerical derivative using the central difference 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(). char() Catalog > char(Integer) ⇒character Returns a character string containing the character numbered Integer from the handheld character set. The valid range for Integer is 0– 65535. c22way Catalog > c22way obsMatrix chi22way obsMatrix Computes a c2 test for association on the two-way table of counts in the observed matrix obsMatrix. A summary of results is stored in the stat.results variable. (See page 97.) For information on the effect of empty elements in a matrix, see “Empty (void) elements” on page 131. Output variable Description stat.c2 Chi square stat: sum (observed - expected)2/expected stat.PVal Smallest level of significance at which the null hypothesis can be rejected stat.df Degrees of freedom for the chi square statistics stat.ExpMat Matrix of expected elemental count table, assuming null hypothesis stat.CompMat Matrix of elemental chi square statistic contributions

c2Cdf() Catalog > c2Cdf(lowBound,upBound,df) ⇒number if lowBound and upBound are numbers, list if lowBound and upBound are lists chi2Cdf(lowBound,upBound,df) ⇒number if lowBound and upBound are numbers, list if lowBound and upBound are lists Computes the c2 distribution probability between lowBound and upBound for the specified degrees of freedom df. For P(X { upBound), set lowBound = 0. For information on the effect of empty elements in a list, see “Empty (void) elements” on page 131. c2GOF Catalog > c2GOF obsList,expList,df chi2GOF obsList,expList,df Performs a test to confirm that sample data is from a population that conforms to a specified distribution. obsList is a list of counts and must contain integers. A summary of results is stored in the stat.results variable. (See page 97.) For information on the effect of empty elements in a list, see “Empty (void) elements” on page 131. Output variable Description stat.c2 Chi square stat: sum((observed - expected)2/expected stat.PVal Smallest level of significance at which the null hypothesis can be rejected stat.df Degrees of freedom for the chi square statistics stat.CompList Elemental chi square statistic contributions c2Pdf() Catalog > c2Pdf(XVal,df) ⇒number if XVal is a number, list if XVal is a list chi2Pdf(XVal,df) ⇒number if XVal is a number, list if XVal is a list Computes the probability density function (pdf) for the c2 distribution at a specified XVal value for the specified degrees of freedom df. For information on the effect of empty elements in a list, see “Empty (void) elements” on page 131. ClearAZ Catalog > ClearAZ Clears all single-character variables in the current problem space. If one or more of the variables are locked, this command displays an error message and deletes only the unlocked variables. See unLock, page 109.

17 ClrErr Catalog > ClrErr Clears the error status and sets system variable errCode to zero. The Else clause of the Try...Else...EndTry block should use ClrErr or PassErr. If the error is to be processed or ignored, use ClrErr. If what to do with the error is not known, use PassErr to send it to the next error handler. If there are no more pending Try...Else...EndTry error handlers, the error dialog box will be displayed as normal. Note: See also PassErr, page 73, and Try, page 105. Note for entering the example: In the Calculator application on the handheld, you can enter multi-line definitions by pressing @ instead of · at the end of each line. On the computer keyboard, hold down Alt and press Enter. For an example of ClrErr, See Example 2 under the Try command, page 105. colAugment() Catalog > colAugment(Matrix1, Matrix2) ⇒matrix Returns a new matrix that is Matrix2 appended to Matrix1. The matrices must have equal column dimensions, and Matrix2 is appended to Matrix1 as new rows. Does not alter Matrix1 or Matrix2. colDim() Catalog > colDim(Matrix) ⇒expression Returns the number of columns contained in Matrix. Note: See also rowDim(). colNorm() Catalog > colNorm(Matrix) ⇒expression Returns the maximum of the sums of the absolute values of the elements in the columns in Matrix. Note: Undefined matrix elements are not allowed. See also rowNorm().

completeSquare() Catalog > completeSquare(ExprOrEqn, Var) ⇒expression or equation completeSquare(ExprOrEqn, Var^Power) ⇒expression or equation completeSquare(ExprOrEqn, Var1, Var2 [,...]) ⇒expression or equation completeSquare(ExprOrEqn, {Var1, Var2 [,...]}) ⇒expression or equation Converts a quadratic polynomial expression of the form a·x2+b·x+c into the form a·(x-h)2+k - or - Converts a quadratic equation of the form a·x2+b·x+c=d into the form a·(x-h)2=k The first argument must be a quadratic expression or equation in standard form with respect to the second argument. The Second argument must be a single univariate term or a single univariate term raised to a rational power, for example x, y2, or z(1/3). The third and fourth syntax attempt to complete the square with respect to variables Var1, Var2 [,… ]). conj() Catalog > conj(Value1) ⇒value conj(List1) ⇒list conj(Matrix1) ⇒matrix Returns the complex conjugate of the argument. constructMat() Catalog > constructMat(Expr,Var1,Var2,numRows,numCols) ⇒matrix Returns a matrix based on the arguments. Expr is an expression in variables Var1 and Var2. Elements in the resulting matrix are formed by evaluating Expr for each incremented value of Var1 and Var2. Var1 is automatically incremented from 1 through numRows. Within each row, Var2 is incremented from 1 through numCols. CopyVar Catalog > CopyVar Var1, Var2 CopyVar Var1., Var2. CopyVar Var1, Var2 copies the value of variable Var1 to variable Var2, creating Var2 if necessary. Variable Var1 must have a value. If Var1 is the name of an existing user-defined function, copies the definition of that function to function Var2. Function Var1 must be defined. Var1 must meet the variable-naming requirements or must be an indirection expression that simplifies to a variable name meeting the requirements.

19 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() Catalog > corrMat(List1,List2[,…[,List20]]) Computes the correlation matrix for the augmented matrix [List1, List2, ..., List20]. cos() μ key cos(Value1) ⇒value cos(List1) ⇒list cos(Value1) returns the cosine of the argument as a value. cos(List1) returns a list of the cosines of all elements in List1. Note: The argument is interpreted as a degree, gradian or radian angle, according to the current angle mode setting. You can use ¡, G, or R to override the angle mode temporarily. In Degree angle mode: In Gradian angle mode: In Radian angle mode: CopyVar Catalog >

cos(squareMatrix1) ⇒squareMatrix Returns the matrix cosine of squareMatrix1. This is not the same as calculating the cosine of each element. When a scalar function f(A) operates on squareMatrix1 (A), the result is calculated by the algorithm: Compute the eigenvalues (li) and eigenvectors (Vi) of A. squareMatrix1 must be diagonalizable. Also, it cannot have symbolic variables that have not been assigned a value. Form the matrices: Then A = X B X/and f(A) = X f(B) X/. For example, cos(A) = X cos(B) X/ where: cos(B) = All computations are performed using floating-point arithmetic. In Radian angle mode: cos/() μ key cos/(Value1) ⇒value cos/(List1) ⇒list cos/(Value1) returns the angle whose cosine is Value1. cos/(List1) returns a list of the inverse cosines of each element of List1. Note: The result is returned as a degree, gradian or radian angle, according to the current angle mode setting. Note: You can insert this function from the keyboard by typing arccos(...). In Degree angle mode: In Gradian angle mode: In Radian angle mode: cos/(squareMatrix1) ⇒squareMatrix 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. In Radian angle mode and Rectangular Complex Format: To see the entire result, press £ and then use ¡ and ¢ to move the cursor. cos() μ key

21 cosh() Catalog > cosh(Value1) ⇒value cosh(List1) ⇒list cosh(Value1) returns the hyperbolic cosine of the argument. cosh(List1) returns a list of the hyperbolic cosines of each element 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/() Catalog > cosh/(Value1) ⇒value cosh/(List1) ⇒list cosh/(Value1) returns the inverse hyperbolic cosine of the argument. cosh/(List1) returns a list of the inverse hyperbolic cosines of each element of List1. Note: You can insert this function from the keyboard by typing arccosh(...). cosh/(squareMatrix1) ⇒squareMatrix Returns the matrix inverse hyperbolic cosine of squareMatrix1. This is not the same as calculating the inverse hyperbolic cosine of each element. For information about the calculation method, refer to cos(). squareMatrix1 must be diagonalizable. The result always contains floating-point numbers. In Radian angle mode and In Rectangular Complex Format: To see the entire result, press £ and then use ¡ and ¢ to move the cursor. cot() μ key cot(Value1) ⇒ value cot(List1) ⇒ list Returns the cotangent of Value1 or returns a list of the cotangents of all elements in List1. Note: The argument is interpreted as a degree, gradian or radian angle, according to the current angle mode setting. You can use ¡, G, or R to override the angle mode temporarily. In Degree angle mode: In Gradian angle mode: In Radian angle mode:

cot/() μ key cot/(Value1) ⇒value cot/(List1) ⇒list Returns the angle whose cotangent is Value1 or returns a list containing the inverse cotangents of each element of List1. Note: The result is returned as a degree, gradian or radian angle, according to the current angle mode setting. Note: You can insert this function from the keyboard by typing arccot(...). In Degree angle mode: In Gradian angle mode: In Radian angle mode: coth() Catalog > coth(Value1) ⇒value coth(List1) ⇒list Returns the hyperbolic cotangent of Value1 or returns a list of the hyperbolic cotangents of all elements of List1. coth/() Catalog > coth/(Value1) ⇒value coth/(List1) ⇒list Returns the inverse hyperbolic cotangent of Value1 or returns a list containing the inverse hyperbolic cotangents of each element of List1. Note: You can insert this function from the keyboard by typing arccoth(...). count() Catalog > count(Value1orList1 [,Value2orList2 [,...]]) ⇒value Returns the accumulated count of all elements in the arguments that evaluate to numeric values. Each argument can be an expression, value, list, or matrix. You can mix data types and use arguments of various dimensions. For a list, matrix, or range of cells, each element is evaluated to determine if it should be included in the count. Within the Lists & Spreadsheet application, you can use a range of cells in place of any argument. Empty (void) elements are ignored. For more information on empty elements, see page 131.

23 countif() Catalog > countif(List,Criteria) ⇒value Returns the accumulated count of all elements in List that meet the specified Criteria. Criteria can be: • A value, expression, or string. For example, 3 counts only those elements in List that simplify to the value 3. • A Boolean expression containing the symbol ? as a placeholder for each element. For example, ?<5 counts only those elements in List that are less than 5. Within the Lists & Spreadsheet application, you can use a range of cells in place of List. Empty (void) elements in the list are ignored. For more information on empty elements, see page 131. Note: See also sumIf(), page 100, and frequency(), page 39. Counts the number of elements equal to 3. Counts the number of elements equal to “def.” Counts 1 and 3. Counts 3, 5, and 7. Counts 1, 3, 7, and 9. cPolyRoots() Catalog > cPolyRoots(Poly,Var) ⇒list cPolyRoots(ListOfCoeffs) ⇒list The first syntax, cPolyRoots(Poly,Var), returns a list of complex roots of polynomial Poly with respect to variable Var. Poly must be a polynomial in expanded form in one variable. Do not use unexpanded forms such as y2·y+1 or x·x+2·x+1 The second syntax, cPolyRoots(ListOfCoeffs), returns a list of complex roots for the coefficients in ListOfCoeffs. Note: See also polyRoots(), page 74. crossP() Catalog > crossP(List1, List2) ⇒list Returns the cross product of List1 and List2 as a list. List1 and List2 must have equal dimension, and the dimension must be either 2 or 3. crossP(Vector1, Vector2) ⇒vector Returns a row or column vector (depending on the arguments) that is the cross product of Vector1 and Vector2. Both Vector1 and Vector2 must be row vectors, or both must be column vectors. Both vectors must have equal dimension, and the dimension must be either 2 or 3.

csc() μ key csc(Value1) ⇒value csc(List1) ⇒list Returns the cosecant of Value1 or returns a list containing the cosecants of all elements in List1. In Degree angle mode: In Gradian angle mode: In Radian angle mode: csc/() μ key csc/(Value1) ⇒ value csc/(List1) ⇒ list Returns the angle whose cosecant is Value1 or returns a list containing the inverse cosecants of each element of List1. Note: The result is returned as a degree, gradian or radian angle, according to the current angle mode setting. Note: You can insert this function from the keyboard by typing arccsc(...). In Degree angle mode: In Gradian angle mode: In Radian angle mode: csch() Catalog > csch(Value1) ⇒ value csch(List1) ⇒ list Returns the hyperbolic cosecant of Value1 or returns a list of the hyperbolic cosecants of all elements of List1. csch/() Catalog > csch/(Value) ⇒ value csch/(List1) ⇒ list Returns the inverse hyperbolic cosecant of Value1 or returns a list containing the inverse hyperbolic cosecants of each element of List1. Note: You can insert this function from the keyboard by typing arccsch(...).

25 CubicReg Catalog > CubicReg X, Y[, [Freq] [, Category, Include]] Computes the cubic polynomial regression y = a·x3+b· x2+c·x+d on lists X and Y with frequency Freq. A summary of results is stored in the stat.results variable. (See page 97.) All the lists must have equal dimension except for Include. X and Y are lists of independent and dependent variables. Freq is an optional list of frequency values. Each element in Freq specifies the frequency of occurrence for each corresponding X and Y data point. The default value is 1. All elements must be integers | 0. Category is a list of numeric or string category codes for the corresponding X and Y data. Include is a list of one or more of the category codes. Only those data items whose category code is included in this list are included in the calculation. For information on the effect of empty elements in a list, see “Empty (void) elements” on page 131. Output variable Description stat.RegEqn Regression equation: a·x3+b·x2+c·x+d stat.a, stat.b, stat.c, stat.d Regression coefficients stat.R2 Coefficient of determination stat.Resid Residuals from the regression stat.XReg List of data points in the modified X List actually used in the regression based on restrictions of Freq, Category List, and Include Categories stat.YReg List of data points in the modified Y List actually used in the regression based on restrictions of Freq, Category List, and Include Categories stat.FreqReg List of frequencies corresponding to stat.XReg and stat.YReg cumulativeSum() Catalog > cumulativeSum(List1) ⇒list Returns a list of the cumulative sums of the elements in List1, starting at element 1. cumulativeSum(Matrix1) ⇒matrix Returns a matrix of the cumulative sums of the elements in Matrix1. Each element is the cumulative sum of the column from top to bottom. An empty (void) element in List1 or Matrix1 produces a void element in the resulting list or matrix. For more information on empty elements, see page 131.

D Cycle Catalog > Cycle Transfers control immediately to the next iteration of the current loop (For, While, or Loop). Cycle is not allowed outside the three looping structures (For, While, or Loop). 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. Function listing that sums the integers from 1 to 100 skipping 50. 4Cylind Catalog > Vector 4Cylind Note: You can insert this operator from the computer keyboard by typing @>Cylind. Displays the row or column vector in cylindrical form [r,±q, z]. Vector must have exactly three elements. It can be either a row or a column. dbd() Catalog > dbd(date1,date2) ⇒value Returns the number of days between date1 and date2 using the actual-day-count method. date1 and date2 can be numbers or lists of numbers within the range of the dates on the standard calendar. If both date1 and date2 are lists, they must be the same length. date1 and date2 must be between the years 1950 through 2049. You can enter the dates in either of two formats. The decimal placement differentiates between the date formats. MM.DDYY (format used commonly in the United States) DDMM.YY (format use commonly in Europe)

27 4DD Catalog > Expr1 4DD ⇒value List1 4DD ⇒list Matrix1 4DD ⇒matrix Note: You can insert this operator from the computer keyboard by typing @>DD. Returns the decimal equivalent of the argument expressed in degrees. The argument is a number, list, or matrix that is interpreted by the Angle mode setting in gradians, radians or degrees. In Degree angle mode: In Gradian angle mode: In Radian angle mode: 4Decimal Catalog > Number1 4Decimal ⇒value List1 4Decimal ⇒value Matrix1 4Decimal ⇒value Note: You can insert this operator from the computer keyboard by typing @>Decimal. Displays the argument in decimal form. This operator can be used only at the end of the entry line. Define Catalog > Define Var = Expression Define Function(Param1, Param2, ...) = Expression Defines the variable Var or the user-defined function Function. Parameters, such as Param1, provide placeholders for passing arguments to the function. When calling a user-defined function, you must supply arguments (for example, values or variables) that correspond to the parameters. When called, the function evaluates Expression using the supplied arguments. Var and Function cannot be the name of a system variable or built-in function or command. Note: This form of Define is equivalent to executing the expression: expression & Function(Param1,Param2).

Define Function(Param1, Param2, ...) = Func Block EndFunc Define Program(Param1, Param2, ...) = Prgm Block EndPrgm In this form, the user-defined function or program can execute a block of multiple statements. Block can be either a single statement or a series of statements on separate lines. Block also can include expressions and instructions (such as If, Then, Else, and For). Note for entering the example: In the Calculator application on the handheld, you can enter multi-line definitions by pressing @ instead of · at the end of each line. On the computer keyboard, hold down Alt and press Enter. Note: See also Define LibPriv, page 28, and Define LibPub, page 28. Define LibPriv Catalog > Define LibPriv Var = Expression Define LibPriv Function(Param1, Param2, ...) = Expression Define LibPriv Function(Param1, Param2, ...) = Func Block EndFunc Define LibPriv Program(Param1, Param2, ...) = Prgm Block EndPrgm Operates the same as Define, except defines a private library variable, function, or program. Private functions and programs do not appear in the Catalog. Note: See also Define, page 27, and Define LibPub, page 28. Define LibPub Catalog > Define LibPub Var = Expression Define LibPub Function(Param1, Param2, ...) = Expression Define LibPub Function(Param1, Param2, ...) = Func Block EndFunc Define LibPub Program(Param1, Param2, ...) = Prgm Block EndPrgm Operates the same as Define, except defines a public library variable, function, or program. Public functions and programs appear in the Catalog after the library has been saved and refreshed. Note: See also Define, page 27, and Define LibPriv, page 28. Define Catalog >

29 deltaList() See @List(), page 55. DelVar Catalog > DelVar Var1[, Var2] [, Var3] ... DelVar Var. Deletes the specified variable or variable group from memory. If one or more of the variables are locked, this command displays an error message and deletes only the unlocked variables. See unLock, page 109. DelVar Var. deletes all members of the Var. variable group (such as the statistics stat.nn results or variables created using the LibShortcut() function). The dot (.) in this form of the DelVar command limits it to deleting a variable group; the simple variable Var is not affected. delVoid() Catalog > delVoid(List1) ⇒list Returns a list that has the contents of List1 with all empty (void) elements removed. For more information on empty elements, see page 131. det() Catalog > det(squareMatrix[, Tolerance]) ⇒expression Returns the determinant of squareMatrix. Optionally, any matrix element is treated as zero if its absolute value is less than Tolerance. This tolerance is used only if the matrix has floating-point entries and does not contain any symbolic variables that have not been assigned a value. Otherwise, Tolerance is ignored. • If you use /· or set the Auto or Approximate mode to Approximate, computations are done using floating- point arithmetic. • If Tolerance is omitted or not used, the default tolerance is calculated as: 5EM14 ·max(dim(squareMatrix))· rowNorm(squareMatrix)

diag() Catalog > diag(List) ⇒matrix diag(rowMatrix) ⇒matrix diag(columnMatrix) ⇒matrix Returns a matrix with the values in the argument list or matrix in its main diagonal. diag(squareMatrix) ⇒rowMatrix Returns a row matrix containing the elements from the main diagonal of squareMatrix. squareMatrix must be square. dim() Catalog > dim(List) ⇒integer Returns the dimension of List. dim(Matrix) ⇒list Returns the dimensions of matrix as a two-element list {rows, columns}. dim(String) ⇒integer Returns the number of characters contained in character string String. Disp Catalog > Disp [exprOrString1] [, exprOrString2] ... Displays the arguments in the Calculator history. The arguments are displayed in succession, with thin spaces as separators. Useful mainly in programs and functions to ensure the display of intermediate calculations. Note for entering the example: In the Calculator application on the handheld, you can enter multi-line definitions by pressing @ instead of · at the end of each line. On the computer keyboard, hold down Alt and press Enter.

31 E 4DMS Catalog > Value 4DMS List 4DMS Matrix 4DMS Note: You can insert this operator from the computer keyboard by typing @>DMS. Interprets the argument as an angle and displays the equivalent DMS (DDDDDD¡MM'SS.ss'') number. See ¡, ', '' on page 127 for DMS (degree, minutes, seconds) format. Note: 4DMS will convert from radians to degrees when used in radian mode. If the input is followed by a degree symbol ¡ , no conversion will occur. You can use 4DMS only at the end of an entry line. In Degree angle mode: dotP() Catalog > dotP(List1, List2) ⇒expression Returns the “dot” product of two lists. dotP(Vector1, Vector2) ⇒expression Returns the “dot” product of two vectors. Both must be row vectors, or both must be column vectors. e^() u key e^(Value1) ⇒value Returns e raised to the Value1 power. Note: See also e exponent template, page 2. Note: Pressing u to display e^( is different from pressing the character E on the keyboard. You can enter a complex number in rei q polar form. However, use this form in Radian angle mode only; it causes a Domain error in Degree or Gradian angle mode. e^(List1) ⇒list Returns e raised to the power of each element in List1. e^(squareMatrix1) ⇒squareMatrix Returns the matrix exponential of squareMatrix1. This is not the same as calculating e raised to the power of each element. For information about the calculation method, refer to cos(). squareMatrix1 must be diagonalizable. The result always contains floating-point numbers.

eff() Catalog > eff(nominalRate,CpY) ⇒value Financial function that converts the nominal interest rate nominalRate to an annual effective rate, given CpY as the number of compounding periods per year. nominalRate must be a real number, and CpY must be a real number > 0. Note: See also nom(), page 68. eigVc() Catalog > eigVc(squareMatrix) ⇒matrix Returns a matrix containing the eigenvectors for a real or complex squareMatrix, where each column in the result corresponds to an eigenvalue. Note that an eigenvector is not unique; it may be scaled by any constant factor. The eigenvectors are normalized, meaning that if V = [x1, x2, … , xn], then: x1 2 + x2 2 + … + xn 2 = 1 squareMatrix is first balanced with similarity transformations until the row and column norms are as close to the same value as possible. The squareMatrix is then reduced to upper Hessenberg form and the eigenvectors are computed via a Schur factorization. In Rectangular Complex Format: To see the entire result, press £ and then use ¡ and ¢ to move the cursor. eigVl() Catalog > eigVl(squareMatrix) ⇒list Returns a list of the eigenvalues of a real or complex squareMatrix. squareMatrix is first balanced with similarity transformations until the row and column norms are as close to the same value as possible. The squareMatrix is then reduced to upper Hessenberg form and the eigenvalues are computed from the upper Hessenberg matrix. In Rectangular complex format mode: To see the entire result, press £ and then use ¡ and ¢ to move the cursor. Else See If, page 45.

33 ElseIf Catalog > If BooleanExpr1 Then Block1 ElseIf BooleanExpr2 Then Block2 © ElseIf BooleanExprN Then BlockN EndIf © Note for entering the example: In the Calculator application on the handheld, you can enter multi-line definitions by pressing @ instead of · at the end of each line. On the computer keyboard, hold down Alt and press Enter. EndFor See For, page 38. EndFunc See Func, page 40. EndIf See If, page 45. EndLoop See Loop, page 60. EndPrgm See Prgm, page 76. EndTry See Try, page 105. EndWhile See While, page 111.

euler() Catalog > euler(Expr, Var, depVar, {Var0, VarMax}, depVar0, VarStep [, eulerStep]) ⇒matrix euler(SystemOfExpr, Var, ListOfDepVars, {Var0, VarMax}, ListOfDepVars0, VarStep [, eulerStep]) ⇒matrix euler(ListOfExpr, Var, ListOfDepVars, {Var0, VarMax}, ListOfDepVars0, VarStep [, eulerStep]) ⇒matrix Uses the Euler method to solve the system = Expr(Var, depVar) with depVar(Var0)=depVar0 on the interval [Var0,VarMax]. Returns a matrix whose first row defines the Var output values and whose second row defines the value of the first solution component at the corresponding Var values, and so on. Expr is the right-hand side that defines the ordinary differential equation (ODE). SystemOfExpr is the system of right-hand sides that define the system of ODEs (corresponds to order of dependent variables in ListOfDepVars). ListOfExpr is a list of right-hand sides that define the system of ODEs (corresponds to the order of dependent variables in ListOfDepVars). Var is the independent variable. ListOfDepVars is a list of dependent variables. {Var0, VarMax} is a two-element list that tells the function to integrate from Var0 to VarMax. ListOfDepVars0 is a list of initial values for dependent variables. VarStep is a nonzero number such that sign(VarStep) = sign(VarMax-Var0) and solutions are returned at Var0+i·VarStep for all i=0,1,2,… such that Var0+i·VarStep is in [var0,VarMax] (there may not be a solution value at VarMax). eulerStep is a positive integer (defaults to 1) that defines the number of euler steps between output values. The actual step size used by the euler method is VarStepàeulerStep. Differential equation: y'=0.001*y*(100-y) and y(0)=10 To see the entire result, press £ and then use ¡ and ¢ to move the cursor. System of equations: with y1(0)=2 and y2(0)=5 Exit Catalog > Exit Exits the current For, While, or Loop block. Exit is not allowed outside the three looping structures (For, While, or Loop). Note for entering the example: In the Calculator application on the handheld, you can enter multi-line definitions by pressing @ instead of · at the end of each line. On the computer keyboard, hold down Alt and press Enter. Function listing: depVar d Var d ----------------------

35 exp() u key exp(Value1) ⇒value Returns e raised to the Value1 power. Note: See also e exponent template, page 2. You can enter a complex number in rei q polar form. However, use this form in Radian angle mode only; it causes a Domain error in Degree or Gradian angle mode. exp(List1) ⇒list Returns e raised to the power of each element in List1. exp(squareMatrix1) ⇒squareMatrix Returns the matrix exponential of squareMatrix1. This is not the same as calculating e raised to the power of each element. For information about the calculation method, refer to cos(). squareMatrix1 must be diagonalizable. The result always contains floating-point numbers. expr() Catalog > expr(String) ⇒expression Returns the character string contained in String as an expression and immediately executes it. ExpReg Catalog > ExpReg X, Y [, [Freq] [, Category, Include]] Computes the exponential regression y = a·(b)x on lists X and Y with frequency Freq. A summary of results is stored in the stat.results variable. (See page 97.) All the lists must have equal dimension except for Include. X and Y are lists of independent and dependent variables. Freq is an optional list of frequency values. Each element in Freq specifies the frequency of occurrence for each corresponding X and Y data point. The default value is 1. All elements must be integers | 0. Category is a list of numeric or string category codes for the corresponding X and Y data. Include is a list of one or more of the category codes. Only those data items whose category code is included in this list are included in the calculation. For information on the effect of empty elements in a list, see “Empty (void) elements” on page 131. Output variable Description stat.RegEqn Regression equation: a·(b)x stat.a, stat.b Regression coefficients stat.r2 Coefficient of linear determination for transformed data stat.r Correlation coefficient for transformed data (x, ln(y))

F stat.Resid Residuals associated with the exponential model stat.ResidTrans Residuals associated with linear fit of transformed data stat.XReg List of data points in the modified X List actually used in the regression based on restrictions of Freq, Category List, and Include Categories stat.YReg List of data points in the modified Y List actually used in the regression based on restrictions of Freq, Category List, and Include Categories stat.FreqReg List of frequencies corresponding to stat.XReg and stat.YReg factor() Catalog > factor(rationalNumber) returns the rational number factored into primes. For composite numbers, the computing time grows exponentially with the number of digits in the second-largest factor. For example, factoring a 30-digit integer could take more than a day, and factoring a 100-digit number could take more than a century. To stop a calculation manually, • Windows®: Hold down the F12 key and press Enter repeatedly. • Macintosh®: Hold down the F5 key and press Enter repeatedly. • Handheld: Hold down the c key and press · repeatedly. If you merely want to determine if a number is prime, use isPrime() instead. It is much faster, particularly if rationalNumber is not prime and if the second-largest factor has more than five digits. FCdf() Catalog > FCdf(lowBound,upBound,dfNumer,dfDenom) ⇒number if lowBound and upBound are numbers, list if lowBound and upBound are lists FCdf(lowBound,upBound,dfNumer,dfDenom) ⇒number if lowBound and upBound are numbers, list if lowBound and upBound are lists Computes the F distribution probability between lowBound and upBound for the specified dfNumer (degrees of freedom) and dfDenom. For P(X { upBound), set lowBound = 0. Fill Catalog > Fill Value, matrixVar ⇒matrix Replaces each element in variable matrixVar with Value. matrixVar must already exist. Output variable Description

37 Fill Value, listVar ⇒list Replaces each element in variable listVar with Value. listVar must already exist. FiveNumSummary Catalog > FiveNumSummary X[,[Freq][,Category,Include]] Provides an abbreviated version of the 1-variable statistics on list X. A summary of results is stored in the stat.results variable. (See page 97.) X represents a list containing the data. Freq is an optional list of frequency values. Each element in Freq specifies the frequency of occurrence for each corresponding X and Y data point. The default value is 1. Category is a list of numeric category codes for the corresponding X data. Include is a list of one or more of the category codes. Only those data items whose category code is included in this list are included in the calculation. An empty (void) element in any of the lists X, Freq, or Category results in a void for the corresponding element of all those lists. For more information on empty elements, see page 131. Output variable Description stat.MinX Minimum of x values. stat.Q1X 1st Quartile of x. stat.MedianX Median of x. stat.Q3X 3rd Quartile of x. stat.MaxX Maximum of x values. floor() Catalog > floor(Value1) ⇒integer Returns the greatest integer that is { the argument. This function is identical to int(). The argument can be a real or a complex number. floor(List1) ⇒list floor(Matrix1) ⇒matrix Returns a list or matrix of the floor of each element. Note: See also ceiling() and int(). Fill Catalog >

For Catalog > For Var, Low, High [, Step] Block EndFor Executes the statements in Block iteratively for each value of Var, from Low to High, in increments of Step. Var must not be a system variable. Step can be positive or negative. The default value is 1. Block can be either a single statement or a series of statements separated with the “:” character. Note for entering the example: In the Calculator application on the handheld, you can enter multi-line definitions by pressing @ instead of · at the end of each line. On the computer keyboard, hold down Alt and press Enter. format() Catalog > format(Value[, formatString]) ⇒string Returns Value as a character string based on the format template. formatString is a string and must be in the form: “F[n]”, “S[n]”, “E[n]”, “G[n][c]”, where [ ] indicate optional portions. F[n]: Fixed format. n is the number of digits to display after the decimal point. S[n]: Scientific format. n is the number of digits to display after the decimal point. E[n]: Engineering format. n is the number of digits after the first significant digit. The exponent is adjusted to a multiple of three, and the decimal point is moved to the right by zero, one, or two digits. G[n][c]: Same as fixed format but also separates digits to the left of the radix into groups of three. c specifies the group separator character and defaults to a comma. If c is a period, the radix will be shown as a comma. [Rc]: Any of the above specifiers may be suffixed with the Rc radix flag, where c is a single character that specifies what to substitute for the radix point. fPart() Catalog > fPart(Expr1) ⇒expression fPart(List1) ⇒list fPart(Matrix1) ⇒matrix Returns the fractional part of the argument. For a list or matrix, returns the fractional parts of the elements. The argument can be a real or a complex number. FPdf() Catalog > FPdf(XVal,dfNumer,dfDenom) ⇒number if XVal is a number, list if XVal is a list Computes the F distribution probability at XVal for the specified dfNumer (degrees of freedom) and dfDenom.

39 freqTable4list() Catalog > freqTable4list(List1,freqIntegerList) ⇒list Returns a list containing the elements from List1 expanded according to the frequencies in freqIntegerList. This function can be used for building a frequency table for the Data & Statistics application. List1 can be any valid list. freqIntegerList must have the same dimension as List1 and must contain non-negative integer elements only. Each element specifies the number of times the corresponding List1 element will be repeated in the result list. A value of zero excludes the corresponding List1 element. Note: You can insert this function from the computer keyboard by typing freqTable@>list(...). Empty (void) elements are ignored. For more information on empty elements, see page 131. frequency() Catalog > frequency(List1,binsList) ⇒list Returns a list containing counts of the elements in List1. The counts are based on ranges (bins) that you define in binsList. If binsList is {b(1), b(2), …, b(n)}, the specified ranges are {?{b(1), b(1)?}. The resulting list is one element longer than binsList. Each element of the result corresponds to the number of elements from List1 that are in the range of that bin. Expressed in terms of the countIf() function, the result is { countIf(list, ?{b(1)), countIf(list, b(1)?)}. Elements of List1 that cannot be “placed in a bin” are ignored. Empty (void) elements are also ignored. For more information on empty elements, see page 131. Within the Lists & Spreadsheet application, you can use a range of cells in place of both arguments. Note: See also countIf(), page 23. Explanation of result: 2 elements from Datalist are {2.5 4 elements from Datalist are >2.5 and {4.5 3 elements from Datalist are >4.5 The element “hello” is a string and cannot be placed in any of the defined bins. FTest_2Samp Catalog > FTest_2Samp List1,List2[,Freq1[,Freq2[,Hypoth]]] FTest_2Samp List1,List2[,Freq1[,Freq2[,Hypoth]]] (Data list input) FTest_2Samp sx1,n1,sx2,n2[,Hypoth] FTest_2Samp sx1,n1,sx2,n2[,Hypoth] (Summary stats input) Performs a two-sample F test. A summary of results is stored in the stat.results variable. (See page 97.) For Ha: s1 > s2, set Hypoth>0 For Ha: s1 ƒ s2 (default), set Hypoth =0 For Ha: s1 < s2, set Hypoth<0 For information on the effect of empty elements in a list, see “Empty (void) elements” on page 131.

G Output variable Description stat.F Calculated F statistic for the data sequence stat.PVal Smallest level of significance at which the null hypothesis can be rejected stat.dfNumer numerator degrees of freedom = n1-1 stat.dfDenom denominator degrees of freedom = n2-1 stat.sx1, stat.sx2 Sample standard deviations of the data sequences in List 1 and List 2 stat.x1_bar stat.x2_bar Sample means of the data sequences in List 1 and List 2 stat.n1, stat.n2 Size of the samples Func Catalog > Func Block EndFunc Template for creating a user-defined function. Block can be a single statement, a series of statements separated with the “:” character, or a series of statements on separate lines. The function can use the Return instruction to return a specific result. Note for entering the example: In the Calculator application on the handheld, you can enter multi-line definitions by pressing @ instead of · at the end of each line. On the computer keyboard, hold down Alt and press Enter. Define a piecewise function: Result of graphing g(x) gcd() Catalog > gcd(Number1, Number2) ⇒expression Returns the greatest common divisor of the two arguments. The gcd of two fractions is the gcd of their numerators divided by the lcm of their denominators. In Auto or Approximate mode, the gcd of fractional floating-point numbers is 1.0. gcd(List1, List2) ⇒list Returns the greatest common divisors of the corresponding elements in List1 and List2. gcd(Matrix1, Matrix2) ⇒matrix Returns the greatest common divisors of the corresponding elements in Matrix1 and Matrix2.

41 geomCdf() Catalog > geomCdf(p,lowBound,upBound) ⇒number if lowBound and upBound are numbers, list if lowBound and upBound are lists geomCdf(p,upBound) for P(1{X{upBound) ⇒number if upBound is a number, list if upBound is a list Computes a cumulative geometric probability from lowBound to upBound with the specified probability of success p. For P(X { upBound), set lowBound = 1. geomPdf() Catalog > geomPdf(p,XVal) ⇒number if XVal is a number, list if XVal is a list Computes a probability at XVal, the number of the trial on which the first success occurs, for the discrete geometric distribution with the specified probability of success p. getDenom() Catalog > getDenom(Fraction1) ⇒value Transforms the argument into an expression having a reduced common denominator, and then returns its denominator. getLangInfo() Catalog > getLangInfo() ⇒string Returns a string that corresponds to the short name of the currently active language. You can, for example, use it in a program or function to determine the current language. English = “en” Danish = “da” German = “de” Finnish = “fi” French = “fr” Italian = “it” Dutch = “nl” Belgian Dutch = “nl_BE” Norwegian = “no” Portuguese = “pt” Spanish = “es” Swedish = “sv”

getLockInfo() Catalog > getLockInfo(Var) ⇒value Returns the current locked/unlocked state of variable Var. value =0: Var is unlocked or does not exist. value =1: Var is locked and cannot be modified or deleted. See Lock, page 57, and unLock, page 109. getMode() Catalog > getMode(ModeNameInteger) ⇒value getMode(0) ⇒list getMode(ModeNameInteger) returns a value representing the current setting of the ModeNameInteger mode. getMode(0) returns a list containing number pairs. Each pair consists of a mode integer and a setting integer. For a listing of the modes and their settings, refer to the table below. If you save the settings with getMode(0) & var, you can use setMode(var) in a function or program to temporarily restore the settings within the execution of the function or program only. See setMode(), page 90. Mode Name Mode Integer Setting Integers Display Digits 1 1=Float, 2=Float1, 3=Float2, 4=Float3, 5=Float4, 6=Float5, 7=Float6, 8=Float7, 9=Float8, 10=Float9, 11=Float10, 12=Float11, 13=Float12, 14=Fix0, 15=Fix1, 16=Fix2, 17=Fix3, 18=Fix4, 19=Fix5, 20=Fix6, 21=Fix7, 22=Fix8, 23=Fix9, 24=Fix10, 25=Fix11, 26=Fix12 Angle 2 1=Radian, 2=Degree, 3=Gradian Exponential Format 3 1=Normal, 2=Scientific, 3=Engineering Real or Complex 4 1=Real, 2=Rectangular, 3=Polar Auto or Approx. 5 1=Auto, 2=Approximate Vector Format 6 1=Rectangular, 2=Cylindrical, 3=Spherical Base 7 1=Decimal, 2=Hex, 3=Binary

43 getNum() Catalog > getNum(Fraction1) ⇒value Transforms the argument into an expression having a reduced common denominator, and then returns its numerator. getType() Catalog > getType(var) ⇒ string Returns a string that indicates the data type of variable var. If var has not been defined, returns the string "NONE". getVarInfo() Catalog > getVarInfo() ⇒matrix or string getVarInfo(LibNameString) ⇒matrix or string getVarInfo() returns a matrix of information (variable name, type, library accessibility, and locked/unlocked state) for all variables and library objects defined in the current problem. If no variables are defined, getVarInfo() returns the string "NONE". getVarInfo(LibNameString) returns a matrix of information for all library objects defined in library LibNameString. LibNameString must be a string (text enclosed in quotation marks) or a string variable. If the library LibNameString does not exist, an error occurs.

Note the example to the left, in which the result of getVarInfo() is assigned to variable vs. Attempting to display row 2 or row 3 of vs returns an “Invalid list or matrix” error because at least one of elements in those rows (variable b, for example) revaluates to a matrix. This error could also occur when using Ans to reevaluate a getVarInfo() result. The system gives the above error because the current version of the software does not support a generalized matrix structure where an element of a matrix can be either a matrix or a list. Goto Catalog > Goto labelName Transfers control to the label labelName. labelName must be defined in the same function using a Lbl instruction. Note for entering the example: In the Calculator application on the handheld, you can enter multi-line definitions by pressing @ instead of · at the end of each line. On the computer keyboard, hold down Alt and press Enter. 4Grad Catalog > Expr1 4 Grad ⇒expression Converts Expr1 to gradian angle measure. Note: You can insert this operator from the computer keyboard by typing @>Grad. In Degree angle mode: In Radian angle mode: getVarInfo() Catalog >

45 I identity() Catalog > identity(Integer) ⇒matrix Returns the identity matrix with a dimension of Integer. Integer must be a positive integer. If Catalog > If BooleanExpr Statement If BooleanExpr Then Block EndIf If BooleanExpr evaluates to true, executes the single statement Statement or the block of statements Block before continuing execution. If BooleanExpr evaluates to false, continues execution without executing the statement or block of statements. Block can be either a single statement or a sequence of statements separated with the “:” character. Note for entering the example: In the Calculator application on the handheld, you can enter multi-line definitions by pressing @ instead of · at the end of each line. On the computer keyboard, hold down Alt and press Enter. If BooleanExpr Then Block1 Else Block2 EndIf If BooleanExpr evaluates to true, executes Block1 and then skips Block2. If BooleanExpr evaluates to false, skips Block1 but executes Block2. Block1 and Block2 can be a single statement.

If BooleanExpr1 Then Block1 ElseIf BooleanExpr2 Then Block2 © ElseIf BooleanExprN Then BlockN EndIf Allows for branching. If BooleanExpr1 evaluates to true, executes Block1. If BooleanExpr1 evaluates to false, evaluates BooleanExpr2, and so on. ifFn() Catalog > ifFn(BooleanExpr,Value_If_true [,Value_If_false [,Value_If_unknown]]) ⇒expression, list, or matrix Evaluates the boolean expression BooleanExpr (or each element from BooleanExpr ) and produces a result based on the following rules: • BooleanExpr can test a single value, a list, or a matrix. • If an element of BooleanExpr evaluates to true, returns the corresponding element from Value_If_true. • If an element of BooleanExpr evaluates to false, returns the corresponding element from Value_If_false. If you omit Value_If_false, returns undef. • If an element of BooleanExpr is neither true nor false, returns the corresponding element Value_If_unknown. If you omit Value_If_unknown, returns undef. • If the second, third, or fourth argument of the ifFn() function is a single expression, the Boolean test is applied to every position in BooleanExpr. Note: If the simplified BooleanExpr statement involves a list or matrix, all other list or matrix arguments must have the same dimension(s), and the result will have the same dimension(s). Test value of 1 is less than 2.5, so its corresponding Value_If_True element of 5 is copied to the result list. Test value of 2 is less than 2.5, so its corresponding Value_If_True element of 6 is copied to the result list. Test value of 3 is not less than 2.5, so its corresponding Value_If_False element of 10 is copied to the result list. Value_If_true is a single value and corresponds to any selected position. Value_If_false is not specified. Undef is used. One element selected from Value_If_true. One element selected from Value_If_unknown. imag() Catalog > imag(Value1) ⇒value Returns the imaginary part of the argument. imag(List1) ⇒list Returns a list of the imaginary parts of the elements. If Catalog >

47 imag(Matrix1) ⇒matrix Returns a matrix of the imaginary parts of the elements. Indirection See #(), page 126. inString() Catalog > inString(srcString, subString[, Start]) ⇒integer Returns the character position in string srcString at which the first occurrence of string subString begins. Start, if included, specifies the character position within srcString where the search begins. Default = 1 (the first character of srcString). If srcString does not contain subString or Start is > the length of srcString, returns zero. int() Catalog > int(Value) ⇒integer int(List1) ⇒list int(Matrix1) ⇒matrix Returns the greatest integer that is less than or equal to the argument. This function is identical to floor(). The argument can be a real or a complex number. For a list or matrix, returns the greatest integer of each of the elements. intDiv() Catalog > intDiv(Number1, Number2) ⇒integer intDiv(List1, List2) ⇒list intDiv(Matrix1, Matrix2) ⇒matrix Returns the signed integer part of (Number1 ÷ Number2). For lists and matrices, returns the signed integer part of (argument 1 ÷ argument 2) for each element pair. imag() Catalog >

interpolate() Catalog > interpolate(xValue, xList, yList, yPrimeList) ⇒list This function does the following: Given xList, yList=f(xList), and yPrimeList=f'(xList) for some unknown function f, a cubic interpolant is used to approximate the function f at xValue. It is assumed that xList is a list of monotonically increasing or decreasing numbers, but this function may return a value even when it is not. This function walks through xList looking for an interval [xList[i], xList[i+1]] that contains xValue. If it finds such an interval, it returns an interpolated value for f(xValue); otherwise, it returns undef. xList, yList, and yPrimeList must be of equal dimension | 2 and contain expressions that simplify to numbers. xValue can be a number or a list of numbers. Differential equation: y'=-3·y+6·t+5 and y(0)=5 To see the entire result, press £ and then use ¡ and ¢ to move the cursor. Use the interpolate() function to calculate the function values for the xvaluelist: invc2() Catalog > invc2(Area,df) invChi2(Area,df) Computes the Inverse cumulative c2 (chi-square) probability function specified by degree of freedom, df for a given Area under the curve. invF() Catalog > invF(Area,dfNumer,dfDenom) invF(Area,dfNumer,dfDenom) computes the Inverse cumulative F distribution function specified by dfNumer and dfDenom for a given Area under the curve. invNorm() Catalog > invNorm(Area[,m[,s]]) Computes the inverse cumulative normal distribution function for a given Area under the normal distribution curve specified by m and s. invt() Catalog > invt(Area,df) Computes the inverse cumulative student-t probability function specified by degree of freedom, df for a given Area under the curve.

49 iPart() Catalog > iPart(Number) ⇒integer iPart(List1) ⇒list iPart(Matrix1) ⇒matrix Returns the integer part of the argument. For lists and matrices, returns the integer part of each element. The argument can be a real or a complex number. irr() Catalog > irr(CF0,CFList [,CFFreq]) ⇒value Financial function that calculates internal rate of return of an investment. CF0 is the initial cash flow at time 0; it must be a real number. CFList is a list of cash flow amounts after the initial cash flow CF0. CFFreq is an optional list in which each element specifies the frequency of occurrence for a grouped (consecutive) cash flow amount, which is the corresponding element of CFList. The default is 1; if you enter values, they must be positive integers < 10,000. Note: See also mirr(), page 63. isPrime() Catalog > isPrime(Number) ⇒Boolean constant expression Returns true or false to indicate if number is a whole number | 2 that is evenly divisible only by itself and 1. If Number exceeds about 306 digits and has no factors {1021, isPrime(Number) displays an error message. 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. Function to find the next prime after a specified number: isVoid() Catalog > isVoid(Var) ⇒Boolean constant expression isVoid(Expr) ⇒Boolean constant expression isVoid(List) ⇒list of Boolean constant expressions Returns true or false to indicate if the argument is a void data type. For more information on void elements, see page 131.

L Lbl Catalog > Lbl labelName Defines a label with the name labelName within a function. You can use a Goto labelName instruction to transfer control to the instruction immediately following the label. labelName must meet the same naming requirements as a variable name. Note for entering the example: In the Calculator application on the handheld, you can enter multi-line definitions by pressing @ instead of · at the end of each line. On the computer keyboard, hold down Alt and press Enter. lcm() Catalog > lcm(Number1, Number2) ⇒expression lcm(List1, List2) ⇒list lcm(Matrix1, Matrix2) ⇒matrix Returns the least common multiple of the two arguments. The lcm of two fractions is the lcm of their numerators divided by the gcd of their denominators. The lcm of fractional floating-point numbers is their product. For two lists or matrices, returns the least common multiples of the corresponding elements. left() Catalog > left(sourceString[, Num]) ⇒string Returns the leftmost Num characters contained in character string sourceString. If you omit Num, returns all of sourceString. left(List1[, Num]) ⇒list Returns the leftmost Num elements contained in List1. If you omit Num, returns all of List1. left(Comparison) ⇒expression Returns the left-hand side of an equation or inequality.

51 libShortcut() Catalog > libShortcut(LibNameString, ShortcutNameString [, LibPrivFlag]) ⇒list of variables Creates a variable group in the current problem that contains references to all the objects in the specified library document libNameString. Also adds the group members to the Variables menu. You can then refer to each object using its ShortcutNameString. Set LibPrivFlag=0 to exclude private library objects (default) Set LibPrivFlag=1 to include private library objects To copy a variable group, see CopyVar on page 18. To delete a variable group, see DelVar on page 29. This example assumes a properly stored and refreshed library document named linalg2 that contains objects defined as clearmat, gauss1, and gauss2. LinRegBx Catalog > LinRegBx X,Y[,[Freq][,Category,Include]] Computes the linear regression y = a+b·x on lists X and Y with frequency Freq. A summary of results is stored in the stat.results variable. (See page 97.) All the lists must have equal dimension except for Include. X and Y are lists of independent and dependent variables. Freq is an optional list of frequency values. Each element in Freq specifies the frequency of occurrence for each corresponding X and Y data point. The default value is 1. All elements must be integers | 0. Category is a list of numeric or string category codes for the corresponding X and Y data. Include is a list of one or more of the category codes. Only those data items whose category code is included in this list are included in the calculation. For information on the effect of empty elements in a list, see “Empty (void) elements” on page 131. Output variable Description stat.RegEqn Regression Equation: a+b·x stat.a, stat.b Regression coefficients stat.r2 Coefficient of determination stat.r Correlation coefficient stat.Resid Residuals from the regression stat.XReg List of data points in the modified X List actually used in the regression based on restrictions of Freq, Category List, and Include Categories stat.YReg List of data points in the modified Y List actually used in the regression based on restrictions of Freq, Category List, and Include Categories stat.FreqReg List of frequencies corresponding to stat.XReg and stat.YReg

LinRegMx Catalog > LinRegMx X,Y[,[Freq][,Category,Include]] Computes the linear regression y = m·x+b on lists X and Y with frequency Freq. A summary of results is stored in the stat.results variable. (See page 97.) All the lists must have equal dimension except for Include. X and Y are lists of independent and dependent variables. Freq is an optional list of frequency values. Each element in Freq specifies the frequency of occurrence for each corresponding X and Y data point. The default value is 1. All elements must be integers | 0. Category is a list of numeric or string category codes for the corresponding X and Y data. Include is a list of one or more of the category codes. Only those data items whose category code is included in this list are included in the calculation. For information on the effect of empty elements in a list, see “Empty (void) elements” on page 131. Output variable Description stat.RegEqn Regression Equation: y = m·x+b stat.m, stat.b Regression coefficients stat.r2 Coefficient of determination stat.r Correlation coefficient stat.Resid Residuals from the regression stat.XReg List of data points in the modified X List actually used in the regression based on restrictions of Freq, Category List, and Include Categories stat.YReg List of data points in the modified Y List actually used in the regression based on restrictions of Freq, Category List, and Include Categories stat.FreqReg List of frequencies corresponding to stat.XReg and stat.YReg LinRegtIntervals Catalog > LinRegtIntervals X,Y[,F[,0[,CLev]]] For Slope. Computes a level C confidence interval for the slope. LinRegtIntervals X,Y[,F[,1,Xval[,CLev]]] For Response. Computes a predicted y-value, a level C prediction interval for a single observation, and a level C confidence interval for the mean response. A summary of results is stored in the stat.results variable. (See page 97.) All the lists must have equal dimension. X and Y are lists of independent and dependent variables. F is an optional list of frequency values. Each element in F specifies the frequency of occurrence for each corresponding X and Y data point. The default value is 1. All elements must be integers | 0. For information on the effect of empty elements in a list, see “Empty (void) elements” on page 131.

53 For Slope type only For Response type only Output variable Description stat.RegEqn Regression Equation: a+b·x stat.a, stat.b Regression coefficients stat.df Degrees of freedom stat.r2 Coefficient of determination stat.r Correlation coefficient stat.Resid Residuals from the regression Output variable Description [stat.CLower, stat.CUpper] Confidence interval for the slope stat.ME Confidence interval margin of error stat.SESlope Standard error of slope stat.s Standard error about the line Output variable Description [stat.CLower, stat.CUpper] Confidence interval for the mean response stat.ME Confidence interval margin of error stat.SE Standard error of mean response [stat.LowerPred, stat.UpperPred] Prediction interval for a single observation stat.MEPred Prediction interval margin of error stat.SEPred Standard error for prediction stat.y a + b·XVal

LinRegtTest Catalog > LinRegtTest X,Y[,Freq[,Hypoth]] Computes a linear regression on the X and Y lists and a t test on the value of slope b and the correlation coefficient r for the equation y=a+bx. It tests the null hypothesis H0:b=0 (equivalently, r=0) against one of three alternative hypotheses. All the lists must have equal dimension. X and Y are lists of independent and dependent variables. Freq is an optional list of frequency values. Each element in Freq specifies the frequency of occurrence for each corresponding X and Y data point. The default value is 1. All elements must be integers | 0. Hypoth is an optional value specifying one of three alternative hypotheses against which the null hypothesis (H0:b=r=0) will be tested. For Ha: bƒ0 and rƒ0 (default), set Hypoth=0 For Ha: b<0 and r<0, set Hypoth<0 For Ha: b>0 and r>0, set Hypoth>0 A summary of results is stored in the stat.results variable. (See page 97.) For information on the effect of empty elements in a list, see “Empty (void) elements” on page 131. Output variable Description stat.RegEqn Regression equation: a + b·x stat.t t-Statistic for significance test stat.PVal Smallest level of significance at which the null hypothesis can be rejected stat.df Degrees of freedom stat.a, stat.b Regression coefficients stat.s Standard error about the line stat.SESlope Standard error of slope stat.r2 Coefficient of determination stat.r Correlation coefficient stat.Resid Residuals from the regression

55 linSolve() Catalog > linSolve( SystemOfLinearEqns, Var1, Var2, ...) ⇒list linSolve(LinearEqn1 and LinearEqn2 and ..., Var1, Var2, ...) ⇒list linSolve({LinearEqn1, LinearEqn2, ...}, Var1, Var2, ...) ⇒list linSolve(SystemOfLinearEqns, {Var1, Var2, ...}) ⇒list linSolve(LinearEqn1 and LinearEqn2 and ..., {Var1, Var2, ...}) ⇒list linSolve({LinearEqn1, LinearEgn2, ...}, {Var1, Var2, ...}) ⇒list Returns a list of solutions for the variables Var1, Var2, ... The first argument must evaluate to a system of linear equations or a single linear equation. Otherwise, an argument error occurs. For example, evaluating linSolve(x=1 and x=2,x) produces an “Argument Error” result. @List() Catalog > @List(List1) ⇒list Note: You can insert this function from the keyboard by typing deltaList(...). Returns a list containing the differences between consecutive elements in List1. Each element of List1 is subtracted from the next element of List1. The resulting list is always one element shorter than the original List1. list4mat() Catalog > list4mat(List [, elementsPerRow]) ⇒matrix Returns a matrix filled row-by-row with the elements from List. elementsPerRow, if included, specifies the number of elements per row. Default is the number of elements in List (one row). If List does not fill the resulting matrix, zeros are added. Note: You can insert this function from the computer keyboard by typing list@>mat(...). ln() /u keys ln(Value1) ⇒value ln(List1) ⇒list Returns the natural logarithm of the argument. For a list, returns the natural logarithms of the elements. If complex format mode is Real: If complex format mode is Rectangular:

ln(squareMatrix1) ⇒squareMatrix Returns the matrix natural logarithm of squareMatrix1. This is not the same as calculating the natural logarithm of each element. For information about the calculation method, refer to cos() on. squareMatrix1 must be diagonalizable. The result always contains floating-point numbers. In Radian angle mode and Rectangular complex format: To see the entire result, press £ and then use ¡ and ¢ to move the cursor. LnReg Catalog > LnReg X, Y[, [Freq] [, Category, Include]] Computes the logarithmic regression y = a+b·ln(x) on lists X and Y with frequency Freq. A summary of results is stored in the stat.results variable. (See page 97.) All the lists must have equal dimension except for Include. X and Y are lists of independent and dependent variables. Freq is an optional list of frequency values. Each element in Freq specifies the frequency of occurrence for each corresponding X and Y data point. The default value is 1. All elements must be integers | 0. Category is a list of numeric or string category codes for the corresponding X and Y data. Include is a list of one or more of the category codes. Only those data items whose category code is included in this list are included in the calculation. For information on the effect of empty elements in a list, see “Empty (void) elements” on page 131. Output variable Description stat.RegEqn Regression equation: a+b·ln(x) stat.a, stat.b Regression coefficients stat.r2 Coefficient of linear determination for transformed data stat.r Correlation coefficient for transformed data (ln(x), y) stat.Resid Residuals associated with the logarithmic model stat.ResidTrans Residuals associated with linear fit of transformed data stat.XReg List of data points in the modified X List actually used in the regression based on restrictions of Freq, Category List, and Include Categories stat.YReg List of data points in the modified Y List actually used in the regression based on restrictions of Freq, Category List, and Include Categories stat.FreqReg List of frequencies corresponding to stat.XReg and stat.YReg ln() /u keys

57 Local Catalog > Local Var1[, Var2] [, Var3] ... Declares the specified vars as local variables. Those variables exist only during evaluation of a function and are deleted when the function finishes execution. Note: Local variables save memory because they only exist temporarily. Also, they do not disturb any existing global variable values. Local variables must be used for For loops and for temporarily saving values in a multi-line function since modifications on global variables are not allowed in a function. Note for entering the example: In the Calculator application on the handheld, you can enter multi-line definitions by pressing @ instead of · at the end of each line. On the computer keyboard, hold down Alt and press Enter. Lock Catalog > Lock Var1[, Var2] [, Var3] ... Lock Var. Locks the specified variables or variable group. Locked variables cannot be modified or deleted. You cannot lock or unlock the system variable Ans, and you cannot lock the system variable groups stat. or tvm. Note: The Lock command clears the Undo/Redo history when applied to unlocked variables. See unLock, page 109, and getLockInfo(), page 42.

log() /s keys log(Value1[,Value2]) ⇒value log(List1[,Value2]) ⇒list Returns the base-Value2 logarithm of the first argument. Note: See also Log template, page 2. For a list, returns the base-Value2 logarithm of the elements. If the second argument is omitted, 10 is used as the base. If complex format mode is Real: If complex format mode is Rectangular: log(squareMatrix1[,Value]) ⇒squareMatrix Returns the matrix base-Value logarithm of squareMatrix1. This is not the same as calculating the base-Value logarithm of each element. For information about the calculation method, refer to cos(). squareMatrix1 must be diagonalizable. The result always contains floating-point numbers. If the base argument is omitted, 10 is used as base. In Radian angle mode and Rectangular complex format: To see the entire result, press £ and then use ¡ and ¢ to move the cursor. Logistic Catalog > Logistic X, Y[, [Freq] [, Category, Include]] Computes the logistic regression y = (c/(1+a·e-bx)) on lists X and Y with frequency Freq. A summary of results is stored in the stat.results variable. (See page 97.) All the lists must have equal dimension except for Include. X and Y are lists of independent and dependent variables. Freq is an optional list of frequency values. Each element in Freq specifies the frequency of occurrence for each corresponding X and Y data point. The default value is 1. All elements must be integers | 0. Category is a list of numeric or string category codes for the corresponding X and Y data. Include is a list of one or more of the category codes. Only those data items whose category code is included in this list are included in the calculation. For information on the effect of empty elements in a list, see “Empty (void) elements” on page 131.

59 Output variable Description stat.RegEqn Regression equation: c/(1+a·e-bx) stat.a, stat.b, stat.c Regression coefficients stat.Resid Residuals from the regression stat.XReg List of data points in the modified X List actually used in the regression based on restrictions of Freq, Category List, and Include Categories stat.YReg List of data points in the modified Y List actually used in the regression based on restrictions of Freq, Category List, and Include Categories stat.FreqReg List of frequencies corresponding to stat.XReg and stat.YReg LogisticD Catalog > LogisticD X, Y [ , [Iterations] , [Freq] [, Category, Include] ] Computes the logistic regression y = (c/(1+a·e-bx)+d) on lists X and Y with frequency Freq, using a specified number of Iterations. A summary of results is stored in the stat.results variable. (See page 97.) All the lists must have equal dimension except for Include. X and Y are lists of independent and dependent variables. Freq is an optional list of frequency values. Each element in Freq specifies the frequency of occurrence for each corresponding X and Y data point. The default value is 1. All elements must be integers | 0. Category is a list of numeric or string category codes for the corresponding X and Y data. Include is a list of one or more of the category codes. Only those data items whose category code is included in this list are included in the calculation. For information on the effect of empty elements in a list, see “Empty (void) elements” on page 131. Output variable Description stat.RegEqn Regression equation: c/(1+a·e-bx)+d) stat.a, stat.b, stat.c, stat.d Regression coefficients stat.Resid Residuals from the regression stat.XReg List of data points in the modified X List actually used in the regression based on restrictions of Freq, Category List, and Include Categories stat.YReg List of data points in the modified Y List actually used in the regression based on restrictions of Freq, Category List, and Include Categories stat.FreqReg List of frequencies corresponding to stat.XReg and stat.YReg

M Loop Catalog > Loop Block EndLoop Repeatedly executes the statements in Block. Note that the loop will be executed endlessly, unless a Goto or Exit instruction is executed within Block. Block is a sequence of statements separated with the “:” character. Note for entering the example: In the Calculator application on the handheld, you can enter multi-line definitions by pressing @ instead of · at the end of each line. On the computer keyboard, hold down Alt and press Enter. LU Catalog > LU Matrix, lMatrix, uMatrix, pMatrix[,Tol] Calculates the Doolittle LU (lower-upper) decomposition of a real or complex matrix. The lower triangular matrix is stored in lMatrix, the upper triangular matrix in uMatrix, and the permutation matrix (which describes the row swaps done during the calculation) in pMatrix. lMatrix · uMatrix = pMatrix · matrix Optionally, any matrix element is treated as zero if its absolute value is less than Tol. This tolerance is used only if the matrix has floating- point entries and does not contain any symbolic variables that have not been assigned a value. Otherwise, Tol is ignored. • If you use /· or set the Auto or Approximate mode to Approximate, computations are done using floating- point arithmetic. • If Tol is omitted or not used, the default tolerance is calculated as: 5EM14 ·max(dim(Matrix)) ·rowNorm(Matrix) The LU factorization algorithm uses partial pivoting with row interchanges. mat4list() Catalog > mat4list(Matrix) ⇒list Returns a list filled with the elements in Matrix. The elements are copied from Matrix row by row. Note: You can insert this function from the computer keyboard by typing mat@>list(...).

61 max() Catalog > max(Value1, Value2) ⇒expression max(List1, List2) ⇒list max(Matrix1, Matrix2) ⇒matrix Returns the maximum of the two arguments. If the arguments are two lists or matrices, returns a list or matrix containing the maximum value of each pair of corresponding elements. max(List) ⇒expression Returns the maximum element in list. max(Matrix1) ⇒matrix Returns a row vector containing the maximum element of each column in Matrix1. Empty (void) elements are ignored. For more information on empty elements, see page 131. Note: See also min(). mean() Catalog > mean(List[, freqList]) ⇒expression Returns the mean of the elements in List. Each freqList element counts the number of consecutive occurrences of the corresponding element in List. mean(Matrix1[, freqMatrix]) ⇒matrix Returns a row vector of the means of all the columns in Matrix1. Each freqMatrix element counts the number of consecutive occurrences of the corresponding element in Matrix1. Empty (void) elements are ignored. For more information on empty elements, see page 131. In Rectangular vector format: median() Catalog > median(List[, freqList]) ⇒expression Returns the median of the elements in List. Each freqList element counts the number of consecutive occurrences of the corresponding element in List.

median(Matrix1[, freqMatrix]) ⇒matrix Returns a row vector containing the medians of the columns in Matrix1. Each freqMatrix element counts the number of consecutive occurrences of the corresponding element in Matrix1. Notes: • All entries in the list or matrix must simplify to numbers. • Empty (void) elements in the list or matrix are ignored. For more information on empty elements, see page 131. MedMed Catalog > MedMed X,Y [, Freq] [, Category, Include]] Computes the median-median line y = (m·x+b) on lists X and Y with frequency Freq. A summary of results is stored in the stat.results variable. (See page 97.) All the lists must have equal dimension except for Include. X and Y are lists of independent and dependent variables. Freq is an optional list of frequency values. Each element in Freq specifies the frequency of occurrence for each corresponding X and Y data point. The default value is 1. All elements must be integers | 0. Category is a list of numeric or string category codes for the corresponding X and Y data. Include is a list of one or more of the category codes. Only those data items whose category code is included in this list are included in the calculation. For information on the effect of empty elements in a list, see “Empty (void) elements” on page 131. Output variable Description stat.RegEqn Median-median line equation: m·x+b stat.m, stat.b Model coefficients stat.Resid Residuals from the median-median line stat.XReg List of data points in the modified X List actually used in the regression based on restrictions of Freq, Category List, and Include Categories stat.YReg List of data points in the modified Y List actually used in the regression based on restrictions of Freq, Category List, and Include Categories stat.FreqReg List of frequencies corresponding to stat.XReg and stat.YReg mid() Catalog > mid(sourceString, Start[, Count]) ⇒string Returns Count characters from character string sourceString, beginning with character number Start. If Count is omitted or is greater than the dimension of sourceString, returns all characters from sourceString, beginning with character number Start. Count must be | 0. If Count = 0, returns an empty string. median() Catalog >

63 mid(sourceList, Start [, Count]) ⇒list Returns Count elements from sourceList, beginning with element number Start. If Count is omitted or is greater than the dimension of sourceList, returns all elements from sourceList, beginning with element number Start. Count must be | 0. If Count = 0, returns an empty list. mid(sourceStringList, Start[, Count]) ⇒list Returns Count strings from the list of strings sourceStringList, beginning with element number Start. min() Catalog > min(Value1, Value2) ⇒expression min(List1, List2) ⇒list min(Matrix1, Matrix2) ⇒matrix Returns the minimum of the two arguments. If the arguments are two lists or matrices, returns a list or matrix containing the minimum value of each pair of corresponding elements. min(List) ⇒expression Returns the minimum element of List. min(Matrix1) ⇒matrix Returns a row vector containing the minimum element of each column in Matrix1. Note: See also max(). mirr() Catalog > mirr(financeRate,reinvestRate,CF0,CFList[,CFFreq]) Financial function that returns the modified internal rate of return of an investment. financeRate is the interest rate that you pay on the cash flow amounts. reinvestRate is the interest rate at which the cash flows are reinvested. CF0 is the initial cash flow at time 0; it must be a real number. CFList is a list of cash flow amounts after the initial cash flow CF0. CFFreq is an optional list in which each element specifies the frequency of occurrence for a grouped (consecutive) cash flow amount, which is the corresponding element of CFList. The default is 1; if you enter values, they must be positive integers < 10,000. Note: See also irr(), page 49. mid() Catalog >

mod() Catalog > mod(Value1, Value2) ⇒expression mod(List1, List2) ⇒list mod(Matrix1, Matrix2) ⇒matrix Returns the first argument modulo the second argument as defined by the identities: mod(x,0) = x mod(x,y) = x - y floor(x/y) When the second argument is non-zero, the result is periodic in that argument. The result is either zero or has the same sign as the second argument. If the arguments are two lists or two matrices, returns a list or matrix containing the modulo of each pair of corresponding elements. Note: See also remain(), page 83 mRow() Catalog > mRow(Value, Matrix1, Index) ⇒matrix Returns a copy of Matrix1 with each element in row Index of Matrix1 multiplied by Value. mRowAdd() Catalog > mRowAdd(Value, Matrix1, Index1, Index2) ⇒matrix Returns a copy of Matrix1 with each element in row Index2 of Matrix1 replaced with: Value · row Index1 + row Index2 MultReg Catalog > MultReg Y, X1[,X2[,X3,…[,X10]]] Calculates multiple linear regression of list Y on lists X1, X2, …, X10. A summary of results is stored in the stat.results variable. (See page 97.) All the lists must have equal dimension. For information on the effect of empty elements in a list, see “Empty (void) elements” on page 131. Output variable Description stat.RegEqn Regression Equation: b0+b1·x1+b2·x2+ ... stat.b0, stat.b1, ... Regression coefficients stat.R2 Coefficient of multiple determination stat.yList yList = b0+b1·x1+ ... stat.Resid Residuals from the regression

65 Outputs MultRegIntervals Catalog > MultRegIntervals Y, X1[,X2[,X3,…[,X10]]],XValList[,CLevel] Computes a predicted y-value, a level C prediction interval for a single observation, and a level C confidence interval for the mean response. A summary of results is stored in the stat.results variable. (See page 97.) All the lists must have equal dimension. For information on the effect of empty elements in a list, see “Empty (void) elements” on page 131. Output variable Description stat.RegEqn Regression Equation: b0+b1·x1+b2·x2+ ... stat.y A point estimate: y = b0 + b1 · xl + ... for XValList stat.dfError Error degrees of freedom stat.CLower, stat.CUpper Confidence interval for a mean response stat.ME Confidence interval margin of error stat.SE Standard error of mean response stat.LowerPred, stat.UpperrPred Prediction interval for a single observation stat.MEPred Prediction interval margin of error stat.SEPred Standard error for prediction stat.bList List of regression coefficients, {b0,b1,b2,...} stat.Resid Residuals from the regression MultRegTests Catalog > MultRegTests Y, X1[,X2[,X3,…[,X10]]] Multiple linear regression test computes a multiple linear regression on the given data and provides the global F test statistic and t test statistics for the coefficients. A summary of results is stored in the stat.results variable. (See page 97.) For information on the effect of empty elements in a list, see “Empty (void) elements” on page 131. Output variable Description stat.RegEqn Regression Equation: b0+b1·x1+b2·x2+ ... stat.F Global F test statistic stat.PVal P-value associated with global F statistic stat.R2 Coefficient of multiple determination

N stat.AdjR2 Adjusted coefficient of multiple determination stat.s Standard deviation of the error stat.DW Durbin-Watson statistic; used to determine whether first-order auto correlation is present in the model stat.dfReg Regression degrees of freedom stat.SSReg Regression sum of squares stat.MSReg Regression mean square stat.dfError Error degrees of freedom stat.SSError Error sum of squares stat.MSError Error mean square stat.bList {b0,b1,...} List of coefficients stat.tList List of t statistics, one for each coefficient in the bList stat.PList List P-values for each t statistic stat.SEList List of standard errors for coefficients in bList stat.yList yList = b0+b1·x1+ . . . stat.Resid Residuals from the regression stat.sResid Standardized residuals; obtained by dividing a residual by its standard deviation stat.CookDist Cook’s distance; measure of the influence of an observation based on the residual and leverage stat.Leverage Measure of how far the values of the independent variable are from their mean values nCr() Catalog > nCr(Value1, Value2) ⇒expression For integer Value1 and Value2 with Value1 | Value2 | 0, nCr() is the number of combinations of Value1 things taken Value2 at a time. (This is also known as a binomial coefficient.) nCr(Value, 0) ⇒1 nCr(Value, negInteger) ⇒0 nCr(Value, posInteger) ⇒ Value·(ValueN1)... (ValueNposInteger+1)/ posInteger! nCr(Value, nonInteger) ⇒expression!/ ((ValueNnonInteger)!·nonInteger!) nCr(List1, List2) ⇒list Returns a list of combinations based on the corresponding element pairs in the two lists. The arguments must be the same size list. nCr(Matrix1, Matrix2) ⇒matrix Returns a matrix of combinations based on the corresponding element pairs in the two matrices. The arguments must be the same size matrix. Output variable Description

67 nDerivative() Catalog > nDerivative(Expr1,Var=Value[,Order]) ⇒value nDerivative(Expr1,Var[,Order]) | Var=Value ⇒value Returns the numerical derivative calculated using auto differentiation methods. When Value is specified, it overrides any prior variable assignment or any current “with” substitution for the variable. If the variable Var does not contain a numeric value, you must provide Value. Order of the derivative must be 1 or 2. Note: The nDerivative() algorithm has a limitiation: it works recursively through the unsimplified expression, computing the numeric value of the first derivative (and second, if applicable) and the evaluation of each subexpression, which may lead to an unexpected result. Consider the example on the right. The first derivative of x·(x^2+x)^(1/3) at x=0 is equal to 0. However, because the first derivative of the subexpression (x^2+x)^(1/3) is undefined at x=0, and this value is used to calculate the derivative of the total expression, nDerivative() reports the result as undefined and displays a warning message. If you encounter this limitation, verify the solution graphically. You can also try using centralDiff(). newList() Catalog > newList(numElements) ⇒list Returns a list with a dimension of numElements. Each element is zero. newMat() Catalog > newMat(numRows, numColumns) ⇒matrix Returns a matrix of zeros with the dimension numRows by numColumns. nfMax() Catalog > nfMax(Expr, Var) ⇒value nfMax(Expr, Var, lowBound) ⇒value nfMax(Expr, Var, lowBound, upBound) ⇒value nfMax(Expr, Var) | lowBound

nfMin() Catalog > nfMin(Expr, Var) ⇒value nfMin(Expr, Var, lowBound) ⇒value nfMin(Expr, Var, lowBound, upBound) ⇒value nfMin(Expr, Var) | lowBound nInt(Expr1, Var, Lower, Upper) ⇒expression If the integrand Expr1 contains no variable other than Var, and if Lower and Upper are constants, positive ˆ, or negative ˆ, then nInt() returns an approximation of ‰(Expr1, Var, Lower, Upper). This approximation is a weighted average of some sample values of the integrand in the interval Lower nom(effectiveRate,CpY) ⇒value Financial function that converts the annual effective interest rate effectiveRate to a nominal rate, given CpY as the number of compounding periods per year. effectiveRate must be a real number, and CpY must be a real number > 0. Note: See also eff(), page 32. norm() Catalog > norm(Matrix) ⇒expression norm(Vector) ⇒expression Returns the Frobenius norm.

69 normCdf() Catalog > normCdf(lowBound,upBound[,m[,s]]) ⇒number if lowBound and upBound are numbers, list if lowBound and upBound are lists Computes the normal distribution probability between lowBound and upBound for the specified m (default=0) and s (default=1). For P(X { upBound), set lowBound = .9E999. normPdf() Catalog > normPdf(XVal[,m[,s]]) ⇒number if XVal is a number, list if XVal is a list Computes the probability density function for the normal distribution at a specified XVal value for the specified m and s. not Catalog > not BooleanExpr ⇒Boolean expression Returns true, false, or a simplified form of the argument. not Integer1 ⇒integer Returns the one’s complement of a real integer. Internally, Integer1 is converted to a signed, 64-bit binary number. The value of each bit is flipped (0 becomes 1, and vice versa) for the one’s complement. Results are displayed according to the Base mode. You can enter the integer in any number base. For a binary or hexadecimal entry, you must use the 0b or 0h prefix, respectively. Without a prefix, the integer is treated as decimal (base 10). 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 12. In Hex base mode: In Bin base mode: To see the entire result, press £ and then use ¡ and ¢ to move the cursor. Note: A binary entry can have up to 64 digits (not counting the 0b prefix). A hexadecimal entry can have up to 16 digits. nPr() Catalog > nPr(Value1, Value2) ⇒expression For integer Value1 and Value2 with Value1 | Value2 | 0, nPr() is the number of permutations of Value1 things taken Value2 at a time. nPr(Value, 0) ⇒1 nPr(Value, negInteger) ⇒ 1/((Value+1)·(Value+2)... (ValueNnegInteger)) nPr(Value, posInteger) ⇒ Value·(ValueN1)... (ValueNposInteger+1) nPr(Value, nonInteger) ⇒Value! / (ValueNnonInteger)! nPr(List1, List2) ⇒list Returns a list of permutations based on the corresponding element pairs in the two lists. The arguments must be the same size list. Important: Zero, not the letter O.

nPr(Matrix1, Matrix2) ⇒matrix Returns a matrix of permutations based on the corresponding element pairs in the two matrices. The arguments must be the same size matrix. npv() Catalog > npv(InterestRate,CFO,CFList[,CFFreq]) Financial function that calculates net present value; the sum of the present values for the cash inflows and outflows. A positive result for npv indicates a profitable investment. InterestRate is the rate by which to discount the cash flows (the cost of money) over one period. CF0 is the initial cash flow at time 0; it must be a real number. CFList is a list of cash flow amounts after the initial cash flow CF0. CFFreq is a list in which each element specifies the frequency of occurrence for a grouped (consecutive) cash flow amount, which is the corresponding element of CFList. The default is 1; if you enter values, they must be positive integers < 10,000. nSolve() Catalog > nSolve(Equation,Var[=Guess]) ⇒number or error_string nSolve(Equation,Var[=Guess],lowBound) ⇒number or error_string nSolve(Equation,Var[=Guess],lowBound,upBound) ⇒number or error_string nSolve(Equation,Var[=Guess]) | lowBound

71 O OneVar Catalog > OneVar [1,]X[,[Freq][,Category,Include]] OneVar [n,]X1,X2[X3[,…[,X20]]] Calculates 1-variable statistics on up to 20 lists. A summary of results is stored in the stat.results variable. (See page 97.) All the lists must have equal dimension except for Include. Freq is an optional list of frequency values. Each element in Freq specifies the frequency of occurrence for each corresponding X and Y data point. The default value is 1. All elements must be integers | 0. Category is a list of numeric category codes for the corresponding X values. Include is a list of one or more of the category codes. Only those data items whose category code is included in this list are included in the calculation. An empty (void) element in any of the lists X, Freq, or Category results in a void for the corresponding element of all those lists. An empty element in any of the lists X1 through X20 results in a void for the corresponding element of all those lists. For more information on empty elements, see page 131. Output variable Description stat.v Mean of x values stat.Gx Sum of x values stat.Gx2 Sum of x2 values stat.sx Sample standard deviation of x stat.sx Population standard deviation of x stat.n Number of data points stat.MinX Minimum of x values stat.Q1X 1st Quartile of x stat.MedianX Median of x stat.Q3X 3rd Quartile of x stat.MaxX Maximum of x values stat.SSX Sum of squares of deviations from the mean of x

P or Catalog > BooleanExpr1 or BooleanExpr2 ⇒Boolean expression Returns true or false or a simplified form of the original entry. Returns true if either or both expressions simplify to true. Returns false only if both expressions evaluate to false. Note: See xor. Note for entering the example: In the Calculator application on the handheld, you can enter multi-line definitions by pressing @ instead of · at the end of each line. On the computer keyboard, hold down Alt and press Enter. Integer1 or Integer2 ⇒integer Compares two real integers bit-by-bit using an or operation. Internally, both integers are converted to signed, 64-bit binary numbers. When corresponding bits are compared, the result is 1 if either bit is 1; the result is 0 only if both bits are 0. The returned value represents the bit results, and is displayed according to the Base mode. You can enter the integers in any number base. For a binary or hexadecimal entry, you must use the 0b or 0h prefix, respectively. Without a prefix, integers are treated as decimal (base 10). 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 12. Note: See xor. In Hex base mode: Important: Zero, not the letter O. In Bin base mode: Note: A binary entry can have up to 64 digits (not counting the 0b prefix). A hexadecimal entry can have up to 16 digits. ord() Catalog > ord(String) ⇒integer ord(List1) ⇒list Returns the numeric code of the first character in character string String, or a list of the first characters of each list element. P4Rx() Catalog > P4Rx(rExpr, qExpr) ⇒expression P4Rx(rList, qList) ⇒list P4Rx(rMatrix, qMatrix) ⇒matrix Returns the equivalent x-coordinate of the (r, q) pair. Note: The q argument is interpreted as either a degree, gradian or radian angle, according to the current angle mode. If the argument is an expression, you can use ¡, G or R to override the angle mode setting temporarily. Note: You can insert this function from the computer keyboard by typing P@>Rx(...). In Radian angle mode:

73 P4Ry() Catalog > P4Ry(rValue, qValue) ⇒value P4Ry(rList, qList) ⇒list P4Ry(rMatrix, qMatrix) ⇒matrix Returns the equivalent y-coordinate of the (r, q) pair. Note: The q argument is interpreted as either a degree, radian or gradian angle, according to the current angle mode.¡R Note: You can insert this function from the computer keyboard by typing P@>Ry(...). In Radian angle mode: PassErr Catalog > PassErr Passes an error to the next level. If system variable errCode is zero, PassErr does not do anything. The Else clause of the Try...Else...EndTry block should use ClrErr or PassErr. If the error is to be processed or ignored, use ClrErr. If what to do with the error is not known, use PassErr to send it to the next error handler. If there are no more pending Try...Else...EndTry error handlers, the error dialog box will be displayed as normal. Note: See also ClrErr, page 17, and Try, page 105. Note for entering the example: In the Calculator application on the handheld, you can enter multi-line definitions by pressing @ instead of · at the end of each line. On the computer keyboard, hold down Alt and press Enter. For an example of PassErr, See Example 2 under the Try command, page 105. piecewise() Catalog > piecewise(Expr1 [, Cond1 [, Expr2 [, Cond2 [, … ]]]]) Returns definitions for a piecewise function in the form of a list. You can also create piecewise definitions by using a template. Note: See also Piecewise template, page 2. poissCdf() Catalog > poissCdf(l,lowBound,upBound) ⇒number if lowBound and upBound are numbers, list if lowBound and upBound are lists poissCdf(l,upBound) for P(0{X{upBound) ⇒number if upBound is a number, list if upBound is a list Computes a cumulative probability for the discrete Poisson distribution with specified mean l. For P(X { upBound), set lowBound=0 poissPdf() Catalog > poissPdf(l,XVal) ⇒number if XVal is a number, list if XVal is a list Computes a probability for the discrete Poisson distribution with the specified mean l.

4Polar Catalog > Vector 4Polar Note: You can insert this operator from the computer keyboard by typing @>Polar. Displays vector in polar form [r ±q]. The vector must be of dimension 2 and can be a row or a column. Note: 4Polar is a display-format instruction, not a conversion function. You can use it only at the end of an entry line, and it does not update ans. Note: See also 4Rect, page 81. complexValue 4Polar Displays complexVector in polar form. • Degree angle mode returns (r±q). • Radian angle mode returns reiq. complexValue can have any complex form. However, an reiq entry causes an error in Degree angle mode. Note: You must use the parentheses for an (r±q) polar entry. In Radian angle mode: In Gradian angle mode: In Degree angle mode: polyEval() Catalog > polyEval(List1, Expr1) ⇒expression polyEval(List1, List2) ⇒expression Interprets the first argument as the coefficient of a descending-degree polynomial, and returns the polynomial evaluated for the value of the second argument. polyRoots() Catalog > polyRoots(Poly,Var) ⇒list polyRoots(ListOfCoeffs) ⇒list The first syntax, polyRoots(Poly,Var), returns a list of real roots of polynomial Poly with respect to variable Var. If no real roots exist, returns an empty list: { }. Poly must be a polynomial in expanded form in one variable. Do not use unexpanded forms such as y2·y+1 or x·x+2·x+1 The second syntax, polyRoots(ListOfCoeffs), returns a list of real roots for the coefficients in ListOfCoeffs. Note: See also cPolyRoots(), page 23.

75 PowerReg Catalog > PowerReg X,Y [, Freq] [, Category, Include]] Computes the power regression y = (a·(x)b) on lists X and Y with frequency Freq. A summary of results is stored in the stat.results variable. (See page 97.) All the lists must have equal dimension except for Include. X and Y are lists of independent and dependent variables. Freq is an optional list of frequency values. Each element in Freq specifies the frequency of occurrence for each corresponding X and Y data point. The default value is 1. All elements must be integers | 0. Category is a list of numeric or string category codes for the corresponding X and Y data. Include is a list of one or more of the category codes. Only those data items whose category code is included in this list are included in the calculation. For information on the effect of empty elements in a list, see “Empty (void) elements” on page 131. Output variable Description stat.RegEqn Regression equation: a·(x)b stat.a, stat.b Regression coefficients stat.r2 Coefficient of linear determination for transformed data stat.r Correlation coefficient for transformed data (ln(x), ln(y)) stat.Resid Residuals associated with the power model stat.ResidTrans Residuals associated with linear fit of transformed data stat.XReg List of data points in the modified X List actually used in the regression based on restrictions of Freq, Category List, and Include Categories stat.YReg List of data points in the modified Y List actually used in the regression based on restrictions of Freq, Category List, and Include Categories stat.FreqReg List of frequencies corresponding to stat.XReg and stat.YReg

Prgm Catalog > Prgm Block EndPrgm Template for creating a user-defined program. Must be used with the Define, Define LibPub, or Define LibPriv command. Block can be a single statement, a series of statements separated with the “:” character, or a series of statements on separate lines. Note for entering the example: In the Calculator application on the handheld, you can enter multi-line definitions by pressing @ instead of · at the end of each line. On the computer keyboard, hold down Alt and press Enter. Calculate GCD and display intermediate results. prodSeq() See Π(), page 124. Product (PI) See Π(), page 124. product() Catalog > product(List[, Start[, End]]) ⇒expression Returns the product of the elements contained in List. Start and End are optional. They specify a range of elements. product(Matrix1[, Start[, End]]) ⇒matrix Returns a row vector containing the products of the elements in the columns of Matrix1. Start and end are optional. They specify a range of rows. Empty (void) elements are ignored. For more information on empty elements, see page 131.

77 Q propFrac() Catalog > propFrac(Value1[, Var]) ⇒value propFrac(rational_number) returns rational_number as the sum of an integer and a fraction having the same sign and a greater denominator magnitude than numerator magnitude. propFrac(rational_expression,Var) returns the sum of proper ratios and a polynomial with respect to Var. The degree of Var in the denominator exceeds the degree of Var in the numerator in each proper ratio. Similar powers of Var are collected. The terms and their factors are sorted with Var as the main variable. If Var is omitted, a proper fraction expansion is done with respect to the most main variable. The coefficients of the polynomial part are then made proper with respect to their most main variable first and so on. You can use the propFrac() function to represent mixed fractions and demonstrate addition and subtraction of mixed fractions. QR Catalog > QR Matrix, qMatrix, rMatrix[, Tol] Calculates the Householder QR factorization of a real or complex matrix. The resulting Q and R matrices are stored to the specified Matrix. The Q matrix is unitary. The R matrix is upper triangular. Optionally, any matrix element is treated as zero if its absolute value is less than Tol. This tolerance is used only if the matrix has floating- point entries and does not contain any symbolic variables that have not been assigned a value. Otherwise, Tol is ignored. • If you use /· or set the Auto or Approximate mode to Approximate, computations are done using floating- point arithmetic. • If Tol is omitted or not used, the default tolerance is calculated as: 5EL14 ·max(dim(Matrix)) ·rowNorm(Matrix) The floating-point number (9.) in m1 causes results to be calculated in floating-point form. The QR factorization is computed numerically using Householder transformations. The symbolic solution is computed using Gram- Schmidt. The columns in qMatName are the orthonormal basis vectors that span the space defined by matrix.

QuadReg Catalog > QuadReg X,Y [, Freq] [, Category, Include]] Computes the quadratic polynomial regression y = a·x2+b·x+c on lists X and Y with frequency Freq. A summary of results is stored in the stat.results variable. (See page 97.) All the lists must have equal dimension except for Include. X and Y are lists of independent and dependent variables. Freq is an optional list of frequency values. Each element in Freq specifies the frequency of occurrence for each corresponding X and Y data point. The default value is 1. All elements must be integers | 0. Category is a list of numeric or string category codes for the corresponding X and Y data. Include is a list of one or more of the category codes. Only those data items whose category code is included in this list are included in the calculation. For information on the effect of empty elements in a list, see “Empty (void) elements” on page 131. Output variable Description stat.RegEqn Regression equation: a·x2+b·x+c stat.a, stat.b, stat.c Regression coefficients stat.R2 Coefficient of determination stat.Resid Residuals from the regression stat.XReg List of data points in the modified X List actually used in the regression based on restrictions of Freq, Category List, and Include Categories stat.YReg List of data points in the modified Y List actually used in the regression based on restrictions of Freq, Category List, and Include Categories stat.FreqReg List of frequencies corresponding to stat.XReg and stat.YReg QuartReg Catalog > QuartReg X,Y [, Freq] [, Category, Include]] Computes the quartic polynomial regression y = a·x4+b·x3+c· x2+d·x+e on lists X and Y with frequency Freq. A summary of results is stored in the stat.results variable. (See page 97.) All the lists must have equal dimension except for Include. X and Y are lists of independent and dependent variables. Freq is an optional list of frequency values. Each element in Freq specifies the frequency of occurrence for each corresponding X and Y data point. The default value is 1. All elements must be integers | 0. Category is a list of numeric or string category codes for the corresponding X and Y data. Include is a list of one or more of the category codes. Only those data items whose category code is included in this list are included in the calculation. For information on the effect of empty elements in a list, see “Empty (void) elements” on page 131.

79 R Output variable Description stat.RegEqn Regression equation: a·x4+b·x3+c· x2+d·x+e stat.a, stat.b, stat.c, stat.d, stat.e Regression coefficients stat.R2 Coefficient of determination stat.Resid Residuals from the regression stat.XReg List of data points in the modified X List actually used in the regression based on restrictions of Freq, Category List, and Include Categories stat.YReg List of data points in the modified Y List actually used in the regression based on restrictions of Freq, Category List, and Include Categories stat.FreqReg List of frequencies corresponding to stat.XReg and stat.YReg R4Pq() Catalog > R4Pq (xValue, yValue) ⇒value R4Pq (xList, yList) ⇒list R4Pq (xMatrix, yMatrix) ⇒matrix Returns the equivalent q-coordinate of the (x,y) pair arguments. Note: The result is returned as a degree, gradian or radian angle, according to the current angle mode setting. Note: You can insert this function from the computer keyboard by typing R@>Ptheta(...). In Degree angle mode: In Gradian angle mode: In Radian angle mode: R4Pr() Catalog > R4Pr (xValue, yValue) ⇒value R4Pr (xList, yList) ⇒list R4Pr (xMatrix, yMatrix) ⇒matrix Returns the equivalent r-coordinate of the (x,y) pair arguments. Note: You can insert this function from the computer keyboard by typing R@>Pr(...). In Radian angle mode:

4Rad Catalog > Value14Rad ⇒value Converts the argument to radian angle measure. Note: You can insert this operator from the computer keyboard by typing @>Rad. In Degree angle mode: In Gradian angle mode: rand() Catalog > rand() ⇒expression rand(#Trials) ⇒list rand() returns a random value between 0 and 1. rand(#Trials) returns a list containing #Trials random values between 0 and 1. randBin() Catalog > randBin(n, p) ⇒expression randBin(n, p, #Trials) ⇒list randBin(n, p) returns a random real number from a specified Binomial distribution. randBin(n, p, #Trials) returns a list containing #Trials random real numbers from a specified Binomial distribution. randInt() Catalog > randInt(lowBound,upBound) ⇒expression randInt(lowBound,upBound ,#Trials) ⇒list randInt(lowBound,upBound) returns a random integer within the range specified by lowBound and upBound integer bounds. randInt(lowBound,upBound ,#Trials) returns a list containing #Trials random integers within the specified range. randMat() Catalog > randMat(numRows, numColumns) ⇒matrix Returns a matrix of integers between -9 and 9 of the specified dimension. Both arguments must simplify to integers. Note: The values in this matrix will change each time you press ·. randNorm() Catalog > randNorm(m, s) ⇒expression randNorm(m, s, #Trials) ⇒list randNorm(m, s) returns a decimal number from the specified normal distribution. It could be any real number but will be heavily concentrated in the interval [mN3·s, m+3·s]. randNorm(m, s, #Trials) returns a list containing #Trials decimal numbers from the specified normal distribution. Sets the random-number seed.

81 randPoly() Catalog > randPoly(Var, Order) ⇒expression Returns a polynomial in Var of the specified Order. The coefficients are random integers in the range L9 through 9. The leading coefficient will not be zero. Order must be 0–99. randSamp() Catalog > randSamp(List,#Trials[,noRepl]) ⇒list Returns a list containing a random sample of #Trials trials from List with an option for sample replacement (noRepl=0), or no sample replacement (noRepl=1). The default is with sample replacement. RandSeed Catalog > RandSeed Number If Number = 0, sets the seeds to the factory defaults for the random- number generator. If Number ƒ 0, it is used to generate two seeds, which are stored in system variables seed1 and seed2. real() Catalog > real(Value1) ⇒value Returns the real part of the argument. real(List1) ⇒list Returns the real parts of all elements. real(Matrix1) ⇒matrix Returns the real parts of all elements. 4Rect Catalog > Vector 4Rect Note: You can insert this operator from the computer keyboard by typing @>Rect. Displays Vector in rectangular form [x, y, z]. The vector must be of dimension 2 or 3 and can be a row or a column. Note: 4Rect is a display-format instruction, not a conversion function. You can use it only at the end of an entry line, and it does not update ans. Note: See also 4Polar, page 74.

complexValue 4Rect Displays complexValue in rectangular form a+bi. The complexValue can have any complex form. However, an reiq entry causes an error in Degree angle mode. Note: You must use parentheses for an (r±q) polar entry. In Radian angle mode: In Gradian angle mode: In Degree angle mode: Note: To type ±, select it from the symbol list in the Catalog. ref() Catalog > ref(Matrix1[, Tol]) ⇒matrix Returns the row echelon form of Matrix1. Optionally, any matrix element is treated as zero if its absolute value is less than Tol. This tolerance is used only if the matrix has floating- point entries and does not contain any symbolic variables that have not been assigned a value. Otherwise, Tol is ignored. • If you use /· or set the Auto or Approximate mode to Approximate, computations are done using floating- point arithmetic. • If Tol is omitted or not used, the default tolerance is calculated as: 5EL14 ·max(dim(Matrix1)) ·rowNorm(Matrix1) Avoid undefined elements in Matrix1. They can lead to unexpected results. For example, if a is undefined in the following expression, a warning message appears and the result is shown as: The warning appears because the generalized element 1/a would not be valid for a=0. You can avoid this by storing a value to a beforehand or by using the “|” substitution mechanism, as shown in the following example. Note: See also rref(), page 87. 4Rect Catalog >

83 remain() Catalog > remain(Value1, Value2) ⇒value remain(List1, List2) ⇒list remain(Matrix1, Matrix2) ⇒matrix Returns the remainder of the first argument with respect to the second argument as defined by the identities: remain(x,0)  x remain(x,y)  xNy·iPart(x/y) As a consequence, note that remain(Nx,y)  Nremain(x,y). The result is either zero or it has the same sign as the first argument. Note: See also mod(), page 64. Request Catalog > Request promptString, var[, DispFlag [, statusVar]] Request promptString, func(arg1, ...argn) [, DispFlag [, statusVar]] Programming command: Pauses the program and displays a dialog box containing the message promptString and an input box for the user’s response. When the user types a response and clicks OK, the contents of the input box are assigned to variable var. If the user clicks Cancel, the program proceeds without accepting any input. The program uses the previous value of var if var was already defined. The optional DispFlag argument can be any expression. • If DispFlag is omitted or evaluates to 1, the prompt message and user’s response are displayed in the Calculator history. • If DispFlag evaluates to 0, the prompt and response are not displayed in the history. Define a program: Define request_demo()=Prgm Request “Radius: ”,r Disp “Area = “,pi*r2 EndPrgm Run the program and type a response: request_demo() Result after selecting OK: Radius: 6/2 Area= 28.2743 The optional statusVar argument gives the program a way to determine how the user dismissed the dialog box. Note that statusVar requires the DispFlag argument. • If the user clicked OK or pressed Enter or Ctrl+Enter, variable statusVar is set to a value of 1. • Otherwise, variable statusVar is set to a value of 0. The func() argument allows a program to store the user’s response as a function definition. This syntax operates as if the user executed the command: Define func(arg1, ...argn) = user’s response The program can then use the defined function func(). The promptString should guide the user to enter an appropriate user’s response that completes the function definition. Note: You can use the Request command within a user-defined program but not within a function. To stop a program that contains a Request command inside an infinite loop: • Windows®: Hold down the F12 key and press Enter repeatedly. • Macintosh®: Hold down the F5 key and press Enter repeatedly. • Handheld: Hold down the c key and press · repeatedly. Note: See also RequestStr, page 84. Define a program: Define polynomial()=Prgm Request "Enter a polynomial in x:",p(x) Disp "Real roots are:",polyRoots(p(x),x) EndPrgm Run the program and type a response: polynomial() Result after selecting OK: Enter a polynomial in x: x^3+3x+1 Real roots are: {-0.322185}

RequestStr Catalog > RequestStr promptString, var[, DispFlag] Programming command: Operates identically to the first syntax of the Request command, except that the user’s response is always interpreted as a string. By contrast, the Request command interprets the response as an expression unless the user encloses it in quotation marks (““). Note: You can use the RequestStr command within a user- defined program but not within a function. To stop a program that contains a RequestStr command inside an infinite loop: • Windows®: Hold down the F12 key and press Enter repeatedly. • Macintosh®: Hold down the F5 key and press Enter repeatedly. • Handheld: Hold down the c key and press · repeatedly. Note: See also Request, page 83. Define a program: Define requestStr_demo()=Prgm RequestStr “Your name:”,name,0 Disp “Response has “,dim(name),” characters.” EndPrgm Run the program and type a response: requestStr_demo() 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. Return Catalog > Return [Expr] Returns Expr as the result of the function. Use within a Func...EndFunc block. Note: Use Return without an argument within a Prgm...EndPrgm block to exit a program. Note for entering the example: In the Calculator application on the handheld, you can enter multi-line definitions by pressing @ instead of · at the end of each line. On the computer keyboard, hold down Alt and press Enter. right() Catalog > right(List1[, Num]) ⇒list Returns the rightmost Num elements contained in List1. If you omit Num, returns all of List1. right(sourceString[, Num]) ⇒string Returns the rightmost Num characters contained in character string sourceString. If you omit Num, returns all of sourceString. right(Comparison) ⇒expression Returns the right side of an equation or inequality.

85 rk23() Catalog > rk23(Expr, Var, depVar, {Var0, VarMax}, depVar0, VarStep [, diftol]) ⇒matrix rk23(SystemOfExpr, Var, ListOfDepVars, {Var0, VarMax}, ListOfDepVars0, VarStep [, diftol]) ⇒matrix rk23(ListOfExpr, Var, ListOfDepVars, {Var0, VarMax}, ListOfDepVars0, VarStep [, diftol]) ⇒matrix Uses the Runge-Kutta method to solve the system = Expr(Var, depVar) with depVar(Var0)=depVar0 on the interval [Var0,VarMax]. Returns a matrix whose first row defines the Var output values as defined by VarStep. The second row defines the value of the first solution component at the corresponding Var values, and so on. Expr is the right hand side that defines the ordinary differential equation (ODE). SystemOfExpr is a system of right-hand sides that define the system of ODEs (corresponds to order of dependent variables in ListOfDepVars). ListOfExpr is a list of right-hand sides that define the system of ODEs (corresponds to order of dependent variables in ListOfDepVars). Var is the independent variable. ListOfDepVars is a list of dependent variables. {Var0, VarMax} is a two-element list that tells the function to integrate from Var0 to VarMax. ListOfDepVars0 is a list of initial values for dependent variables. If VarStep evaluates to a nonzero number: sign(VarStep) = sign(VarMax-Var0) and solutions are returned at Var0+i*VarStep for all i=0,1,2,… such that Var0+i*VarStep is in [var0,VarMax] (may not get a solution value at VarMax). if VarStep evaluates to zero, solutions are returned at the "Runge- Kutta" Var values. diftol is the error tolerance (defaults to 0.001). Differential equation: y'=0.001*y*(100-y) and y(0)=10 To see the entire result, press £ and then use ¡ and ¢ to move the cursor. Same equation with diftol set to 1.E•6 System of equations: with y1(0)=2 and y2(0)=5 root() Catalog > root(Value) ⇒ root root(Value1, Value2) ⇒ root root(Value) returns the square root of Value. root(Value1, Value2) returns the Value2 root of Value1. Value1 can be a real or complex floating point constant or an integer or complex rational constant. Note: See also Nth root template, page 1. rotate() Catalog > rotate(Integer1[,#ofRotations]) ⇒integer Rotates the bits in a binary integer. You can enter Integer1 in any number base; it is converted automatically to a signed, 64-bit binary form. If the magnitude of Integer1 is too large for this form, a symmetric modulo operation brings it within the range. For more information, see 4Base2, page 12. In Bin base mode: To see the entire result, press £ and then use ¡ and ¢ to move the cursor. depVar d Var d ----------------------

If #ofRotations is positive, the rotation is to the left. If #ofRotations is negative, the rotation is to the right. The default is L1 (rotate right one bit). For example, in a right rotation: In Hex base mode: Each bit rotates right. 0b00000000000001111010110000110101 Rightmost bit rotates to leftmost. produces: 0b10000000000000111101011000011010 The result is displayed according to the Base mode. Important: To enter a binary or hexadecimal number, always use the 0b or 0h prefix (zero, not the letter O). rotate(List1[,#ofRotations]) ⇒list Returns a copy of List1 rotated right or left by #of Rotations elements. Does not alter List1. If #ofRotations is positive, the rotation is to the left. If #of Rotations is negative, the rotation is to the right. The default is L1 (rotate right one element). In Dec base mode: rotate(String1[,#ofRotations]) ⇒string Returns a copy of String1 rotated right or left by #ofRotations characters. Does not alter String1. If #ofRotations is positive, the rotation is to the left. If #ofRotations is negative, the rotation is to the right. The default is L1 (rotate right one character). round() Catalog > round(Value1[, digits]) ⇒value Returns the argument rounded to the specified number of digits after the decimal point. digits must be an integer in the range 0–12. If digits is not included, returns the argument rounded to 12 significant digits. Note: Display digits mode may affect how this is displayed. round(List1[, digits]) ⇒list Returns a list of the elements rounded to the specified number of digits. round(Matrix1[, digits]) ⇒matrix Returns a matrix of the elements rounded to the specified number of digits. rowAdd() Catalog > rowAdd(Matrix1, rIndex1, rIndex2) ⇒matrix Returns a copy of Matrix1 with row rIndex2 replaced by the sum of rows rIndex1 and rIndex2. rotate() Catalog >

87 rowDim() Catalog > rowDim(Matrix) ⇒expression Returns the number of rows in Matrix. Note: See also colDim(), page 17. rowNorm() Catalog > rowNorm(Matrix) ⇒expression Returns the maximum of the sums of the absolute values of the elements in the rows in Matrix. Note: All matrix elements must simplify to numbers. See also colNorm(), page 17. rowSwap() Catalog > rowSwap(Matrix1, rIndex1, rIndex2) ⇒matrix Returns Matrix1 with rows rIndex1 and rIndex2 exchanged. rref() Catalog > rref(Matrix1[, Tol]) ⇒matrix Returns the reduced row echelon form of Matrix1. Optionally, any matrix element is treated as zero if its absolute value is less than Tol. This tolerance is used only if the matrix has floating- point entries and does not contain any symbolic variables that have not been assigned a value. Otherwise, Tol is ignored. • If you use /· or set the Auto or Approximate mode to Approximate, computations are done using floating- point arithmetic. • If Tol is omitted or not used, the default tolerance is calculated as: 5EL14 ·max(dim(Matrix1)) ·rowNorm(Matrix1) Note: See also ref(), page 82.

S sec() μ key sec(Value1) ⇒ value sec(List1) ⇒ list Returns the secant of Value1 or returns a list containing the secants of all elements in List1. Note: The argument is interpreted as a degree, gradian or radian angle, according to the current angle mode setting. You can use ¡, G, or R to override the angle mode temporarily. In Degree angle mode: sec/() μ key sec/(Value1) ⇒ value sec/(List1) ⇒ list Returns the angle whose secant is Value1 or returns a list containing the inverse secants of each element of List1. Note: The result is returned as a degree, gradian or radian angle, according to the current angle mode setting. Note: You can insert this function from the keyboard by typing arcsec(...). In Degree angle mode: In Gradian angle mode: In Radian angle mode: sech() Catalog > sech(Value1) ⇒ value sech(List1) ⇒ list Returns the hyperbolic secant of Value1 or returns a list containing the hyperbolic secants of the List1 elements. sech/() Catalog > sech/(Value1) ⇒ value sech/ (List1) ⇒ list Returns the inverse hyperbolic secant of Value1 or returns a list containing the inverse hyperbolic secants of each element of List1. Note: You can insert this function from the keyboard by typing arcsech(...). In Radian angle and Rectangular complex mode:

89 seq() Catalog > seq(Expr, Var, Low, High[, Step]) ⇒list Increments Var from Low through High by an increment of Step, evaluates Expr, and returns the results as a list. The original contents of Var are still there after seq() is completed. The default value for Step = 1. Press Ctrl+Enter /· (Macintosh®: “+Enter) to evaluate: seqGen() Catalog > seqGen(Expr, Var, depVar, {Var0, VarMax}[, ListOfInitTerms [, VarStep [, CeilingValue]]]) ⇒list Generates a list of terms for sequence depVar(Var)=Expr as follows: Increments independent variable Var from Var0 through VarMax by VarStep, evaluates depVar(Var) for corresponding values of Var using the Expr formula and ListOfInitTerms, and returns the results as a list. seqGen(ListOrSystemOfExpr, Var, ListOfDepVars, {Var0, VarMax} [, MatrixOfInitTerms [, VarStep [, CeilingValue]]]) ⇒matrix Generates a matrix of terms for a system (or list) of sequences ListOfDepVars(Var)=ListOrSystemOfExpr as follows: Increments independent variable Var from Var0 through VarMax by VarStep, evaluates ListOfDepVars(Var) for corresponding values of Var using ListOrSystemOfExpr formula and MatrixOfInitTerms, and returns the results as a matrix. The original contents of Var are unchanged after seqGen() is completed. The default value for VarStep = 1. Generate the first 5 terms of the sequence u(n) = u(n-1)2/2, with u(1)=2 and VarStep=1. Example in which Var0=2: System of two sequences: Note: The Void (_) in the initial term matrix above is used to indicate that the initial term for u1(n) is calculated using the explicit sequence formula u1(n)=1/n.

seqn() Catalog > seqn(Expr(u, n [, ListOfInitTerms[, nMax [, CeilingValue]]]) ⇒list Generates a list of terms for a sequence u(n)=Expr(u, n) as follows: Increments n from 1 through nMax by 1, evaluates u(n) for corresponding values of n using the Expr(u, n) formula and ListOfInitTerms, and returns the results as a list. seqn(Expr(n [, nMax [, CeilingValue]]) ⇒list Generates a list of terms for a non-recursive sequence u(n)=Expr(n) as follows: Increments n from 1 through nMax by 1, evaluates u(n) for corresponding values of n using the Expr(n) formula, and returns the results as a list. If nMax is missing, nMax is set to 2500 If nMax=0, nMax is set to 2500 Note: seqn() calls seqGen( ) with n0=1 and nstep =1 Generate the first 6 terms of the sequence u(n) = u(n-1)/2, with u(1)=2. setMode() Catalog > setMode(modeNameInteger, settingInteger) ⇒ integer setMode(list) ⇒ integer list Valid only within a function or program. setMode(modeNameInteger, settingInteger) temporarily sets mode modeNameInteger to the new setting settingInteger, and returns an integer corresponding to the original setting of that mode. The change is limited to the duration of the program/ function’s execution. modeNameInteger specifies which mode you want to set. It must be one of the mode integers from the table below. settingInteger specifies the new setting for the mode. It must be one of the setting integers listed below for the specific mode you are setting. setMode(list) lets you change multiple settings. list contains pairs of mode integers and setting integers. setMode(list) returns a similar list whose integer pairs represent the original modes and settings. If you have saved all mode settings with getMode(0) & var, you can use setMode(var) to restore those settings until the function or program exits. See getMode(), page 42. Note: The current mode settings are passed to called subroutines. If any subroutine changes a mode setting, the mode change will be lost when control returns to the calling routine. Note for entering the example: In the Calculator application on the handheld, you can enter multi-line definitions by pressing @ instead of · at the end of each line. On the computer keyboard, hold down Alt and press Enter. Display approximate value of p using the default setting for Display Digits, and then display p with a setting of Fix2. Check to see that the default is restored after the program executes. Mode Name Mode Integer Setting Integers Display Digits 1 1=Float, 2=Float1, 3=Float2, 4=Float3, 5=Float4, 6=Float5, 7=Float6, 8=Float7, 9=Float8, 10=Float9, 11=Float10, 12=Float11, 13=Float12, 14=Fix0, 15=Fix1, 16=Fix2, 17=Fix3, 18=Fix4, 19=Fix5, 20=Fix6, 21=Fix7, 22=Fix8, 23=Fix9, 24=Fix10, 25=Fix11, 26=Fix12 Angle 2 1=Radian, 2=Degree, 3=Gradian

91 Exponential Format 3 1=Normal, 2=Scientific, 3=Engineering Real or Complex 4 1=Real, 2=Rectangular, 3=Polar Auto or Approx. 5 1=Auto, 2=Approximate Vector Format 6 1=Rectangular, 2=Cylindrical, 3=Spherical Base 7 1=Decimal, 2=Hex, 3=Binary shift() Catalog > shift(Integer1[,#ofShifts]) ⇒integer Shifts the bits in a binary integer. You can enter Integer1 in any number base; it is converted automatically to a signed, 64-bit binary form. If the magnitude of Integer1 is too large for this form, a symmetric modulo operation brings it within the range. For more information, see 4Base2, page 12. If #ofShifts is positive, the shift is to the left. If #ofShifts is negative, the shift is to the right. The default is L1 (shift right one bit). In a right shift, the rightmost bit is dropped and 0 or 1 is inserted to match the leftmost bit. In a left shift, the leftmost bit is dropped and 0 is inserted as the rightmost bit. For example, in a right shift: Each bit shifts right. 0b0000000000000111101011000011010 Inserts 0 if leftmost bit is 0, or 1 if leftmost bit is 1. produces: 0b00000000000000111101011000011010 The result is displayed according to the Base mode. Leading zeros are not shown. In Bin base mode: In Hex base mode: Important: To enter a binary or hexadecimal number, always use the 0b or 0h prefix (zero, not the letter O). shift(List1 [,#ofShifts]) ⇒list Returns a copy of List1 shifted right or left by #ofShifts elements. Does not alter List1. If #ofShifts is positive, the shift is to the left. If #ofShifts is negative, the shift is to the right. The default is L1 (shift right one element). Elements introduced at the beginning or end of list by the shift are set to the symbol “undef”. In Dec base mode: shift(String1 [,#ofShifts]) ⇒string Returns a copy of String1 shifted right or left by #ofShifts characters. Does not alter String1. If #ofShifts is positive, the shift is to the left. If #ofShifts is negative, the shift is to the right. The default is L1 (shift right one character). Characters introduced at the beginning or end of string by the shift are set to a space. Mode Name Mode Integer Setting Integers

sign() Catalog > sign(Value1) ⇒value sign(List1) ⇒list sign(Matrix1) ⇒matrix For real and complex Value1, returns Value1 / abs(Value1) when Value1 ƒ 0. Returns 1 if Value1 is positive. Returns L1 if Value1 is negative. sign(0) returns „1 if the complex format mode is Real; otherwise, it returns itself. sign(0) represents the unit circle in the complex domain. For a list or matrix, returns the signs of all the elements. If complex format mode is Real: simult() Catalog > simult(coeffMatrix, constVector[, Tol]) ⇒matrix Returns a column vector that contains the solutions to a system of linear equations. Note: See also linSolve(), page 55. coeffMatrix must be a square matrix that contains the coefficients of the equations. constVector must have the same number of rows (same dimension) as coeffMatrix and contain the constants. Optionally, any matrix element is treated as zero if its absolute value is less than Tol. This tolerance is used only if the matrix has floating- point entries and does not contain any symbolic variables that have not been assigned a value. Otherwise, Tol is ignored. • If you set the Auto or Approximate mode to Approximate, computations are done using floating-point arithmetic. • If Tol is omitted or not used, the default tolerance is calculated as: 5EL14 ·max(dim(coeffMatrix)) ·rowNorm(coeffMatrix) Solve for x and y: x + 2y = 1 3x + 4y = L1 The solution is x=L3 and y=2. Solve: ax + by = 1 cx + dy = 2 simult(coeffMatrix, constMatrix[, Tol]) ⇒matrix Solves multiple systems of linear equations, where each system has the same equation coefficients but different constants. Each column in constMatrix must contain the constants for a system of equations. Each column in the resulting matrix contains the solution for the corresponding system. Solve: x + 2y = 1 3x + 4y = L1 x + 2y = 2 3x + 4y = L3 For the first system, x=L3 and y=2. For the second system, x=L7 and y=9/2.

93 sin() μ key sin(Value1) ⇒value sin(List1) ⇒list sin(Value1) returns the sine of the argument. sin(List1) returns a list of the sines of all elements in List1. Note: The argument is interpreted as a degree, gradian or radian angle, according to the current angle mode. You can use ¡,G, or R to override the angle mode setting temporarily. In Degree angle mode: In Gradian angle mode: In Radian angle mode: sin(squareMatrix1) ⇒squareMatrix Returns the matrix sine of squareMatrix1. This is not the same as calculating the sine of each element. For information about the calculation method, refer to cos(). squareMatrix1 must be diagonalizable. The result always contains floating-point numbers. In Radian angle mode: sin/() μ key sin/(Value1) ⇒value sin/(List1) ⇒list sin/(Value1) returns the angle whose sine is Value1. sin/(List1) returns a list of the inverse sines of each element of List1. Note: The result is returned as a degree, gradian or radian angle, according to the current angle mode setting. Note: You can insert this function from the keyboard by typing arcsin(...). In Degree angle mode: In Gradian angle mode: In Radian angle mode: sin/(squareMatrix1) ⇒squareMatrix Returns the matrix inverse sine of squareMatrix1. This is not the same as calculating the inverse sine of each element. For information about the calculation method, refer to cos(). squareMatrix1 must be diagonalizable. The result always contains floating-point numbers. In Radian angle mode and Rectangular complex format mode: To see the entire result, press £ and then use ¡ and ¢ to move the cursor.

sinh() Catalog > sinh(Numver1) ⇒value sinh(List1) ⇒list sinh (Value1) returns the hyperbolic sine of the argument. sinh (List1) returns a list of the hyperbolic sines of each element of List1. sinh(squareMatrix1) ⇒squareMatrix Returns the matrix hyperbolic sine of squareMatrix1. This is not the same as calculating the hyperbolic sine of each element. For information about the calculation method, refer to cos(). squareMatrix1 must be diagonalizable. The result always contains floating-point numbers. In Radian angle mode: sinh/() Catalog > sinh/(Value1) ⇒value sinh/(List1) ⇒list sinh/(Value1) returns the inverse hyperbolic sine of the argument. sinh/(List1) returns a list of the inverse hyperbolic sines of each element of List1. Note: You can insert this function from the keyboard by typing arcsinh(...). sinh/(squareMatrix1) ⇒squareMatrix Returns the matrix inverse hyperbolic sine of squareMatrix1. This is not the same as calculating the inverse hyperbolic sine of each element. For information about the calculation method, refer to cos(). squareMatrix1 must be diagonalizable. The result always contains floating-point numbers. In Radian angle mode: