TI-Nspire™ CAS Reference Guide This guidebook applies to TI-Nspire™ software version 4.5. To obtain the latest version of the documentation, go to education.ti.com/go/download.
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Contents Important Information ii Expression Templates 1 Alphabetical Listing 8 A B C D E F G I L M N O P Q R S T U V W X Z 8 17 20 45 57 68 77 87 96 112 120 129 131 140 143 157 182 197 198 199 201 202 iii
Symbols 210 Empty (Void) Elements 236 Shortcuts for Entering Math Expressions 238 EOS™ (Equation Operating System) Hierarchy 240 Constants and Values 242 Error Codes and Messages 243 Warning Codes and Messages 251 Support and Service 253 Texas Instruments Support and Service Service and Warranty Information Index iv 253 253 254
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. Position the cursor on each element, and type a value or expression for the element. /p keys Fraction template Example: Note: See also / (divide) , page 212.
/l keys Nth root template u keys e exponent template Example: Natural exponential e raised to a power Note: See also e^() , page 57. /s key Log template Example: Calculates log to a specified base. For a default of base 10, omit the base. Note: See also log() , page 107. Piecewise template (2-piece) Catalog > Example: Lets you create expressions and conditions for a two-piece piecewise function. To add a piece, click in the template and repeat the template. Note: See also piecewise() , page 133.
Piecewise template (N-piece) Lets you create expressions and conditions for an N-piece piecewise function. Prompts for N. Catalog > Example: See the example for Piecewise template (2piece). Note: See also piecewise() , page 133. System of 2 equations template Catalog > Example: Creates a system of two equations. To add a row to an existing system, click in the template and repeat the template. Note: See also system() , page 182. System of N equations template Lets you create a system of N equations.
Absolute value template Catalog > dd° mm’ss.ss’’ template Catalog > Example: Lets you enter angles in dd°mm’ss.ss ’’ format, where dd is the number of decimal degrees, mm is the number of minutes, and ss.ss is the number of seconds. Matrix template (2 x 2) Catalog > Example: Creates a 2 x 2 matrix. Matrix template (1 x 2) . Catalog > Example: Matrix template (2 x 1) Catalog > Example: Matrix template (m x n) The template appears after you are prompted to specify the number of rows and columns.
Matrix template (m x n) Catalog > Note: If you create a matrix with a large number of rows and columns, it may take a few moments to appear. Sum template (Σ) Catalog > Example: Note: See also Σ() ( sumSeq), page 224. Product template (Π) Catalog > Example: Note: See also Π() ( prodSeq), page 223. First derivative template Catalog > Example: The first derivative template can also be used to calculate first derivative at a point. Note: See also d() (derivative) , page 221.
Second derivative template Catalog > Example: The second derivative template can also be used to calculate second derivative at a point. Note: See also d() (derivative) , page 221. Nth derivative template Catalog > Example: The nth derivative template can be used to calculate the nth derivative. Note: See also d() (derivative) , page 221. Definite integral template Catalog > Example: Note: See also∫() integral() , page 221.
Limit template Use − or ( −) for left hand limit. Use + for Catalog > right hand limit. Note: See also limit() , page 6.
Alphabetical Listing Items whose names are not alphabetic (such as +, !, and >) are listed at the end of this section, page 210. 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() abs(Expr1) ⇒ expression Catalog > abs(List1) ⇒ list abs(Matrix1) ⇒ matrix Returns the absolute value of the argument. Note: See also Absolute value template, page 3.
Catalog > amortTbl() 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 ΣInt() and ΣPrn() , page 225, and bal() , page 17.
angle() angle(Expr1) ⇒ expression Catalog > In Degree angle mode: Returns the angle of the argument, interpreting the argument as a complex number. Note: All undefined variables are treated as In Gradian angle mode: real variables. 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.
Output variable Description stat.dfError Degrees of freedom of the errors stat.SSError Sum of squares of the errors stat.MSError Mean square for the errors stat.sp Pooled standard deviation stat.xbarlist Mean of the input of the lists stat.CLowerList 95% confidence intervals for the mean of each input list stat.
Output variable Description 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 COLUMN FACTOR Outputs Output variable Description stat. Fcol F statistic of the column factor stat.PValCol Probability value of the column factor stat.dfCol Degrees of freedom of the column factor stat.SSCol Sum of squares of the column factor stat.
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. approx() approx(Expr1) ⇒ expression Catalog > Returns the evaluation of the argument as an expression containing decimal values, when possible, regardless of the current Auto or Approximate mode.
►approxFraction() Catalog > Note: You can insert this function from the computer keyboard by typing @>approxFraction(...). approxRational() approxRational(Expr[, Tol ]) ⇒ expression Catalog > 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⁻¹(), page 31. arccosh() See cosh⁻¹(), page 32. arccot() See cot ⁻¹(), page 33.
arcLen() arcLen(Expr1,Var,Start ,End) ⇒ expression Catalog > Returns the arc length of Expr1 from Start to End with respect to variable Var. Arc length is calculated as an integral assuming a function mode definition. arcLen(List1,Var,Start ,End) ⇒ list Returns a list of the arc lengths of each element of List1 from Start to End with respect to Var. arcsec() See sec ⁻¹(), page 158. arcsech() See sech⁻¹(), page 158. arcsin() See sin⁻¹(), page 168. arcsinh() See sinh⁻¹(), page 169.
augment() Catalog > 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 bal() bal(NPmt ,N,I,PV ,[Pmt ], [FV], [PpY], [CpY], [PmtAt ], [roundValue ]) ⇒ value Catalog > 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 195. 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 195.
►Base2 Catalog > Converts Integer1 to a binary number. Binary or hexadecimal numbers always have a 0b or 0h prefix, respectively. Use a zero, not the letter O, followed by b or h. 0b binaryNumber 0h hexadecimalNumber A binary number can have up to 64 digits. A hexadecimal number can have up to 16. Without a prefix, Integer1 is treated as decimal (base 10). The result is displayed in binary, regardless of the Base mode. Negative numbers are displayed in “two's complement” form.
►Base10 Catalog > 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.
binomCdf() binomCdf(n,p) ⇒ list Catalog > 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.
centralDiff() centralDiff(Expr1,Var [=Value ][,Step]) ⇒ expression Catalog > 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 “|” substitution for the variable. Step is the step value.
cFactor() cFactor( Expr1,Var) returns Expr1 factored with respect to variable Var. Catalog > Expr1 is factored as much as possible toward factors that are linear in Var, with perhaps non-real constants, even if it introduces irrational constants or subexpressions that are irrational in other variables. The factors and their terms are sorted with Var as the main variable. Similar powers of Var are collected in each factor.
charPoly() charPoly(squareMatrix,Var) ⇒ polynomial expression Catalog > charPoly(squareMatrix,Expr) ⇒ polynomial expression charPoly(squareMatrix1,Matrix2) ⇒ polynomial expression Returns the characteristic polynomial of squareMatrix . The characteristic polynomial of n×n matrix A, denoted by p A ( λ), is the polynomial defined by p (λ) = det(λ•I−A) A where I denotes the n×n identity matrix. squareMatrix1 and squareMatrix2 must have the equal dimensions.
χ2Cdf() Catalog > χ 2Cdf(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 χ 2 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,” page 236.
χ2Pdf() Catalog > chi2Pdf(XVal ,df ) ⇒ number if XVal is a number, list if XVal is a list Computes the probability density function (pdf) for the χ 2 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,” page 236. ClearAZ Catalog > ClearAZ Clears all single-character variables in the current problem space.
colAugment() colAugment(Matrix1, Matrix2) ⇒ matrix Catalog > Returns a new matrix that is Matrix2 appended to Matrix1. The matrices must have equal column dimensions, and Matrix2 is appended to Matrix1 as new rows. Does not alter Matrix1 or Matrix2. colDim() colDim(Matrix ) ⇒ expression Catalog > Returns the number of columns contained in Matrix . Note: See also rowDim() .
comDenom() comDenom( Expr1,Var) returns a reduced Catalog > ratio of numerator and denominator expanded with respect to Var. The terms and their factors are sorted with Var as the main variable. Similar powers of Var are collected. There might be some incidental factoring of the collected coefficients. Compared to omitting Var, this often saves time, memory, and screen space, while making the expression more comprehensible.
completeSquare () Catalog > - 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 [,… ]).
CopyVar CopyVar Var1, Var2 Catalog > 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 userdefined function, copies the definition of that function to function Var2. Function Var1 must be defined. Var1 must meet the variable-naming requirements or must be an indirection expression that simplifies to a variable name meeting the requirements. CopyVar Var1., Var2.
Catalog > ►cos ►cos reduces all powers of sin(...) modulo 1−cos(...)^2 so that any remaining powers of cos(...) have exponents in the range (0, 2). Thus, the result will be free of sin(...) if and only if sin(...) occurs in the given expression only to even powers. Note: This conversion operator is not supported in Degree or Gradian Angle modes. Before using it, make sure that the Angle mode is set to Radians and that Expr does not contain explicit references to degree or gradian angles.
µ key cos() When a scalar function f(A) operates on squareMatrix1 (A), the result is calculated by the algorithm: Compute the eigenvalues ( λ ) and i 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⁻¹ and f(A) = X f(B) X⁻¹. For example, cos(A) = X cos(B) X⁻¹ where: cos(B) = All computations are performed using floating-point arithmetic.
cos⁻¹() cos⁻¹(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. µ key In Radian angle mode and Rectangular Complex Format: To see the entire result, press £ and then use ¡ and ¢ to move the cursor.
cosh⁻¹() cosh⁻¹( List1) returns a list of the inverse Catalog > hyperbolic cosines of each element of List1. Note: You can insert this function from the keyboard by typing arccosh(...). cosh⁻¹(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.
µ key cot⁻¹() Note: The result is returned as a degree, gradian or radian angle, according to the current angle mode setting. In Radian angle mode: Note: You can insert this function from the keyboard by typing arccot(...). coth() coth(Expr1) ⇒ expression Catalog > coth(List1) ⇒ list Returns the hyperbolic cotangent of Expr1 or returns a list of the hyperbolic cotangents of all elements of List1.
Catalog > 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 236. Catalog > countif() countif(List ,Criteria) ⇒ value Returns the accumulated count of all elements in List that meet the specified Criteria. Counts the number of elements equal to 3. Criteria can be: • • A value, expression, or string.
Catalog > cPolyRoots() 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 one variable. The second syntax, cPolyRoots ( ListOfCoeffs) , returns a list of complex roots for the coefficients in ListOfCoeffs. Note: See also polyRoots() , page 137.
µ key csc() In Radian angle mode: csc ⁻¹() csc⁻¹(Expr1) ⇒ expression µ key In Degree angle mode: csc⁻¹(List1) ⇒ list Returns the angle whose cosecant is Expr1 or returns a list containing the inverse cosecants of each element of List1. In Gradian angle mode: Note: The result is returned as a degree, gradian or radian angle, according to the current angle mode setting. In Radian angle mode: Note: You can insert this function from the keyboard by typing arccsc(...).
cSolve() cSolve(Equation, Var) ⇒ Boolean expression Catalog > cSolve(Equation, Var=Guess) ⇒ Boolean expression cSolve(Inequality , Var) ⇒ Boolean expression Returns candidate complex solutions of an equation or inequality for Var. The goal is to produce candidates for all real and nonreal solutions. Even if Equation is real, cSolve() allows non-real results in Real result Complex Format.
cSolve() Catalog > You should also use var_ for any other variables in Equation that might have unreal values. Otherwise, you may receive unexpected results. cSolve(Eqn1andEqn2 [and…], VarOrGuess1, VarOrGuess2 [, … ]) ⇒ Boolean expression cSolve(SystemOfEqns, VarOrGuess1, VarOrGuess2 [, …]) ⇒ Boolean expression Returns candidate complex solutions to the simultaneous algebraic equations, where each varOrGuess specifies a variable that you want to solve for.
cSolve() You can also include solution variables that do not appear in the equations. These solutions show how families of solutions might contain arbitrary constants of the form ck , where k is an integer suffix from 1 through 255. For polynomial systems, computation time or memory exhaustion may depend strongly on the order in which you list solution variables. If your initial choice exhausts memory or your patience, try rearranging the variables in the equations and/or varOrGuess list.
Catalog > CubicReg All the lists must have equal dimension except for Include . X and Y are lists of independent and dependent variables. Freq is an optional list of frequency values. Each element in Freq specifies the frequency of occurrence for each corresponding X and Y data point. The default value is 1. All elements must be integers ≥ 0. Category is a list of category codes for the corresponding X and Y data. Include is a list of one or more of the category codes.
cumulativeSum() cumulativeSum(Matrix1) ⇒ matrix Catalog > 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 236. Cycle Cycle Transfers control immediately to the next iteration of the current loop ( For, While, or Loop).
cZeros() Returns a list of candidate real and non-real values of Var that make Expr=0. cZeros() does this by computing exp►list(cSolve( Expr=0,Var) ,Var) . Otherwise, cZeros() is similar to zeros() . Note: See also cSolve() , solve() , and zeros() . Catalog > To see the entire result, press £ and then use ¡ and ¢ to move the cursor. Note: If Expr is non-polynomial with functions such as abs() , angle() , conj() , real () , or imag() , you should place an underscore (press /_) at the end of Var.
Catalog > cZeros() Complex zeros can include both real and non-real zeros, as in the example to the right. Each row of the resulting matrix represents an alternate zero, with the components ordered the same as the VarOrGuess list. To extract a row, index the matrix by [row]. Extract row 2: Simultaneous polynomials can have extra variables that have no values, but represent given numeric values that could be substituted later. You can also include unknown variables that do not appear in the expressions.
Catalog > cZeros() If a system is neither polynomial in all of its variables nor linear in its unknowns, cZeros () determines at most one zero using an approximate iterative method. To do so, the number of unknowns must equal the number of expressions, and all other variables in the expressions must simplify to numbers. A non-real guess is often necessary to determine a non-real zero. For convergence, a guess might have to be rather close to a zero.
Catalog > ►DD 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.
Define Var and Function cannot be the name of a Catalog > 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.
Define LibPriv Catalog > ...) = 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 46, and Define LibPub, page 48. Define LibPub Define LibPub Var = Expression Define LibPub Function(Param1, Param2, ...) = Expression Catalog > Define LibPub Function(Param1, Param2, ...) = Func Block EndFunc Define LibPub Program(Param1, Param2, ...
DelVar DelVar Var1[, Var2] [, Var3] ... Catalog > 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 197. 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 ( .
deSolve() • the 1st derivative of the dependent variable with respect to the independent variable. Use two prime symbols to denote the corresponding second derivative. The prime symbol is used for derivatives within deSolve() only. In other cases, use d () . The general solution of a 1st-order equation contains an arbitrary constant of the form ck , where k is an integer suffix from 1 through 255. The solution of a 2nd-order equation contains two such constants.
deSolve() deSolve(2ndOrderODE and initCond1 and initCond2, Var, depVar) ⇒ particular solution Catalog > Returns a particular solution that satisfies 2nd Order ODE and has a specified value of the dependent variable and its first derivative at one point.
det() • Catalog > computations are done using floatingpoint arithmetic. If Tolerance is omitted or not used, the default tolerance is calculated as: 5E ⁻14 •max(dim( squareMatrix )) •rowNorm( squareMatrix ) diag() diag(List ) ⇒ matrix diag(rowMatrix ) ⇒ matrix diag(columnMatrix ) ⇒ matrix Catalog > Returns a matrix with the values in the argument list or matrix in its main diagonal. diag(squareMatrix ) ⇒ rowMatrix Returns a row matrix containing the elements from the main diagonal of squareMatrix .
Catalog > Disp 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: For instructions on entering multi-line program and function definitions, refer to the Calculator section of your product guidebook. Catalog > DispAt DispAt int ,expr1 [,expr2 ...] ...
Catalog > DispAt Define z()= Output Prgm z() For n,1,3 Iteration 1: DispAt 1,"N: ",n Line 1: N:1 Disp "Hello" Line 2: Hello EndFor Iteration 2: EndPrgm Line 1: N:2 Line 2: Hello Line 3: Hello Iteration 3: Line 1: N:3 Line 2: Hello Line 3: Hello Line 4: Hello Define z1()= z1() Prgm For n,1,3 DispAt 1,"N: ",n EndFor Line 1: N:3 Line 2: Hello Line 3: Hello Line 4: Hello Line 5: Hello For n,1,4 Disp "Hello" EndFor EndPrgm Error conditions: Error Message Description DispAt line number must be between 1 an
Error Message Description for the void (if the callback is defined) Conversion operator: DispAt 2_ft @> _m, "Hello World" CAS: Datatype Error is thrown (if the callback is defined) Numeric: Conversion will be evaluated and if the result is a valid argument, DispAt print the string at the result line. Catalog > ►DMS Expr ►DMS In Degree angle mode: List ►DMS Matrix ►DMS Note: You can insert this operator from the computer keyboard by typing @>DMS.
domain() Catalog > Certain functions cannot be used as arguments for domain() , regardless of whether they appear explicitly or within user-defined variables and functions. In the following example, the expression cannot be simplified because ∫() is a disallowed function.
dominantTerm() Catalog > If the series or one of its derivatives has a jump discontinuity at Point , the result is likely to contain sub-expressions of the form sign(…) or abs(…) for a real expansion variable or (-1) floor(…angle(…)…) for a complex expansion variable, which is one ending with “_”. If you intend to use the dominant term only for values on one side of Point , then append to dominantTerm( ...
u key e^() Note: Pressing u to display e^( is different from pressing the character E on the keyboard. You can enter a complex number in reiθ 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.
eigVc() Catalog > 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 To see the entire result, press £ and then use ¡ and ¢ to move the cursor.
ElseIf If BooleanExpr1 Then Block1 ElseIf BooleanExpr2 Then Block2 Catalog > ⋮ ElseIf BooleanExprN Then BlockN EndIf ⋮ Note for entering the example: For instructions on entering multi-line program and function definitions, refer to the Calculator section of your product guidebook. EndFor EndFunc EndIf See For, page 73. See Func, page 76. See If, page 87. EndLoop See Loop, page 111. EndPrgm See Prgm, page 138. EndTry EndWhile 60 Alphabetical Listing See Try, page 191.
euler () euler(Expr, Var, depVar, {Var0, VarMax }, depVar0, VarStep [, eulerStep]) ⇒ matrix Catalog > Differential equation: y'=0.001*y*(100-y) and y(0)=10 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 To see the entire result, press £ and then use ¡ and ¢ to move the cursor.
Catalog > euler () 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 VarStep ⁄ eulerStep.
eval () Hub Menu Although eval() does not display its result, you can view the resulting Hub command string after executing the command by inspecting any of the following special variables. iostr.SendAns iostr.GetAns iostr.GetStrAns Note: See also Get (page 78), GetStr (page 85), and Send (page 159).
►exp Catalog > Expr►exp Represents Expr in terms of the natural exponential e . This is a display conversion operator. It can be used only at the end of the entry line. Note: You can insert this operator from the computer keyboard by typing @>exp. exp() exp(Expr1) ⇒ expression u key Returns e raised to the Expr1 power. Note: See also e exponent template, page 2. You can enter a complex number in reiθ polar form.
exp►list() Examines Expr for equations that are Catalog > separated by the word “or,” and returns a list containing the right-hand sides of the equations of the form Var=Expr. This gives you an easy way to extract some solution values embedded in the results of the solve() , cSolve() , fMin() , and fMax() functions. Note: exp►list() is not necessary with the zeros() and cZeros() functions because they return a list of solution values directly.
expand() Catalog > Even when there is only one variable, using Var might make the denominator factorization used for partial fraction expansion more complete. Hint: For rational expressions, propFrac() is a faster but less extreme alternative to expand() . Note: See also comDenom() for an expanded numerator over an expanded denominator. expand( Expr1,[Var]) also distributes logarithms and fractional powers regardless of Var.
Catalog > ExpReg All the lists must have equal dimension except for Include . X and Y are lists of independent and dependent variables. Freq is an optional list of frequency values. Each element in Freq specifies the frequency of occurrence for each corresponding X and Y data point. The default value is 1. All elements must be integers ≥ 0. Category is a list of category codes for the corresponding X and Y data. Include is a list of one or more of the category codes.
F factor() factor(Expr1[, Var]) ⇒ expression factor(List1[,Var]) ⇒ list factor(Matrix1[,Var]) ⇒ matrix factor( Expr1) returns Expr1 factored with respect to all of its variables over a common denominator. Expr1 is factored as much as possible toward linear rational factors without introducing new non-real subexpressions. This alternative is appropriate if you want factorization with respect to more than one variable. factor( Expr1,Var) returns Expr1 factored with respect to variable Var.
factor() Catalog > Note: See also cFactor() for factoring all the way to complex coefficients in pursuit of linear factors. 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 100digit number could take more than a century.
FCdf() Catalog > Computes the F distribution probability between lowBound and upBound for the specified dfNumer (degrees of freedom) and dfDenom. For P( X ≤ upBound), set lowBound = 0. Fill Catalog > Fill Expr, matrixVar ⇒ matrix Replaces each element in variable matrixVar with Expr. matrixVar must already exist. Fill Expr, listVar ⇒ list Replaces each element in variable listVar with Expr. listVar must already exist.
Catalog > FiveNumSummary 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 236. Output variable Description stat.MinX Minimum of x values. stat.Q X 1st Quartile of x. stat.MedianX Median of x. stat.Q X 3rd Quartile of x. stat.MaxX Maximum of x values. 1 3 floor() floor(Expr1) ⇒ integer Catalog > Returns the greatest integer that is ≤ the argument.
fMax() Catalog > You can use the constraint (“|”) operator to restrict the solution interval and/or specify other constraints. For the Approximate setting of the Auto or Approximate mode, fMax() iteratively searches for one approximate local maximum. This is often faster, particularly if you use the “|” operator to constrain the search to a relatively small interval that contains exactly one local maximum. Note: See also fMin() and max() .
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.
format() Catalog > 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.
Catalog > freqTable►list() freqIntegerList must have the same dimension as List1 and must contain nonnegative 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 236.
Catalog > FTest_2Samp 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 177.
Catalog > Func 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: For instructions on entering multi-line program and function definitions, refer to the Calculator section of your product guidebook.
geomCdf() if lowBound and upBound are numbers, list if lowBound and upBound are lists Catalog > 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.
Get Hub Menu Implicit simplification takes place. For example, a received string of "123" is interpreted as a numeric value. To preserve the string, use GetStr instead of Get. If you include the optional argument statusVar, it is assigned a value based on the success of the operation. A value of zero means that no data was received. In the second syntax, the func () argument allows a program to store the received string as a function definition.
Catalog > getKey() • keypressed := getKey() will return a key or an empty string if no key has been pressed. This call will return immediately. keypressed := getKey(1) will wait till a key is pressed. This call will pause execution of the program till a key is pressed.
Handheld Device/Emulator Key Desktop Return Value Templates n/a "template" Catalog n/a "cat" ^ ^ "^" X^2 n/a "square" / (division key) / "/" * (multiply key) * "*" e^x n/a "exp" 10^x n/a "10power" + + "+" - - "-" ( ( "(" ) ) ")" . . ".
Handheld Device/Emulator Key Desktop Return Value Space Space " " (space) Inaccessible Special Character Keys like @,!,^, etc. The character is returned n/a Function Keys No returned character n/a Special desktop control keys No returned character Inaccessible Other desktop keys that are Same character you get in not available on the Notes (not in a math box) calculator while getkey() is waiting for a keystroke. ({, },;, :, ...
exit the program the TIInnovator™ Hub is still working with the handheld. getLangInfo() getLangInfo() ⇒ string Catalog > 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.
getMode() getMode(ModeNameInteger) ⇒ value Catalog > 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.
Catalog > getNum() getNum(Expr1) ⇒ expression Transforms the argument into an expression having a reduced common denominator, and then returns its numerator. GetStr GetStr [promptString,] var[, statusVar] Hub Menu For examples, see Get . GetStr [promptString,] func (arg1, ...argn) [, statusVar] Programming command: Operates identically to the Get command, except that the retrieved value is always interpreted as a string.
getVarInfo() 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.
Catalog > Goto 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: For instructions on entering multi-line program and function definitions, refer to the Calculator section of your product guidebook. Catalog > ►Grad Expr1►Grad ⇒ expression In Degree angle mode: Converts Expr1 to gradian angle measure. Note: You can insert this operator from the computer keyboard by typing @>Grad.
Catalog > If 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.
Catalog > ifFn() 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: • • • • • Test value of 1 is less than 2.5, so its corresponding Value_If_True element of 5 is copied to the result list. BooleanExpr can test a single value, a list, or a matrix.
imag() Catalog > Note: All undefined variables are treated as real variables. See also real(), page 147 imag(List1) ⇒ list Returns a list of the imaginary parts of the elements. imag(Matrix1) ⇒ matrix Returns a matrix of the imaginary parts of the elements. impDif() impDif(Equation, Var, dependVar[,Ord]) ⇒ expression Catalog > where the order Ord defaults to 1. Computes the implicit derivative for equations in which one variable is defined implicitly in terms of another.
Catalog > int() int(Expr) ⇒ integer int(List1) ⇒ list int(Matrix1) ⇒ matrix Returns the greatest integer that is less than or equal to the argument. This function is identical to floor() . The argument can be a real or a complex number. For a list or matrix, returns the greatest integer of each of the elements. Catalog > intDiv() intDiv(Number1, Number2) ⇒ integer intDiv(List1, List2) ⇒ list intDiv(Matrix1, Matrix2) ⇒ matrix Returns the signed integer part of ( Number1 ÷ Number2).
interpolate () Given xList , yList =f( xList ) , and yPrimeList =f'( xList ) for some unknown Catalog > Use the interpolate() function to calculate the function values for the xvaluelist: 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.
invBinom() invBinom (CumulativeProb,NumTrials,Prob, OutputForm)⇒ scalar or matrix Inverse binomial. Given the number of trials ( NumTrials) and the probability of success of each trial ( Prob), this function returns the minimum number of successes, k , such that the value, k , is greater than or equal to the given cumulative probability ( CumulativeProb). Catalog > Example: Mary and Kevin are playing a dice game. Mary has to guess the maximum number of times 6 shows up in 30 rolls.
invt() Catalog > Computes the inverse cumulative student-t probability function specified by degree of freedom, df for a given Area under the curve. iPart() iPart(Number) ⇒ integer iPart(List1) ⇒ list iPart(Matrix1) ⇒ matrix Catalog > 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.
isPrime() Returns true or false to indicate if number is a whole number ≥ 2 that is evenly divisible only by itself and 1. Catalog > Function to find the next prime after a specified number: If Number exceeds about 306 digits and has no factors ≤1021, isPrime( Number) displays an error message. If you merely want to determine if Number is prime, use isPrime() instead of factor() . It is much faster, particularly if Number is not prime and has a second-largest factor that exceeds about five digits.
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: For instructions on entering multi-line program and function definitions, refer to the Calculator section of your product guidebook.
left() Catalog > 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. libShortcut() 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.
limit() or lim() Catalog > Limits at positive ∞ and at negative ∞ are always converted to one-sided limits from the finite side. Depending on the circumstances, limit() returns itself or undef when it cannot determine a unique limit. This does not necessarily mean that a unique limit does not exist. undef means that the result is either an unknown number with finite or infinite magnitude, or it is the entire set of such numbers.
LinRegBx Freq is an optional list of frequency values. Each element in Freq specifies the Catalog > frequency of occurrence for each corresponding X and Y data point. The default value is 1. All elements must be integers ≥ 0. Category is a list of category codes for the corresponding X and Y data. Include is a list of one or more of the category codes. Only those data items whose category code is included in this list are included in the calculation.
LinRegMx X and Y are lists of independent and Catalog > dependent variables. Freq is an optional list of frequency values. Each element in Freq specifies the frequency of occurrence for each corresponding X and Y data point. The default value is 1. All elements must be integers ≥ 0. Category is a list of category codes for the corresponding X and Y data. Include is a list of one or more of the category codes.
Catalog > LinRegtIntervals 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 177.) 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.
Output variable Description 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 LinRegtTest X,Y[,Freq[,Hypoth]] Computes a linear regression on the X and Y lists and a t test on the value of slope β and the correlation coefficient ρ for the equation y =α +βx.
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.r 2 Coefficient of determination stat.r Correlation coefficient stat.
ΔList() Catalog > ΔList(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. list ►mat() list►mat(List [, elementsPerRow]) ⇒ matrix Catalog > Returns a matrix filled row-by-row with the elements from List .
ln() /u keys Returns the natural logarithm of the argument. For a list, returns the natural logarithms of the elements. 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.
LnReg Include is a list of one or more of the Catalog > 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,” page 236. Output variable Description stat.RegEqn Regression equation: a+b•ln(x) stat.a, stat.b Regression coefficients stat.r 2 Coefficient of linear determination for transformed data stat.
Local Catalog > Note for entering the example: For instructions on entering multi-line program and function definitions, refer to the Calculator section of your product guidebook. Lock LockVar1[, Var2] [, Var3] ... LockVar. Catalog > 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.
log() log( squareMatrix1[,Expr]) ⇒ squareMatrix /s keys In Radian angle mode and Rectangular complex format: Returns the matrix base-Expr logarithm of squareMatrix1. This is not the same as calculating the base-Expr logarithm of each element. For information about the calculation method, refer to cos() . squareMatrix1 must be diagonalizable. The result always contains floating-point numbers. If the base argument is omitted, 10 is used as base.
Logistic Category is a list of category codes for the corresponding X and Y data. Catalog > 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,” page 236. Output variable Description stat.RegEqn Regression equation: c/(1+a•e-bx) stat.a, stat.b, stat.c Regression coefficients stat.
LogisticD Freq is an optional list of frequency values. Each element in Freq specifies the Catalog > frequency of occurrence for each corresponding X and Y data point. The default value is 1. All elements must be integers ≥ 0. Category is a list of category codes for the corresponding X and Y data. Include is a list of one or more of the category codes. Only those data items whose category code is included in this list are included in the calculation.
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: For instructions on entering multi-line program and function definitions, refer to the Calculator section of your product guidebook.
Catalog > LU The LU factorization algorithm uses partial pivoting with row interchanges. M mat ►list() mat►list(Matrix ) ⇒ list Catalog > 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 (...). max() max(Expr1, Expr2) ⇒ expression max(List1, List2) ⇒ list max(Matrix1, Matrix2) ⇒ matrix Returns the maximum of the two arguments.
max() Catalog > Empty (void) elements are ignored. For more information on empty elements, see page 236. Note: See also fMax() and min(). mean() mean(List [, freqList ]) ⇒ expression Catalog > Returns the mean of the elements in List . Each freqList element counts the number of consecutive occurrences of the corresponding element in List . mean(Matrix1[, freqMatrix ]) ⇒ matrix In Rectangular vector format: Returns a row vector of the means of all the columns in Matrix1.
Catalog > median() 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 236. MedMed 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 177.) All the lists must have equal dimension except for Include .
Output variable Description 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.
min() min(Expr1, Expr2) ⇒ expression Catalog > min(List1, List2) ⇒ list min(Matrix1, Matrix2) ⇒ matrix Returns the minimum of the two arguments. If the arguments are two lists or matrices, returns a list or matrix containing the minimum value of each pair of corresponding elements. min(List ) ⇒ expression Returns the minimum element of List . min(Matrix1) ⇒ matrix Returns a row vector containing the minimum element of each column in Matrix1. Note: See also fMin() and max().
mirr() Catalog > Note: See also irr() , page 94. mod() mod(Expr1, Expr2) ⇒ expression Catalog > 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.
MultReg MultReg Y, X1[,X2[,X3,…[,X10]]] Catalog > 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 177.) All the lists must have equal dimension. For information on the effect of empty elements in a list, see “Empty (Void) Elements,” page 236. Output variable Description stat.RegEqn Regression Equation: b0+b1•x1+b2•x2+ ... stat.b0, stat.b1, ... Regression coefficients stat.
Output variable Description 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.
Output variable Description 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.
nand Integer1 nand Integer2 ⇒ integer /= keys Compares two real integers bit-by-bit using a nand operation. Internally, both integers are converted to signed, 64-bit binary numbers. When corresponding bits are compared, the result is 1 if both bits are 1; otherwise, the result is 0. The returned value represents the bit results, and is displayed according to the Base mode. You can enter the integers in any number base. For a binary or hexadecimal entry, you must use the 0b or 0h prefix, respectively.
nCr() Catalog > Returns a matrix of combinations based on the corresponding element pairs in the two matrices. The arguments must be the same size matrix. nDerivative() nDerivative(Expr1,Var=Value [,Order]) ⇒ value Catalog > 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 “|” substitution for the variable.
nfMax() Catalog > Returns a candidate numerical value of variable Var where the local maximum of Expr occurs. If you supply lowBound and upBound, the function looks in the closed interval [lowBound,upBound] for the local maximum. Note: See also fMax() and d() .
nInt() Catalog > The goal is six significant digits. The adaptive algorithm terminates when it seems likely that the goal has been achieved, or when it seems unlikely that additional samples will yield a worthwhile improvement. A warning is displayed (“Questionable accuracy”) when it seems that the goal has not been achieved. Nest nInt() to do multiple numeric integration. Integration limits can depend on integration variables outside them. Note: See also ∫() , page 221.
nor Integer1 nor Integer2 ⇒ integer /= keys Compares two real integers bit-by-bit using a nor operation. Internally, both integers are converted to signed, 64-bit binary numbers. When corresponding bits are compared, the result is 1 if both bits are 1; otherwise, the result is 0. The returned value represents the bit results, and is displayed according to the Base mode. You can enter the integers in any number base. For a binary or hexadecimal entry, you must use the 0b or 0h prefix, respectively.
Catalog > normCdf() normCdf(lowBound,upBound[,μ[,σ]]) ⇒ 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 μ (default=0) and σ (default=1). For P(X ≤ upBound), set lowBound = ⁻∞.
nPr() nPr(Expr1, Expr2) ⇒ expression Catalog > For integer Expr1 and Expr2 with Expr1 ≥ Expr2 ≥ 0, nPr() is the number of permutations of Expr1 things taken Expr2 at a time. Both arguments can be integers or symbolic expressions. nPr(Expr, 0 ⇒ 1 nPr(Expr, negInteger) ⇒ 1 / ((Expr+1)• (Expr+2) ... (expression−negInteger)) nPr(Expr, posInteger) ⇒ Expr•(Expr−1) ...
npv() CFFreq is a list in which each element Catalog > 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.
Catalog > nSolve() Note: See also cSolve() , cZeros() , solve() , and zeros() . O Catalog > OneVar 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 177.) All the lists must have equal dimension except for Include . Freq is an optional list of frequency values.
Output variable Description stat.sx Sample standard deviation of x stat. σx Population standard deviation of x stat.n Number of data points stat.MinX Minimum of x values stat.Q X 1st Quartile of x stat.MedianX Median of x stat.Q X 3rd Quartile of x stat.MaxX Maximum of x values stat.
Catalog > or 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. Note: A binary entry can have up to 64 digits (not counting the 0b prefix). A hexadecimal entry can have up to 16 digits.
Catalog > P►Rx() Note: The θ 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(...).
PassErr Catalog > Note: See also ClrErr, page 25, and Try, page 191. Note for entering the example: For instructions on entering multi-line program and function definitions, refer to the Calculator section of your product guidebook. piecewise() piecewise(Expr1[, Cond1[, Expr2 [, Cond2 Catalog > [, … ]]]]) 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 3.
Catalog > ►Polar Vector ►Polar Note: You can insert this operator from the computer keyboard by typing @>Polar. Displays vector in polar form [r∠ θ]. The vector must be of dimension 2 and can be a row or a column. Note: ►Polar 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 ►Rect, page 147. complexValue ►Polar In Radian angle mode: Displays complexVector in polar form.
polyCoeffs() Catalog > polyDegree() polyDegree(Poly [,Var]) ⇒ value Catalog > Returns the degree of polynomial expression Poly with respect to variable Var. If you omit Var, the polyDegree() function selects a default from the variables contained in the polynomial Poly . Constant polynomials Poly must be a polynomial expression in Var. We recommend that you do not omit Var unless Poly is an expression in a single variable. The degree can be extracted even though the coefficients cannot.
polyGcd() polyGcd(Expr1,Expr2) ⇒ expression Catalog > Returns greatest common divisor of the two arguments. Expr1 and Expr2 must be polynomial expressions. List, matrix, and Boolean arguments are not allowed. polyQuotient() polyQuotient(Poly1,Poly2 [,Var]) ⇒ expression Catalog > Returns the quotient of polynomial Poly1 divided by polynomial Poly2 with respect to the specified variable Var. Poly1 and Poly2 must be polynomial expressions in Var.
polyRemainder() Catalog > polyRoots() polyRoots(Poly ,Var) ⇒ list Catalog > 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 one variable. The second syntax, polyRoots ( ListOfCoeffs) , returns a list of real roots for the coefficients in ListOfCoeffs. Note: See also cPolyRoots() , page 36.
Catalog > PowerReg Category is a list of category codes for the corresponding X and Y data. Include is a list of one or more of the category codes. Only those data items whose category code is included in this list are included in the calculation. For information on the effect of empty elements in a list, see “Empty (Void) Elements,” page 236. Output variable Description stat.RegEqn Regression equation: a•(x)b stat.a, stat.b Regression coefficients stat.
Prgm Catalog > Note for entering the example: For instructions on entering multi-line program and function definitions, refer to the Calculator section of your product guidebook. prodSeq() See Π (), page 223. Product (PI) See Π (), page 223. product() product(List [, Start [, End]]) ⇒ expression Catalog > Returns the product of the elements contained in List . Start and End are optional. They specify a range of elements.
propFrac() propFrac( rational_expression,Var) returns Catalog > 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.
Catalog > QR • computations are done using floatingpoint arithmetic. If Tol is omitted or not used, the default tolerance is calculated as: 5E −14 •max(dim(Matrix )) •rowNorm (Matrix ) 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 Include is a list of one or more of the Catalog > 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,” page 236. Output variable Description stat.RegEqn Regression equation: a•x 2+b•x+c stat.a, stat.b, stat.c Regression coefficients stat.R 2 Coefficient of determination stat.Resid Residuals from the regression stat.
Catalog > QuartReg Category is a list of category codes for the corresponding X and Y data. Include is a list of one or more of the category codes. Only those data items whose category code is included in this list are included in the calculation. For information on the effect of empty elements in a list, see “Empty (Void) Elements,” page 236. Output variable Description stat.RegEqn Regression equation: a•x 4+b•x 3+c• x 2+d•x+e stat.a, stat.b, stat.c, stat.d, stat.e Regression coefficients stat.
Catalog > R►Pθ() R►Pr() R►Pr (xExpr, yExpr) ⇒ expression Catalog > In Radian angle mode: R►Pr (xList , yList ) ⇒ list R►Pr (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(...). Catalog > ►Rad Expr1►Rad ⇒ expression In Degree angle mode: Converts the argument to radian angle measure. Note: You can insert this operator from the computer keyboard by typing @>Rad.
randBin() randBin(n, p) ⇒ expression randBin(n, p, #Trials) ⇒ list Catalog > 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.
randNorm() randNorm(μ, σ) ⇒ expression randNorm(μ, σ, #Trials) ⇒ list Catalog > randNorm( μ, σ) returns a decimal number from the specified normal distribution. It could be any real number but will be heavily concentrated in the interval [μ−3•σ, μ+3•σ]. randNorm( μ, σ, #Trials) returns a list containing #Trials decimal numbers from the specified normal distribution. randPoly() randPoly(Var, Order) ⇒ expression Catalog > Returns a polynomial in Var of the specified Order.
Catalog > real() real(Expr1) ⇒ expression Returns the real part of the argument. Note: All undefined variables are treated as real variables. See also imag() , page 89. real(List1) ⇒ list Returns the real parts of all elements. real(Matrix1) ⇒ matrix Returns the real parts of all elements. Catalog > ►Rect Vector ►Rect Note: You can insert this operator from the computer keyboard by typing @>Rect. Displays Vector in rectangular form [x, y, z].
ref() 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 floatingpoint arithmetic.
Catalog > RefreshProbeVars RefreshProbeVars Example Allows you to access sensor data from all connected sensor probes in your TI-Basic program. Define temp()= Prgm © Check if system is ready StatusVar Value Status statusVar Normal (continue with the =0 program) The Vernier DataQuest™ application is in data collection mode. statusVar Note: The Vernier DataQuest™ =1 application must be in meter mode for this command to work.
Catalog > remain() remain(Expr1, Expr2) ⇒ expression remain(List1, List2) ⇒ list remain(Matrix1, Matrix2) ⇒ matrix Returns the remainder of the first argument with respect to the second argument as defined by the identities: remain(x,0) x remain(x,y) x−y•iPart(x/y) As a consequence, note that remain( −x,y) − remain( x,y) . The result is either zero or it has the same sign as the first argument. Note: See also mod() , page 117.
Catalog > Request 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.
Catalog > RequestStr 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 (““). Define requestStr_demo()=Prgm RequestStr “Your name:”,name,0 Disp “Response has “,dim(name),” characters.
Catalog > right() 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. rk23 () rk23(Expr, Var, depVar, {Var0, VarMax }, depVar0, VarStep [, diftol ]) ⇒ matrix Catalog > Differential equation: y'=0.
Catalog > rk23 () ListOfExpr is a list of right-hand sides that define the system of ODEs (corresponds to order of dependent variables in ListOfDepVars). with y1(0)=2 and y2(0)=5 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.
Catalog > rotate() 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 ►Base2, page 17. If #ofRotations is positive, the rotation is to the left. If #ofRotations is negative, the rotation is to the right. The default is −1 (rotate right one bit).
round() round(Expr1[, digits]) ⇒ expression Catalog > 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.
Catalog > rowSwap() rowSwap(Matrix1, rIndex1, rIndex2) ⇒ matrix Returns Matrix1 with rows rIndex1 and rIndex2 exchanged. Catalog > rref() 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.
µ key sec() 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. sec ⁻¹() sec⁻¹(Expr1) ⇒ expression µ key In Degree angle mode: sec⁻¹(List1) ⇒ list Returns the angle whose secant is Expr1 or returns a list containing the inverse secants of each element of List1.
Send Send exprOrString1 [, exprOrString2] ... Programming command: Sends one or more TI-Innovator™ Hub commands to a connected hub. exprOrString must be a valid TI-Innovator™ Hub Command. Typically, exprOrString contains a "SET ..." command to control a device or a "READ ..." command to request data. Hub Menu Example: Turn on the blue element of the built-in RGB LED for 0.5 seconds. Example: Request the current value of the hub's built-in light-level sensor.
seqGen() 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. Catalog > Generate the first 5 terms of the sequence u (n ) = u (n -1)2/2, with u (1)=2 and VarStep =1.
seqn() Catalog > 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.
series() Point defaults to 0. Point can be ∞ or −∞, Catalog > in which cases the expansion is through degree Order in 1/( Var − Point ). series(...) returns “series(...) ” if it is unable to determine such a representation, such as for essential singularities such as sin(1/z) at z=0, e−1/z at z=0, or ez at z = ∞ or −∞.
setMode() setMode( modeNameInteger, settingInteger) temporarily sets mode modeNameInteger to the new setting settingInteger, and returns an integer Catalog > 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.
Mode Name Mode Integer Setting Integers Angle 2 1=Radian, 2=Degree, 3=Gradian Exponential Format 3 1=Normal, 2=Scientific, 3=Engineering Real or Complex 4 1=Real, 2=Rectangular, 3=Polar Auto or Approx. 5 1=Auto, 2=Approximate, 3=Exact Vector Format 6 1=Rectangular, 2=Cylindrical, 3=Spherical Base 7 1=Decimal, 2=Hex, 3=Binary Unit system 8 1=SI, 2=Eng/US shift() shift(Integer1[,#ofShifts]) ⇒ integer Shifts the bits in a binary integer.
Catalog > shift() 0b00000000000000111101011000011010 The result is displayed according to the Base mode. Leading zeros are not shown. shift(List1[,#ofShifts]) ⇒ list In Dec base mode: Returns a copy of List1 shifted right or left by #ofShifts elements. Does not alter List1. If #ofShifts is positive, the shift is to the left. If #ofShifts is negative, the shift is to the right. The default is −1 (shift right one element).
simult() simult(coeffMatrix , constVector[, Tol ]) ⇒ matrix Returns a column vector that contains the solutions to a system of linear equations. Catalog > Solve for x and y: x + 2y = 1 3x + 4y = −1 Note: See also linSolve() , page 103. coeffMatrix must be a square matrix that contains the coefficients of the equations. The solution is x=−3 and y=2. constVector must have the same number of rows (same dimension) as coeffMatrix and contain the constants.
Catalog > ►sin Represents Expr in terms of sine. This is a display conversion operator. It can be used only at the end of the entry line. ►sin reduces all powers of cos(...) modulo 1−sin(...)^2 so that any remaining powers of sin(...) have exponents in the range (0, 2). Thus, the result will be free of cos(...) if and only if cos(...) occurs in the given expression only to even powers. Note: This conversion operator is not supported in Degree or Gradian Angle modes.
µ key sin() 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. sin⁻¹() sin⁻¹(Expr1) ⇒ expression µ key In Degree angle mode: sin⁻¹(List1) ⇒ list sin⁻¹( Expr1) returns the angle whose sine is Expr1 as an expression.
sinh() sinh ( List1) returns a list of the hyperbolic sines of each element of List1. sinh(squareMatrix1) ⇒ squareMatrix Catalog > In Radian angle mode: Returns the matrix hyperbolic sine of squareMatrix1. This is not the same as calculating the hyperbolic sine of each element. For information about the calculation method, refer to cos() . squareMatrix1 must be diagonalizable. The result always contains floating-point numbers.
Catalog > SinReg All the lists must have equal dimension except for Include . X and Y are lists of independent and dependent variables. Iterations is a value that specifies the maximum number of times (1 through 16) a solution will be attempted. If omitted, 8 is used. Typically, larger values result in better accuracy but longer execution times, and vice versa. Period specifies an estimated period. If omitted, the difference between values in X should be equal and in sequential order.
Catalog > solve() solve(Equation, Var) ⇒ Boolean expression solve(Equation, Var=Guess) ⇒ Boolean expression solve(Inequality , Var) ⇒ Boolean expression Returns candidate real solutions of an equation or an inequality for Var. The goal is to return candidates for all solutions. However, there might be equations or inequalities for which the number of solutions is infinite. Solution candidates might not be real finite solutions for some combinations of values for undefined variables.
Catalog > solve() false is returned when no real solutions are found. true is returned if solve() can determine that any finite real value of Var satisfies the equation or inequality. Since solve() always returns a Boolean result, you can use “and,” “or,” and “not” to combine results from solve() with each other or with other Boolean expressions. Solutions might contain a unique new undefined constant of the form nj with j being an integer in the interval 1–255.
solve() Catalog > You can separate the equations with the and operator, or you can enter a SystemOfEqns using a template from the Catalog. The number of VarOrGuess arguments must match the number of equations. Optionally, you can specify an initial guess for a variable. Each VarOrGuess must have the form: variable – or – variable = real or non-real number For example, x is valid and so is x=3.
solve() Catalog > For polynomial systems, computation time or memory exhaustion may depend strongly on the order in which you list solution variables. If your initial choice exhausts memory or your patience, try rearranging the variables in the equations and/or varOrGuess list. If you do not include any guesses and if any equation is non-polynomial in any variable but all equations are linear in the solution variables, solve() uses Gaussian elimination to attempt to determine all real solutions.
Catalog > SortA Empty (void) elements within the first argument move to the bottom. For more information on empty elements, see page 236. Catalog > SortD SortD List1[, List2][, List3]... SortD Vector1[,Vector2][,Vector3]... Identical to SortA, except SortD sorts the elements in descending order. Empty (void) elements within the first argument move to the bottom. For more information on empty elements, see page 236.
►Sphere Catalog > sqrt() sqrt(Expr1) ⇒ expression Catalog > sqrt(List1) ⇒ list Returns the square root of the argument. For a list, returns the square roots of all the elements in List1. Note: See also Square root template, page 1.
Catalog > stat.results stat.results Displays results from a statistics calculation. The results are displayed as a set of namevalue pairs. The specific names shown are dependent on the most recently evaluated statistics function or command. You can copy a name or value and paste it into other locations. Note: Avoid defining variables that use the same names as those used for statistical analysis. In some cases, an error condition could occur.
stat.CUpperList stat.d stat.ME stat.MedianX stat.Q1Y stat.SS Note: Each time the Lists & Spreadsheet application calculates statistical results, it copies the “stat.” group variables to a “stat#.” group, where # is a number that is incremented automatically. This lets you maintain previous results while performing multiple calculations. stat.values stat.values Catalog > See the stat.results example.
stDevPop() Note:Matrix1must have at least two rows. Catalog > Empty (void) elements are ignored. For more information on empty elements, see page 236. stDevSamp() stDevSamp(List [, freqList ]) ⇒ expression Catalog > Returns the sample standard deviation of the elements in List . Each freqList element counts the number of consecutive occurrences of the corresponding element in List . Note:List must have at least two elements. Empty (void) elements are ignored.
Stop Catalog > Note for entering the example: For instructions on entering multi-line program and function definitions, refer to the Calculator section of your product guidebook. Store string() string(Expr) ⇒ string See →(store), page 233. Catalog > Simplifies Expr and returns the result as a character string. subMat() subMat(Matrix1[, startRow][, startCol ][, endRow][, endCol ]) ⇒ matrix Catalog > Returns the specified submatrix of Matrix1.
sum() sum(Matrix1[, Start [, End]]) ⇒ matrix Catalog > Returns a row vector containing the sums of all elements in the columns in Matrix1. Start and End are optional. They specify a range of rows. Any void argument produces a void result. Empty (void) elements in Matrix1 are ignored. For more information on empty elements, see page 236. sumIf() sumIf(List ,Criteria[, SumList ]) ⇒ value Catalog > Returns the accumulated sum of all elements in List that meet the specified Criteria.
Catalog > sumIf() Empty (void) elements are ignored. For more information on empty elements, see page 236. Note: See also countIf() , page 35. sumSeq() See Σ(), page 224. Catalog > system() system(Eqn1[, Eqn2[, Eqn3[, ...]]]) system(Expr1[, Expr2[, Expr3[, ...]]]) Returns a system of equations, formatted as a list. You can also create a system by using a template. Note: See also System of equations , page 3.
µ key tan() Note: The argument is interpreted as a degree, gradian or radian angle, according to the current angle mode. You can use °, g or r to override the angle mode setting temporarily. In Gradian angle mode: In Radian angle mode: tan(squareMatrix1) ⇒ squareMatrix In Radian angle mode: Returns the matrix tangent of squareMatrix1. This is not the same as calculating the tangent of each element. For information about the calculation method, refer to cos() . squareMatrix1 must be diagonalizable.
µ key tan⁻¹() Returns the matrix inverse tangent of squareMatrix1. This is not the same as calculating the inverse tangent of each element. For information about the calculation method, refer to cos() . squareMatrix1 must be diagonalizable. The result always contains floating-point numbers. Catalog > tangentLine() tangentLine(Expr1,Var,Point ) ⇒ expression tangentLine(Expr1,Var=Point ) ⇒ expression Returns the tangent line to the curve represented by Expr1 at the point specified in Var=Point .
tanh⁻¹() tanh⁻¹(Expr1) ⇒ expression Catalog > In Rectangular complex format: tanh⁻¹(List1) ⇒ list tanh⁻¹( Expr1) returns the inverse hyperbolic tangent of the argument as an expression. tanh⁻¹( List1) returns a list of the inverse hyperbolic tangents of each element of List1. Note: You can insert this function from the keyboard by typing arctanh(...). tanh⁻¹(squareMatrix1) ⇒ squareMatrix Returns the matrix inverse hyperbolic tangent of squareMatrix1.
tCdf() tCdf(lowBound,upBound,df ) ⇒ number if lowBound and upBound are numbers, list if lowBound and upBound are lists Catalog > Computes the Student-t distribution probability between lowBound and upBound for the specified degrees of freedom df . For P(X ≤ upBound), set lowBound = ⁻∞.
Catalog > tExpand() Note: Degree-mode scaling by π/180 interferes with the ability of tExpand() to recognize expandable forms. For best results, tExpand() should be used in Radian mode. Text TextpromptString[, DispFlag] Programming command: Pauses the program and displays the character string promptString in a dialog box. When the user selects OK, program execution continues. Catalog > Define a program that pauses to display each of five random numbers in a dialog box. Within the Prgm...
Catalog > tInterval tInterval v, sx , n[, CLevel ] (Summary stats input) Computes a t confidence interval. A summary of results is stored in the stat.results variable. (See page 177.) For information on the effect of empty elements in a list, see “Empty (Void) Elements,” page 236. Output variable Description stat.CLower, stat.CUpper Confidence interval for an unknown population mean stat. v Sample mean of the data sequence from the normal random distribution stat.ME Margin of error stat.
Output variable Description stat.CLower, stat.CUpper Confidence interval containing confidence level probability of distribution stat. v1-v2 Sample means of the data sequences from the normal random distribution stat.ME Margin of error stat.df Degrees of freedom stat. v1, stat. v2 Sample means of the data sequences from the normal random distribution stat. σx1, stat. σx2 Sample standard deviations for List 1 and List 2 stat.n1, stat.n2 Number of samples in data sequences stat.
ΔtmpCnv() Catalog > ΔtmpCnv(Expr_°tempUnit , _°tempUnit2) ⇒ expression _°tempUnit2 Note: You can insert this function from the keyboard by typing deltaTmpCnv(...). Converts a temperature range (the difference between two temperature values) specified by Expr from one unit to another. Valid temperature units are: Note: You can use the Catalog to select temperature units. _°C Celsius _°F Fahrenheit _°K Kelvin _°R Rankine To enter °, select it from the Symbol Palette or type @d. To type _ , press /_.
Catalog > Try Try block1 Else block2 EndTry Executes block1 unless an error occurs. Program execution transfers to block2 if an error occurs in block1. System variable errCode contains the error code to allow the program to perform error recovery. For a list of error codes, see “Error codes and messages,” page 251. block1 and block2 can be either a single statement or a series of statements separated with the “:” character.
tTest tTest μ0,List [,Freq[,Hypoth]] Catalog > (Data list input) tTest μ0,v,sx ,n,[Hypoth] (Summary stats input) Performs a hypothesis test for a single unknown population mean μ when the population standard deviation σ is unknown. A summary of results is stored in the stat.results variable. (See page 177.
Catalog > tTest_2Samp Computes a two-sample t test. A summary of results is stored in the stat.results variable. (See page 177.) Test H : μ1 = μ2, against one of the 0 following: For H : μ1< μ2, set Hypoth<0 a For H : μ1≠ μ2 (default), set Hypoth=0 a For H : μ1> μ2, set Hypoth>0 a Pooled=1 pools variances Pooled=0 does not pool variances For information on the effect of empty elements in a list, see “Empty (Void) Elements,” page 236. Output variable Description stat.
tvmI() Catalog > Financial function that calculates the interest rate per year. Note: Arguments used in the TVM functions are described in the table of TVM arguments, page 195. See also amortTbl() , page 8. tvmN() tvmN(I,PV,Pmt ,FV,[PpY],[CpY],[PmtAt ]) ⇒ value Catalog > Financial function that calculates the number of payment periods. Note: Arguments used in the TVM functions are described in the table of TVM arguments, page 195. See also amortTbl() , page 8.
TVM argument* Description Data type N Number of payment periods real number I Annual interest rate real number PV Present value real number Pmt Payment amount real number FV Future value real number PpY Payments per year, default=1 integer > 0 CpY Compounding periods per year, default=1 integer > 0 PmtAt Payment due at the end or beginning of each period, default=end integer (0=end, 1=beginning) * These time-value-of-money argument names are similar to the TVM variable names (such
Catalog > TwoVar 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 236. Output variable Description stat. v Mean of x values stat. Σ x Sum of x values stat. Σ x2 Sum of x2 values stat.sx Sample standard deviation of x stat.
Output variable Description stat.MaxY Maximum of y values stat. Σ (x-v)2 Sum of squares of deviations from the mean of x stat. Σ (y-w)2 Sum of squares of deviations from the mean of y U unitV() unitV(Vector1) ⇒ vector Catalog > Returns either a row- or column-unit vector, depending on the form of Vector1. Vector1 must be either a single-row matrix or a single-column matrix. To see the entire result, press £ and then use ¡ and ¢ to move the cursor. unLock unLock Var1[, Var2] [, Var3] ...
V varPop() varPop(List [, freqList ]) ⇒ expression Catalog > Returns the population variance of List . Each freqList element counts the number of consecutive occurrences of the corresponding element in List . Note: List must contain at least two elements. If an element in either list is empty (void), that element is ignored, and the corresponding element in the other list is also ignored. For more information on empty elements, see page 236.
Catalog > varSamp() If an element in either matrix is empty (void), that element is ignored, and the corresponding element in the other matrix is also ignored. For more information on empty elements, see page 236. Note: Matrix1 must contain at least two rows. W Catalog > Wait Wait timeInSeconds To wait 4 seconds: Suspends execution for a period of timeInSeconds seconds.
warnCodes () warnCodes(Expr1, StatusVar) ⇒ expression Evaluates expression Expr1, returns the result, and stores the codes of any generated warnings in the StatusVar list variable. If no warnings are generated, this function assigns StatusVar an empty list. Expr1 can be any valid TI-Nspire™ or TI-Nspire™ CAS math expression. You cannot use a command or assignment as Expr1. Catalog > To see the entire result, press £ and then use ¡ and ¢ to move the cursor. StatusVar must be a valid variable name.
Catalog > While While Condition Block EndWhile Executes the statements in Block as long as Condition is true. Block can be either a single statement or a sequence of statements separated with the “:” character. Note for entering the example: For instructions on entering multi-line program and function definitions, refer to the Calculator section of your product guidebook.
Catalog > xor You can enter the integers in any number base. For a binary or hexadecimal entry, you must use the 0b or 0h prefix, respectively. Without a prefix, integers are treated as decimal (base 10). Note: A binary entry can have up to 64 digits (not counting the 0b prefix). A hexadecimal entry can have up to 16 digits. If you enter a decimal integer that is too large for a signed, 64-bit binary form, a symmetric modulo operation is used to bring the value into the appropriate range.
Catalog > zeros() variable – or – variable = real or non-real number For example, x is valid and so is x=3. If all of the expressions are polynomials and if you do NOT specify any initial guesses, zeros() uses the lexical Gröbner/Buchberger elimination method to attempt to determine all real zeros. For example, suppose you have a circle of radius r at the origin and another circle of radius r centered where the first circle crosses the positive x-axis. Use zeros() to find the intersections.
Catalog > zeros() If you do not include any guesses and if any expression is non-polynomial in any variable but all expressions are linear in the unknowns, zeros() uses Gaussian elimination to attempt to determine all real zeros. If a system is neither polynomial in all of its variables nor linear in its unknowns, zeros() determines at most one zero using an approximate iterative method.
Output variable Description stat.n Length of the data sequence with sample mean stat. σ Known population standard deviation for data sequence List zInterval_1Prop zInterval_1Prop x ,n [,CLevel ] Catalog > Computes a one-proportion z confidence interval. A summary of results is stored in the stat.results variable. (See page 177.) x is a non-negative integer. For information on the effect of empty elements in a list, see “Empty (Void) Elements,” page 236. Output variable Description stat.
Output variable Description stat. Ç 1 First sample proportion estimate stat. Ç 2 Second sample proportion estimate stat.n1 Sample size in data sequence one stat.n2 Sample size in data sequence two zInterval_2Samp zInterval_2Samp σ1 ,σ2 ,List1,List2[,Freq1 [,Freq2,[CLevel ]]] Catalog > (Data list input) zInterval_2Samp σ1 ,σ2 ,v 1,n1,v 2,n2 [,CLevel ] (Summary stats input) Computes a two-sample z confidence interval. A summary of results is stored in the stat.results variable. (See page 177.
Catalog > zTest (Data list input) zTest μ0,σ,v,n[,Hypoth] (Summary stats input) Performs a z test with frequency freqlist . A summary of results is stored in the stat.results variable. (See page 177.) Test H : μ = μ0, against one of the 0 following: For H : μ < μ0, set Hypoth<0 a For H : μ ≠ μ0 (default), set Hypoth=0 a For H : μ > μ0, set Hypoth>0 a For information on the effect of empty elements in a list, see “Empty (Void) Elements,” page 236. Output variable Description stat.
Catalog > zTest_2Prop Computes a two-proportion z test. A summary of results is stored in the stat.results variable. (See page 177.) x1 and x2 are non-negative integers. Test H : p1 = p2, against one of the 0 following: For H : p1 > p2, set Hypoth>0 a For H : p1 ≠ p2 (default), set Hypoth=0 a For H : p < p0, set Hypoth<0 a For information on the effect of empty elements in a list, see “Empty (Void) Elements,” page 236. Output variable Description stat.
Catalog > zTest_2Samp For information on the effect of empty elements in a list, see “Empty (Void) Elements,” page 236. Output variable Description stat.z Standard normal value computed for the difference of means stat.PVal Smallest level of significance at which the null hypothesis can be rejected stat. x1, stat. x2 Sample means of the data sequences in List1 and List2 stat.sx1, stat.sx2 Sample standard deviations of the data sequences in List1 and List2 stat.n1, stat.
Symbols + (add) Expr1 + Expr2 ⇒ expression + key Returns the sum of the two arguments. List1 + List2 ⇒ list Matrix1 + Matrix2 ⇒ matrix Returns a list (or matrix) containing the sums of corresponding elements in List1 and List2 (or Matrix1 and Matrix2). Dimensions of the arguments must be equal. Expr + List1 ⇒ list List1 + Expr ⇒ list Returns a list containing the sums of Expr and each element in List1.
− (subtract) - key Subtracts each element in List2 (or Matrix2) from the corresponding element in List1 (or Matrix1), and returns the results. Dimensions of the arguments must be equal. Expr − List1 ⇒ list List1 − Expr ⇒ list Subtracts each List1 element from Expr or subtracts Expr from each List1 element, and returns a list of the results. Expr − Matrix1 ⇒ matrix Matrix1 − Expr ⇒ matrix Expr − Matrix1 returns a matrix of Expr times the identity matrix minus Matrix1. Matrix1 must be square.
• (multiply) r key Expr •List1 ⇒ list List1•Expr ⇒ list Returns a list containing the products of Expr and each element in List1. Expr •Matrix1 ⇒ matrix Matrix1•Expr ⇒ matrix Returns a matrix containing the products of Expr and each element in Matrix1. Note: Use .•(dot multiply) to multiply an expression by each element. ⁄ (divide) Expr1 ⁄ Expr2 ⇒ expression Returns the quotient of Expr1 divided by Expr2. Note: See also Fraction template, page 1.
⁄ (divide) p key Note: Use . ⁄ (dot divide) to divide an expression by each element. ^ (power) Expr1 ^ Expr2⇒ expression l key List1 ^ List2 ⇒ list Returns the first argument raised to the power of the second argument. Note: See also Exponent template, page 1. For a list, returns the elements in List1 raised to the power of the corresponding elements in List2.
x2 (square) Expr12⇒ expression q key Returns the square of the argument. List12 ⇒ list Returns a list containing the squares of the elements in List1. squareMatrix12 ⇒ matrix Returns the matrix square of squareMatrix1. This is not the same as calculating the square of each element. Use .^2 to calculate the square of each element. .+ (dot add) Matrix1 .+ Matrix2 ⇒ matrix ^+ keys Expr .+ Matrix1⇒ matrix Matrix1.
. •(dot mult.) Matrix1 .• Matrix2⇒ matrix ^r keys Expr .• Matrix1 ⇒ matrix Matrix1.• Matrix2 returns a matrix that is the product of each pair of corresponding elements in Matrix1 and Matrix2. Expr .• Matrix1 returns a matrix containing the products of Expr and each element in Matrix1. . ⁄ (dot divide) Matrix1. ⁄ Matrix2 ⇒ matrix ^p keys Expr . ⁄ Matrix1⇒ matrix Matrix1 . ⁄ Matrix2 returns a matrix that is the quotient of each pair of corresponding elements in Matrix1 and Matrix2. Expr .
v key − (negate) Returns the negation of the argument. For a list or matrix, returns all the elements negated. In Bin base mode: Important: Zero, not the letter O. If the argument is a binary or hexadecimal integer, the negation gives the two’s complement. To see the entire result, press £ and then use ¡ and ¢ to move the cursor. % (percent) Expr1% ⇒ expression List1% ⇒ list Matrix1% ⇒ matrix /k keys Note: To force an approximate result, Handheld: Press / ·. Windows®: Press Ctrl+Enter .
= key = (equal) Note for entering the example: For instructions on entering multi-line program and function definitions, refer to the Calculator section of your product guidebook. /= keys ≠ (not equal) Expr1≠Expr2 ⇒ Boolean expression See “=” (equal) example. List1≠List2 ⇒ Boolean list Matrix1≠Matrix2 ⇒ Boolean matrix Returns true if Expr1 is determined to be not equal to Expr2. Returns false if Expr1 is determined to be equal to Expr2. Anything else returns a simplified form of the equation.
/= keys < (less than) Anything else returns a simplified form of the equation. For lists and matrices, returns comparisons element by element. /= keys ≤ (less or equal) Expr1≤Expr2 ⇒ Boolean expression See “=” (equal) example. List1≤List2 ⇒ Boolean list Matrix1 ≤Matrix2 ⇒ Boolean matrix Returns true if Expr1 is determined to be less than or equal to Expr2. Returns false if Expr1 is determined to be greater than Expr2. Anything else returns a simplified form of the equation.
/= keys ≥ (greater or equal) Expr1≥Expr2 ⇒ Boolean expression See “=” (equal) example. List1≥List2 ⇒ Boolean list Matrix1 ≥Matrix2 ⇒ Boolean matrix Returns true if Expr1 is determined to be greater than or equal to Expr2. Returns false if Expr1 is determined to be less than Expr2. Anything else returns a simplified form of the equation. For lists and matrices, returns comparisons element by element.
⇔ (logical double implication, XNOR) /= keys BooleanExpr1 ⇔ BooleanExpr2 returns Boolean expression BooleanList1 ⇔ BooleanList2 returns Boolean list BooleanMatrix1 ⇔ BooleanMatrix2 returns Boolean matrix Integer1 ⇔ Integer2 returns Integer Returns the negation of an XOR Boolean operation on the two arguments. Returns true, false, or a simplified form of the equation. For lists and matrices, returns comparisons element by element.
d() (derivative) Catalog > d(Expr1, Var[, Order]) ⇒ expression d(List1, Var[, Order]) ⇒ list d(Matrix1,Var[, Order]) ⇒ matrix Returns the first derivative of the first argument with respect to variable Var. Order, if included, must be an integer. If the order is less than zero, the result will be an anti-derivative. Note: You can insert this function from the keyboard by typing derivative(...).
∫() (integral) Catalog > Returns the integral of Expr1 with respect to the variable Var from Lower to Upper. Note: See also Definite or Indefinite integral template, page 6. Note: You can insert this function from the keyboard by typing integral(...). If Lower and Upper are omitted, returns an anti-derivative. A symbolic constant of integration is omitted unless you provide the Constant argument. Equally valid anti-derivatives might differ by a numeric constant.
∫() (integral) Catalog > ∫() can be nested to do multiple integrals. Integration limits can depend on integration variables outside them. Note: See also nInt() , page 123. √() (square root) /q keys √(Expr1) ⇒ expression √(List1) ⇒ list Returns the square root of the argument. For a list, returns the square roots of all the elements in List1. Note: You can insert this function from the keyboard by typing sqrt(...) Note: See also Square root template, page 1.
Π() (prodSeq) Catalog > Π(Expr1, Var, Low, Low−1) ⇒ 1 Π(Expr1, Var, Low, High) ⇒ 1/Π(Expr1, Var, High+1, Low−1) if High < Low−1 The product formulas used are derived from the following reference: Ronald L. Graham, Donald E. Knuth, and Oren Patashnik. Concrete Mathematics: A Foundation for Computer Science . Reading, Massachusetts: Addison-Wesley, 1994. Σ() (sumSeq) Σ(Expr1, Var, Low, High) ⇒ expression Note: You can insert this function from the keyboard by typing sumSeq(...).
ΣInt() Catalog > ΣInt(NPmt1, NPmt2, N, I, PV ,[Pmt ], [FV], [PpY], [CpY], [PmtAt ], [roundValue ]) ⇒ value ΣInt(NPmt1,NPmt2,amortTable ) ⇒ value Amortization function that calculates the sum of the interest during a specified range of payments. NPmt1 and NPmt2 define the start and end boundaries of the payment range. N, I, PV, Pmt , FV, PpY, CpY, and PmtAt are described in the table of TVM arguments, page 195. • • • If you omit Pmt , it defaults to Pmt =tvmPmt ( N,I,PV,FV,PpY,CpY,PmtAt ).
ΣPrn() Catalog > NPmt1 and NPmt2 define the start and end boundaries of the payment range. N, I, PV, Pmt , FV, PpY, CpY, and PmtAt are described in the table of TVM arguments, page 195. • • • 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.
E (scientific notation) i key mantissaEexponent Enters a number in scientific notation. The number is interpreted as mantissa × 10exponent. Hint: If you want to enter a power of 10 without causing a decimal value result, use 10^integer. Note: You can insert this operator from the computer keyboard by typing @E. for example, type 2.3@E4 to enter 2.3E 4.
¹ key r(radian) This function gives you a way to specify a radian angle while in Degree or Gradian mode. In Degree angle mode, multiplies the argument by 180/ π. In Radian angle mode, returns the argument unchanged. In Gradian mode, multiplies the argument by 200/ π. Hint: Use r if you want to force radians in a function definition regardless of the mode that prevails when the function is used. Note: You can insert this symbol from the computer keyboard by typing @r.
/k keys °, ', '' (degree/minute/second) dd A positive or negative number mm A non-negative number ss.ss A non-negative number Returns dd+( mm/60)+( ss.ss/3600). This base-60 entry format lets you: • • Enter an angle in degrees/minutes/seconds without regard to the current angle mode. Enter time as hours/minutes/seconds. Note: Follow ss.ss with two apostrophes (''), not a quote symbol (").
/k keys ∠ (angle) º key ' (prime) variable ' variable ' ' Enters a prime symbol in a differential equation. A single prime symbol denotes a 1st-order differential equation, two prime symbols denote a 2nd-order, and so on. _ (underscore as an empty element) See “Empty (Void) Elements,” page 236. /_ keys _ (underscore as unit designator) Expr_Unit Designates the units for an Expr. All unit names must begin with an underscore. You can use pre-defined units or create your own units.
► (convert) /k keys Expr_Unit1►_Unit2 ⇒ Expr_Unit2 Converts an expression from one unit to another. The _ underscore character designates the units. The units must be in the same category, such as Length or Area. For a list of pre-defined units, open the Catalog and display the Unit Conversions tab: • • You can select a unit name from the list. You can select the conversion operator, ►, from the top of the list. You can also type unit names manually.
^ ⁻¹ (reciprocal) Expr1 ^⁻¹ ⇒ expression Catalog > List1 ^⁻¹ ⇒ list Returns the reciprocal of the argument. For a list, returns the reciprocals of the elements in List1. squareMatrix1 ^⁻¹ ⇒ squareMatrix Returns the inverse of squareMatrix1. squareMatrix1 must be a non-singular square matrix. | (constraint operator) Expr | BooleanExpr1[and BooleanExpr2]... Expr | BooleanExpr1[ orBooleanExpr2]... The constraint (“|”) symbol serves as a binary operator. The operand to the left of | is an expression.
| (constraint operator) /k keys Interval constraints take the form of one or more inequalities joined by logical “and” or “or” operators. Interval constraints also permit simplification that otherwise might be invalid or not computable. Exclusions use the “not equals” (/= or ≠) relational operator to exclude a specific value from consideration. They are used primarily to exclude an exact solution when using cSolve() , cZeros() , fMax() , fMin() , solve() , zeros() , and so on.
→ (store) /h key Hint: If you plan to do symbolic computations using undefined variables, avoid storing anything into commonly used, one-letter variables such as a, b, c, x, y, z, and so on. Note: You can insert this operator from the keyboard by typing =: as a shortcut. For example, type pi/4 =: myvar. := (assign) Var := Expr Var := List Var := Matrix Function(Param1,...) := Expr Function(Param1,...) := List Function(Param1,...
/k keys © (comment) © [text ] © processes text as a comment line, allowing you to annotate functions and programs that you create. © can be at the beginning or anywhere in the line. Everything to the right of © , to the end of the line, is the comment. Note for entering the example: For instructions on entering multi-line program and function definitions, refer to the Calculator section of your product guidebook.
Empty (Void) Elements When analyzing real-world data, you might not always have a complete data set. TI-Nspire™ CAS Software allows empty, or void, data elements so you can proceed with the nearly complete data rather than having to start over or discard the incomplete cases. You can find an example of data involving empty elements in the Lists & Spreadsheet chapter, under “Graphing spreadsheet data.” The delVoid() function lets you remove empty elements from a list.
List arguments containing void elements In regressions, a void in an X or Y list introduces a void for the corresponding element of the residual. An omitted category in regressions introduces a void for the corresponding element of the residual. A frequency of 0 in regressions introduces a void for the corresponding element of the residual.
Shortcuts for Entering Math Expressions Shortcuts let you enter elements of math expressions by typing instead of using the Catalog or Symbol Palette. For example, to enter the expression √6, you can type sqrt (6) on the entry line. When you press ·, the expression sqrt(6) is changed to √6. Some shortcuts are useful from both the handheld and the computer keyboard. Others are useful primarily from the computer keyboard.
To enter this: Type this shortcut: n1, n2, ... (integer constants) @n1, @n2, ... i (imaginary constant) @i e (natural log base e) @e (scientific notation) @E T (transpose) @t r (radians) @r ° (degrees) @d g @g E (gradians) ∠ (angle) @< ► (conversion) @> ►Decimal, ►approxFraction() , and so on. @>Decimal, @>approxFraction(), and so on.
EOS™ (Equation Operating System) Hierarchy This section describes the Equation Operating System (EOS™) that is used by the TI-Nspire™ CAS math and science learning technology. Numbers, variables, and functions are entered in a simple, straightforward sequence. EOS™ software evaluates expressions and equations using parenthetical grouping and according to the priorities described below.
The number of opening and closing parentheses, brackets, and braces must be the same within an expression or equation. If not, an error message is displayed that indicates the missing element. For example, (1+2)/(3+4 will display the error message “Missing ).” Note: Because the TI-Nspire™ CAS software allows you to define your own functions, a variable name followed by an expression in parentheses is considered a “function call” instead of implied multiplication.
Constants and Values The following table lists the constants and their values that are available when performing unit conversions. They can be typed in manually or selected from the Constants list in Utilities > Unit Conversions (Handheld: Press k 3). Constant Name Value _c Speed of light 299792458 _m/_s _Cc Coulomb constant 8987551787.3682 _m/_F _Fc Faraday constant 96485.33289 _coul/_mol _g Acceleration of gravity 9.80665 _m/_s2 _Gc Gravitational constant 6.
Error Codes and Messages When an error occurs, its code is assigned to variable errCode . User-defined programs and functions can examine errCode to determine the cause of an error. For an example of using errCode , See Example 2 under the Try command, page 191. Note: Some error conditions apply only to TI-Nspire™ CAS products, and some apply only to TI-Nspire™ products. Error code Description 10 A function did not return a value 20 A test did not resolve to TRUE or FALSE.
Error code Description 180 Break The d or c key was pressed during a long calculation or during program execution. 190 Circular definition This message is displayed to avoid running out of memory during infinite replacement of variable values during simplification. For example, a+1->a, where a is an undefined variable, will cause this error.
Error code Description 345 Inconsistent units 350 Index out of range 360 Indirection string is not a valid variable name 380 Undefined Ans Either the previous calculation did not create Ans, or no previous calculation was entered. 390 Invalid assignment 400 Invalid assignment value 410 Invalid command 430 Invalid for the current mode settings 435 Invalid guess 440 Invalid implied multiply For example, x(x+1) is invalid; whereas, x*(x+1) is the correct syntax.
Error code Description 600 Invalid table 605 Invalid use of units 610 Invalid variable name in a Local statement 620 Invalid variable or function name 630 Invalid variable reference 640 Invalid vector syntax 650 Link transmission A transmission between two units was not completed. Verify that the connecting cable is connected firmly to both ends. 665 Matrix not diagonalizable 670 Low Memory 1. Delete some data in this document 2.
Error code Description To allow complex results, change the “Real or Complex” Mode Setting to RECTANGULAR or POLAR. 830 Overflow 850 Program not found A program reference inside another program could not be found in the provided path during execution. 855 Rand type functions not allowed in graphing 860 Recursion too deep 870 Reserved name or system variable 900 Argument error Median-median model could not be applied to data set.
Error code Description 1000 Window variables domain 1010 Zoom 1020 Internal error 1030 Protected memory violation 1040 Unsupported function. This function requires Computer Algebra System. Try TI-Nspire™ CAS. 1045 Unsupported operator. This operator requires Computer Algebra System. Try TI-Nspire™ CAS. 1050 Unsupported feature. This operator requires Computer Algebra System. Try TI-Nspire™ CAS. 1060 Input argument must be numeric. Only inputs containing numeric values are allowed.
Error code Description A pathname must be in the form xxx\yyy, where: • • The xxx part can have 1 to 16 characters. The yyy part can have 1 to 15 characters. See the Library section in the documentation for more details. 1170 Invalid use of library pathname • • 1180 A value cannot be assigned to a pathname using Define, :=, or sto → . A pathname cannot be declared as a Local variable or be used as a parameter in a function or program definition. Invalid library variable name.
Error code Description Trigonometric conversion operators are not supported in Degree or Gradian angle modes. 1250 Argument Error Use a system of linear equations. Example of a system of two linear equations with variables x and y: 3x+7y=5 2y-5x=-1 1260 Argument Error: The first argument of nfMin or nfMax must be an expression in a single variable. It cannot contain a non-valued variable other than the variable of interest. 1270 Argument Error Order of the derivative must be equal to 1 or 2.
Warning Codes and Messages You can use the warnCodes() function to store the codes of warnings generated by evaluating an expression. This table lists each numeric warning code and its associated message. For an example of storing warning codes, see warnCodes() , page 200. Warning code Message 10000 Operation might introduce false solutions. 10001 Differentiating an equation may produce a false equation. 10002 Questionable solution 10003 Questionable accuracy 10004 Operation might lose solutions.
Warning code Message 10022 Specifying appropriate lower and upper bounds might produce a solution. 10023 Scalar has been multiplied by the identity matrix. 10024 Result obtained using approximate arithmetic. 10025 Equivalence cannot be verified in EXACT mode. 10026 Constraint might be ignored.
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Index ^, power 213 _ -, subtract _, unit designation ! !, factorial | |, constraint operator 220 " ", second notation 228 #, indirection #, indirection operator ′ minute notation ′, prime 226 241 216 & &, append 220 +, add ≠, not equal ≤, less than or equal ≥, greater than or equal >, greater than =, equal ∏, product 214 215 215 215 214 ∑( ), sum ∑Int( ) ∑Prn( ) 224 225 225 √ √, square root / 223 ∠ 212 ∠ (angle) : :=, assign 223 ∑ . /, divide 217 218 219 218 216 ∏ 211 .
► ►, convert units ►approxFraction( ) ►Base10, display as decimal integer ►Base16, display as hexadecimal ►Base2, display as binary ►cos, display in terms of cosine ►Cylind, display as cylindrical vector ►DD, display as decimal angle ►Decimal, display result as decimal ►DMS, display as degree/minute/second ►exp, display in terms of e ►Grad, convert to gradian angle ►Polar, display as polar vector ►Rad, convert to radian angle ►Rect, display as rectangular vector ►sin, display in terms of sine ►Sphere, displ
average rate of change, avgRC( ) avgRC( ), average rate of change 16 16 B binary display, ►Base2 indicator, 0b binomCdf( ) binomPdf( ) Boolean operators ⇒ ⇔ and nand nor not or xor 17 235 20, 93 20 219, 238 220 9 120 124 126 130 201 C Cdf( ) 69 ceiling( ), ceiling 20 ceiling, ceiling( ) 20-21, 36 centralDiff( ) 21 cFactor( ), complex factor 21 char( ), character string 22 character string, char( ) 22 characters numeric code, ord( ) 131 string, char( ) 22 charPoly( ) 23 χ²2way 23 clear error, ClrErr 25 C
countif( ) count items in a list, count( ) count( ), count items in a list countif( ), conditionally count items in a list cPolyRoots() cross product, crossP( ) crossP( ), cross product csc⁻¹( ), inverse cosecant csc( ), cosecant csch⁻¹( ), inverse hyperbolic cosecant csch( ), hyperbolic cosecant cSolve( ), complex solve cubic regression, CubicReg CubicReg, cubic regression cumulative sum, cumulativeSum( ) cumulativeSum( ), cumulative sum cycle, Cycle Cycle, cycle cylindrical vector display, ►Cylind cZeros(
poissPdf( ) tCdf( ) tPdf( ) χ²2way( ) χ²Cdf( ) χ²GOF( ) χ²Pdf( ) divide, / domain function, domain( ) domain( ), domain function dominant term, dominantTerm( ) dominantTerm( ), dominant term dot addition, .+ division, ./ multiplication, .* power, .^ product, dotP( ) subtraction, .
Fill, matrix fill financial functions, tvmFV( ) financial functions, tvmI( ) financial functions, tvmN( ) financial functions, tvmPmt( ) financial functions, tvmPV( ) first derivative template for FiveNumSummary floor( ), floor floor, floor( ) fMax( ), function maximum fMin( ), function minimum For for, For For, for format string, format( ) format( ), format string fpart( ), function part fractions propFrac template for freqTable( ) frequency( ) Frobenius norm, norm( ) Func, function Func, program function
imaginary part, imag( ) ImpDif( ), implicit derivative implicit derivative, Impdif( ) indefinite integral template for indirection operator (#) indirection, # input, Input Input, input inString( ), within string int( ), integer intDiv( ), integer divide integer divide, intDiv( ) integer part, iPart( ) integer, int( ) integral, ∫ interpolate( ), interpolate inverse cumulative normal distribution (invNorm( ) inverse, ^⁻¹ invF( ) invNorm( ), inverse cumulative normal distribution) invt( ) Invχ²( ) iPart( ), in
local variable, Local 106 local, Local 106 Local, local variable 106 Lock, lock variable or variable group 107 locking variables and variable groups 107 Log template for 2 logarithmic regression, LnReg 105 logarithms 104 logical double implication, ⇔ 220 logical implication, ⇒ 219, 238 logistic regression, Logistic 108 logistic regression, LogisticD 109 Logistic, logistic regression 108 LogisticD, logistic regression 109 loop, Loop 111 Loop, loop 111 LU, matrix lower-upper 111 decomposition M mat►list( ),
mixed fractions, using propFrac(› with mod( ), modulo mode settings, getMode( ) modes setting, setMode( ) modified internal rate of return, mirr () modulo, mod( ) mRow( ), matrix row operation mRowAdd( ), matrix row multiplication and addition Multiple linear regression t test multiply, * MultReg MultRegIntervals( ) MultRegTests( ) 139 117 84 162 116 117 117 117 119 211 118 118 119 N nand, Boolean operator natural logarithm, ln( ) nCr( ), combinations nDerivative( ), numeric derivative negation, entering
vector display, ►Polar 134 polyCoef( ) 134 polyDegree( ) 135 polyEval( ), evaluate polynomial 135 polyGcd( ) 136 polynomials evaluate, polyEval( ) 135 random, randPoly( ) 146 PolyRoots() 137 power of ten, 10^( ) 231 power regression, 137, 150-151, 187 PowerReg power, ^ 213 PowerReg, power regression 137 Prgm, define program 138 prime number test, isPrime( ) 94 prime, ′ 230 probability densiy, normPdf( ) 126 prodSeq() 139 product( ), product 139 product, ∏( ) 223 template for 5 product, product( ) 139 progra
quartic, QuartReg 142 sinusoidal, SinReg 169 remain( ), remainder 150 remainder, remain( ) 150 remove void elements from list 49 Request 150 RequestStr 151 result display in terms of cosine 29 display in terms of e 64 display in terms of sine 166 result values, statistics 178 results, statistics 177 return, Return 152 Return, return 152 right( ), right 152 right, right( ) 27, 61, 91, 152-153 rk23( ), Runge Kutta function 153 rotate( ), rotate 154 rotate, rotate( ) 154 round( ), round 156 round, round( ) 156
random number seed, 146 RandSeed standard deviation, stdDev 178-179, 198 () two-variable results, TwoVar 195 variance, variance( ) 198 stdDevPop( ), population standard 178 deviation stdDevSamp( ), sample standard 179 deviation Stop command 179 store variable (→) 233 storing symbol, & 234 string dimension, dim( ) 52 length 52 string( ), expression to string 180 strings append, & 220 character code, ord( ) 131 character string, char( ) 22 expression to string, string( ) 180 format, format( ) 73 formatting 73
second derivative 6 square root 1 sum, ∑( ) 5 system of equations (23 equation) system of equations (N3 equation) test for void, isVoid( ) 95 Test_2S, 2-sample F test 76 tExpand( ), trigonometric expansion 186 Text command 187 time value of money, Future Value 193 time value of money, Interest 193 time value of money, number of 194 payments time value of money, payment 194 amount time value of money, present value 194 tInterval, t confidence interval 187 tInterval_2Samp, twosample t 188 confidence interval
within string, inString( ) 90 X x², square XNOR xor, Boolean exclusive or 214 220 201 Z zeroes( ), zeroes zeroes, zeroes( ) zInterval, z confidence interval zInterval_1Prop, one-proportion z confidence interval zInterval_2Prop, two-proportion z confidence interval zInterval_2Samp, two-sample z confidence interval zTest zTest_1Prop, one-proportion z test zTest_2Prop, two-proportion z test zTest_2Samp, two-sample z test 202 202 204 205 205 206 206 207 207 208 Χ χ²Cdf( ) χ²GOF χ²Pdf( ) 267 Index 24 24
