ceiling(List1) ⇒ list
ceiling(Matrix1) ⇒ matrix

Returns a list or matrix of the ceiling of each element.

centralDiff(Expr1,Var [=Value][,Step]) ⇒ expression

centralDiff(Expr1,Var [,Step])|Var=Value ⇒ expression

centralDiff(Expr1,Var [=Value][,List]) ⇒ list

centralDiff(List1,Var [=Value][,Step]) ⇒ list

centralDiff(Matrix1,Var [=Value][,Step]) ⇒ matrix

Returns the numerical derivative using the central difference quotient formula.

When Value is specified, it overrides any prior variable assignment or any current “|” substitution for the variable.

Step is the step value. If Step is omitted, it defaults to 0.001.

When using List1 or Matrix1, the operation gets mapped across the values in the list or across the matrix elements.

Note: See also avgRC() and d().

For the Auto setting of the Auto or Approximate mode, including Var also permits approximation with floating-point coefficients where irrational coefficients cannot be explicitly expressed concisely in terms of the built-in functions. Even when there is only one variable, including Var might yield more complete factorization.

Note: See also factor().

char(Integer) ⇒ character

Returns a character string containing the character numbered Integer from the handheld character set. The valid range for Integer is 0–65535.

charPoly(squareMatrix,Var) ⇒ polynomial expression

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 pA(λ), is the polynomial defined by

pA(λ) = det(λ•I−A)

where I denotes the n×n identity matrix.

squareMatrix1 and squareMatrix2 must have the equal dimensions.

χ22way obsMatrix

chi22way obsMatrix

Computes a χ2 test for association on the two-way table of counts in the observed matrix obsMatrix. A summary of results is stored in the stat.results variable. (here)

For information on the effect of empty elements in a matrix, see “Empty (Void) Elements,” here.

χ2Cdf(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 χ2 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,” here.

χ2GOF obsList,expList,df

chi2GOF obsList,expList,df

Performs a test to confirm that sample data is from a population that conforms to a specified distribution. obsList is a list of counts and must contain integers. A summary of results is stored in the stat.results variable. (See here.)

For information on the effect of empty elements in a list, see “Empty (Void) Elements,” here.

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

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

Computes the probability density function (pdf) for the χ2 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,” here.

ClearAZ

Clears all single-character variables in the current problem space.

If one or more of the variables are locked, this command displays an error message and deletes only the unlocked variables. See unLock, here.

ClrErr

Clears the error status and sets system variable errCode to zero.

The Else clause of the Try...Else...EndTry block should use ClrErr or PassErr. If the error is to be processed or ignored, use ClrErr. If what to do with the error is not known, use PassErr to send it to the next error handler. If there are no more pending Try...Else...EndTry error handlers, the error dialog box will be displayed as normal.

Note: See also PassErr, here, and Try, here.

Note for entering the example: For instructions on entering multi-line program and function definitions, refer to the Calculator section of your product guidebook.

colAugment(Matrix1, Matrix2) ⇒ matrix

Returns a new matrix that is Matrix2 appended to Matrix1. The matrices must have equal column dimensions, and Matrix2 is appended to Matrix1 as new rows. Does not alter Matrix1 or Matrix2.

colDim(Matrix) ⇒ expression

Returns the number of columns contained in Matrix.

Note: See also rowDim().

colNorm(Matrix) ⇒ expression

Returns the maximum of the sums of the absolute values of the elements in the columns in Matrix.

Note: Undefined matrix elements are not allowed. See also rowNorm().

Even when there is no denominator, the comden function is often a fast way to achieve partial factorization if factor() is too slow or if it exhausts memory.

Hint: Enter this comden() function definition and routinely try it as an alternative to comDenom() and factor().

completeSquare(ExprOrEqn, Var) ⇒ expression or equation

completeSquare(ExprOrEqn, Var^Power) ⇒ expression or equation

completeSquare(ExprOrEqn, Var1, Var2 [,...]) ⇒ expression or equation

completeSquare(ExprOrEqn, {Var1, Var2 [,...]}) ⇒ expression or equation

Converts a quadratic polynomial expression of the form a•x2+b•x+c into the form a•(x-h)2+k

- or -

Converts a quadratic equation of the form a•x2+b•x+c=d into the form a•(x-h)2=k

The first argument must be a quadratic expression or equation in standard form with respect to the second argument.

The Second argument must be a single univariate term or a single univariate term raised to a rational power, for example x, y2, or z(1/3).

The third and fourth syntax attempt to complete the square with respect to variables Var1, Var2 [,… ]).

conj(Expr1) ⇒ expression

conj(List1) ⇒ list

conj(Matrix1) ⇒ matrix

Returns the complex conjugate of the argument.

Note: All undefined variables are treated as real variables.

constructMat(Expr,Var1,Var2,numRows,numCols) ⇒ matrix

Returns a matrix based on the arguments.

Expr is an expression in variables Var1 and Var2. Elements in the resulting matrix are formed by evaluating Expr for each incremented value of Var1 and Var2.

Var1 is automatically incremented from 1 through numRows. Within each row, Var2 is incremented from 1 through numCols.

CopyVar Var1., Var2. copies all members of the Var1. variable group to the Var2. group, creating Var2. if necessary.

Var1. must be the name of an existing variable group, such as the statistics stat.nn results, or variables created using the LibShortcut() function. If Var2. already exists, this command replaces all members that are common to both groups and adds the members that do not already exist. If one or more members of Var2. are locked, all members of Var2. are left unchanged.

corrMat(List1,List2[,…[,List20]])

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

Expr ►cos

Note: You can insert this operator from the computer keyboard by typing @>cos.

Represents Expr in terms of cosine. This is a display conversion operator. It can be used only at the end of the entry line.

►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.

cos(squareMatrix1) ⇒ squareMatrix

Returns the matrix cosine of squareMatrix1. This is not the same as calculating the cosine of each element.

When a scalar function f(A) operates on squareMatrix1 (A), the result is calculated by the algorithm:

Compute the eigenvalues (λi) and eigenvectors (Vi) of A.

squareMatrix1 must be diagonalizable. Also, it cannot have symbolic variables that have not been assigned a value.

Form the matrices:

Then A = X B X⁻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(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.

cosh(squareMatrix1) ⇒ squareMatrix

Returns the matrix hyperbolic cosine of squareMatrix1. This is not the same as calculating the hyperbolic cosine of each element. For information about the calculation method, refer to cos().

squareMatrix1 must be diagonalizable. The result always contains floating-point numbers.

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. The result always contains floating-point numbers.

cot(Expr1) ⇒ expression

cot(List1) ⇒ list

Returns the cotangent of Expr1 or returns a list of the cotangents of all elements in List1.

Note: The argument is interpreted as a degree, gradian or radian angle, according to the current angle mode setting. You can use °, G, or r to override the angle mode temporarily.

cot⁻¹(Expr1) ⇒ expression

cot⁻¹(List1) ⇒ list

Returns the angle whose cotangent is Expr1 or returns a list containing the inverse cotangents of each element of List1.

Note: The result is returned as a degree, gradian or radian angle, according to the current angle mode setting.

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

coth(Expr1) ⇒ expression

coth(List1) ⇒ list

Returns the hyperbolic cotangent of Expr1 or returns a list of the hyperbolic cotangents of all elements of List1.

coth⁻¹(Expr1) ⇒ expression

coth⁻¹(List1) ⇒ list

Returns the inverse hyperbolic cotangent of Expr1 or returns a list containing the inverse hyperbolic cotangents of each element of List1.

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

count(Value1orList1 [,Value2orList2 [,...]]) ⇒ value

Returns the accumulated count of all elements in the arguments that evaluate to numeric values.

Each argument can be an expression, value, list, or matrix. You can mix data types and use arguments of various dimensions.

For a list, matrix, or range of cells, each element is evaluated to determine if it should be included in the count.

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

Empty (void) elements are ignored. For more information on empty elements, see here.

countif(List,Criteria) ⇒ value

Returns the accumulated count of all elements in List that meet the specified Criteria.

Criteria can be:

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

Empty (void) elements in the list are ignored. For more information on empty elements, see here.

Note: See also sumIf(), here, and frequency(), here.

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(), here.

crossP(Vector1, Vector2) ⇒ vector

Returns a row or column vector (depending on the arguments) that is the cross product of Vector1 and Vector2.

Both Vector1 and Vector2 must be row vectors, or both must be column vectors. Both vectors must have equal dimension, and the dimension must be either 2 or 3.

csc(Expr1) ⇒ expression

csc(List1) ⇒ list

Returns the cosecant of Expr1 or returns a list containing the cosecants of all elements in List1.

csc⁻¹(Expr1) ⇒expression

csc⁻¹(List1) ⇒list

Returns the angle whose cosecant is Expr1 or returns a list containing the inverse cosecants of each element of List1.

Note: The result is returned as a degree, gradian or radian angle, according to the current angle mode setting.

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

csch(Expr1) ⇒ expression

csch(List1) ⇒ list

Returns the hyperbolic cosecant of Expr1 or returns a list of the hyperbolic cosecants of all elements of List1.

csch⁻¹(Expr1) ⇒ expression

csch⁻¹(List1) ⇒ list

Returns the inverse hyperbolic cosecant of Expr1 or returns a list containing the inverse hyperbolic cosecants of each element of List1.

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

A non-real guess is often necessary to determine a non-real solution. For convergence, a guess might have to be rather close to a solution.

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

Computes the cubic polynomial regression y=a•x3+b•x2+c•x+d on lists X and Y with frequency Freq. A summary of results is stored in the stat.results variable. (See here.)

All the lists must have equal dimension except for Include.

X and Y are lists of independent and dependent variables.

Freq is an optional list of frequency values. Each element in Freq specifies the frequency of occurrence for each corresponding X and Y data point. The default value is 1. All elements must be integers ≥ 0.

Category is a list of category codes for the corresponding X and Y data.

Include is a list of one or more of the category codes. Only those data items whose category code is included in this list are included in the calculation.

For information on the effect of empty elements in a list, see “Empty (Void) Elements,” here.

cumulativeSum(Matrix1) ⇒ matrix

Returns a matrix of the cumulative sums of the elements in Matrix1. Each element is the cumulative sum of the column from top to bottom.

An empty (void) element in List1 or Matrix1 produces a void element in the resulting list or matrix. For more information on empty elements, see here.

Cycle

Transfers control immediately to the next iteration of the current loop (For, While, or Loop).

Cycle is not allowed outside the three looping structures (For, While, or Loop).

Note for entering the example: For instructions on entering multi-line program and function definitions, refer to the Calculator section of your product guidebook.

Vector ►Cylind

Note: You can insert this operator from the computer keyboard by typing @>Cylind.

Displays the row or column vector in cylindrical form [r,∠θ, z].

Vector must have exactly three elements. It can be either a row or a column.

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.