e^(squareMatrix1) ⇒ squareMatrix

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

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

eff(nominalRate,CpY) ⇒ value

Financial function that converts the nominal interest rate nominalRate to an annual effective rate, given CpY as the number of compounding periods per year.

nominalRate must be a real number, and CpY must be a real number > 0.

Note: See also nom(), here.

eigVc(squareMatrix) ⇒ matrix

Returns a matrix containing the eigenvectors for a real or complex squareMatrix, where each column in the result corresponds to an eigenvalue. Note that an eigenvector is not unique; it may be scaled by any constant factor. The eigenvectors are normalized, meaning that:

if  V = [x1, x2, … , xn]

then x12 + x22 + … + xn2 = 1

squareMatrix is first balanced with similarity transformations until the row and column norms are as close to the same value as possible. The squareMatrix is then reduced to upper Hessenberg form and the eigenvectors are computed via a Schur factorization.

eigVl(squareMatrix) ⇒ list

Returns a list of the eigenvalues of a real or complex squareMatrix.

squareMatrix is first balanced with similarity transformations until the row and column norms are as close to the same value as possible. The squareMatrix is then reduced to upper Hessenberg form and the eigenvalues are computed from the upper Hessenberg matrix.

If BooleanExpr1 Then
     Block1
ElseIf BooleanExpr2 Then
     Block2
⋮
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.

euler(Expr, Var, depVar, {Var0, VarMax}, depVar0, VarStep [, eulerStep]) ⇒ matrix

euler(SystemOfExpr, Var, ListOfDepVars, {Var0, VarMax},      ListOfDepVars0, VarStep [, eulerStep]) ⇒ matrix

euler(ListOfExpr, Var, ListOfDepVars, {Var0, VarMax}, ListOfDepVars0, VarStep [, eulerStep]) ⇒ matrix

Uses the Euler method to solve the system

with depVar(Var0)=depVar0 on the interval [Var0,VarMax]. Returns a matrix whose first row defines the Var output values and whose second row defines the value of the first solution component at the corresponding Var values, and so on.

Expr is the right-hand side that defines the ordinary differential equation (ODE).

SystemOfExpr is the system of right-hand sides that define the system of ODEs (corresponds to order of dependent variables in ListOfDepVars).

ListOfExpr is a list of right-hand sides that define the system of ODEs (corresponds to the order of dependent variables in ListOfDepVars).

Var is the independent variable.

ListOfDepVars is a list of dependent variables.

{Var0, VarMax} is a two-element list that tells the function to integrate from Var0 to VarMax.

ListOfDepVars0 is a list of initial values for dependent variables.

VarStep is a nonzero number such that sign(VarStep) = sign(VarMax‑Var0) and solutions are returned at Var0+i•VarStep for all i=0,1,2,… such that Var0+i•VarStep is in [var0,VarMax] (there may not be a solution value at VarMax).

eulerStep is a positive integer (defaults to 1) that defines the number of euler steps between output values. The actual step size used by the euler method is VarStep ⁄ eulerStep.

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 (here), GetStr (here), and Send (here).

exact(Expr1 [, Tolerance]) ⇒ expression
exact(List1 [, Tolerance]) ⇒ list
exact(Matrix1 [, Tolerance]) ⇒ matrix

Uses Exact mode arithmetic to return, when possible, the rational-number equivalent of the argument.

Tolerance specifies the tolerance for the conversion; the default is 0 (zero).

Exit

Exits the current For, While, or Loop block.

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

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

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(squareMatrix1) ⇒ squareMatrix

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

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

exp►list(Expr,Var) ⇒ list

Examines Expr for equations that are separated by the word “or,” and returns a list containing the right-hand sides of the equations of the form Var=Expr. This gives you an easy way to extract some solution values embedded in the results of the solve(), cSolve(), fMin(), and fMax() functions.

Note: exp►list() is not necessary with the zeros() and cZeros() functions because they return a list of solution values directly.

You can insert this function from the keyboard by typing exp@>list(...).

expand(Expr1,[Var]) also distributes logarithms and fractional powers regardless of Var. For increased distribution of logarithms and fractional powers, inequality constraints might be necessary to guarantee that some factors are nonnegative.

expand(Expr1, [Var]) also distributes absolute values, sign(), and exponentials, regardless of Var.

Note: See also tExpand() for trigonometric angle-sum and multiple-angle expansion.

expr(String) ⇒ expression

Returns the character string contained in String as an expression and immediately executes it.

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

Computes the exponential regression y = a•(b)x on lists X and Y with frequency Freq. A summary of results is stored in the stat.results variable. (See 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.