Input/Output:

 

 

 

 

 

Level 1/Argument 1

 

Level 3/Item 1

Level 2/Item 2

Level 1/Item 3

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

[[ matrix ]]A

→

[[ matrix ]]L

[[ matrix ]]U

[[ matrix ]]P

 

DET, INV,

 

 

 

 

 

See also:

LSQ, /

 

 

 

 

LVAR

 

 

 

 

 

 

 

 

 

Type:

Command

 

 

 

 

Description:

Returns a list of variables in an algebraic object. Differs from LNAME above in that functions of

 

variables, such as COS(X) or LN(AB) are returned, instead of the variable names, X or AB. INV()

 

and SQ() are not treated as functions. Compare the example here with the same example in

 

LNAME.

 

 

 

 

Access:

Catalog, …µ

 

 

 

 

Input:

An algebraic object.

 

 

 

 

Output:

Level 2/Item 1: The algebraic object.

 

 

 

 

Level 1/Item 2: A list which includes both the original expression and a vector containing the

 

variable names. Variable names include functions of variables, as described above. The names are

 

sorted by length, longest first, and ones of equal length are sorted alphabetically.

 

Flags:

Exact mode must be set (flag –105 clear).

 

 

 

 

Numeric mode must not be set (flag –3 clear).

 

 

Example:

List the variables and function names in the expression COS(B)/2*A + MYFUNC(PQ) + 1/T.

Command:

LVAR(COS(B)/2*A + MYFUNC(PQ) + INV(T))

 

 

Result:

{COS(B)/2*A + MYFUNC(PQ) + 1/T, [MYFUNC(PQ),COS(B),A,T]}

 

See also:

LNAME

 

 

 

 

MAD

 

 

 

 

 

 

 

 

 

Type:

Command

 

 

 

 

Description:

Returns details of a square matrix, including the information needed to obtain the adjoint matrix.

 

The adjoint matrix is obtained by multiplying the inverse matrix by the determinant.

Access:

Matrices, !Ø OPERATIONS L

 

 

 

Input:

A square matrix

 

 

 

 

Output:

Level 4/Item 1: The determinant.

 

 

 

 

 

Level 3/Item 2: The formal inverse.

 

 

 

 

Level 2/Item 3: The matrix coefficients of the polynomial, p, defined by

 

 

(xi–a)p(x)=m(x)i, where a is the matrix, and m is the characteristic polynomial of a.

 

 

Level 1/Item 4: The characteristic polynomial.

 

 

Flags:

Exact mode must be set (flag –105 clear).

 

 

 

 

Numeric mode must not be set (flag –3 clear).

 

 

Example:

Obtain the adjoint matrix of:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0 –1

 

 

 

 

 

 

 

1

0

 

 

 

 

 

 

Command:

 

 

 

 

 

 

 

MAD([[0, -1][1, 0]])

 

 

 

 

Result:

{1,[[0, 1][-1, 0]],{[[1, 0][0, 1]], [[0, -1][1, 0]]}, X^2+1}

 

 

The determinant is 1, so the adjoint is the second item[[0, 1][-1, 0]].

 

See also:

LNAME

 

 

 

 

3-140 Full Command and Function Reference