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MatrixPolynomialAlgebra

  

LeftDivision

  

compute a left quotient and remainder of 2 matrices of polynomials

  

RightDivision

  

compute a right quotient and remainder of 2 matrices of polynomials

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

LeftDivision(A, B, x)

RightDivision(A, B, x)

Parameters

A

-

Matrix of polynomials

B

-

Matrix of polynomials

x

-

variable name of the polynomial domain

Description

• 

The LeftDivision(A, B, x) command computes a left quotient Q and a remainder R such that A=B.Q+R where B1.R is strictly proper.  That is,  limzB1z.Rz is a zero matrix. The input matrices must have the same number of rows, and B must be a square nonsingular matrix of polynomials.

• 

The RightDivision(A, B, x) command computes a right quotient Q and a remainder R such that A=Q.B+R where R.B1 is strictly proper.  That is,  limzRz.B1z is a zero matrix. The input matrices must have the same number of columns, and B must be a square nonsingular matrix of polynomials.

• 

The quotient Q and the remainder R are returned in a list.

Examples

withMatrixPolynomialAlgebra:

AMatrix2,2,9z23z+1,12z2+10z,3z3+2z2z,4z3+2z2z2:

BMatrix2,2,3z3+6z2+5z+1,12z213z,z4+z3+z2,4z33z+3z2:

Q,RopLeftDivisionA,B,z

Q,R:=00341,274z+13z14z2+54zz2z

(1)

mapexpand,AB.Q+R

0000

(2)

mapf→limz→∞f,LinearAlgebra:-MatrixInverseB.R

0000

(3)

Q,RopRightDivisionA,B,z

Q,R:=12016z+133612,6z212z+3232z36z2+72z512z3+76z29536z133653z2+18736z

(4)

mapexpand,AQ.B+R

0000

(5)

mapf→limz→∞f,R.LinearAlgebra:-MatrixInverseB

0000

(6)

See Also

expand

LinearAlgebra[MatrixInverse]

map

Matrix

MatrixPolynomialAlgebra

op

 


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