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
LeftDivision(A, B, x)
RightDivision(A, B, x)
A
-
Matrix of polynomials
B
x
variable name of the polynomial domain
The LeftDivision(A, B, x) command computes a left quotient Q and a remainder R such that A=B·Q+R where B−1·R is strictly proper. That is, limz→∞B−1z.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·B−1 is strictly proper. That is, limz→∞Rz.B−1z 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.
withMatrixPolynomialAlgebra:
A≔Matrix2,2,−9z2−3z+1,12z2+10z,−3z3+2z2−z,4z3+2z−2z2:
B≔Matrix2,2,−3z3+6z2+5z+1,−12z2−13z,z4+z3+z2,−4z3−3z+3z2:
Q,R≔opLeftDivisionA,B,z
Q,R≔0034−1,27z4+1−3z−14z2+54zz2−z
mapexpand,A−B·Q+R
0000
mapf↦limitf,z=∞,LinearAlgebra:-MatrixInverseB·R
Q,R≔opRightDivisionA,B,z
Q,R≔−120−z6+1336−12,−6z2−12z+32−32z36z2+72z−512z3+76z2−9536z−133653z2+18736z
mapexpand,A−Q·B+R
mapf↦limitf,z=∞,R·LinearAlgebra:-MatrixInverseB
See Also
expand
LinearAlgebra[MatrixInverse]
map
Matrix
op
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