MatrixPolynomialAlgebra - Maple Programming Help

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MatrixPolynomialAlgebra

 Degree
 compute the degree of a matrix of polynomials.
 Ldegree
 compute the low degree of a matrix of polynomials.

 Calling Sequence Degree(A, x) Degree[row](A, x) Degree[column](A, x) Ldegree(A, x) Ldegree[row](A, x) Ldegree[column](A, x)

Parameters

 A - Matrix x - name; specify the variable in which the entries of A are rational polynomials over Q

Description

 • The Degree(A,x) and Ldegree(A,x) commands compute the highest degree and the lowest degree of a matrix of polynomials.
 • The Degree[row](A,x) and Ldegree[row](A,x) commands compute the highest degree and lowest degree of each row of a matrix of polynomials. The row degree is returned as a list of integers.
 • The Degree[column](A,x) and Ldegree[column](A,x) commands compute the highest degree and lowest degree of each column of a matrix of polynomials.  The column degree is returned as a list of integers.

Examples

 > $\mathrm{with}\left(\mathrm{MatrixPolynomialAlgebra}\right):$
 > $A≔⟨⟨3+x,4{x}^{2},{x}^{2}-1⟩|⟨1,x,4⟩|⟨-4{x}^{3},2x,-{x}^{3}⟩⟩$
 ${A}{:=}\left[\begin{array}{ccc}{3}{+}{x}& {1}& {-}{4}{}{{x}}^{{3}}\\ {4}{}{{x}}^{{2}}& {x}& {2}{}{x}\\ {{x}}^{{2}}{-}{1}& {4}& {-}{{x}}^{{3}}\end{array}\right]$ (1)
 > $\mathrm{Degree}\left(A,x\right)$
 ${3}$ (2)
 > $\mathrm{Degree}[\mathrm{row}]\left(A,x\right)$
 $\left[{3}{,}{2}{,}{3}\right]$ (3)
 > $\mathrm{Degree}[\mathrm{column}]\left(A,x\right)$
 $\left[{2}{,}{1}{,}{3}\right]$ (4)
 > $\mathrm{Ldegree}\left(A,x\right)$
 ${0}$ (5)
 > $\mathrm{Ldegree}[\mathrm{row}]\left(A,x\right)$
 $\left[{0}{,}{1}{,}{0}\right]$ (6)
 > $\mathrm{Ldegree}[\mathrm{column}]\left(A,x\right)$
 $\left[{0}{,}{0}{,}{1}\right]$ (7)