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.

$\mathrm{with}\left(\mathrm{MatrixPolynomialAlgebra}\right)\:$

$A≔⟨⟨3+x\,4x^2\,x^2-1⟩\left|⟨1\,x\,4⟩\right|⟨-4x^3\,2x\,-x^3⟩⟩$

$A≔\left[\begin{array}{ccc}3+x& 1& -4x^3\\ 4x^2& x& 2x\\ x^2-1& 4& -x^3\end{array}\right]$

$\mathrm{Degree}\left(A\,x\right)$

$3$

$\mathrm{Degree}\left[\mathrm{row}\right]\left(A\,x\right)$

$\left[3\,2\,3\right]$

$\mathrm{Degree}\left[\mathrm{column}\right]\left(A\,x\right)$

$\left[2\,1\,3\right]$

$\mathrm{Ldegree}\left(A\,x\right)$

$0$

$\mathrm{Ldegree}\left[\mathrm{row}\right]\left(A\,x\right)$

$\left[0\,1\,0\right]$

$\mathrm{Ldegree}\left[\mathrm{column}\right]\left(A\,x\right)$

$\left[0\,0\,1\right]$