TITLE: (Efficient) computation of symmetric powers of square matrices
QUESTION [6 upvotes]: I'm looking for software that can compute symmetric powers of medium-size square (say rational, 100 by 100) matrices, and ideally can do so efficiently if the matrix is sparse enough. I haven't found any function for symmetric power in Sage or sympy, and a google search hasn't turned up anything. (An aside: Do people studying matrix algorithms have a different name for symmetric power, or they just aren't interested?) Any suggestions?
Edit: Macaulay2 only does symmetric powers of one-rowed matrices, it seems. Singular seems hopelessly inefficient on medium-sized sparse matrices (20 by 20).

REPLY [4 votes]: Sage can compute symmetric powers of matrices via a Singular function, we just discussed this here the other day. Or, indeed, you can use Singular directly.
Posted from mobile, sorry for lack of details.
PS. GAP has an undocumented function SymmetricPower, which computes symmetric powers of square matrices, but it is unfortunately quite slow.