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).