# Solve symbolic matrix equations

Let $S$ be a given matrix belonging to some matrix space over a ring. I wonder if SAGE can find matrices, say $A, B, $ in such a space, satisfying the equations $A + B = S$ and $AB = S$. Is there a way to do this? Thanks!

This is a long standing ticket in Sage: http://trac.sagemath.org/ticket/5201