1 | initial version |
Aladin Virmaux has written some code (ported from Florent Hivert's implementation in MuPAD) that computes the Cartan matrix of a finite dimensional algebra by constructing orthogonal idempotents and building the sandwiches e_i A e_j. The code is meant to go into Sage at some point, but it still needs polishing and has a couple dependencies.
Probably something could be extracted out of it for your need, but I don't expect it to do better than the naive implementation: building the a basis of the projective module e_i A by repeated multiplication on the right by the generators and so on.
If your algebra is the algebra of a monoid or semigroup, let us know for there we have much more under hand :-)
What kind of dimension do you have in mind?