Group algebras would be natural and interesting. I would suggest that they derive from FreeAlgebra, and improve those if the performance was inadequate. This gives a sparse representation, and as I remember, for finite dimensional (quotient) algebras, I use the explicit matrix representation on finite dimensional vector spaces. However, for large (finite) groups one would not want to use the (dense) basis representation.
The module decomposition problem is only easier over finite fields because the modules are finite; the theory is more subtle than in characteristic zero. It is computationally harder to find the splittings since the generating basis elements can be large (in terms of a fixed group algebra basis), but my understanding is that the character theory and resulting representation theory is better understood. Doing local decompositions over p-adics integer rings and number/function rings would give insight into both the modular theory (i.e. over finite fields) and characteristic zero, so the computational infrastructure should be set up generically. --David --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://sage.scipy.org/sage/ and http://modular.math.washington.edu/sage/ -~----------~----~----~----~------~----~------~--~---
