Hi all, thanks for the tip-off in CombinatorialFreeModule, I have been trying to use this, but cannot find any sensible way to make it work.
sage: G = SymmetricGroup(3) sage: B = sorted(list(G)) sage: n = len(B) sage: K = CyclotomicField(n) sage: A = GroupAlgebra(G,K) sage: V = CombinatorialFreeModule(K,B) sage: X = G.irreducible_characters() up to here everything goes fine. Now I need to compute the idempotent elements as elements of the group algebra, and I simply do this: sage: E = [K(x(G(1))/n)*A(FormalSum([(x(g),g) for g in B], parent=FormalSums(K))) for x in X] and still no problem. Finally, I get the generators for the blocks for the AW-decomp as sage: Block_gens = [[e*A(g)*e for g in B] for e in E] What now I'd like to do is take each of the sublists in Block_gens and convert it to a list of vectors so that I can extract a basis from them. Eventually, I'd like to take the obtained vectors and bring them back to the group algebra. Is there a way of doing of this with the current CombinatorialFreeModule? On Feb 17, 8:43 pm, Florent Hivert <florent.hiv...@univ-rouen.fr> wrote: > So maybe this is was you want: > > sage: MPR = a.parent(); MPR > Multivariate Polynomial Ring in a, b over Rational Field > sage: C = CombinatorialFreeModule(QQ, MPR) > sage: C(a^2) > B[a^2] > sage: C(a^2)+C(b^2) > B[b^2] + B[a^2] Unfortunately that trick is not useful for my purposes (getting rid of linearly dependent expressions on the group algebra). In an ideal world, GroupAlgebra(G,K) would automatically be a "vector space over K with basis G" and one could do something like sage: V = A.vector_space() sage: Blocks = [V.subspace(x).basis() for x in Block_gens] Any hints on this direction? Cheers J -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
