javier wrote: > If that you want are the cosets you can get them simply using > > cosets = Set([Set([h*g for h in H]) for g in G]) > > or if you want to get a representative of each coset you can then use > > reps = [x[0] for x in cosets] > > this should work even if H is not normal, the only issue being that > the set of cosets is not a group. Not sure if it will help with your > problem, though. >
Yes, I will use that, for now, although I was hoping to get a "nice" representation of the set of cosets, in terms of generators. Anyway, it looks like I wasn't expecting too much after all. On http://en.wikipedia.org/wiki/Group_action or S. Lang: Algebra (p. 28) I find exactly what I want, supposing a group G acts transitively on a set X: "If G does not act faithfully on X, one can easily modify the group to obtain a faithful action. If we define N = {g in G : g·x = x for all x in X}, then N is a normal subgroup of G; indeed, it is the kernel of the homomorphism G → Sym(X). The factor group G/N acts faithfully on X by setting (gN)·x = g·x. The original action of G on X is faithful if and only if N = {e}." So what I need, computationally, is not a map from G -> G/N, but more the other way round. More explicitly I want a (nice, simple, concise) description of X (= orbit of G) in terms of elements of G. The cosets will do that, but not really simpler than X itself. Provided I come up with something sufficiently general, there will be a patch with a new feature :-) Thanks, again -- Robert Schwarz <[email protected]> Get my public key at http://rschwarz.net/key.asc --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to [email protected] 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://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
