On Sat, Oct 3, 2009 at 1:30 PM, David Joyner <wdjoy...@gmail.com> wrote: > > The abelian group class needs to be rewritten. The basic idea > was to try to use GAP as much as possible and use > Python/Sage to parse input and output. For various > technical reasons, that did not work as nicely as hoped. > The correct solution, may be to rewrite it from scratch completely > separate from GAP.
And this has already been almost completed by David Loeffler based on work by me. http://trac.sagemath.org/sage_trac/ticket/6449 David is done working on that so somebody else has a chance to be a hero and step up and finish it. Go somebody! Whoever you are, if you finish this, you'll be the first to successfully "rewrite abelian groups", after about 7 people have tried and failed. Time to clime Everest. -- William > > This doesn't answer your question, but I hope gives you confidence > that if you think that something is odd about the implementation > and you want to change it, then you are probably correct. > > > On Sat, Oct 3, 2009 at 3:43 PM, Rob Beezer <goo...@beezer.cotse.net> wrote: >> >> The AbelianGroup class has an extremely welcome method that >> manufactures all subgroups of a finite abelian group. These groups >> are a big part of an introductory group theory course, so to be able >> to list and inspect all subgroups is a really great feature that I >> wish was more widespread. However, I've stumbled across the following >> behavior (demonstrated here in Z/2Z x Z/4Z), which I think will be >> very confusing to students, since it gave me pause: >> >> sage: G=AbelianGroup([2,4]) >> sage: K=G.subgroups()[1] >> sage: K >> >> Multiplicative Abelian Group isomorphic to C2 x C2, >> which is the subgroup of Multiplicative Abelian Group >> isomorphic to C2 x C4 generated by [f1^2, f0] >> >> sage: K.gens() >> [f1^2, f0] >> sage: K.list() >> [1, f1, f0, f0*f1] >> >> At first glance it looks like the generator f1^2 is not an element of >> the subgroup! The explanation is that the generators are reported in >> terms of the two generators of the full Z/2Z x Z/4Z group G (f0, f1), >> while the elements of the subgroup K are reported using conceptually >> "new" names for its two generators. In effect there are assignments >> f1 = f1^2, f0 = f0 in moving to the elements of the subgroup. Other >> examples with smaller subgroups of larger groups can get more >> complicated, where the indexing also seems to "shift" downward for the >> subgroup. >> >> So subgroups are being reported as isomorphic copies rather than as >> subsets of the group, while retaining enough information to >> reconstruct them as subsets. This certainly makes great sense for a >> compact manageable internal representation, but does it make sense to >> report elements of the subgroup relative to the isomorphic >> representation or in terms of the full (ambient) group? >> >> Seemingly related to this, subgroups are implemented with their own >> class, which does not seem to permit always obtaining subgroups of >> subgroups - there appears to be something like a check that the set of >> names used are equal, which raises an error since they can be more >> mismatched than in the above example. In the definition of K above, >> switch the index to 5 and ask for K's subgroups to see this error >> behavior. At a minimum this would seem to be a bug, because this >> action seems to work correctly for the original K. >> >> I'm building a class for the group of units mod n, mostly on top of >> this AbelianGroup implementation. So far, I just represent subgroups >> with the same class that I use for the "full" group. Would this be a >> bad idea for the AbelianGroup class (or is it a bad idea for the class >> I'm building)? Or would there be a way to (optionally) have a >> subgroup report its elements in terms of the full group? I don't see >> a command to realize a subgroup as a subset of the original group, but >> maybe the reverse would make sense: you get a subgroup that is a >> subset, unless you ask explicitly for an isomorphic version? Is the >> current, or the suggested, behavior totally inconsistent with what is >> done elsewhere in Sage? >> >> Clarifications, unexplored commands, workarounds, policies, >> suggestions, opinions, sympathy all welcome. Thanks. >> >> Rob >> >> >> > >> > > > > -- William Stein Associate Professor of Mathematics University of Washington http://wstein.org --~--~---------~--~----~------------~-------~--~----~ 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 -~----------~----~----~----~------~----~------~--~---
