Sorry, I've just seen William's earlier post in this thread, and I see that there was no need for my rather combative previous post -- I apologise for any offence I may have caused.
David On Oct 4, 2:05 am, William Stein <wst...@gmail.com> wrote: > 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 Washingtonhttp://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 -~----------~----~----~----~------~----~------~--~---
