I think it should be considered a bug, because it is sage, not the user, that decides what presentation to use. In this example, the group A is not considered equal to the subgroup generated by its generators (groups that are not only isomorphic, but really equal), because internally the presentation of the subgroup differs from that of the ambient group. On the other hand, there are isomorphic groups with different presentations that are considered equal: AbelianGroup([6]) == AbelianGroup([1,6]) True
On May 8, 10:16 am, "John Cremona" <[EMAIL PROTECTED]> wrote: > Is this actually a bug? It would certainly wrong if the test being > performed was isomorphism rather than equality, but I think it is > actually reasonable for two finite abelian groups to only be reported > as "equal" when they are presented the same way. > > John Cremona > > 2008/5/7 William Stein <[EMAIL PROTECTED]>: > > > > > On Wed, May 7, 2008 at 3:18 PM, Utpal Sarkar <[EMAIL PROTECTED]> wrote: > > > > Hi there, > > > > When I define an abelian group > > > A = AbelianGroup(1,[6]) > > > and then generate a subgroup that actually is the whole group itself, > > > and then compare it to the original group: > > > A.subgroup(list(A.gens())) == A > > > the result may be either True or False. In this example it is False. > > > When defining A as > > > A = AbelianGroup(2,[3,2]) > > > it is False as well, but when I define it as > > > A = AbelianGroup(2,[2,3]) > > > it is True. > > > My guess is that this is because comparison of finite Abelian groups > > > is implemented using their invariant factors, but when you create the > > > group using factors that are not in canonical form or not in > > > increasing order, these are used instead of the ordered list of > > > invariant factors anyway. > > > > Greetings, > > > > Utpal > > > Thanks for reporting this bug! We are tracking it here: > > > http://trac.sagemath.org/sage_trac/ticket/3127 > > > -- William --~--~---------~--~----~------------~-------~--~----~ 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-support URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
