2015-01-12 16:08 UTC+01:00, William Stein <wst...@gmail.com>:
> By the way, yesterday at the Sage booth at the Joint Math meetings somebody
> walked up and said, "can you use Sage to enumerate the groups of order 16?"
>   For a group theorist, this is a very natural basic question.     I tried
> groups.[tab] and found nothing useful.  I tried searching the sage
> reference manual and couldn't figure it out.  I then of course googled for
> GAP and that sort of question, and found how to do it directly with GAP and
> did.  However, I could not figure out how to convert a gap group back to
> Sage.  And I couldn't figure out how to list the elements of a GAP group.
>  So I'm definitely not so happy with the group theory functionality in
> Sage, or at least its documentation.
> Remember, this was all in front of an impatient *potential* Sage users, so
> I don't get 20 minutes to try to figure out each thing -- if I can't in 1
> minute, we lose.

That's a pity... we have everything

1) gap stuff

sage: for g in gap.AllGroups(12): print g
Group( [ f1, f2, f3 ] )
Group( [ f1, f2, f3 ] )
Group( [ f1, f2, f3 ] )
Group( [ f1, f2, f3 ] )
Group( [ f1, f2, f3 ] )

2) gap wrappers for finitely presented groups

sage: G.<a,b> = FreeGroup()
sage: H = G / [a, b^3]
sage: H
Finitely presented group < a, b | a, b^3 >

But there is currently no way to initialize 2) with a group from GAP!
Too bad. I created #17627 for that.

Vincent

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