Ticket #10722 (closed enhancement: fixed)
All cosets of a permutation group
|Reported by:||rbeezer||Owned by:||joyner|
|Cc:||dimpase, wdj||Work issues:|
|Report Upstream:||N/A||Reviewers:||Dmitrii Pasechnik|
|Authors:||Rob Beezer||Merged in:||sage-4.6.2.alpha4|
Description (last modified by rbeezer) (diff)
New method for permutation groups generates a list of all of the cosets of a subgroup in a group.
This is intended for instructional use, to allow students to experiment with cosets (say, actually defining a product on the raw cosets). This is a companion to #10685 and I think completes my wish-list of fundamental brute-force computations that help with teaching introductory group theory.
I had this all written using representatives from GAP, but GAP's "canonical" representatives are only guaranteed to be identical on a per-GAP-session basis. For this reason,I couldn't get (a) predictable output, (b) subgroup as first coset, (c) coset "structure" identical to subgroup "structure", (d) doctest-able output and (e) a fairly straightforward technique for a naive check on normality. Well, I could get almost all of that, but it got to where it was requiring about two or three times as many computations.
- Cc dimpase, wdj added
- Status changed from new to needs_review
- Description modified (diff)
- Authors set to Rob Beezer