#10722: All cosets of a permutation group
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Reporter: rbeezer | Owner: joyner
Type: enhancement | Status: new
Priority: minor | Milestone: sage-4.6.2
Component: group theory | Keywords:
Author: | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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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.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10722>
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