#10722: All cosets of a permutation group
----------------------------+-----------------------------------------------
Reporter: rbeezer | Owner: joyner
Type: enhancement | Status: needs_review
Priority: minor | Milestone: sage-4.6.2
Component: group theory | Keywords:
Author: Rob Beezer | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
----------------------------+-----------------------------------------------
Changes (by newvalueoldvalue):
* cc: dimpase, wdj (added)
* status: new => needs_review
* author: => Rob Beezer
Old description:
> 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.
New description:
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.
Depends: #10685
--
Comment:
This will need #10685 on 4.6.2.alpha3 so it will apply properly, but there
is no logical dependence.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10722#comment:1>
Sage <http://www.sagemath.org>
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