#20445: Iteration through finite Coxeter groups
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Reporter: | Owner:
stumpc5 | Status: new
Type: | Milestone: sage-7.2
enhancement | Resolution:
Priority: major | Merged in:
Component: | Reviewers:
combinatorics | Work issues:
Keywords: | Commit:
Authors: | abfff5ffdf5e3d7a90bdaa542ecca3ba2691bffe
Report Upstream: N/A | Stopgaps:
Branch: |
u/stumpc5/20445 |
Dependencies: |
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Comment (by tscrim):
Replying to [comment:25 stumpc5]:
> I would propose to first work out the implementation here and then see
if we can use it also in the other places. I only don't see how to
actually do the implementation in an optimal way, so some support of yours
and/or Travis is appreciated.
I'm really starting to consider that what we should do is create our own
separate project where we write all of this independently (in, say,
C/C++). At this stage, I'm somewhat concerned with the additional overhead
that Cython could impose and the lack of complete memory control. Although
I cannot commit serious time to working on this for then next two weeks (I
will be in grading and math mode). Over the summer starting in June, I
should be able to do so.
> Some concrete questions:
>
> 1. It seems that we should use the same data structure as for
{{{PermutationGroupElement}}}:
> {{{
> self.perm = <int *>sig_malloc(sizeof(int) * self.N)
> }}}
> Do you agree? Can we even get anything significantly better than
sticking to {{{PermutationGroupElement}}} if we do it ourselves?
I think we can avoid a bit of overhead of maintaining the GAP and category
information. Although it is hard to tell how much of an impact this will
have on things.
> This also asks whether we can do better when multiplying elements, I
do not see what
> {{{
> cdef PermutationGroupElement prod =
PermutationGroupElement.__new__(PermutationGroupElement)
> }}}
> does or how long it takes, see the method {{{_new_mul_}}} in
{{{reflection_group_c.pyx}}}.
This creates a new element in memory, but it does not call the `__init__`.
It is essential and done in Python kernel, so we won't get any better.
> 3. It seems that we are using {{{PermutationGroupElement}}} in a few
places (when talking to {{{GAP3}}}}), but this might just be that we need
the cycle string representation for that.
GAP4 doesn't store things as cycle strings AFAIK, and so I doubt GAP3 does
either.
--
Ticket URL: <http://trac.sagemath.org/ticket/20445#comment:27>
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