#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 stumpc5):
Replying to [comment:23 nthiery]:
> Replying to [comment:17 stumpc5]:
> This business sounds of the same nature as what we have for affine
> permutations (in window notation). Would there be a way to use the
> same implementation behind the scene?
And also with colored permutations, isn't it? The main difference is that
here (and also in signed permutations) one works mod N, for colored
permutations one works "+N mod kN", and for affine permutation one does
not work mod anything.
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.
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? 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}}}.
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.
--
Ticket URL: <http://trac.sagemath.org/ticket/20445#comment:25>
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