Added colored and signed permutations

[tscrim]

Currently we do not have classes for colored nor signed permutations. Implemented as a group by using the wreath product construction.

[tscrim]

New commits:

​f1aa77e	Initial implementation of colored permutations.
​2737b19	Merge branch 'develop' into public/combinat/colored_permutation_groups-TBA
​7525680	Fixing things and added full coverage.
​184b4f9	Added some more methods and some comments.

[vdelecroix]

Hi Travis,

I think it is needed to have ._gap_() implemented on all these wreath product constructions. I am trying to do that right now.

Vincent

[tscrim]

Hey Vincent,

I agree that we probably should have a _gap_ method. Were you able to add that code?

[tscrim]

See also #16010 for specialized code on signed permutations.

[chapoton]

One failing doctest, see patchbot report

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​9f8921f	Merge branch 'public/combinat/colored_permutation_groups-17411' of trac.sagemath.org:sage into public/combinat/colored_permutation_groups-17411
​d063050	Fix doctest from update to Coxeter groups.

[tscrim]

Fixed (failure was due to Coxeter groups better understanding their category).

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​5f32618

trac #17411 a few doc typo corrections and also some pep8 code changes

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​66a2290	trac #17411 final pep8 cleanup
​0350849	trac #17411 insertion in module_list

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​0b56cd3

trac #17411 one typo found

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​24b4b4f

trac #17411 lazy import

[tscrim]

Let me know if what you're doing/done counts as a review and if so, when you're done (thus far, I'm good with your changes).

[chapoton]

OOps, sorry. I just realized that I had pushed without giving my name or commenting. Yes, I am more or less doing a review. In my spare time, so this may take longer..

[tscrim]

No worries. Thank you for all the recent reviews you have been doing.

[kdilks]

Comments so far:

• Make 'number_reflecting_hyperplanes' 'number_of_reflecting_hyperplanes', because that's the way permutation statistics names methods.
• Documentation should mention somewhere that \ell is the number of degrees is the rank. Some docstrings just refer to \ell, and maybe you could look back and see that \ell is the number of degrees, but then nothing mentions that the number of the degrees is the same as the rank.
• Why just left descent and not right descent?
• Colored permutations should have an inverse operation.
• There should be element constructors ColoredPermutation and SignedPermutation.
• For m=2, there should be a way to get between thinking of something as a SignedPermutation and a ColoredPermutation.
• Codegree documentation needs a .. Math:: around the formula.
• Preliminary docstring/index of functions would be nice, but possibly a task for another ticket.

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​e9d30dc	Merge branch 'public/combinat/colored_permutation_groups-17411' of trac.sagemath.org:sage into public/combinat/colored_permutation_groups-17411
​4595847	Making changes based upon Kevin's comments.