Implement all G(r,p,m) complex reflection groups

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Implement all G(r,p,m) complex reflection groups #37848

Open tscrim opened 3 weeks ago

tscrim commented 3 weeks ago

We provide an implementation of the whole family of G(r, p, n) complex reflection groups by realizing them as a subgroup of ColoredPermutations.

:memo: Checklist

[x] The title is concise and informative.
[x] The description explains in detail what this PR is about.
[x] I have linked a relevant issue or discussion.
[x] I have created tests covering the changes.
[x] I have updated the documentation and checked the documentation preview.

:hourglass: Dependencies

tscrim commented 3 weeks ago

This has a merge conflict with the splitting of the combinat/all.py. I will deal with that once this is reviewed (if that is still an issue at that time).

fchapoton commented 4 days ago

where does the merge conflict comes from ? which pull request ?

fchapoton commented 4 days ago

maybe the choice of the name ComplexReflectionGroup is a bit confusing with a category.

tscrim commented 4 days ago

It came from the one that split the all.py files, which has then been reverted. So there shouldn’t be a conflict anymore.

It’s the same situation with, e.g., WeylGroup(s). This is most naturally called a complex reflection group at this level of generality; I can’t really call it $G(r,p,n)$. Of course, this isn’t all such groups, but it is the unique infinite family. I guess the $p > 1$ case could be called the ImprimitiveComplexReflectionGroup (with $p=1$ being the colored permutations). What do you think?

fchapoton commented 4 days ago

no, ok, I was just asking. It is indeed reasonable to keep your proposed name, with appropriate documentation

tscrim commented 15 hours ago

I thought a bit more, and I found a name that is perhaps reasonable: "Shephard-Todd family complex reflection group" (abbreviated as STFamilyComplexReflectionGroup for the class name).

I added a bit more documentation as well. Let me know if there is anything else you would like changed/added.

github-actions[bot] commented 13 hours ago

Documentation preview for this PR (built with commit 068040bbf644896fc82d1cad37f64b3c558e9bbf; changes) is ready! :tada: This preview will update shortly after each push to this PR.