Various improvements to Weyl character rings

[tscrim]

📚 Description

We provide a number of improvements to the Weyl character ring:

1. We make it know that it is commutative (along with its ambient ring).
2. We speedup the _demazure_helper method by only doing operations based upon the support of the simple roots.

   sage: F = FusionRing(['B',10], 2, base_ring=QQ)
   sage: dd = {(1,0,0,1,0,0,0,0,0,0): 1}
   sage: %time X = F._demazure_helper(dd)
   CPU times: user 3.1 s, sys: 12 ms, total: 3.11 s
   Wall time: 3.11 s
   

   Previously took ~6s.
3. We don't set the FusionRing as a subobject of the WeightRing.

📝 Checklist

• I have made sure that the title is self-explanatory and the description concisely explains the PR.
• I have linked an issue or discussion.
• I have created tests covering the changes.
• I have updated the documentation accordingly.

⌛ Dependencies

[tscrim]

@dwbump @willieab Here are some improvements to the WCR which also improves the fusion rings.

[github-actions]

Documentation preview for this PR is ready! 🎉
Built with commit: d008a9c

[dwbump]

I built the commit and verified the speedup, which is pretty good if the rank is moderately large. The Demazure character formula is used to compute characters, which also underly the calculations of tensor products. The exception is that for reductive groups that are not semisimple such as GL(r), the Demazure character formula is not used, in lieu of the Freudenthal multiplicity formula. Because of this here is no speedup for WeylCharacterRings in Type A unless you make the WeylCharacterRing with style="coroots" but this is the default for FusionRings.

Nothing in the patch would require doctest revisions. I can recommend a positive review.

[tscrim]

Someone with sufficient powers (e.g., @mkoeppe @dimpase) needs to approve the PR request (and also upgrade @dwbump to the triage team since he is a long-term contributor).

[dimpase]

as requested by @tscrim

[dimpase]

@dwbump is a member of triage team

[tscrim]

Thank you @dimpase!