modernize coercion for Hecke algebras

[fchapoton]

Small changes that switch Hecke algebras to the modern coercion framework.

Also avoiding the auld class CommutativeRing and use the categories instead.

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[tscrim]

Are we sure we are not losing the methods:

• ideal_monoid
• extension
• frobenius_endomorphism
• derivation_module
• derivation

(as they are all provided by CommutativeRing generically)? Unfortunately I think we have to address this now, and I don't think they are provided. We probably just need to copy them to the CommutativeRings() category.

(localization and fraction_field are for integral domains, so not having them is an improvement (unless Hecke algebras are always an integral domain, but I don't think so?). Actually, are these provided by the category? I don't see them in there. krull_dimension is generically a NotImplementedError.)

[fchapoton]

I would prefer to keep this one small, as there is already the big #37719 blocking the view. I am trying to move by little steps only. Here we are getting rid of the last class using CommutativeRing outside of the ring folder.
I understand your concerns, but there is no doctest. Of course, people could use that in the wilderness.

Would it be ok to perform the move of these methods to the category later ? Probably copying them is easier, but there is no doctest ready for testing these copied methods.

[tscrim]

I don't think a subclass must include doctests/examples showing the methods defined in a base class work; so I don't find that to be a convincing argument. For ideal_monoid and derivation_module, we can just use the classes at hand here. We could ask one of the number theory people if they have any thoughts (for this specific case) and/or suggestions for such doctests.

I am also happy to do the changes on a separate PR that would become a dependency of this one.

[fchapoton]

ok, I will do another PR, but probably not soon

[tscrim]

LGTM. Thank you.