Change behavior of base_ring for UniversalPolyRing

[SoongNoonien]

As mentioned here, I've adjusted the behavior of base_ring to eliminate more polynomial-specific code in the implementation of UniversalPolyRing in preparation for #2172.

[SoongNoonien]

Ok, I forgot to replace all original occurrences of base_ring by coefficient_ring...

[SoongNoonien]

I noticed that things like change_base_ring might be a bit unintuitive now.

[codecov]

Codecov Report

❌ Patch coverage is 87.50000% with 4 lines in your changes missing coverage. Please review.
✅ Project coverage is 87.95%. Comparing base (0bc9419) to head (3a0ec26).

Files with missing lines	Patch %	Lines
src/generic/UnivPoly.jl	87.50%	4 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #2182      +/-   ##
==========================================
- Coverage   87.95%   87.95%   -0.01%     
==========================================
  Files         127      127              
  Lines       31771    31769       -2     
==========================================
- Hits        27945    27943       -2     
  Misses       3826     3826              

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[SoongNoonien]

The error seem to be related to the serialization in Oscar. To obtain the type of the coefficients of a given universal polynomial p Oscar uses elem_type(base_ring(parent(p))) where instead elem_type(coefficient_ring(parent(p))) (or even elem_type(coefficient_ring(p))) should be used now. In general I'd say using coefficient_ring is the better choice as it is easier to understand what's happening. I'll provide a PR which fixes this in Oscar.

[SoongNoonien]

It is still failing because I overlooked some occurrences of base_ring in the serialization code. I'll investigate further...

[SoongNoonien]

The tests are still failing... The experimental action polynomial rings of Oscar which use universal polynomial rings seem to be the issue. I've isolated the respective use of base_ring and will provide yet another PR to clean up the usage of base_ring.

[fingolfin]

Has a merge conflict now.

We had a look, the OSCAR booktest error is due to GenericCharactertables, @SoongNoonien is work on it.

[SoongNoonien]

I think this should be good to go now.