Remove redundancy in UniversalPolyRing

[SoongNoonien]

In preparation for #2172 I'm trying to simplify the implementation of universal polynomial rings.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 87.93%. Comparing base (f69ac97) to head (b73e495).
⚠️ Report is 2 commits behind head on master.

Additional details and impacted files

@@           Coverage Diff           @@
##           master    #2176   +/-   ##
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  Coverage   87.92%   87.93%           
=======================================
  Files         127      127           
  Lines       31780    31792   +12     
=======================================
+ Hits        27943    27955   +12     
  Misses       3837     3837           

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[fingolfin]

Really nice, thank you! Just one minor quirk mentioned above

[fingolfin]

Before this PR (and for the copy call: with PR #2178):

julia> R,(x,y) = universal_polynomial_ring(QQ, [:x, :y]; cached=false);

julia> @b gen(R, :x)
124.765 ns (16 allocs: 608 bytes)

julia> @b copy(x)
46.943 ns (6 allocs: 256 bytes)

With this PR:

julia> R,(x,y) = universal_polynomial_ring(QQ, [:x, :y]; cached=false);

julia> @b gen(R, :x)
140.961 ns (17 allocs: 640 bytes)

So this PR still allocates more and is a tad slower

[fingolfin]

This is probably the extra allocation. But also idx is a redundant allocation when we are in the gen case.

All in all I think my version which added a separate gen method is still desirable.

[fingolfin]

In hindsight this definition of base_ring was wrong: it should have been

Suggested change

	base_ring(S::UniversalPolyRing) = base_ring(mpoly_ring(S))::base_ring_type(S)
	base_ring(S::UniversalPolyRing) = mpoly_ring(S))::base_ring_type(S)

(obviously with base_ring_type changed as well), and then coefficient_ring(S) would return base_ring(base_ring(S)).

That would then also fit naturally with the new UniversalRing{T} type: anything that uses mpoly_ring now would simply use base_ring.

[fingolfin]

Thinking about this some more, I would suggest we actually really change this for UniversalRing -- then it would be a breaking change (assuming that we'd replace UniversalPolyRing{T} by UniversalRing{mpoly_type(T)}), but this would only affect GenericCharacterTables.jl (at least in the known OSCAR-verse -- someone else might rely on it, but in the release notes for the "breaking" item, we'd just suggest that affected code should use coefficient_ring instead of base_ring.

(And we'd keep providing mpoly_ring, but only as mpoly_ring(S::UniversalRing{<:MPolyRingElem}))

All of this is not for this PR, though