Add several is_known methods for characteristic and is_perfect

[fingolfin]

• Merge characteristic docstrings (moved to Merge characteristic docstrings #2271)
• Implement is_known(characteristic, ::NCRing)
• Implement is_known(is_perfect, ::Field)
• Implement is_known(is_finite, ::NCRing)
• Remove incorrect characteristic(R::ResidueField) method

Extracted from PR #1996

[codecov]

Codecov Report

❌ Patch coverage is 39.21569% with 31 lines in your changes missing coverage. Please review.
✅ Project coverage is 88.22%. Comparing base (bcc2923) to head (74b7ac6).
⚠️ Report is 7 commits behind head on master.

Files with missing lines	Patch %	Lines
src/Rings.jl	40.00%	3 Missing ⚠️
src/NCPoly.jl	0.00%	2 Missing ⚠️
src/generic/SparsePoly.jl	0.00%	2 Missing ⚠️
src/AbsMSeries.jl	50.00%	1 Missing ⚠️
src/Fraction.jl	50.00%	1 Missing ⚠️
src/FreeAssociativeAlgebra.jl	0.00%	1 Missing ⚠️
src/LaurentPoly.jl	0.00%	1 Missing ⚠️
src/MatRing.jl	50.00%	1 Missing ⚠️
src/NumFields.jl	0.00%	1 Missing ⚠️
src/Poly.jl	50.00%	1 Missing ⚠️
... and 17 more

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #2270      +/-   ##
==========================================
- Coverage   88.30%   88.22%   -0.08%     
==========================================
  Files         126      126              
  Lines       31784    31798      +14     
==========================================
- Hits        28068    28055      -13     
- Misses       3716     3743      +27     

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[lgoettgens]

Since a large chunk of this is #2271, I am waiting for a rebase before looking at the changes here

[lgoettgens]

I just rebased this on top of current master to exclude everything from #2271

[lgoettgens]

This (as well as all other isknown(::typeof(is_finite), ...) methods in this PR) are wrong.
If we know that the base ring is not trivial, we know nothing about the FreeAssAlgebra, but this is_known would return true.

Suggested change

	is_known(::typeof(is_finite), R::FreeAssociativeAlgebra) = is_known(is_trivial, base_ring(R)) || (nvars(R) == 0 && is_known(is_finite, base_ring(R)))
	is_known(::typeof(is_finite), R::FreeAssociativeAlgebra) = (is_known(is_trivial, base_ring(R)) && is_trivial(base_ring(R))) || (nvars(R) == 0 && is_known(is_finite, base_ring(R)) && is_finite(base_ring(R))) || (is_known(is_trivial, base_ring(R)) && !is_trivial(base_ring(R)) && (nvars(R) > 0 || (is_known(is_finite, base_ring(R)) && !is_finite(base_ring(R)))))

(no guarantee of correctness, but I think this is more or less what one needs to do)

[fingolfin]

You are of course right, argh! This is why I really prefer to have someone review my PRs. Thank you, very embarrassing.

Anyway, I have now removed the is_finite part of this PR, and will resubmit it separately, but it shouldn't hold up the other changes.

To fix things, I am contemplating introducing internal helpers is_known_to_be_trivial, is_known_to_be_nontrivial, is_known_to_be_finite, is_known_to_be_infinite or so (or maybe... is_known_to_be(is_finite, R), is_known_to_be(!is_finite, R), ... ????)