Add Puiseux polynomials

[ollieclarke8787]

Working repository for adding Puiseux Polynomials to AA, this should supersede oscar-system/Oscar.jl#5861

[codecov]

Codecov Report

❌ Patch coverage is 0% with 198 lines in your changes missing coverage. Please review.
✅ Project coverage is 87.59%. Comparing base (3355a14) to head (d6e032a).

Files with missing lines	Patch %	Lines
src/PuiseuxMPoly.jl	0.00%	198 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #2391      +/-   ##
==========================================
- Coverage   88.12%   87.59%   -0.53%     
==========================================
  Files         128      129       +1     
  Lines       32886    33084     +198     
==========================================
  Hits        28981    28981              
- Misses       3905     4103     +198     

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[joschmitt]

The test file needs to be included explicitly to be executed (there is no magic like in OSCAR). I assume it could fit in the list of includes in test/Rings-test.jl.

[YueRen]

@lgoettgens Good point, I suggest we remove these for now and once this PR is merged and a new release of AA has happened, I will open a PR in OSCAR.

[thofma]

We plan to do a new release soonish. Do you guys want to get it in? Not sure what the status is here. I still see some "Oscar" references in the test code.

[YueRen]

@ollieclarke8787 Do you have some time to finish the pull request at the beginning of next week?

[ollieclarke8787]

@ollieclarke8787 Do you have some time to finish the pull request at the beginning of next week?

Definitely, I think we just need to remove the Oscar references from the tests, everything else should still be working.

[ollieclarke8787]

Update: Most parts work as intended. Two remaining issues:

1. base_ring_type(::Type{PuiseuxMPolyRing{T}}) where T <: RingElement = AA.Generic.LaurentMPolyRing{T} is not correct - I'm not sure what it should be so that typeof(base_ring(R)) == AA.Generic.LaurentMPolyWrapRing{T}
2. There is an issue with divexact(f, a) where a lies in the coefficient ring, see the example in the code.