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.

[lgoettgens]

Suggested change

	#################################################################################
	#
	# tropical semiring maps for puiseux polynomials
	#
	#################################################################################
	@doc raw"""
	tropical_semiring_map(K::Field, minOrMax::Union{typeof(min),typeof(max)}=min)
	Return a map `nu` from `K` to the min (default) or max tropical semiring `T` such that `nu(0)=zero(T)` and `nu(c)=one(T)` for `c` non-zero. In other words, `nu` extends the trivial valuation on `K`.
	# Examples
	```jldoctest
	julia> nu = tropical_semiring_map(QQ) # arbitrary rings possible
	Map into Min tropical semiring encoding the trivial valuation on Rational field
	julia> nu(1)
	(0)
	julia> nu(0)
	infty
	julia> nu = tropical_semiring_map(QQ,max) # arbitrary rings possible
	Map into Max tropical semiring encoding the trivial valuation on Rational field
	julia> nu(1)
	(0)
	julia> nu(0)
	-infty
	```
	"""
	function tropical_semiring_map(R::PuiseuxMPolyRing, t::PuiseuxMPolyRingElem, minOrMax::Union{typeof(min),typeof(max)}=min)
	@assert ngens(R) == 1 "The tropical_semiring_map is only implemented for Puiseux polynomial rings in one variable."
	@assert t == first(gens(R)) "The uniformizer must be the generator of the Puiseux polynomial ring."
	valuedField = nothing
	uniformizerField = nothing
	valuedRing = R
	uniformizerRing = t
	residueField = base_ring(R)
	tropicalSemiring = tropical_semiring(minOrMax)
	return TropicalSemiringMap{typeof(R),typeof(t),typeof(minOrMax)}(
	valuedField,
	uniformizerField,
	valuedRing,
	uniformizerRing,
	residueField,
	tropicalSemiring)
	end
	# Print string
	function Base.show(io::IO, nu::TropicalSemiringMap{<:PuiseuxMPolyRing,<:PuiseuxMPolyRingElem,MinOrMax}) where {MinOrMax<:Union{typeof(min),typeof(max)}}
	print(io, "Map into $(tropical_semiring(nu)) encoding the $(uniformizer(nu))-adic valuation on $(Oscar.valued_ring(nu))")
	end
	# Mapping an element of the valued field or ring to the tropical semiring
	function (nu::TropicalSemiringMap{<:PuiseuxMPolyRing,<:PuiseuxMPolyRingElem,MinOrMax})(c::PuiseuxMPolyRingElem) where MinOrMax<:Union{typeof(min),typeof(max)}
	# return tropical zero if c is zero and valuation otherwise
	iszero(c) && return zero(tropical_semiring(nu))
	# preserve_ordering ensures that valuation is negated if convention(nu)==max
	return tropical_semiring(nu)(valuation(c); preserve_ordering=true)
	end
	# Mapping an element of the valued field or ring to the residue field
	function initial(c::PuiseuxMPolyRingElem, nu::TropicalSemiringMap{<:PuiseuxMPolyRing,<:PuiseuxMPolyRingElem,MinOrMax}) where MinOrMax<:Union{typeof(min),typeof(max)}
	# return residue field zero if c is zero and the correct non-zero residue otherwise
	iszero(c) && return zero(residue_field(nu))
	C = collect(coefficients(c))
	return last(C)
	end

this part belongs into Oscar

[lgoettgens]

this file contains multiple references to Oscar which won't work here

[lgoettgens]

Suggested change

	@testset "TrivialTests" begin
	@test 1+1==2
	@test 1+2==3
	# @test 1+1==3 # this one fails
	end

[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.