Merge branch 'oscar-system:master' into cohomology_rings

Author: wgabrielong

docs/src/CommutativeAlgebra/ideals.md

@@ -297,6 +297,14 @@ true
 ```
 
 ## Vanishing sets and solving multivariate polynomial systems
+For solving multivariate polynomial systems using the below functions
+we provide an introductory tutorial
+[here](https://www.oscar-system.org/tutorials/CommutativeAlgebra).
+
+
+```@docs
+real_solutions
+```
 
 ```@docs
 rational_solutions

src/Rings/FreeAssociativeAlgebraIdeal.jl

@@ -77,12 +77,6 @@ function Base.:+(a::FreeAssociativeAlgebraIdeal{T}, b::FreeAssociativeAlgebraIde
   return ideal(R, vcat(gens(a), gens(b)))
 end
 
-function Base.:*(a::FreeAssociativeAlgebraIdeal{T}, b::FreeAssociativeAlgebraIdeal{T}) where T
-  R = base_ring(a)
-  @req R == base_ring(b) "parent mismatch"
-  return ideal(R, [i*j for i in gens(a) for j in gens(b)])
-end
-
 AbstractAlgebra.normal_form(f::FreeAssociativeAlgebraElem, I::FreeAssociativeAlgebraIdeal) = normal_form(f, gens(I))
 AbstractAlgebra.normal_form(f::FreeAssociativeAlgebraElem, I::IdealGens{<:FreeAssociativeAlgebraElem}) = normal_form(f, collect(I))
 

src/Rings/PBWAlgebra.jl

@@ -1,8 +1,8 @@
 @attributes mutable struct PBWAlgRing{T, S} <: NCRing
   sring::Singular.PluralRing{S}
   relations::Singular.smatrix{Singular.spoly{S}}
-  coeff_ring
-  poly_ring
+  coeff_ring::Ring
+  poly_ring::MPolyRing{T}
   opposite::PBWAlgRing{T, S}
 
   function PBWAlgRing{T, S}(sring, relations, coeff_ring, poly_ring) where {T, S}
@@ -62,11 +62,11 @@ parent(a::PBWAlgElem) = a.parent
 
 symbols(a::PBWAlgRing) = symbols(a.sring)
 
-coefficient_ring(a::PBWAlgRing) = a.coeff_ring
+coefficient_ring(a::PBWAlgRing{T}) where T = a.coeff_ring::parent_type(T)
 
 coefficient_ring(a::PBWAlgElem) = coefficient_ring(parent(a))
 
-base_ring(a::PBWAlgRing) = a.poly_ring
+base_ring(a::PBWAlgRing{T}) where T = a.poly_ring::mpoly_ring_type(T)
 
 function Base.deepcopy_internal(a::PBWAlgElem, dict::IdDict)
   return PBWAlgElem(parent(a), deepcopy_internal(a.sdata, dict))
@@ -343,7 +343,7 @@ function (R::PBWAlgRing)(cs::AbstractVector, es::AbstractVector{Vector{Int}})
 end
 
 function (R::PBWAlgRing)(a::MPolyRingElem)
-  @assert parent(a) == R.poly_ring
+  @assert parent(a) == base_ring(R)
   z = build_ctx(R)
   for (c, e) in zip(AbstractAlgebra.coefficients(a), AbstractAlgebra.exponent_vectors(a))
     push_term!(z, c, e)
@@ -537,7 +537,7 @@ function _opposite(a::PBWAlgRing{T, S}) where {T, S}
     for i in 1:n-1, j in i+1:n
       bsrel[i,j] = _unsafe_coerce(bspolyring, a.relations[n+1-j,n+1-i], true)
     end
-    b = PBWAlgRing{T, S}(bsring, bsrel, a.coeff_ring, polynomial_ring(a.coeff_ring, revs; cached = false)[1])
+    b = PBWAlgRing{T, S}(bsring, bsrel, coefficient_ring(a), polynomial_ring(coefficient_ring(a), revs; cached = false)[1])
     a.opposite = b
     b.opposite = a
   end
@@ -1154,7 +1154,7 @@ function _left_eliminate_via_given_ordering(I::Singular.sideal{<:Singular.splura
 end
 
 function _left_eliminate(R::PBWAlgRing, I::Singular.sideal, sigma, sigmaC, ordering)
-  r = R.poly_ring
+  r = base_ring(R)
   if !isnothing(ordering)
     @assert is_elimination_ordering(ordering, sigmaC)
     @assert is_admissible_ordering(R, ordering)
@@ -1217,7 +1217,7 @@ function eliminate(I::PBWAlgIdeal{D, T, S}, sigmaC::Vector{Int}; ordering = noth
     sigmaop = reverse!(n + 1 .- sigma)
     sigmaCop = reverse!(n + 1 .- sigmaC)
     orderingop = isnothing(ordering) ? ordering :
-                                     opposite_ordering(Rop.poly_ring, ordering)
+                                     opposite_ordering(base_ring(Rop), ordering)
     zop = _left_eliminate(Rop, get_sopdata(I), sigmaop, sigmaCop, orderingop)
     z = _opmap(R, zop, Rop)
     return PBWAlgIdeal{D, T, S}(R, z, zop)

src/Rings/solving.jl

@@ -2,7 +2,7 @@
     real_solutions(I::MPolyIdeal, <keyword arguments>)
 
 Given an ideal `I` with a finite solution set over the complex numbers, return a pair `r,p` where `p` is the rational parametrization of the solution set and `r` represents the real roots of `Ì`  with a given precision (default 32 bits).
-See [BES21](@cite) for more information.
+See [BES-E-D21](@cite) for more information.
 
 **Note**: At the moment only QQ is supported as ground field. If the dimension of `I`
 is greater than zero an empty array is returned.

test/Rings/FreeAssociativeAlgebraIdeal.jl

@@ -30,7 +30,6 @@ end
   @test ideal_membership(f1, I2.gens)
   gb = groebner_basis(I2, 3; protocol=false)
   @test isdefined(I2, :gb)
-  @test length(gens(I * I2)) == 2
 end
 
 @testset "FreeAssociativeAlgebraIdeal.utils" begin