Replace deprecated alias MPolyElem by MPolyRingElem (oscar-system#2932)

docs/src/AlgebraicGeometry/AlgebraicSets/AffineAlgebraicSet.md

@@ -91,8 +91,8 @@ AbsAffineAlgebraicSet
 ## Constructors
 One can create an algebraic set from an ideal or a multivariate polynomial.
 ```@docs
-algebraic_set(I::MPolyIdeal{<:MPolyElem}; check::Bool=true)
-algebraic_set(f::MPolyElem; check::Bool=true)
+algebraic_set(I::MPolyIdeal{<:MPolyRingElem}; check::Bool=true)
+algebraic_set(f::MPolyRingElem; check::Bool=true)
 ```
 Convert an affine scheme to an affine algebraic set in order to ignore
 its (non-reduced) scheme structure.

experimental/Schemes/elliptic_surface.jl

@@ -1126,7 +1126,7 @@ function two_neighbor_step(X::EllipticSurface, F::Vector{QQFieldElem})
   @assert scheme(parent(u)) === weierstrass_model(X)[1]
 
   # Helper function
-  my_const(u::MPolyElem) = is_zero(u) ? zero(coefficient_ring(parent(u))) : first(coefficients(u))
+  my_const(u::MPolyRingElem) = is_zero(u) ? zero(coefficient_ring(parent(u))) : first(coefficients(u))
 
   # transform to a quartic y'^2 = q(x)
   if iszero(P[3])  #  P = O
@@ -1456,13 +1456,13 @@ end
 
 
 @doc raw"""
-    elliptic_surface(g::MPolyElem, x::MPolyElem, y::MPolyElem, P::Vector{<:RingElem})
+    elliptic_surface(g::MPolyRingElem, x::MPolyRingElem, y::MPolyRingElem, P::Vector{<:RingElem})
 
 Transform a bivariate polynomial `g` of the form `y^2 - Q(x)` with `Q(x)` of
 degree at most ``4`` to Weierstrass form and return the corresponding
 elliptic surface as well as the coordinate transformation.
 """
-function elliptic_surface(g::MPolyElem, P::Vector{<:RingElem})
+function elliptic_surface(g::MPolyRingElem, P::Vector{<:RingElem})
   R = parent(g)
   (x, y) = gens(R)
   P = base_ring(R).(P)
@@ -1480,14 +1480,14 @@ function elliptic_surface(g::MPolyElem, P::Vector{<:RingElem})
 end
 
 @doc raw"""
-    transform_to_weierstrass(g::MPolyElem, x::MPolyElem, y::MPolyElem, P::Vector{<:RingElem})
+    transform_to_weierstrass(g::MPolyRingElem, x::MPolyRingElem, y::MPolyRingElem, P::Vector{<:RingElem})
 
 Transform a bivariate polynomial `g` of the form `y^2 - Q(x)` with `Q(x)` of degree ``≤ 4``
 to Weierstrass form. This returns a pair `(f, trans)` where `trans` is an endomorphism of the 
 `fraction_field` of `parent(g)` and `f` is the transform. The input `P` must be a rational point 
 on the curve defined by `g`, i.e. `g(P) == 0`.
 """
-function transform_to_weierstrass(g::MPolyElem, x::MPolyElem, y::MPolyElem, P::Vector{<:RingElem})
+function transform_to_weierstrass(g::MPolyRingElem, x::MPolyRingElem, y::MPolyRingElem, P::Vector{<:RingElem})
   R = parent(g)
   @assert ngens(R) == 2 "input polynomial must be bivariate"
   @assert x in gens(R) "second argument must be a variable of the parent of the first"
@@ -1568,11 +1568,11 @@ function transform_to_weierstrass(g::MPolyElem, x::MPolyElem, y::MPolyElem, P::V
   return result, trans
 end
 
-function _is_in_weierstrass_form(f::MPolyElem)
+function _is_in_weierstrass_form(f::MPolyRingElem)
   R = parent(f)
   @req ngens(R) == 2 "polynomial must be bivariate"
   # Helper function
-  my_const(u::MPolyElem) = is_zero(u) ? zero(coefficient_ring(parent(u))) : first(coefficients(u))
+  my_const(u::MPolyRingElem) = is_zero(u) ? zero(coefficient_ring(parent(u))) : first(coefficients(u))
 
   (x, y) = gens(R)
   f = -inv(my_const(coeff(f, [x, y], [0, 2]))) * f
@@ -1645,7 +1645,7 @@ function _elliptic_parameter_conversion(X::EllipticSurface, u::VarietyFunctionFi
   FS = fraction_field(S)
 
   # Helper function
-  my_const(u::MPolyElem) = is_zero(u) ? zero(coefficient_ring(parent(u))) : first(coefficients(u))
+  my_const(u::MPolyRingElem) = is_zero(u) ? zero(coefficient_ring(parent(u))) : first(coefficients(u))
 
   # We verify the assumptions made on p. 44 of
   #   A. Kumar: "Elliptic Fibrations on a generic Jacobian Kummer surface"

src/AlgebraicGeometry/Schemes/AffineAlgebraicSet/Objects/Constructors.jl

@@ -31,7 +31,7 @@ defined by ideal(x^3 + y^2 + y + 1, x)
 
 ```
 """
-function algebraic_set(I::MPolyIdeal{<:MPolyElem}; is_radical::Bool=false, check::Bool=true)
+function algebraic_set(I::MPolyIdeal{<:MPolyRingElem}; is_radical::Bool=false, check::Bool=true)
   X = Spec(base_ring(I), I)
   return algebraic_set(X, is_reduced=is_radical, check=check)
 end

src/Rings/MPolyQuo.jl

@@ -1230,7 +1230,7 @@ function vector_space(K::AbstractAlgebra.Field, Q::MPolyQuoRing)
   # quotient; see Greuel/Pfister "A singular introduction to Commutative Algebra".
   function prim(a::MPolyQuoRingElem)
     @assert parent(a) === Q
-    b = lift(a)::MPolyElem
+    b = lift(a)::MPolyRingElem
     o = default_ordering(R)
     # TODO: Make sure the ordering is the same as the one used for the _kbase above
     @assert is_global(o) "ordering must be global"

src/Rings/mpoly-ideals.jl

@@ -1282,7 +1282,7 @@ julia> codim(I)
 2
 ```
 """
-codim(I::MPolyIdeal{T}) where {T<:MPolyElem{<:FieldElem}}= nvars(base_ring(I)) - dim(I)
+codim(I::MPolyIdeal{T}) where {T<:MPolyRingElem{<:FieldElem}}= nvars(base_ring(I)) - dim(I)
 codim(I::MPolyIdeal) = dim(base_ring(I)) - dim(I)
 
 # Some fixes which were necessary for the above

src/Rings/mpoly-localizations.jl

@@ -3095,7 +3095,7 @@ julia> minimal_generating_set(I)
 """
 @attr Vector{<:MPolyLocRingElem} function minimal_generating_set(
     I::MPolyLocalizedIdeal{<:MPolyLocRing{<:Field, <:FieldElem,
-                                          <:MPolyRing, <:MPolyElem,
+                                          <:MPolyRing, <:MPolyRingElem,
                                           <:MPolyComplementOfKPointIdeal}
                           }
   )
@@ -3171,17 +3171,17 @@ julia> small_generating_set(I)
 ```
 """
 small_generating_set(I::MPolyLocalizedIdeal{<:MPolyLocRing{<:Field, <:FieldElem,
-                        <:MPolyRing, <:MPolyElem,
+                        <:MPolyRing, <:MPolyRingElem,
                         <:MPolyComplementOfKPointIdeal}})  = minimal_generating_set(I)
 
 function small_generating_set(I::MPolyLocalizedIdeal{<:MPolyLocRing{<:Field, <:FieldElem,
-                        <:MPolyRing, <:MPolyElem,
+                        <:MPolyRing, <:MPolyRingElem,
                         <:MPolyPowersOfElement}})
   L = base_ring(I)
   R = base_ring(L)
   I_min = L.(small_generating_set(saturated_ideal(I)))
   return filter(!iszero, I_min)
 end
 
-dim(R::MPolyLocRing{<:Field, <:FieldElem, <:MPolyRing, <:MPolyElem, <:MPolyComplementOfPrimeIdeal}) = nvars(base_ring(R)) - dim(prime_ideal(inverted_set(R)))
+dim(R::MPolyLocRing{<:Field, <:FieldElem, <:MPolyRing, <:MPolyRingElem, <:MPolyComplementOfPrimeIdeal}) = nvars(base_ring(R)) - dim(prime_ideal(inverted_set(R)))
 

src/Rings/mpoly.jl

@@ -1296,7 +1296,7 @@ end
 lift(f::MPolyRingElem) = f
 
 ### Hessian matrix
-function hessian_matrix(f::MPolyElem)
+function hessian_matrix(f::MPolyRingElem)
   R = parent(f)
   n = nvars(R)
   df = jacobi_matrix(f)
@@ -1309,5 +1309,5 @@ function hessian_matrix(f::MPolyElem)
   return result
 end
 
-hessian(f::MPolyElem) = det(hessian_matrix(f))
+hessian(f::MPolyRingElem) = det(hessian_matrix(f))
 

src/Rings/mpolyquo-localizations.jl

@@ -2221,7 +2221,7 @@ If the localization is at a point, a minimal set of generators is returned.
 """
 @attr Vector{<:MPolyQuoLocRingElem} function small_generating_set(
       I::MPolyQuoLocalizedIdeal{<:MPolyQuoLocRing{<:Field, <:FieldElem,
-                                          <:MPolyRing, <:MPolyElem,
+                                          <:MPolyRing, <:MPolyRingElem,
                                           <:MPolyComplementOfKPointIdeal},
                               <:Any,<:Any}
   )
@@ -2234,7 +2234,7 @@ end
 
 function small_generating_set(
     I::MPolyQuoLocalizedIdeal{<:MPolyQuoLocRing{<:Field, <:FieldElem,
-                                          <:MPolyRing, <:MPolyElem,
+                                          <:MPolyRing, <:MPolyRingElem,
                                           <:MPolyPowersOfElement}
                           }
   )
@@ -2245,5 +2245,5 @@ function small_generating_set(
   return filter(!iszero, Q.(small_generating_set(J)))
 end
 
-dim(R::MPolyQuoLocRing{<:Field, <:FieldElem, <:MPolyRing, <:MPolyElem, <:MPolyComplementOfPrimeIdeal}) = dim(saturated_ideal(modulus(R))) - dim(prime_ideal(inverted_set(R)))
+dim(R::MPolyQuoLocRing{<:Field, <:FieldElem, <:MPolyRing, <:MPolyRingElem, <:MPolyComplementOfPrimeIdeal}) = dim(saturated_ideal(modulus(R))) - dim(prime_ideal(inverted_set(R)))
 

src/Serialization/Fields.jl

@@ -248,7 +248,7 @@ end
 function load_object(s::DeserializerState, ::Type{<: Union{NfAbsNSElem, Hecke.NfRelNSElem}}, terms::Vector, parents::Vector)
   K = parents[end]
   n = ngens(K)
-  # forces parent of MPolyElem
+  # forces parent of MPolyRingElem
   poly_ring = polynomial_ring(base_field(K), n)
   parents[end - 1], _ = poly_ring
   poly_elem_type = elem_type

src/TropicalGeometry/groebner_fan.jl

@@ -13,7 +13,7 @@
 
 # Computes the space of weight vectors w.r.t. which G is weighted homogeneous
 @doc raw"""
-    homogeneity_space(G::Vector{<:MPolyElem})
+    homogeneity_space(G::Vector{<:MPolyRingElem})
 
 Return a `Cone` that is the space of all weight vectors under which all elements of `G` are weighted homogeneous.  The cone will be a linear subspace without any rays.
 
@@ -56,7 +56,7 @@ julia> rays_modulo_lineality(homogeneity_space(G3))
 
 ```
 """
-function homogeneity_space(G::Vector{<:MPolyElem})
+function homogeneity_space(G::Vector{<:MPolyRingElem})
     inequalities = fmpq_mat(0,0)
     equations = Vector{Vector{Int}}()
     for g in G
@@ -71,7 +71,7 @@ end
 
 
 @doc raw"""
-    homogeneity_vector(G::Vector{<:MPolyElem})
+    homogeneity_vector(G::Vector{<:MPolyRingElem})
 
 Return a positive `Vector{fmpz}` under which every element of `G` is weighted
 homogeneous. If no such vector exists, return `nothing`.
@@ -119,7 +119,7 @@ true
 
 ```
 """
-function homogeneity_vector(G::Vector{<:MPolyElem})
+function homogeneity_vector(G::Vector{<:MPolyRingElem})
     homogeneitySpace = homogeneity_space(G)
 
     # return nothing if homogeneitySpace is the origin
@@ -150,7 +150,7 @@ end
 
 
 @doc raw"""
-    maximal_groebner_cone(G::Oscar.IdealGens{<:MPolyElem}; homogeneityWeight::Union{Nothing,Vector{fmpz}}=nothing)
+    maximal_groebner_cone(G::Oscar.IdealGens{<:MPolyRingElem}; homogeneityWeight::Union{Nothing,Vector{fmpz}}=nothing)
 
 Returns the maximal Groebner cone of a Groebner basis `G`, i.e., the closure of all weight vectors with respect to whose weighted ordering `G` is a Groebner basis (independent of tie-breaker).
 
@@ -180,36 +180,36 @@ julia> rays_modulo_lineality(maximal_groebner_cone(G))
 
 ```
 """
-function maximal_groebner_cone(G::Oscar.IdealGens{<:MPolyElem})
+function maximal_groebner_cone(G::Oscar.IdealGens{<:MPolyRingElem})
     @assert is_groebner_basis(G)
     ord = ordering(G)
     G = collect(G)
     homogeneityWeight = homogeneity_vector(G)
     return maximal_groebner_cone(G,ord,homogeneityWeight)
 end
 
-function maximal_groebner_cone(G::Oscar.IdealGens{<:MPolyElem}, homogeneityWeight::Union{Vector{fmpz},Nothing})
+function maximal_groebner_cone(G::Oscar.IdealGens{<:MPolyRingElem}, homogeneityWeight::Union{Vector{fmpz},Nothing})
     @assert is_groebner_basis(G)
     ord = ordering(G)
     G = collect(G)
     return maximal_groebner_cone(G,ord,homogeneityWeight)
 end
 
-function maximal_groebner_cone(G::Vector{<:MPolyElem}, ord::MonomialOrdering, homogeneityWeight::Nothing)
+function maximal_groebner_cone(G::Vector{<:MPolyRingElem}, ord::MonomialOrdering, homogeneityWeight::Nothing)
     # calling with `nothing` as homogeneityWeight
     # means that C needs to be restricted to the positive orthant
     C = maximal_groebner_cone_extended(G,ord)
     positiveOrthant = positive_hull(identity_matrix(ZZ,ambient_dim(C)))
     return intersect(C,positiveOrthant)
 end
 
-function maximal_groebner_cone(G::Vector{<:MPolyElem}, ord::MonomialOrdering, homogeneityWeight::Vector{fmpz})
+function maximal_groebner_cone(G::Vector{<:MPolyRingElem}, ord::MonomialOrdering, homogeneityWeight::Vector{fmpz})
     # calling with a positive homogeneityWeight
     # means that C does not be restricted to the positive orthant
     return maximal_groebner_cone_extended(G,ord)
 end
 
-function maximal_groebner_cone_extended(G::Vector{<:MPolyElem}, ord::MonomialOrdering)
+function maximal_groebner_cone_extended(G::Vector{<:MPolyRingElem}, ord::MonomialOrdering)
     # iterate over all elements of G and construct the inequalities
     inequalities = Vector{Vector{Int}}()
     for g in G
@@ -268,7 +268,7 @@ end
 
 # Returns the initial form of polynomial g with respect to weight vector u.
 # Requires a monomial ordering that is compatible with respect to u, i.e., the leading monomial is of highest weighted degree.
-function initial(g::MPolyElem, ordering::MonomialOrdering, u::Vector{fmpz})
+function initial(g::MPolyRingElem, ordering::MonomialOrdering, u::Vector{fmpz})
     lt,tail = Iterators.peel(terms(g,ordering=ordering));
     d = dot(u,fmpz.(leading_exponent_vector(lt)))
     initial_terms = [s for s in tail if dot(u,fmpz.(leading_exponent_vector(s)))==d]
@@ -277,7 +277,7 @@ function initial(g::MPolyElem, ordering::MonomialOrdering, u::Vector{fmpz})
 end
 
 # Applies the function above to each polynomial in a list of polynomials.
-function initial(G::Vector{<:MPolyElem}, ord::MonomialOrdering, u::Vector{fmpz})
+function initial(G::Vector{<:MPolyRingElem}, ord::MonomialOrdering, u::Vector{fmpz})
     return initial.(G,Ref(ord),Ref(u))
 end
 
@@ -287,7 +287,7 @@ end
 # - G is a Groebner basis with respect to ord
 # Returns:
 # - a reduced Groebner basis with respect to ord
-function interreduce(G::Vector{<:MPolyElem}, ord::MonomialOrdering)
+function interreduce(G::Vector{<:MPolyRingElem}, ord::MonomialOrdering)
     # sort G by its leading monomials (result is smallest first)
     # then reduce G[i] by G[1:i-1] for i=length(G),...,2
     sort!(G,
@@ -307,9 +307,9 @@ end
 # - ordH and ordG are adjacent orderings
 # Returns:
 # - Gnew, a Groebner basis of the original ideal w.r.t. ordH
-function groebner_lift(Hnew::Vector{<:MPolyElem},
+function groebner_lift(Hnew::Vector{<:MPolyRingElem},
                        ordH::MonomialOrdering,
-                       G::Vector{<:MPolyElem},
+                       G::Vector{<:MPolyRingElem},
                        ordG::MonomialOrdering)
     # lift to groebner basis
     Gnew = Hnew - reduce(Hnew,G,ordering=ordG,complete_reduction=true)
@@ -327,7 +327,7 @@ end
 # Returns:
 # - the reduced Groebner basis with respect to the adjacent ordering
 #     in direction v
-function groebner_flip(G::Vector{<:MPolyElem},
+function groebner_flip(G::Vector{<:MPolyRingElem},
                        ordG::MonomialOrdering,
                        homogeneityVector::Union{Vector{fmpz},Nothing},
                        interior_facet_point::Vector{fmpz},