Update to AbstractAlgebra 0.48 and Nemo 0.54.

Project.toml

@@ -31,26 +31,26 @@ f4ncgb_jll = "160f184c-7e1a-5d95-af1f-70d62a450302"
 lib4ti2_jll = "1493ae25-0f90-5c0e-a06c-8c5077d6d66f"
 
 [compat]
-AbstractAlgebra = "0.47.4"
-AlgebraicSolving = "0.10.1"
+AbstractAlgebra = "0.48.0"
+AlgebraicSolving = "0.10.3"
 Compat = "4.13.0"
 Distributed = "1.6"
-GAP = "0.16.2"
-Hecke = "0.39.7"
+GAP = "0.16.3"
+Hecke = "0.39.10"
 JSON = "1.0.1"
 JSON3 = "1.13.2"
 LazyArtifacts = "1.6"
 Markdown = "1.6"
 Mongoc = "0.9.2, 0.10"
-Nemo = "0.53.2"
+Nemo = "0.54.0"
 NetworkOptions = "1.2.0"
 Pkg = "1.6"
-Polymake = "0.13.4"
+Polymake = "0.13.6"
 ProgressMeter = "1.10.2"
 Random = "1.6"
 RandomExtensions = "0.4.3"
 Serialization = "1.6"
-Singular = "0.28.3"
+Singular = "0.28.7"
 TOPCOM_jll = "0.17.8"
 UUIDs = "1.6"
 cohomCalg_jll = "0.32.0"

docs/oscar_references.bib

@@ -2533,6 +2533,14 @@ @Book{Mar18
   doi           = {10.1007/978-3-319-90233-3}
 }
 
+@Misc{Mil20,
+  author        = {Milne, J. S.},
+  title         = {Class Field Theory (v4.03)},
+  pages         = {287+viii},
+  year          = {2020},
+  url           = {https://www.jmilne.org/math/CourseNotes/cft.html}
+}
+
 @Article{Moe93,
   author        = {Moeller, H. Michael},
   title         = {On Decomposing Systems of Polynomial Equations with Finitely Many Solutions},

docs/src/DeveloperDocumentation/styleguide.md

@@ -293,7 +293,7 @@ the user's convenience.
 Let's see an example. Say, you want to implement the characteristic 
 polynomial of a matrix. You could do it as follows:
 ```julia
-function characteristic_polynomial(A::MatrixElem)
+function characteristic_polynomial(A::MatElem)
   kk = base_ring(A)
   P, x = kk[:x]
   AP = change_base_ring(P, A)
@@ -310,7 +310,7 @@ To solve this, we should have implemented the function differently:
 ```julia
 # Implementation of the recommended keyword argument signature:
 function characteristic_polynomial(
-    A::MatrixElem;
+    A::MatElem;
     parent::AbstractAlgebra.Ring=polynomial_ring(base_ring(A), :t)[1]
   )
   AP = change_base_ring(parent, A)
@@ -322,7 +322,7 @@ end
 # output's parent as the first argument:
 function characteristic_polynomial(
     P::PolyRing,
-    A::MatrixElem
+    A::MatElem
   )
   coefficient_ring(P) === base_ring(A) || error("coefficient rings incompatible")
   return characteristic_polynomial(A, parent=P)

docs/src/Groups/matgroup.md

@@ -243,7 +243,6 @@ matrix(A::Vector{AbstractAlgebra.Generic.FreeModuleElem{T}}) where T <: RingElem
 conjugate_transpose(x::MatElem{T}) where T <: FinFieldElem
 complement(V::AbstractAlgebra.Generic.FreeModule{T}, W::AbstractAlgebra.Generic.Submodule{T}) where T <: FieldElem
 permutation_matrix(R::NCRing, Q::AbstractVector{<:IntegerUnion})
-is_alternating(M::MatrixElem)
 is_hermitian(B::MatElem{T}) where T <: FinFieldElem
 ```
 

examples/Reynolds.jl

@@ -238,7 +238,7 @@ function action_on_monomials(R::MPolyRing, d::Int, A::Vector{QQMatrix})
     bb = Vector{QQFieldElem}[]
     h = [x^a for x = g]
     for x = m
-      b = zeros(QQ, length(m))
+      b = zeros(QQFieldElem, length(m))
       y = evaluate(x, h)
       for (c,v) = zip(AbstractAlgebra.coefficients(y), AbstractAlgebra.monomials(y))
         b[findfirst(==(v), m)] = c

experimental/AlgebraicShifting/src/PartialShiftGraph.jl

@@ -194,7 +194,7 @@ function partial_shift_graph(F::Field, complexes::Vector{T},
   if length(complexes) == 1
     @req is_shifted(complexes[1]) "The list of complexes should be closed under shifting by elements of W"
     return (
-      graph_from_adjacency_matrix(Directed, zeros(length(complexes),length(complexes))),
+      graph_from_adjacency_matrix(Directed, zeros(Int,length(complexes),length(complexes))),
       EdgeLabels(),
       complexes) :: Tuple{Graph{Directed}, EdgeLabels, Vector{T}}
   end
@@ -256,7 +256,7 @@ function partial_shift_graph(F::Field, complexes::Vector{T};
                              kwargs...) where T <: ComplexOrHypergraph
   # Deal with trivial case
   if length(complexes) <= 1
-    return (graph_from_adjacency_matrix(Directed, zeros(length(complexes),length(complexes))), EdgeLabels())
+    return (graph_from_adjacency_matrix(Directed, zeros(Int,length(complexes),length(complexes))), EdgeLabels())
   end
 
   n = n_vertices(complexes[1])

experimental/AlgebraicStatistics/src/PhylogeneticModels.jl

@@ -1538,14 +1538,14 @@ Computes specialized Fourier transform from the matrix that represents the full
 This matrix transforms the reduced probability coordinates (corresponding to the equivalent classes) to the reduced Fourier coordinates.
 """
 function fourier_transform(PM::GroupBasedPhylogeneticModel)
-  FRp, p = Oscar.full_model_ring(phylogenetic_model(PM))
-  FRq, q = Oscar.full_model_ring(PM)
+  FRp, p = full_model_ring(phylogenetic_model(PM))
+  FRq, q = full_model_ring(PM)
 
-  Rp, rp = Oscar.model_ring(phylogenetic_model(PM))
-  Rq, rq = Oscar.model_ring(PM)
+  Rp, rp = model_ring(phylogenetic_model(PM))
+  Rq, rq = model_ring(PM)
 
-  p_classes = Oscar.equivalent_classes(phylogenetic_model(PM))
-  q_classes = Oscar.equivalent_classes(PM)
+  p_classes = equivalent_classes(phylogenetic_model(PM))
+  q_classes = equivalent_classes(PM)
 
   np = length(p_classes)
   nq = length(q_classes)
@@ -1556,7 +1556,7 @@ function fourier_transform(PM::GroupBasedPhylogeneticModel)
   # keys_q_classes = collect(keys(q_classes))
   # sort!(keys_q_classes, rev = true)
   H = Rp.(hadamard(matrix_space(ZZ, n_states(PM), n_states(PM))))
-  M = Rp.(Int.(zeros(nq, np)))
+  M = Rp.(zeros(Int, nq, np))
 
   for (i, q_index) in enumerate(sort(collect(keys(rq)); rev=true))
     current_fourier_class = q_classes[q_index]
@@ -1609,7 +1609,7 @@ function inverse_fourier_transform(PM::GroupBasedPhylogeneticModel)
   H = Rq.(hadamard(matrix_space(ZZ, n_states(PM), n_states(PM))))
   Hinv = 1//n_states(PM) * H
 
-  M = zeros(base_ring(Rq), np, nq)
+  M = zero_matrix(base_ring(Rq), np, nq)
   for (i, p_index) in enumerate(sort(collect(keys(rp)); rev=true))
     current_prob_class = p_classes[p_index]
     for (j, q_index) in enumerate(sort(collect(keys(rq)); rev=true))

experimental/DoubleAndHyperComplexes/src/SpectralSequences.jl

@@ -736,8 +736,6 @@ function produce_map(cssp::CSSPage, i::Int, j::Int)
   return hom(dom, cod, elem_type(cod)[cod(v) for v in img_gens]; check=false)
 end
 
-relations(F::FreeMod) = elem_type(F)[]
-
 function multiplication_map(
     ctx::Union{PushForwardCtx, ToricCtx},
     p::MPolyDecRingElem,

experimental/FTheoryTools/src/AbstractFTheoryModels/Methods/blowups.jl

@@ -235,11 +235,11 @@ function _ideal_sheaf_to_minimal_supercone_coordinates(
   defining_ideal = ideal_in_cox_ring(I)
   all(in(gens(base_ring(defining_ideal))), gens(defining_ideal)) || return not_possible
   R = coordinate_ring(X)
-  coords = zeros(QQ, n_rays(X))
+  coords = zeros(QQFieldElem, n_rays(X))
   for i in 1:n_rays(X)
     R[i] in gens(defining_ideal) && (coords[i] = 1)
   end
-  coords == zeros(QQ, n_rays(X)) && return not_possible
+  is_zero(coords) && return not_possible
   is_minimal_supercone_coordinate_vector(polyhedral_fan(X), coords) || return not_possible
   return coords
 end

experimental/FTheoryTools/src/G4Fluxes/auxiliary.jl

@@ -210,21 +210,21 @@ julia> length(collect(keys(cdh22)))
       (my_tuple[1] in bad_positions || my_tuple[2] in bad_positions)
 
       # Represent first variable by list of coefficients, after plugging in the linear relation
-      var1 = zeros(QQ, ncols(my_mat))
+      var1 = zeros(QQFieldElem, ncols(my_mat))
       var1[my_tuple[1]] = 1
       if my_tuple[1] in bad_positions
         var1 = lin_rels[my_tuple[1]]
       end
 
       # Represent second variable by list of coefficients, after plugging in the linear relation
-      var2 = zeros(QQ, ncols(my_mat))
+      var2 = zeros(QQFieldElem, ncols(my_mat))
       var2[my_tuple[2]] = 1
       if my_tuple[2] in bad_positions
         var2 = lin_rels[my_tuple[2]]
       end
 
       # Compute the product of the two variables, which represents the new relation
-      prod = zeros(QQ, N_filtered_quadratic_elements)
+      prod = zeros(QQFieldElem, N_filtered_quadratic_elements)
       for k in 1:length(var1)
         if var1[k] != 0
           for l in 1:length(var2)

experimental/FTheoryTools/src/auxiliary.jl

@@ -341,7 +341,7 @@ function _construct_generic_sample(
   )
   ambient_space_vars = vcat(base_vars, ["x", "y", "z"])
   coordinate_ring_ambient_space = polynomial_ring(QQ, ambient_space_vars; cached=false)[1]
-  ambient_space_grading = zero_matrix(Int, nrows(base_grading) + 1, ncols(base_grading) + 3)
+  ambient_space_grading = zeros(Int, nrows(base_grading) + 1, ncols(base_grading) + 3)
   ambient_space_grading[1:nrows(base_grading), 1:ncols(base_grading)] = base_grading
   ambient_space_grading[1, (ncols(base_grading) + 1):(ncols(base_grading) + 2)] = [2; 3]
   ambient_space_grading[nrows(base_grading) + 1, (ncols(base_grading) + 1):(ncols(base_grading) + 3)] = [

experimental/GModule/src/GaloisCohomology.jl

@@ -1997,7 +1997,7 @@ function Hecke.structure_constant_algebra(CC::GrpCoh.CoChain{2, PermGroupElem, G
   else
     mp = id_hom(k)
   end
-  M = zeros(base_field(k), n*n, n*n, n*n)
+  M = Hecke.zeros_array(base_field(k), n*n, n*n, n*n)
   #basis is prod. basis of basis(k) and e_sigma sigma in G
   # e_sigma * e_tau is via cocycle
   # bas * bas is direct
@@ -2011,7 +2011,7 @@ function Hecke.structure_constant_algebra(CC::GrpCoh.CoChain{2, PermGroupElem, G
     # -> a*b^A * (sigma(A, B)*AB)
     c = a[1] * preimage(mp, mG(a[2])(mp(b[1]))) * preimage(mp, CC(a[2], b[2]).data)
     C = a[2]*b[2]
-    z = zeros(base_field(k), n*n)
+    z = Hecke.zeros_array(base_field(k), n*n)
     bk = basis(k)
     for i=1:length(bk)
       p = findfirst(isequal((bk[i], C)), B)

experimental/GModule/src/Misc.jl

@@ -258,19 +258,19 @@ function relative_field(m::Map{<:AbstractAlgebra.Field, <:AbstractAlgebra.Field}
   coordinates = function(x::FieldElem)
     @assert parent(x) == K
     c = collect(Hecke.coefficients(map_coefficients(k, Qt(x), parent = kt) % h))
-    c = vcat(c, zeros(k, degree(h)-length(c)))
+    c = vcat(c, Hecke.zeros_array(k, degree(h)-length(c)))
     return c
   end
   rep_mat = function(x::FieldElem)
     @assert parent(x) == K
     c = map_coefficients(k, Qt(x), parent = kt) % h
     m = collect(Hecke.coefficients(c))
-    m = vcat(m, zeros(k, degree(h) - length(m)))
+    m = vcat(m, Hecke.zeros_array(k, degree(h) - length(m)))
     r = m
     for i in 2:degree(h)
       c = shift_left(c, 1) % h
       m = collect(Hecke.coefficients(c))
-      m = vcat(m, zeros(k, degree(h) - length(m)))
+      m = vcat(m, Hecke.zeros_array(k, degree(h) - length(m)))
       r = hcat(r, m)
     end
     return transpose(matrix(r))

experimental/GaloisGrp/src/Subfields.jl

@@ -332,10 +332,11 @@ function _subfields(K::AbsSimpleNumField; pStart = 2*degree(K)+1, prime = 0)
   sf = get_attribute(K, :principal_subfields)
   store = sf === nothing
 
-  f = Zx(mapreduce(denominator, lcm, coefficients(defining_polynomial(K)), init = ZZRingElem(1))*defining_polynomial(K))
-  f = divexact(f, content(f))
+  fQ = defining_polynomial(K)
+  fQ /= content(fQ)
+  f = change_base_ring(ZZ, fQ; parent = Zx)
 
-  p, ct = find_prime(Hecke.Globals.Qx(f), pStart = pStart, prime = prime,
+  p, ct = find_prime(fQ, pStart = pStart, prime = prime,
                                           filter_pattern = x->any(t->degree(t) == 1, first.(collect(x))))
   n = degree(K)
   if primitive_by_shape(ct, n)
@@ -358,7 +359,7 @@ function _subfields(K::AbsSimpleNumField; pStart = 2*degree(K)+1, prime = 0)
   b .*= inv(derivative(f)(gen(K)))
   bt = [parent(defining_polynomial(K))(x) for x = b]
   bd = map(denominator, bt)
-  bz = [Zx(bd[i]*bt[i]) for i=1:length(bd)]
+  bz = [change_base_ring(ZZ, bd[i]*bt[i]; parent = Zx) for i=1:length(bd)]
   @assert parent(f) == parent(bz[1])
 
   lf = Hecke.factor_mod_pk(Array, H, 1)

experimental/InjectiveResolutions/src/InjectiveResolutions.jl

@@ -523,7 +523,7 @@ function coefficients(N::SubquoModule{T}, p_F::FaceQ) where {T <: MonoidAlgebraE
   # get socle degrees of indecomposable injectives kQ{a + F - Q}, i.e. compute a k[F]-basis of the localisation (0 :_M P_F)[ZZ F]
   Bp = ZF_basis(N, p_F)
   if is_empty(Bp)
-    return [], zeros(kQ, 1, 1)
+    return Bp, Hecke.zeros_array(kQ, 1, 1)
   end
 
   R = relations(N) #get all relations of N

experimental/InjectiveResolutions/src/MonoidAlgebra.jl

@@ -526,20 +526,6 @@ end
 dim(I::MonoidAlgebraIdeal) = krull_dim(underlying_ideal(I))
 krull_dim(I::MonoidAlgebraIdeal) = krull_dim(underlying_ideal(I))
 
-# some generic functionality which should probably be elsewhere
-function is_subset(I::T, J::T) where {T<:Ideal}
-  return all(x in J for x in gens(I))
-end
-
-function Base.:(==)(I::T, J::T) where {T <: Ideal}
-  return is_subset(I, J) && is_subset(J, I)
-end
-
-function Base.:*(I::T, J::T) where {T<:Ideal}
-  @assert base_ring(I) === base_ring(J)
-  return ideal(base_ring(I), [x*y for x in gens(I) for y in gens(J)])
-end
-
 # user facing constructor
 ideal(A::MonoidAlgebra, v::Vector) = MonoidAlgebraIdeal(A, elem_type(A)[A(x) for x in v])
 

experimental/InvariantTheory/src/InvariantTheory.jl

@@ -533,7 +533,7 @@ function inv_generators(I::MPolyIdeal, G::LinearlyReductiveGroup, ringg::MPolyRi
     end
 
     #map them to the required ring, ringg. 
-    img_genss = vcat(gens(ringg), zeros(ringg, length(xyz)-n))
+    img_genss = vcat(gens(ringg), Hecke.zeros_array(ringg, length(xyz)-n))
     mixed_to_ring = hom(mixed_ring_xy, ringg, img_genss)
     new_gens = Vector{elem_type(ringg)}()
     for elemm in new_gens_wrong_ring

experimental/LieAlgebras/src/AbstractLieAlgebra.jl

@@ -199,7 +199,7 @@ such that $[x_i, x_j] = \sum_k a_{i,j,k} x_k$.
 
 # Examples
 ```jldoctest
-julia> struct_consts = zeros(QQ, 3, 3, 3);
+julia> struct_consts = QQ.(zeros(Int, 3, 3, 3));
 
 julia> struct_consts[1, 2, 3] = QQ(1);
 

experimental/LieAlgebras/test/AbstractLieAlgebra-test.jl

@@ -1,6 +1,6 @@
 @testset "LieAlgebras.AbstractLieAlgebra" begin
   function sl2_struct_consts(R::Field)
-    sc = zeros(R, 3, 3, 3)
+    sc = Hecke.zeros_array(R, 3, 3, 3)
     sc[1, 2, 3] = R(1)
     sc[2, 1, 3] = R(-1)
     sc[3, 1, 1] = R(2)

experimental/LieAlgebras/test/LieAlgebraIdeal-test.jl

@@ -34,7 +34,7 @@
     end
 
     let # Example where ideal basis is only found after two steps
-      sc = zeros(QQ, 4, 4, 4)
+      sc = Hecke.zeros_array(QQ, 4, 4, 4)
       sc[1, 2, 3] = 1
       sc[2, 1, 3] = -1
       sc[1, 3, 4] = 1

experimental/LieAlgebras/test/iso_oscar_gap-test.jl

@@ -40,7 +40,7 @@ end
   @testset for RO in baserings
     @testset "AbstractLieAlgebra" begin
       function sl2_struct_consts(R::Field)
-        sc = zeros(R, 3, 3, 3)
+        sc = Hecke.zeros_array(R, 3, 3, 3)
         sc[1, 2, 3] = R(1)
         sc[2, 1, 3] = R(-1)
         sc[3, 1, 1] = R(2)

experimental/LieAlgebras/test/setup_tests.jl

@@ -51,7 +51,7 @@ if !isdefined(Main, :lie_algebra_conformance_test) || isinteractive()
     end
 
     @testset "parent object call overload" begin
-      @test L() == zero(L) == L(zeros(coefficient_ring(L), dim(L)))
+      @test L() == zero(L) == L(Hecke.zeros_array(coefficient_ring(L), dim(L)))
 
       for _ in 1:num_random_tests
         coeffs = rand(-10:10, dim(L))
@@ -147,7 +147,7 @@ if !isdefined(Main, :lie_algebra_conformance_test) || isinteractive()
               reduce(
                 hcat,
                 [coefficients.(es); coefficients.(fs); coefficients.(hs)];
-                init=zeros(coefficient_ring(L), dim(L), 0),
+                init=Hecke.zeros_array(coefficient_ring(L), dim(L), 0),
               ),
             ),
           )
@@ -304,7 +304,7 @@ if !isdefined(Main, :lie_algebra_module_conformance_test) || isinteractive()
     end
 
     @testset "parent object call overload" begin
-      @test V() == zero(V) == V(zeros(coefficient_ring(V), dim(V)))
+      @test V() == zero(V) == V(Hecke.zeros_array(coefficient_ring(V), dim(V)))
 
       for _ in 1:num_random_tests
         coeffs = rand(-10:10, dim(V))

experimental/MatroidRealizationSpaces/src/realization_space.jl

@@ -669,7 +669,7 @@ end
 function n_new_Sgens(
   x::RingElem, t::RingElem, Sgens::Vector{<:RingElem}, R::Ring, xs::Vector{<:RingElem}
 )
-  preSgens = unique!([sub_v(x, t, f, R, xs) for f in Sgens])
+  preSgens = unique!(elem_type(R)[sub_v(x, t, f, R, xs) for f in Sgens])
   if R(0) in preSgens
     return [R(0)]
   end

experimental/ModStd/src/ModStdQt.jl

@@ -261,7 +261,7 @@ end
 
 function Base.setindex!(v::Vals{T}, c::T, i::Int, j::Int) where {T}
   if i > length(v.v)
-    push!(v.v, zeros(parent(v.v[1][1]), length(v.v[1])))
+    push!(v.v, Hecke.zeros_array(parent(v.v[1][1]), length(v.v[1])))
   end
   if j > length(v.v[i])
     while length(v.v[i]) < j-1

experimental/Schemes/src/ToricBlowups/constructors.jl

@@ -121,7 +121,7 @@ Multivariate polynomial ring in 5 variables over QQ graded by
 ```
 """
 function blow_up(X::NormalToricVarietyType, n::Int; coordinate_name::Union{VarName, Nothing} = nothing)
-  coords = zeros(QQ, n_rays(X))
+  coords = zeros(QQFieldElem, n_rays(X))
   for i in 1:number_of_rays(X)
     cones(X)[n, i] && (coords[i] = QQ(1))
   end