Merge branch 'master' into gf/BasisLieHighestWeight

Project.toml

@@ -31,7 +31,7 @@ AlgebraicSolving = "0.3.6"
 Distributed = "1.6"
 DocStringExtensions = "0.8, 0.9"
 GAP = "0.10.0"
-Hecke = "0.22.5"
+Hecke = "0.22.6"
 JSON = "^0.20, ^0.21"
 LazyArtifacts = "1.6"
 Nemo = "0.37.1"

docs/src/Groups/basics.md

@@ -89,10 +89,13 @@ is_finitelygenerated
 
 ```@docs
 order(::Type{T}, x::Union{GAPGroupElem, GAPGroup}) where T <: IntegerUnion
+abelian_invariants(G::GAPGroup)
+abelian_invariants_schur_multiplier(G::GAPGroup)
 cyclic_generator(G::GAPGroup)
 exponent(G::GAPGroup)
 describe(G::GAPGroup)
 nilpotency_class(G::GAPGroup)
 prime_of_pgroup
 derived_length
+schur_multiplier(G::Union{GAPGroup, GrpAbFinGen})
 ```

docs/src/NumberTheory/galois.md

@@ -145,8 +145,8 @@ julia> r = roots(C, 5)
 4-element Vector{qadic}:
  5*11^0 + 2*11^1 + 6*11^2 + 8*11^3 + 11^4 + O(11^5)
  6*11^0 + 8*11^1 + 4*11^2 + 2*11^3 + 9*11^4 + O(11^5)
- (11^0 + 6*11^1 + 6*11^2 + 2*11^4 + O(11^5))*a + 9*11^0 + 4*11^1 + 6*11^2 + 7*11^3 + 11^4 + O(11^5)
  (10*11^0 + 4*11^1 + 4*11^2 + 10*11^3 + 8*11^4 + O(11^5))*a + 2*11^0 + 6*11^1 + 4*11^2 + 3*11^3 + 9*11^4 + O(11^5)
+ (11^0 + 6*11^1 + 6*11^2 + 2*11^4 + O(11^5))*a + 9*11^0 + 4*11^1 + 6*11^2 + 7*11^3 + 11^4 + O(11^5)
 
 julia> r[1]^2
 3*11^0 + O(11^5)

experimental/GModule/GaloisCohomology.jl

@@ -426,7 +426,7 @@ function Oscar.gmodule(K::Hecke.LocalField, k::Union{Hecke.LocalField, FlintPadi
   mQ = mQ*inv(mS)
 
   if Sylow > 0
-    @assert isprime(Sylow)
+    @assert is_prime(Sylow)
     G, mS = sylow_subgroup(G, Sylow)
     mG = mS*mG
   end

experimental/GaloisGrp/test/runtests.jl

@@ -3,5 +3,12 @@
   K, r = solve(x^3+3*x+5)
   @test absolute_degree(K) == 12
   @test length(r) == 3
+
+  Qt, t = rational_function_field(QQ, "t")
+  Qtx, x = Qt["x"]
+  F, a = function_field(x^6 + 108*t^2 + 108*t + 27)
+  subfields(F)
+  G, = galois_group(F)
+  @test is_isomorphic(G, symmetric_group(3))
 end
 

experimental/OrthogonalDiscriminants/test/data.jl

@@ -26,7 +26,7 @@
   @test length(all_od_infos(orthogonal_discriminant => "O+")) +
         length(all_od_infos(orthogonal_discriminant => "O-")) ==
         length(Oplusminus)
-  @test length(Oplusminus) <= length(all_od_infos(characteristic => ispositive))
+  @test length(Oplusminus) <= length(all_od_infos(characteristic => is_positive))
   deg_1 = all_od_infos(degree => 1);
   deg_other = all_od_infos(degree => (x -> x > 1));
   @test length(all_entries) == length(deg_1) + length(deg_other)

experimental/QuadFormAndIsom/src/embeddings.jl

@@ -1487,7 +1487,7 @@ function _find_admissible_gluing(SAinqA::TorQuadModuleMor,
   phiHA, _ = sub(SB, elem_type(SB)[phi(SA(lift(a))) for a in gens(HA)])
   OSB = orthogonal_group(SB)
   G = GSetByElements(OSB, _on_subgroups, TorQuadModule[HB])
-  ok, g = representative_action(G, phiHA, HB)
+  ok, g = is_conjugate_with_data(G, phiHA, HB)
   @hassert :ZZLatWithIsom 1 ok
   phi_1 = compose(phi, hom(g))
   @hassert :ZZLatWithIsom 1 sub(SB, elem_type(SB)[phi_1(SA(lift(a))) for a in gens(HA)])[1] == HB

experimental/Schemes/AlgebraicCycles.jl

@@ -491,8 +491,8 @@ function ==(D::AbsAlgebraicCycle, E::AbsAlgebraicCycle)
     end
   else
     # Make sure all generators are actually prime so that they can be compared. 
-    all(I->isprime(I), keys(coefficient_dict(D))) || return irreducible_decomposition(D) == E
-    all(I->isprime(I), keys(coefficient_dict(E))) || return D == irreducible_decomposition(E)
+    all(is_prime, keys(coefficient_dict(D))) || return irreducible_decomposition(D) == E
+    all(is_prime, keys(coefficient_dict(E))) || return D == irreducible_decomposition(E)
 
     keys_D = collect(keys(coefficient_dict(D)))
     keys_E = collect(keys(coefficient_dict(E)))

experimental/Schemes/BlowupMorphism.jl

@@ -543,7 +543,7 @@ function strict_transform(p::AbsSimpleBlowdownMorphism, C::EffectiveCartierDivis
                        # sanity check -- we are on a trivializing covering after all!
     h_orig = C(V)[1]
     h_total = pullback(pr_refined[U]).(h_orig)
-    if isunit(h_total)
+    if is_unit(h_total)
       ID[U] = one(OO(U))
       continue
     end
@@ -552,7 +552,7 @@ function strict_transform(p::AbsSimpleBlowdownMorphism, C::EffectiveCartierDivis
     length(E(U)) == 1 || error("exceptional divisor is not principal")
                        # sanity check -- default covering of Y is already trivializing for E!
     e = E(U)[1]
-    if isunit(e)
+    if is_unit(e)
       ID[U] = h_total
       continue
     end

experimental/Schemes/CartierDivisor.jl

@@ -331,7 +331,7 @@ function intersect(W::WeilDivisor, C::EffectiveCartierDivisor; check::Bool=true)
   X = scheme(W)
   result = zero(W)
   for I in components(W)
-    @check isprime(I) "all components of the first argument must be sheaves of prime ideals"
+    @check is_prime(I) "all components of the first argument must be sheaves of prime ideals"
     inc_Y = CoveredClosedEmbedding(X, I, check=false)
     #inc_Y = CoveredClosedEmbedding(X, I, covering=trivializing_covering(C), check=false)
     Y = domain(inc_Y)

experimental/Schemes/CoveredProjectiveSchemes.jl

@@ -519,7 +519,7 @@ function is_regular_sequence(g::Vector{T}) where {T<:RingElem}
   length(g) == 0 && return true
   R = parent(g[1])
   all(x->parent(x)===R, g) || error("elements do not belong to the correct ring")
-  isunit(g[1]) && return false # See Bruns-Herzog: Cohen-Macaulay rings, section 1.1.
+  is_unit(g[1]) && return false # See Bruns-Herzog: Cohen-Macaulay rings, section 1.1.
   is_zero_divisor(g[1]) && return false
   A, p = quo(R, ideal(R, g))
   return is_regular_sequence(p.(g[2:end]))
@@ -1469,7 +1469,7 @@ end
 #        X = hypersurface_complement(subscheme(C, div_list[i]), prod(loc_list[i]))
 #        D = A[row_list[i], column_list[i]]
 #        g = det(D)
-#        isunit(OO(X)(g)) || error("selected minor is not a unit")
+#        is_unit(OO(X)(g)) || error("selected minor is not a unit")
 #      end
 #    end
 #  else
@@ -1678,7 +1678,7 @@ end
 #    A = Df[rl[i], cl[i]]
 #    g = det(A)
 #    U = hypersurface_complement(subscheme(C, ql[i]), h)
-#    @show isunit(OO(U)(g))
+#    @show is_unit(OO(U)(g))
 #  end
 #
 #

experimental/Schemes/FunctionFields.jl

@@ -167,7 +167,7 @@ end
 # try to avoid a groebner basis computation
 iszero(a::VarietyFunctionFieldElem) = iszero(representative(a)) || iszero(OO(representative_patch(parent(a)))(numerator(a)))
 isone(a::VarietyFunctionFieldElem) = isone(representative(a)) || iszero(OO(representative_patch(parent(a)))(numerator(a) - denominator(a)))
-isunit(a::VarietyFunctionFieldElem) = !iszero(representative(a))
+is_unit(a::VarietyFunctionFieldElem) = !iszero(representative(a))
 
 ########################################################################
 # Conversion of rational functions on arbitrary patches                #

experimental/Schemes/MorphismFromRationalFunctions.jl

@@ -601,7 +601,7 @@ end
 function pushforward(Phi::MorphismFromRationalFunctions, D::AbsAlgebraicCycle)
   is_isomorphism(Phi) || error("method not implemented unless for the case of an isomorphism")
   #is_proper(Phi) || error("morphism must be proper")
-  all(x->isprime(x), components(D)) || error("divisor must be given in terms of irreducible components")
+  all(is_prime, components(D)) || error("divisor must be given in terms of irreducible components")
   X = domain(Phi)
   Y = codomain(Phi)
   pushed_comps = IdDict{IdealSheaf, elem_type(coefficient_ring(D))}()

experimental/Schemes/ToricIdealSheaves/constructors.jl

@@ -44,7 +44,7 @@ function IdealSheaf(X::NormalToricVariety, I::MPolyIdeal)
   # 1. All maximal cones are smooth, i.e. the fan is smooth/X is smooth.
   # 2. The dimension of all maximal cones matches the dimension of the fan.
   @req is_smooth(X) "Currently, ideal sheaves are only supported for smooth toric varieties"
-  @req ispure(X) "Currently, ideal sheaves require that all maximal cones have the dimension of the variety"
+  @req is_pure(X) "Currently, ideal sheaves require that all maximal cones have the dimension of the variety"
 
   ideal_dict = IdDict{AbsSpec, Ideal}()
 

experimental/Schemes/WeilDivisor.jl

@@ -429,7 +429,7 @@ function in_linear_system(f::VarietyFunctionFieldElem, D::WeilDivisor; regular_o
   X === variety(parent(f)) || error("schemes not compatible")
   C = simplified_covering(X)
   for I in components(D)
-    @check isprime(I) "components of the divisor must be prime"
+    @check is_prime(I) "components of the divisor must be prime"
     order_on_divisor(f, I, check=false) >= -D[I] || return false
   end
   regular_on_complement && return true
@@ -461,7 +461,7 @@ generated by rational functions ``f₁,…,fᵣ ∈ K(X)``.
     X === variety(KK) || error("input not compatible")
 
     @check begin
-      all(I->isprime(I), components(D)) || error("components of the divisor must be prime")
+      all(is_prime, components(D)) || error("components of the divisor must be prime")
       all(g->in_linear_system(g, D), f) || error("element not in linear system")
     end
     f = Vector{VarietyFunctionFieldElem}(f)

experimental/StandardFiniteFields/src/StandardFiniteFields.jl

@@ -460,7 +460,7 @@ Finite field of degree 24 over GF(3)
 ```
 """
 function standard_finite_field(p::IntegerUnion, n::IntegerUnion)
-  @req isprime(p) "first argument must be a prime"
+  @req is_prime(p) "first argument must be a prime"
   F = GF(p)
   set_standard_prime_field!(F)
 

experimental/SymmetricIntersections/src/representations.jl

@@ -1060,7 +1060,7 @@ function _has_pfr(G::Oscar.GAPGroup, dim::Int)
   f_gap = GG.EpimorphismSchurCover(G_gap)
   H_gap = GG.Source(f_gap)
   n, p = ispower(GG.Size(H_gap))
-  if isprime(p)
+  if is_prime(p)
     fff_gap = GG.EpimorphismPGroup(H_gap, p)
     E_gap = fff_gap(H_gap)
   else

src/AlgebraicGeometry/Schemes/AffineSchemes/Objects/Properties.jl

@@ -153,7 +153,7 @@ function issubset(
   ) where {BRT}
   R = ambient_coordinate_ring(X)
   R === ambient_coordinate_ring(Y) || return false
-  all(x->isunit(OO(X)(x)), denominators(inverted_set(OO(Y)))) || return false
+  all(x->is_unit(OO(X)(x)), denominators(inverted_set(OO(Y)))) || return false
   return iszero(localized_ring(OO(Y))(modulus(OO(X))))
 end
 
@@ -164,7 +164,7 @@ function issubset(
   ) where {BRT}
   R = ambient_coordinate_ring(X)
   R === ambient_coordinate_ring(Y) || return false
-  all(x->isunit(OO(X)(x)), denominators(inverted_set(OO(Y)))) || return false
+  all(x->is_unit(OO(X)(x)), denominators(inverted_set(OO(Y)))) || return false
   return issubset(modulus(OO(Y)), localized_ring(OO(Y))(modulus(OO(X))))
 end
 
@@ -464,7 +464,7 @@ function is_closed_embedding(
   R = ambient_coordinate_ring(X)
   R === ambient_coordinate_ring(Y) || return false
   for f in inverted_set(OO(X))
-    isunit(OO(Y)(f)) || return false
+    is_unit(OO(Y)(f)) || return false
   end
   return true
 end
@@ -479,7 +479,7 @@ function is_closed_embedding(
   R = ambient_coordinate_ring(X)
   R === ambient_coordinate_ring(Y) || return false
   for x in inverted_set(OO(X)) 
-    isunit(OO(Y)(x)) || return false
+    is_unit(OO(Y)(x)) || return false
   end
   for g in gens(modulus(OO(Y)))
     iszero(OO(X)(g)) || return false
@@ -517,7 +517,7 @@ function is_closed_embedding(
                                           <:MPolyPowersOfElement}}
   R = ambient_coordinate_ring(X)
   R === ambient_coordinate_ring(Y) || return false
-  all(x->(isunit(OO(X)(x))), denominators(inverted_set(OO(Y)))) || return false
+  all(x->(is_unit(OO(X)(x))), denominators(inverted_set(OO(Y)))) || return false
   return issubset(modulus(OO(Y)), localized_ring(OO(Y))(modulus(OO(X))))
 end
 

src/AlgebraicGeometry/Schemes/CoveredSchemes/Morphisms/Attributes.jl

@@ -56,8 +56,8 @@ given by the pullback function
     (y//z) -> 0
 ```
 """
-function covering_morphism(f::AbsCoveredSchemeMorphism)::CoveringMorphism
-  return covering_morphism(underlying_morphism(f))
+function covering_morphism(f::AbsCoveredSchemeMorphism)
+  return covering_morphism(underlying_morphism(f))::CoveringMorphism
 end
 
 ### generically derived getters

src/AlgebraicGeometry/Surfaces/K3Auto.jl

@@ -1201,7 +1201,7 @@ function is_S_nondegenerate(L::ZZLat, S::ZZLat, w::QQMatrix)
   D = reduce(vcat, prSDelta_w, init=i)
   P = positive_hull(D)  # the dual cone of C
   # If P has a linear subspace, then its dual C is not of full dimension.
-  return ispointed(P)
+  return is_pointed(P)
 end
 
 function inner_point(L::ZZLat, S::ZZLat, w::QQMatrix)

src/AlgebraicGeometry/ToricVarieties/CohomologyClasses/methods.jl

@@ -88,7 +88,7 @@ julia> integrate(cohomology_class(anticanonical_divisor_class(X))^3)
 62
 ```
 """
-function integrate(c::CohomologyClass)::QQFieldElem
+function integrate(c::CohomologyClass)
     # can only integrate if the variety is simplicial, complete
     @req is_simplicial(toric_variety(c)) && is_complete(toric_variety(c)) "Integration only supported over complete and simplicial toric varieties"
 
@@ -97,30 +97,30 @@ function integrate(c::CohomologyClass)::QQFieldElem
         intersection_dict = _intersection_form_via_exponents(toric_variety(c))
         coeffs = coefficients(c)
         expos = exponents(c)
-        integral = 0
+        integral = zero(QQ)
         for i in 1:nrows(expos)
             if expos[i, :] in keys(intersection_dict)
                 integral += coeffs[i] * intersection_dict[expos[i, :]]
             end
         end
-        return integral
+        return integral::QQFieldElem
     end
 
     # otherwise, proceed "by hand"
     if is_trivial(c)
-        return 0
+        return zero(QQ)
     end
     poly = polynomial(c)
     dict = homogeneous_components(poly)
     elem = base_ring(parent(poly)).D([dim(toric_variety(c))])
     if !(elem in keys(dict))
-        return 0
+        return zero(QQ)
     end
     top_form = dict[elem]
     if iszero(top_form)
-        return 0
+        return zero(QQ)
     end
     n = AbstractAlgebra.leading_coefficient(top_form.f)
     m = AbstractAlgebra.leading_coefficient(polynomial(volume_form(toric_variety(c))).f)
-    return QQFieldElem(n//m)
+    return n//m
 end

src/AlgebraicGeometry/ToricVarieties/NormalToricVarieties/attributes.jl

@@ -1091,7 +1091,7 @@ julia> hilbert_basis(antv)
 """
 @attr ZZMatrix function hilbert_basis(v::AffineNormalToricVariety)
   @req is_pointed(weight_cone(v)) "Weight cone is not pointed"
-  @req isfulldimensional(weight_cone(v)) "Weight cone is not full dimensional"
+  @req is_fulldimensional(weight_cone(v)) "Weight cone is not full dimensional"
   return matrix(ZZ, hilbert_basis(weight_cone(v)))
 end