New linear solving interface + bump dependencies (#3350)

* feat: Use new linear algebra functionality

* Adjust to deleted deprecations/aliases Hecke edition

Project.toml

@@ -26,16 +26,16 @@ UUIDs = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"
 cohomCalg_jll = "5558cf25-a90e-53b0-b813-cadaa3ae7ade"
 
 [compat]
-AbstractAlgebra = "0.37.5"
+AbstractAlgebra = "0.39.0"
 AlgebraicSolving = "0.4.10"
 Distributed = "1.6"
 DocStringExtensions = "0.8, 0.9"
 GAP = "0.10.2"
-Hecke = "0.27.0"
+Hecke = "0.28.0"
 JSON = "^0.20, ^0.21"
 JSON3 = "1.13.2"
 LazyArtifacts = "1.6"
-Nemo = "0.41.3"
+Nemo = "0.42.1"
 Pkg = "1.6"
 Polymake = "0.11.13"
 Preferences = "1"

docs/src/NumberTheory/galois.md

@@ -60,7 +60,7 @@ The main information is included in the number field chapter, see
   - [`Hecke.principal_subfields(K::SimpleNumField)`](@ref)
   - [`subfields(FF::Generic.FunctionField{QQFieldElem})`](@ref)
 
-By setting `set_verbose_level(:Subfields, n::Int)` to 1 or 2
+By setting `set_verbosity_level(:Subfields, n::Int)` to 1 or 2
 information about the progress can be obtained.
 
 ## Galois Group
@@ -75,8 +75,8 @@ find explicit subfields of the splitting field as well.
 
 Information about the progress is available via
 
- - `set_verbose_level(:GaloisGroup, n::Int)`
- - `set_verbose_level(:GaloisInvariants, n::Int)`
+ - `set_verbosity_level(:GaloisGroup, n::Int)`
+ - `set_verbosity_level(:GaloisInvariants, n::Int)`
 
 ```@docs
 galois_group(K::AbsSimpleNumField, extra::Int = 5; useSubfields::Bool = true, pStart::Int = 2*degree(K), prime::Int = 0)

examples/BinomIdeal.jl

@@ -695,7 +695,7 @@ argument, so we make an array prodDeltaC, push to it, then splice it in
 		uv=matrixFromArray(u-v)	#this is the vector of u-v
 		vst=transpose(vs)
 		vstMat=matrix(FlintZZ,size(vst,1), size(vst,2),vst)
-		if(cansolve(transpose(vstMat),uv)[1]==false)
+		if(can_solve(transpose(vstMat),uv)==false)
 			images=[images; nemo(-lead_coeff(tCopy))]
 			#we have to save u-v as generator for the lattice
 			#now concatenate the vector vs on bottom of the matrix vs

examples/BinomIdeal2.jl

@@ -700,7 +700,7 @@ argument, so we make an array prodDeltaC, push to it, then splice it in
                 uv=matrixFromArray(u-v) #this is the vector of u-v
                 vst=transpose(vs)
                 vstMat=matrix(FlintZZ,size(vst,1), size(vst,2),vst)
-                if(cansolve(transpose(vstMat),uv)[1]==false)
+                if(can_solve(transpose(vstMat),uv)==false)
                         images=[images; nemo(-lead_coeff(tCopy))]
                         #we have to save u-v as generator for the lattice
                         #now concatenate the vector vs on bottom of the matrix vs

experimental/FTheoryTools/src/FamilyOfSpaces/attributes.jl

@@ -196,7 +196,7 @@ Ideal generated by
   ring = coordinate_ring(f)
   variables = gens(ring)
   w = weights(f)
-  ideal_gens = right_kernel(ZZMatrix(w))[2]
+  ideal_gens = kernel(ZZMatrix(w); side = :right)
   ideal_gens = [sum([ideal_gens[l,k] * variables[l] for l in 1:nrows(ideal_gens)]) for k in 1:ncols(ideal_gens)]
   return ideal(ideal_gens)
 end

experimental/FTheoryTools/src/auxiliary.jl

@@ -22,7 +22,7 @@ function _ambient_space(base::NormalToricVariety, fiber_amb_space::NormalToricVa
   D2_coeffs = divisor_class(D2).coeff
   m1 = reduce(vcat, [D1_coeffs, D2_coeffs])
   m2 = transpose(f_rays[1:2,:])
-  u_matrix = solve_left(b_grades, (-1)*m2*m1)
+  u_matrix = solve(b_grades, (-1)*m2*m1; side = :left)
 
   # Form toric ambient space
   a_rays = zero_matrix(ZZ, nrows(b_rays) + nrows(f_rays), ncols(b_rays) + ncols(f_rays))

experimental/GITFans/src/GITFans.jl

@@ -207,7 +207,7 @@ function action_on_target(Q::Matrix{Int}, G::PermGroup)
     matgens = typeof(mat)[]
     for ppi in permgens
       matimg = mat[Vector{Int}(ppi), 1:n]  # permute the rows with `ppi`
-      push!(matgens, solve(mat, matimg))
+      push!(matgens, solve(mat, matimg; side = :right))
     end
 
     # Create the matrix group.

experimental/GModule/Brueckner.jl

@@ -418,7 +418,7 @@ function lift(C::GModule, mp::Map)
     @hassert :BruecknerSQ 2 preimage(z, z(chn)) == chn
     GG, GGinj, GGpro, GMtoGG = Oscar.GrpCoh.extension(PcGroup, z(chn))
     @assert is_surjective(GGpro)
-    if get_assert_level(:BruecknerSQ) > 1
+    if get_assertion_level(:BruecknerSQ) > 1
       _GG, _ = Oscar.GrpCoh.extension(z(chn))
       @assert is_isomorphic(GG, _GG)
     end

experimental/GModule/Cohomology.jl

@@ -11,11 +11,11 @@ import Base: parent
 import Oscar: pretty, Lowercase, @show_name, @show_special
 
 function __init__()
-  Hecke.add_verbose_scope(:GroupCohomology)
-  Hecke.add_assert_scope(:GroupCohomology)
+  Hecke.add_verbosity_scope(:GroupCohomology)
+  Hecke.add_assertion_scope(:GroupCohomology)
 
-  Hecke.add_verbose_scope(:GaloisCohomology)
-  Hecke.add_assert_scope(:GaloisCohomology)
+  Hecke.add_verbosity_scope(:GaloisCohomology)
+  Hecke.add_assertion_scope(:GaloisCohomology)
 end
 
 ######################################################################

experimental/GModule/GModule.jl

@@ -213,17 +213,17 @@ end
 
 
 function __init__()
-  add_verbose_scope(:BruecknerSQ)
-  set_verbose_level(:BruecknerSQ, 0)
+  add_verbosity_scope(:BruecknerSQ)
+  set_verbosity_level(:BruecknerSQ, 0)
 
-  add_assert_scope(:BruecknerSQ)
-  set_assert_level(:BruecknerSQ, 0)
+  add_assertion_scope(:BruecknerSQ)
+  set_assertion_level(:BruecknerSQ, 0)
 
-  add_assert_scope(:MinField)
-  set_assert_level(:MinField, 0)
+  add_assertion_scope(:MinField)
+  set_assertion_level(:MinField, 0)
 
-  add_verbose_scope(:MinField)
-  set_verbose_level(:MinField, 0)
+  add_verbosity_scope(:MinField)
+  set_verbosity_level(:MinField, 0)
 end
 
 function irreducible_modules(k::FinField, G::Oscar.GAPGroup)
@@ -914,7 +914,7 @@ function hilbert90_cyclic(A::MatElem{<:FinFieldElem}, s, os::Int)
       @hassert :MinField 2 A == B*inv(map_entries(s, B))
       return B
     else
-      if cnt > 10 && get_assert_level(:MinField) > 1
+      if cnt > 10 && get_assertion_level(:MinField) > 1
         error("")
       end
       cnt += 1
@@ -1259,7 +1259,7 @@ function hom_base(C::_T, D::_T) where _T <: GModule{<:Any, <:AbstractAlgebra.FPM
           push!(S, s)
         end
       end
-      if nbits(pp) > 1000 && get_assert_level(:MinField) > 1
+      if nbits(pp) > 1000 && get_assertion_level(:MinField) > 1
         error("ndw")
       end
       if length(S) == length(T)

experimental/GModule/GaloisCohomology.jl

@@ -1021,7 +1021,7 @@ julia> k, a = number_field(x^4 - 12*x^3 + 36*x^2 - 36*x + 9);
 
 julia> a = ray_class_field(8*3*maximal_order(k), n_quo = 2);
 
-julia> a = filter(isnormal, subfields(a, degree = 2));
+julia> a = filter(is_normal, subfields(a, degree = 2));
 
 julia> I = idel_class_gmodule(k);
 
@@ -1518,7 +1518,7 @@ and explicit 2-cochains.
 function relative_brauer_group(K::AbsSimpleNumField, k::Union{QQField, AbsSimpleNumField} = QQ)
   G, mG = automorphism_group(PermGroup, K)
   if k != QQ 
-    fl, mp = issubfield(k, K)
+    fl, mp = is_subfield(k, K)
     p = mp(gen(k))
     @assert fl
     s, ms = sub(G, [x for x = G if mG(x)(p) == p])
@@ -1631,7 +1631,7 @@ function (a::RelativeBrauerGroupElem)(p::Union{NumFieldOrderIdeal, Hecke.NumFiel
 end
 
 #write (or try to write) `b` as a ZZ-linear combination of the elements in `A`
-function Oscar.cansolve(A::Vector{RelativeBrauerGroupElem}, b::RelativeBrauerGroupElem)
+function cansolve(A::Vector{RelativeBrauerGroupElem}, b::RelativeBrauerGroupElem)
   @assert all(x->parent(x) == parent(b), A)
   lp = Set(collect(keys(b.data)))
   for a = A

experimental/GaloisGrp/src/Solve.jl

@@ -4,8 +4,8 @@ using Oscar
 import Oscar: AbstractAlgebra, Hecke, GaloisGrp.GaloisCtx
 
 function __init__()
-  Hecke.add_verbose_scope(:SolveRadical)
-  Hecke.add_assert_scope(:SolveRadical)
+  Hecke.add_verbosity_scope(:SolveRadical)
+  Hecke.add_assertion_scope(:SolveRadical)
 end
 
 
@@ -420,7 +420,7 @@ a corresponding primitive n-th root of 1, find an isomorphic radical extension
 using Lagrange resolvents.
 """
 function as_radical_extension(K::NumField, aut::Map, zeta::NumFieldElem; simplify::Bool = !false)
-  CHECK = get_assert_level(:SolveRadical) > 0
+  CHECK = get_assertion_level(:SolveRadical) > 0
 
   g = gen(K)
   d = degree(K)
@@ -468,7 +468,7 @@ The necessary roots of unity are not themselves computed as radicals.
 See also [`galois_group`](@ref).
 
 # VERBOSE
-Supports `set_verbose_level(:SolveRadical, i)` to obtain information.
+Supports `set_verbosity_level(:SolveRadical, i)` to obtain information.
 
 
 # Examples
@@ -503,7 +503,7 @@ function Oscar.solve(f::ZZPolyRingElem; max_prec::Int=typemax(Int), show_radical
   @req is_squarefree(f) "Polynomial must be square-free"
 
   #switches check = true in hom and number_field on
-  CHECK = get_assert_level(:SolveRadical) > 0
+  CHECK = get_assertion_level(:SolveRadical) > 0
   @vprint :SolveRadical 1 "computing initial galois group...\n"
   @vtime :SolveRadical 1 G, C = galois_group(f)
   lp = [p for p = keys(factor(order(G)).fac) if p > 2]

experimental/LieAlgebras/src/LieAlgebra.jl

@@ -303,7 +303,8 @@ function center(L::LieAlgebra)
     end
   end
 
-  c_dim, c_basis = left_kernel(mat)
+  c_basis = kernel(mat; side = :left)
+  c_dim = nrows(c_basis)
   return ideal(L, [L(c_basis[i, :]) for i in 1:c_dim]; is_basis=true)
 end
 
@@ -322,7 +323,8 @@ function centralizer(L::LieAlgebra, xs::AbstractVector{<:LieAlgebraElem})
     end
   end
 
-  c_dim, c_basis = left_kernel(mat)
+  c_basis = kernel(mat; side = :left)
+  c_dim = nrows(c_basis)
   return sub(L, [L(c_basis[i, :]) for i in 1:c_dim]; is_basis=true)
 end
 

experimental/LieAlgebras/src/LieAlgebraHom.jl

@@ -159,7 +159,9 @@ end
 Return the kernel of `h` as an ideal of the domain.
 """
 function kernel(h::LieAlgebraHom)
-  ker_dim, ker_b = left_kernel(matrix(h))
+  ker_b = kernel(matrix(h); side = :left)
+  ker_dim = nrows(ker_b)
+
   return ideal(domain(h), [domain(h)(ker_b[i, :]) for i in 1:ker_dim])
 end
 

experimental/LieAlgebras/src/LieSubalgebra.jl

@@ -213,7 +213,8 @@ function normalizer(L::LieAlgebra, S::LieSubalgebra)
       S
     )
   end
-  sol_dim, sol = left_kernel(mat)
+  sol = kernel(mat; side = :left)
+  sol_dim = nrows(sol)
   sol = sol[:, 1:dim(L)]
   c_dim, c_basis = rref(sol)
   return sub(L, [L(c_basis[i, :]) for i in 1:c_dim]; is_basis=true)

experimental/LieAlgebras/src/Util.jl

@@ -24,7 +24,6 @@ function coefficient_vector(M::MatElem{T}, basis::Vector{<:MatElem{T}}) where {T
   for i in 1:nr, j in 1:nc
     rhs[(i - 1) * nc + j, 1] = M[i, j]
   end
-  fl, sol = can_solve_with_solution(lgs, rhs)
-  @assert fl
+  sol = solve(lgs, rhs; side = :right)
   return transpose(sol)
 end

experimental/LieAlgebras/test/LieAlgebraModule-test.jl

@@ -402,7 +402,7 @@
                 b = V()
                 while iszero(a) ||
                         iszero(b) ||
-                        can_solve(
+                        Oscar.can_solve(
                           Oscar.LieAlgebras._matrix(a),
                           Oscar.LieAlgebras._matrix(b);
                           side=:left,

experimental/LinearQuotients/src/cox_rings.jl

@@ -43,8 +43,7 @@ function action_on_basis(G::FinGenAbGroup, G_action::Function, polys::Vector{<:
     # Little bit of a waste to recompute the rref of M all the time.
     # But I don't see how to do it better and mats should not contain many
     # elements anyways.
-    fl, sol = can_solve_with_solution(M, N, side = :left)
-    @assert fl
+    sol = solve(M, N, side = :left)
 
     push!(res, sol)
   end
@@ -140,8 +139,7 @@ function fill_degree!(HBB::HomBasisBuilder, d::Int)
     M = vcat(M, N)
   end
 
-  fl, sol = can_solve_with_solution(V, M, side = :left)
-  @assert fl
+  sol = solve(V, M, side = :left)
 
   # The i-th row of sol gives the coefficient of inhom_gens[row_to_gen[i]] in
   # the basis hom_basisd.

experimental/ModStd/ModStdNF.jl

@@ -7,7 +7,7 @@ import Hecke: modular_lift, modular_proj, modular_env, RecoCtx,
               induce_rational_reconstruction
 
 function __init__()
-  Hecke.add_verbose_scope(:ModStdNF)
+  Hecke.add_verbosity_scope(:ModStdNF)
 end
 
 

experimental/ModStd/ModStdQ.jl

@@ -6,7 +6,7 @@ import Oscar: MPolyIdeal, BiPolyArray, IdealGens, Hecke, AbstractAlgebra
 import Hecke: induce_rational_reconstruction, induce_crt
 
 function __init__()
-  Hecke.add_verbose_scope(:ModStdQ)
+  Hecke.add_verbosity_scope(:ModStdQ)
 end
 
 function (R::fpMPolyRing)(f::QQMPolyRingElem)

experimental/ModStd/ModStdQt.jl

@@ -5,7 +5,7 @@ import Oscar.Nemo
 import Oscar.Hecke
 
 function __init__()
-  Hecke.add_verbose_scope(:ModStdQt)
+  Hecke.add_verbosity_scope(:ModStdQt)
 end
 
 function Oscar.evaluate(f::FracElem{<:MPolyRingElem}, v::Vector{<:RingElem}; ErrorTolerant::Bool = false)
@@ -892,7 +892,7 @@ function Oscar.lift(f::PolyRingElem, g::PolyRingElem, a::AbsSimpleNumFieldElem,
   for i=1:n
     mm[i, 1] = coeff(d*b, i-1)
   end
-  s = solve(m, mm)
+  s = solve(m, mm; side = :right)
   B = q(parent(f)(vec(collect(s))))
   @assert all(x->iszero(evaluate(numerator(x), V)), coefficients(lift(gg(B))))
   o = lift(inv(derivative(gg)(B)))

experimental/QuadFormAndIsom/src/embeddings.jl

@@ -175,7 +175,7 @@ function _overlattice(gamma::TorQuadModuleMap,
     _B = QQ(1, denominator(Fakeglue))*change_base_ring(QQ, numerator(_FakeB))
     C = lattice(ambient_space(A), _B[end-rank(A)-rank(B)+1:end, :])
     fC = block_diagonal_matrix(QQMatrix[fA, fB])
-    _B = solve_left(reduce(vcat, basis_matrix.([A,B])), basis_matrix(C))
+    _B = solve(reduce(vcat, basis_matrix.([A,B])), basis_matrix(C); side = :left)
     fC = _B*fC*inv(_B)
   else
     _glue = Vector{QQFieldElem}[lift(HAinD(a)) + lift(HBinD(gamma(a))) for a in gens(domain(gamma))]
@@ -187,7 +187,7 @@ function _overlattice(gamma::TorQuadModuleMap,
     _B = QQ(1, denominator(Fakeglue))*change_base_ring(QQ, numerator(_FakeB))
     C = lattice(ambient_space(cover(D)), _B[end-rank(A)-rank(B)+1:end, :])
     fC = block_diagonal_matrix(QQMatrix[fA, fB])
-    _B = solve_left(block_diagonal_matrix(basis_matrix.(ZZLat[A, B])), basis_matrix(C))
+    _B = solve(block_diagonal_matrix(basis_matrix.(ZZLat[A, B])), basis_matrix(C); side = :left)
     fC = _B*fC*inv(_B)
   end
   @hassert :ZZLatWithIsom 1 fC*gram_matrix(C)*transpose(fC) == gram_matrix(C)
@@ -377,7 +377,7 @@ function _fitting_isometries(OqfN::AutomorphismGroup{TorQuadModule},
   # To summarize, in the general case, we obtain representatives of fitting
   # isometries by identifying CN-conjugate isometries in the coset fNKN.
   if first
-    reporb = QQMatrix[solve_left(basis_matrix(N), basis_matrix(N)*matrix(_fN))]
+    reporb = QQMatrix[solve(basis_matrix(N), basis_matrix(N)*matrix(_fN); side = :left)]
   else
     KNhat, _ = discrep\(kernel(_actN)[1])
     fNKN = _fN*KNhat
@@ -391,7 +391,7 @@ function _fitting_isometries(OqfN::AutomorphismGroup{TorQuadModule},
       end
     end
   end
-  reporb = QQMatrix[solve_left(basis_matrix(N), basis_matrix(N)*matrix(a[1])) for a in orb_and_rep]
+  reporb = QQMatrix[solve(basis_matrix(N), basis_matrix(N)*matrix(a[1]); side = :left) for a in orb_and_rep]
   return reporb
 end
 
@@ -925,7 +925,8 @@ function _subgroups_orbit_representatives_and_stabilizers_elementary(Vinq::TorQu
 
   F = base_ring(Qp)
   # K is H0 but seen a subvector space of Vp (which is V)
-  k, K = kernel(VptoQp.matrix; side = :left)
+  K = kernel(VptoQp.matrix; side = :left)
+  k = nrows(K)
   gene_H0p = elem_type(Vp)[Vp(vec(collect(K[i,:]))) for i in 1:k]
   orb_and_stab = orbit_representatives_and_stabilizers(MGp, g-k)
 
@@ -1405,8 +1406,8 @@ function primitive_embeddings(G::ZZGenus, M::ZZLat; classification::Symbol = :su
       # L, M3 and N live in a very big ambient space: we redescribed them in the
       # rational span of L so that L has full rank and we keep only the
       # necessary information.
-      bM = solve_left(basis_matrix(L), basis_matrix(M3))
-      bN = solve_left(basis_matrix(L), basis_matrix(N))
+      bM = solve(basis_matrix(L), basis_matrix(M3); side = :left)
+      bN = solve(basis_matrix(L), basis_matrix(N); side = :left)
       L = integer_lattice(; gram = gram_matrix(L))
       M3 = lattice_in_same_ambient_space(L, bM)
       N = lattice_in_same_ambient_space(L, bN)

experimental/QuadFormAndIsom/src/hermitian_miranda_morrison.jl

@@ -576,7 +576,7 @@ function _transfer_discriminant_isometry(res::AbstractSpaceRes,
   B2abs = map_entries(p, B2abs)
 
   # Our local modular solution we have to lift
-  K = solve_left(Bpabs, B2abs)
+  K = solve(Bpabs, B2abs; side = :left)
   K = map_entries(a -> EabstoE(Eabs(p\a)), K)
 
   # If what we have done is correct then K*newBp == newB2 modulo O_p, so all