feat: Use new linear algebra functionality

Project.toml

@@ -26,7 +26,7 @@ UUIDs = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"
 cohomCalg_jll = "5558cf25-a90e-53b0-b813-cadaa3ae7ade"
 
 [compat]
-AbstractAlgebra = "0.37.5"
+AbstractAlgebra = "0.37.6"
 AlgebraicSolving = "0.4.6"
 Distributed = "1.6"
 DocStringExtensions = "0.8, 0.9"
@@ -35,7 +35,7 @@ Hecke = "0.27.0"
 JSON = "^0.20, ^0.21"
 JSON3 = "1.13.2"
 LazyArtifacts = "1.6"
-Nemo = "0.41.3"
+Nemo = "0.41.5"
 Pkg = "1.6"
 Polymake = "0.11.12"
 Preferences = "1"

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 = Solve.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.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

@@ -7,6 +7,8 @@ module GITFans
 # the necessary Julia packages
 using Oscar
 
+import Oscar: AbstractAlgebra.Solve
+
 export git_fan
 
 #############################################################################
@@ -207,7 +209,7 @@ 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.solve(mat, matimg; side = :right))
     end
 
     # Create the matrix group.

experimental/LieAlgebras/src/LieAlgebra.jl

@@ -303,7 +303,8 @@ function center(L::LieAlgebra)
     end
   end
 
-  c_dim, c_basis = left_kernel(mat)
+  c_basis = Solve.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 = Solve.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 = Solve.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/LieAlgebraIdeal.jl

@@ -23,7 +23,7 @@
       left = copy(gens)
       while !isempty(left)
         g = pop!(left)
-        can_solve(basis_matrix, _matrix(g); side=:left) && continue
+        Solve.can_solve(basis_matrix, _matrix(g); side=:left) && continue
         for b in basis(L)
           push!(left, b * g)
         end

experimental/LieAlgebras/src/LieAlgebras.jl

@@ -13,8 +13,10 @@ using AbstractAlgebra: CacheDictType, ProductIterator, get_cached!, ordinal_numb
 
 using AbstractAlgebra.PrettyPrinting
 
+
 # functions with new methods
 import ..Oscar:
+  AbstractAlgebra.Solve,
   _iso_oscar_gap,
   action,
   basis_matrix,

experimental/LieAlgebras/src/LieSubalgebra.jl

@@ -23,7 +23,7 @@
       left = copy(gens)
       while !isempty(left)
         g = pop!(left)
-        can_solve(basis_matrix, _matrix(g); side=:left) && continue
+        Solve.can_solve(basis_matrix, _matrix(g); side=:left) && continue
         for i in 1:nrows(basis_matrix)
           push!(left, g * L(basis_matrix[i, :]))
         end
@@ -160,7 +160,7 @@ end
 Return `true` if `x` is in the Lie subalgebra `S`, `false` otherwise.
 """
 function Base.in(x::LieAlgebraElem, S::LieSubalgebra)
-  return can_solve(basis_matrix(S), _matrix(x); side=:left)
+  return Solve.can_solve(basis_matrix(S), _matrix(x); side=:left)
 end
 
 ###############################################################################
@@ -213,7 +213,8 @@ function normalizer(L::LieAlgebra, S::LieSubalgebra)
       S
     )
   end
-  sol_dim, sol = left_kernel(mat)
+  sol = Solve.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 +24,7 @@ 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)
+  fl, sol = Solve.can_solve_with_solution(lgs, rhs; side = :right)
   @assert fl
   return transpose(sol)
 end

experimental/LieAlgebras/test/LieAlgebraModule-test.jl

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

experimental/ModStd/ModStdQt.jl

@@ -3,6 +3,7 @@ module ModStdQt
 using Oscar
 import Oscar.Nemo
 import Oscar.Hecke
+import Oscar.Solve
 
 function __init__()
   Hecke.add_verbose_scope(:ModStdQt)
@@ -892,7 +893,7 @@ 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.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.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.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.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.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 = Solve.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.solve(basis_matrix(L), basis_matrix(M3); side = :left)
+      bN = Solve.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.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

experimental/QuadFormAndIsom/src/lattices_with_isometry.jl

@@ -1821,7 +1821,7 @@ function _real_kernel_signatures(L::ZZLat, M::MatElem)
   C = base_ring(M)
   G = gram_matrix(L)
   GC = change_base_ring(C, G)
-  _, K = left_kernel(M)
+  K = Solve.kernel(M; side = :left)
   diag = K*GC*transpose(K)
 
   diag = Hecke._gram_schmidt(diag, C)[1]
@@ -1951,7 +1951,7 @@ function kernel_lattice(Lf::ZZLatWithIsom, p::QQPolyRingElem)
   f = isometry(Lf)
   M = p(f)
   d = denominator(M)
-  k, K = left_kernel(change_base_ring(ZZ, d*M))
+  K = Solve.kernel(change_base_ring(ZZ, d*M); side = :left)
   return lattice(ambient_space(Lf), K*basis_matrix(L))
 end
 
@@ -2141,7 +2141,7 @@ function coinvariant_lattice(L::ZZLat, G::MatrixGroup; ambient_representation::B
     if !ambient_representation
       g_ambient = block_diagonal_matrix(QQMatrix[matrix(g), identity_matrix(QQ, nrows(B2))])
       g_ambient = iB3*g_ambient*B3
-      m = solve_left(basis_matrix(C), basis_matrix(C)*g_ambient)
+      m = Solve.solve(basis_matrix(C), basis_matrix(C)*g_ambient; side = :left)
       push!(gene, m)
     else
       push!(gene, matrix(g))
@@ -2216,7 +2216,7 @@ function invariant_coinvariant_pair(L::ZZLat, G::MatrixGroup; ambient_representa
     if !ambient_representation
       g_ambient = block_diagonal_matrix(QQMatrix[matrix(g), identity_matrix(QQ, nrows(B2))])
       g_ambient = iB3*g_ambient*B3
-      m = solve_left(basis_matrix(C), basis_matrix(C)*g_ambient)
+      m = Solve.solve(basis_matrix(C), basis_matrix(C)*g_ambient; side = :left)
       push!(gene, m)
     else
       push!(gene, matrix(g))

experimental/Rings/QQAbAndPChars.jl

@@ -4,6 +4,8 @@ using ..Oscar
 
 import Oscar: IJuliaMime
 
+import Oscar: Solve
+
 ###############################################################################
 #
 #   Partial character functions
@@ -42,7 +44,7 @@ end
 function (Chi::PartialCharacter)(b::ZZMatrix)
   @assert nrows(b) == 1
   @assert Nemo.ncols(b) == Nemo.ncols(Chi.A)
-  s = can_solve_with_solution(Chi.A, b, side = :left)
+  s = Solve.can_solve_with_solution(Chi.A, b, side = :left)
   @assert s[1]
   return evaluate(FacElem(Dict([(Chi.b[i], s[2][1, i]) for i = 1:length(Chi.b)])))
 end

experimental/Schemes/WeilDivisor.jl

@@ -675,7 +675,8 @@ function _subsystem(L::LinearSystem, P::IdealSheaf, n)
       A[i, k] = c
     end
   end
-  r, K = left_kernel(A)
+  K = Solve.kernel(A; side = :left)
+  r = nrows(K)
   new_gens = [sum([K[i,j]*gen(L, j) for j in 1:ncols(K)]) for i in 1:r]
   W = weil_divisor(L)
   PW = WeilDivisor(P, check=false)

experimental/Schemes/elliptic_surface.jl

@@ -1028,7 +1028,8 @@ function _prop217(E::EllipticCurve, P::EllipticCurvePoint, k)
   cc = [[coeff(j, abi) for abi in ab] for j in eqns]
   M = matrix(B, length(eqns), length(ab), reduce(vcat,cc, init=elem_type(base)[]))
   # @assert M == matrix(base, cc) # does not work if length(eqns)==0
-  kerdim, K = kernel(M)
+  K = Solve.kernel(M; side = :right)
+  kerdim = ncols(K)
   result = Tuple{elem_type(Bt),elem_type(Bt)}[]
   t = gen(Bt)
   for j in 1:kerdim
@@ -1358,7 +1359,7 @@ function extended_ade(ADE::Symbol, n::Int)
     G[n,1] = -1
   end
   @assert rank(G) == n
-  return -G, left_kernel(G)[2]
+  return -G, Solve.kernel(G; side = :left)
 end
 
 function basis_representation(X::EllipticSurface, D::WeilDivisor)

experimental/SymmetricIntersections/src/representations.jl

@@ -1280,12 +1280,12 @@ function complement_submodule(rep::LinRep{S, T, U}, M::W) where {S, T, U, W <: M
         B2j = B2[j]
         B2jM = (B2j*M)[1:1,:]
         B1u = reduce(vcat, [BB[1:1,:] for BB in B1])
-        _Kj = solve_left(B1u, B2jM)
+        _Kj = Solve.solve(B1u, B2jM; side = :left)
         for i in 1:d, k in 1:length(B1)
           _K[(k-1)*d + i, i + (j-1)*d] = _Kj[1, k]
         end
       end
-      a, K2 = left_kernel(_K)
+      K2 = Solve.kernel(_K; side = :left)
       Borth = K2*reduce(vcat, B1)
       @assert is_submodule(rep, Borth)
       bas = vcat(bas, Borth)

experimental/SymmetricIntersections/src/symmetric_grassmannians.jl

@@ -508,7 +508,7 @@ function _intersection_with_grassmannian(V::Vector{T}, n::Int, t::Int;
   end
   Grtn = subscheme(X, ideal_Gr)
   B = reduce(vcat, V)
-  _, K = right_kernel(B)
+  K = Solve.kernel(B; side = :right)
 
   if ncols(K) == 0
     return ideal_Gr