From 17afb5c2e097e706bf2753ac380e9f80bb8ffcd5 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Lars=20G=C3=B6ttgens?= Date: Fri, 16 Feb 2024 12:39:07 +0100 Subject: [PATCH 01/29] Change some things from British to American spelling (#3367) * `factorisations` -> `factorizations` * comment and docu fixes * Add `centraliser` -> `centralizer` deprecation * `neighbour` -> `neighbor` --- README.md | 2 +- .../Experimental/Singularities/space_germs.md | 2 +- docs/src/NumberTheory/galois.md | 2 +- experimental/GModule/Cohomology.jl | 4 +-- experimental/GModule/GModule.jl | 2 +- experimental/GModule/GaloisCohomology.jl | 2 +- .../QuadFormAndIsom/src/embeddings.jl | 2 +- experimental/Schemes/SpaceGerms.jl | 2 +- src/Groups/sub.jl | 2 -- src/NumberTheory/GaloisGrp/GaloisGrp.jl | 2 +- src/NumberTheory/GaloisGrp/Qt.jl | 2 +- src/NumberTheory/NmbThy.jl | 6 ++-- src/TropicalGeometry/groebner_fan.jl | 4 +-- src/TropicalGeometry/hypersurface.jl | 2 +- src/TropicalGeometry/linear_space.jl | 8 ++--- src/TropicalGeometry/variety.jl | 30 +++++++++---------- src/deprecations.jl | 3 ++ src/exports.jl | 2 +- test/NumberTheory/nmbthy.jl | 4 +-- 19 files changed, 42 insertions(+), 41 deletions(-) diff --git a/README.md b/README.md index 595a9923be14..e91e73bc2e41 100644 --- a/README.md +++ b/README.md @@ -54,7 +54,7 @@ julia> zk = maximal_order(k) Maximal order of Imaginary quadratic field defined by x^2 + 5 with basis AbsSimpleNumFieldElem[1, sqrt(-5)] -julia> factorisations(zk(6)) +julia> factorizations(zk(6)) 2-element Vector{Fac{AbsSimpleNumFieldOrderElem}}: -1 * -3 * 2 -1 * (-sqrt(-5) - 1) * (-sqrt(-5) + 1) diff --git a/docs/src/Experimental/Singularities/space_germs.md b/docs/src/Experimental/Singularities/space_germs.md index 0e9f215a227e..0457ead8759d 100644 --- a/docs/src/Experimental/Singularities/space_germs.md +++ b/docs/src/Experimental/Singularities/space_germs.md @@ -6,7 +6,7 @@ CurrentModule = Oscar ## [Generalities on Space germs](@id space_germ_generalities) -The geometric notion of a space germ is a local concept. A space germ $(X,x)$ at a point $x$ is an equivalence class of ringed spaces, each of which contains $x$ in its underlying topological space, and the equivalence relation is precisely the existence of an open neighbourhood of $x$ on which the spaces coincide. +The geometric notion of a space germ is a local concept. A space germ $(X,x)$ at a point $x$ is an equivalence class of ringed spaces, each of which contains $x$ in its underlying topological space, and the equivalence relation is precisely the existence of an open neighborhood of $x$ on which the spaces coincide. Depending on the kind of ringed space in question, space germs arise in different forms: diff --git a/docs/src/NumberTheory/galois.md b/docs/src/NumberTheory/galois.md index 3521c038ae44..df8a02f60dd9 100644 --- a/docs/src/NumberTheory/galois.md +++ b/docs/src/NumberTheory/galois.md @@ -41,7 +41,7 @@ between `K` and `k` can be computed as well. ## Automorphism Group -The automorphisms are computed using various specialised factoring +The automorphisms are computed using various specialized factoring algorithms: lifting the roots of the defining polynomial in the given field modulo suitable prime ideal powers and recovering the true roots from this information. diff --git a/experimental/GModule/Cohomology.jl b/experimental/GModule/Cohomology.jl index f4d8fe6cf8f3..6762947010f4 100644 --- a/experimental/GModule/Cohomology.jl +++ b/experimental/GModule/Cohomology.jl @@ -291,7 +291,7 @@ function induce(C::GModule{<:Oscar.GAPGroup, FinGenAbGroup}, h::Map, D = nothing #= C is Z[U] module, we needd C otimes Z[G] - any pure tensor c otimes g can be "normalised" g = u*g_i for one of the + any pure tensor c otimes g can be "normalized" g = u*g_i for one of the reps fixed above, so c otimes g = c otimes u g_i == cu otimes g_i For the G-action we thus get @@ -2080,7 +2080,7 @@ function extension(::Type{PcGroup}, c::CoChain{2,<:Oscar.PcGroupElem}) # F^p = w (order relation) # compute (F, 0)^p = (?, t) = (?, 0)(1, t) # compute (w, 0) = (?, s) = (?, 0)(1, s) - # so (?, 0) = (w, 0)(1,s)^-1= (w, 0)(1,-s) if chain is normalised + # so (?, 0) = (w, 0)(1,s)^-1= (w, 0)(1,-s) if chain is normalized # thus (F, 0)^p = (?, 0)(1, t) = (w, 0)(1,-s)(1, t) # the ? should be identical, namely the collected version of w # then (F, 0)^p = (w, t-s) might be the answer diff --git a/experimental/GModule/GModule.jl b/experimental/GModule/GModule.jl index d52cd4a9dbf4..11dfc8eaff02 100644 --- a/experimental/GModule/GModule.jl +++ b/experimental/GModule/GModule.jl @@ -728,7 +728,7 @@ function _two_cocycle(mA::Map, C::GModule{<:Any, <:AbstractAlgebra.FPModule{AbsS end I = identity_matrix(K, dim(C)) - @vprint :MinField 1 "computing un-normalised 1-chain (of matrices)\n" + @vprint :MinField 1 "computing un-normalized 1-chain (of matrices)\n" # pairs: (g, X_g) with operation (g, X_g)(h, X_h) = (gh, X_g^h * X_h) @vtime :MinField 2 c = closure([(gen(G, i), homs[i]) for i=1:ngens(G)], diff --git a/experimental/GModule/GaloisCohomology.jl b/experimental/GModule/GaloisCohomology.jl index 5d6ff89b807b..bead762397c7 100644 --- a/experimental/GModule/GaloisCohomology.jl +++ b/experimental/GModule/GaloisCohomology.jl @@ -1292,7 +1292,7 @@ end For `K/k` a number field, where `k` has to be Antic or QQField and `K` Antic return a container for the relative Brauer group parametrizing central -simple algebras with center `k` that are split by `K` (thus can be realised +simple algebras with center `k` that are split by `K` (thus can be realized as a 2-cochain with values in `K`) """ mutable struct RelativeBrauerGroup diff --git a/experimental/QuadFormAndIsom/src/embeddings.jl b/experimental/QuadFormAndIsom/src/embeddings.jl index 5015532d4bf6..a0468f772937 100644 --- a/experimental/QuadFormAndIsom/src/embeddings.jl +++ b/experimental/QuadFormAndIsom/src/embeddings.jl @@ -1710,7 +1710,7 @@ function admissible_equivariant_primitive_extensions(A::ZZLatWithIsom, # We look for the GA|GB-invariant and fA|fB-stable subgroups of VA|VB which respectively # contained lpqA|lpqB, where pqA and pqB are respectively the p-primary parts of qA and qB. - # This is done by computing orbits and stabilisers of VA/lpqA (resp VB/lpqB) + # This is done by computing orbits and stabilizers of VA/lpqA (resp VB/lpqB) # seen as a F_p-vector space under the action of GA (resp. GB). Then we check which ones # are fA-stable (resp. fB-stable) subsA = _subgroups_orbit_representatives_and_stabilizers_elementary(VAinqA, GA, p^g, fqA, ZZ(l)) diff --git a/experimental/Schemes/SpaceGerms.jl b/experimental/Schemes/SpaceGerms.jl index 0743396cb9e8..a48a584a6e83 100644 --- a/experimental/Schemes/SpaceGerms.jl +++ b/experimental/Schemes/SpaceGerms.jl @@ -592,7 +592,7 @@ end CompleteIntersectionGerm(X::AbsSpec, p::AbsAffineRationalPoint) CompleteIntersectionGerm(p::AbsAffineRationalPoint) -Return a complete intersection germ `(X,p)` for a given `X`and a rational point `p` on some affine scheme `Y`, provided that $X$ is locally a complete intersection in some neighbourhood of `p`. If no `X` is specified, `Y` is used in its place. +Return a complete intersection germ `(X,p)` for a given `X`and a rational point `p` on some affine scheme `Y`, provided that $X$ is locally a complete intersection in some neighborhood of `p`. If no `X` is specified, `Y` is used in its place. """ CompleteIntersectionGerm(p::AbsAffineRationalPoint) = CompleteIntersectionGerm(codomain(p), coordinates(p)) diff --git a/src/Groups/sub.jl b/src/Groups/sub.jl index 76c606f9cbf5..2932195d1a50 100644 --- a/src/Groups/sub.jl +++ b/src/Groups/sub.jl @@ -354,8 +354,6 @@ function centralizer(G::GAPGroup, x::GAPGroupElem) return _as_subgroup(G, GAP.Globals.Centralizer(G.X, x.X)) end -const centraliser = centralizer # FIXME/TODO: use @alias? - ################################################################################ # # diff --git a/src/NumberTheory/GaloisGrp/GaloisGrp.jl b/src/NumberTheory/GaloisGrp/GaloisGrp.jl index 3f27edfa4751..6bdf9fcf5cb4 100644 --- a/src/NumberTheory/GaloisGrp/GaloisGrp.jl +++ b/src/NumberTheory/GaloisGrp/GaloisGrp.jl @@ -1669,7 +1669,7 @@ function starting_group(GC::GaloisCtx, K::T; useSubfields::Bool = true) where T O = sum_orbits(K, x->mk(pc(map_coeff(GC, x))), map(mk, c)) GC.start = (2, O) - #the factors define a partitioning of pairs, the stabiliser of this + #the factors define a partitioning of pairs, the stabilizer of this #partition is the largest possible group... #code from Max... diff --git a/src/NumberTheory/GaloisGrp/Qt.jl b/src/NumberTheory/GaloisGrp/Qt.jl index bb5e2a311a3e..b6cd7f0c2498 100644 --- a/src/NumberTheory/GaloisGrp/Qt.jl +++ b/src/NumberTheory/GaloisGrp/Qt.jl @@ -710,7 +710,7 @@ function Hecke.newton_polygon(f::T) where T <: Generic.Poly{S} where S <: Union{ dev = collect(coefficients(f)) d = degree(base_ring(f)) a = Tuple{Int, Int}[] - #careful: valuation is q-valued, normalised for val(p) == 1 + #careful: valuation is q-valued, normalized for val(p) == 1 # lines have Int corredinated, so we scale by the degree of the field # => the slopes are also multiplied by this!!! for i = 0:length(dev) -1 diff --git a/src/NumberTheory/NmbThy.jl b/src/NumberTheory/NmbThy.jl index a6670cc19996..50a04d723f84 100644 --- a/src/NumberTheory/NmbThy.jl +++ b/src/NumberTheory/NmbThy.jl @@ -183,11 +183,11 @@ end =# @doc raw""" - factorisations(a::AbsNumFieldOrderElem{AbsSimpleNumField,AbsSimpleNumFieldElem}) -> Vector{Fac{OrdElem}} + factorizations(a::AbsNumFieldOrderElem{AbsSimpleNumField,AbsSimpleNumFieldElem}) -> Vector{Fac{OrdElem}} -Return all factorisations of $a$ into irreducibles. +Return all factorizations of $a$ into irreducibles. """ -function factorisations(a::AbsNumFieldOrderElem{AbsSimpleNumField,AbsSimpleNumFieldElem}) +function factorizations(a::AbsNumFieldOrderElem{AbsSimpleNumField,AbsSimpleNumFieldElem}) O = parent(a) S = collect(keys(factor(a*O))) if length(S) == 0 diff --git a/src/TropicalGeometry/groebner_fan.jl b/src/TropicalGeometry/groebner_fan.jl index 7b960cc551f6..9f568b2b92aa 100644 --- a/src/TropicalGeometry/groebner_fan.jl +++ b/src/TropicalGeometry/groebner_fan.jl @@ -426,8 +426,8 @@ function groebner_fan(I::MPolyIdeal; # Starting cone ### C = maximal_groebner_cone(G,ord,homogeneityWeight) - workingList = [(G,ord,C,unique_identifying_point(C))] # list of Groebner cones whose neighbours may be unknown - finishedList = typeof(workingList)() # list of Groebner cones whose neighbours are known + workingList = [(G,ord,C,unique_identifying_point(C))] # list of Groebner cones whose neighbors may be unknown + finishedList = typeof(workingList)() # list of Groebner cones whose neighbors are known finishedFacets = Vector{Vector{ZZRingElem}}() # list of interior facet points whose facet has been traversed diff --git a/src/TropicalGeometry/hypersurface.jl b/src/TropicalGeometry/hypersurface.jl index a1045642099a..d7ca5a50d099 100644 --- a/src/TropicalGeometry/hypersurface.jl +++ b/src/TropicalGeometry/hypersurface.jl @@ -142,7 +142,7 @@ Min tropical hypersurface """ function tropical_hypersurface(f::MPolyRingElem, nu::Union{Nothing,TropicalSemiringMap}=nothing; weighted_polyhedral_complex_only::Bool=false) - # initialise nu as the trivial valuation if not specified by user + # initialize nu as the trivial valuation if not specified by user isnothing(nu) && (nu=tropical_semiring_map(coefficient_ring(f))) tropf = tropical_polynomial(f,nu) diff --git a/src/TropicalGeometry/linear_space.jl b/src/TropicalGeometry/linear_space.jl index dd8c4413df5b..295d120f7a55 100644 --- a/src/TropicalGeometry/linear_space.jl +++ b/src/TropicalGeometry/linear_space.jl @@ -163,7 +163,7 @@ Min tropical linear space ``` """ function tropical_linear_space(plueckerIndices::Vector{Vector{Int}}, plueckerVector::Vector, nu::Union{Nothing,TropicalSemiringMap}=nothing; weighted_polyhedral_complex_only::Bool=false) - # if nu unspecified, initialise as the trivial valuation + min convention + # if nu unspecified, initialize as the trivial valuation + min convention isnothing(nu) && (nu=tropical_semiring_map(parent(first(plueckerVector)))) TropL = tropical_linear_space(plueckerIndices, @@ -195,7 +195,7 @@ Min tropical linear space ``` """ function tropical_linear_space(k::Int, n::Int, plueckerVector::Vector, nu::Union{Nothing,TropicalSemiringMap}=nothing; weighted_polyhedral_complex_only::Bool=false) - # if nu unspecified, initialise as the trivial valuation + min convention + # if nu unspecified, initialize as the trivial valuation + min convention isnothing(nu) && (nu=tropical_semiring_map(parent(first(plueckerVector)))) TropL = tropical_linear_space(AbstractAlgebra.combinations(1:n,k), nu.(plueckerVector), weighted_polyhedral_complex_only=weighted_polyhedral_complex_only) @@ -261,7 +261,7 @@ Min tropical linear space ``` """ function tropical_linear_space(A::MatElem, nu::Union{Nothing,TropicalSemiringMap}=nothing; weighted_polyhedral_complex_only::Bool=false) - # if nu unspecified, initialise as the trivial valuation + min convention + # if nu unspecified, initialize as the trivial valuation + min convention isnothing(nu) && (nu=tropical_semiring_map(base_ring(A))) n = max(nrows(A), ncols(A)) @@ -302,7 +302,7 @@ Min tropical linear space ``` """ function tropical_linear_space(I::MPolyIdeal, nu::Union{Nothing,TropicalSemiringMap}=nothing; weighted_polyhedral_complex_only::Bool=false) - # initialise nu as the trivial valuation if not specified by user + # initialize nu as the trivial valuation if not specified by user isnothing(nu) && (nu=tropical_semiring_map(coefficient_ring(I))) x = gens(base_ring(I)) diff --git a/src/TropicalGeometry/variety.jl b/src/TropicalGeometry/variety.jl index a6dce2036415..81f9be02a4e7 100644 --- a/src/TropicalGeometry/variety.jl +++ b/src/TropicalGeometry/variety.jl @@ -163,7 +163,7 @@ julia> tropical_variety(I) function tropical_variety(I::Union{MPolyIdeal,MPolyRingElem}, nu::Union{TropicalSemiringMap,Nothing}=nothing; weighted_polyhedral_complex_only::Bool=false, skip_saturation::Bool=false, skip_primary_decomposition::Bool=false) ### # Step 0.a: convert I to ideal if poly, - # initialise nu as the trivial valuation if not specified by user + # initialize nu as the trivial valuation if not specified by user ### if I isa MPolyRingElem I = ideal(parent(I),[I]) @@ -559,8 +559,8 @@ end # # * w is a weight vector with respect to which G is a Groebner basis, # # * w is compatible with coordinate permutations if symmetries exist, # # * instead of comparing C or G it suffices to compare w. -# working_list_todo = [] # list of groebner polyhedra with potentially unknown neighbours -# working_list_done = [] # list of groebner polyhedra with known neighbours +# working_list_todo = [] # list of groebner polyhedra with potentially unknown neighbors +# working_list_done = [] # list of groebner polyhedra with known neighbors # facet_points_done = [] # list of facet points whose tropical links were computed and traversed # compute_starting_points = true @@ -623,29 +623,29 @@ end # directions_to_traverse = tropical_link(ideal(G),val,point_to_traverse) # todo, this output can be wrong # for direction_to_traverse in directions_to_traverse -# # compute neighbour +# # compute neighbor # print("computing groebner_basis for ",point_to_traverse,direction_to_traverse,"... ") -# G_neighbour = groebner_flip(G,val,w,point_to_traverse,direction_to_traverse) +# G_neighbor = groebner_flip(G,val,w,point_to_traverse,direction_to_traverse) # println("done") -# C_neighbour = groebner_polyhedron(G_neighbour,val,point_to_traverse,perturbation=direction_to_traverse) -# w_neighbour = anchor_point(C_neighbour) +# C_neighbor = groebner_polyhedron(G_neighbor,val,point_to_traverse,perturbation=direction_to_traverse) +# w_neighbor = anchor_point(C_neighbor) -# # if neighbour is already in done list, skip +# # if neighbor is already in done list, skip # i = searchsortedfirst(working_list_done, -# (w_neighbour,C_neighbour,G_neighbour), +# (w_neighbor,C_neighbor,G_neighbor), # by=x->x[1]) -# if i<=length(working_list_done) && working_list_done[i][1]==w_neighbour +# if i<=length(working_list_done) && working_list_done[i][1]==w_neighbor # continue # end -# # if neighbour is already in todo list, skip +# # if neighbor is already in todo list, skip # i = searchsortedfirst(working_list_todo, -# (w_neighbour,C_neighbour,G_neighbour), +# (w_neighbor,C_neighbor,G_neighbor), # by=x->x[1]) -# if i<=length(working_list_todo) && working_list_todo[i][1]==w_neighbour +# if i<=length(working_list_todo) && working_list_todo[i][1]==w_neighbor # continue # end -# # otherwise, add neighbour to todo list -# insert!(working_list_todo, i, (w_neighbour,C_neighbour,G_neighbour)) +# # otherwise, add neighbor to todo list +# insert!(working_list_todo, i, (w_neighbor,C_neighbor,G_neighbor)) # end # end # end diff --git a/src/deprecations.jl b/src/deprecations.jl index fc436b0902b4..9c7b6a37fbb1 100644 --- a/src/deprecations.jl +++ b/src/deprecations.jl @@ -70,3 +70,6 @@ Base.@deprecate_binding jacobi_ideal jacobian_ideal @deprecate has_number_small_groups has_number_of_small_groups @deprecate number_transitive_groups number_of_transitive_groups @deprecate has_number_transitive_groups has_number_of_transitive_groups + +@deprecate factorisations factorizations +@deprecate centraliser centralizer diff --git a/src/exports.jl b/src/exports.jl index f129e80404cb..00e174ec89f7 100644 --- a/src/exports.jl +++ b/src/exports.jl @@ -513,7 +513,7 @@ export facet_indices export facet_sizes export facets export factor_of_direct_product -export factorisations +export factorizations export fano_matroid export fano_simplex export fat_ideal diff --git a/test/NumberTheory/nmbthy.jl b/test/NumberTheory/nmbthy.jl index f882f3a9d4a9..058cb21f27e5 100644 --- a/test/NumberTheory/nmbthy.jl +++ b/test/NumberTheory/nmbthy.jl @@ -4,10 +4,10 @@ using Test function evalu(x::Fac) return x.unit * prod(p*k for (p,k) = x.fac) end -@testset "Polymake.factorisations" begin +@testset "Polymake.factorizations" begin k, a = quadratic_field(-5) zk = maximal_order(k) - f = factorisations(zk(6)) + f = factorizations(zk(6)) @test length(f) == 2 @test all(x -> evalu(x) == 6, f) end From b09c7638e3b679c02cecf10fe9b932651a4d52ba Mon Sep 17 00:00:00 2001 From: Benjamin Lorenz Date: Fri, 16 Feb 2024 14:34:42 +0100 Subject: [PATCH 02/29] CI: switch to 1.11-nightly for now (#3379) --- .github/workflows/CI.yml | 6 ++++-- 1 file changed, 4 insertions(+), 2 deletions(-) diff --git a/.github/workflows/CI.yml b/.github/workflows/CI.yml index 135f0f0cee9a..8e54e01828a1 100644 --- a/.github/workflows/CI.yml +++ b/.github/workflows/CI.yml @@ -31,7 +31,8 @@ jobs: - '1.6' - '1.9' # to be removed in the near future - '1.10' - - 'nightly' + - '1.11-nightly' + #- 'nightly' group: [ 'short', 'long' ] os: - ubuntu-latest @@ -112,7 +113,8 @@ jobs: julia-version: - '1.9' # to be removed in the near future - '1.10' - - 'nightly' + - '1.11-nightly' + #- 'nightly' os: - ubuntu-latest depwarn: [ '' ] From eabc53b0bd2040d8dd287c7ae141ea0d050daf17 Mon Sep 17 00:00:00 2001 From: Max Horn Date: Fri, 16 Feb 2024 14:13:12 +0100 Subject: [PATCH 03/29] Performance improvements for PointVector, RayVector, SubObjectIterator (#3369) MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Add type assertions to their getindex methods to improve type stability. Similarly ensure that the return value of `size` is recognized as Tuple{Int}. Silly microbenchmark, before: julia> v = PointVector{ZZRingElem}(matrix(ZZ, [1 2 3 ; ])); julia> @btime prod(v) 1.217 μs (21 allocations: 336 bytes) After: julia> @btime prod(v); 288.449 ns (5 allocations: 80 bytes) --- src/PolyhedralGeometry/iterators.jl | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/src/PolyhedralGeometry/iterators.jl b/src/PolyhedralGeometry/iterators.jl index 2488e881c461..007a58e90c3c 100644 --- a/src/PolyhedralGeometry/iterators.jl +++ b/src/PolyhedralGeometry/iterators.jl @@ -13,7 +13,7 @@ for (T, _t) in ((:PointVector, :point_vector), (:RayVector, :ray_vector)) end Base.IndexStyle(::Type{<:$T}) = IndexLinear() - Base.getindex(po::$T, i::Base.Integer) = po.p[1, i] + Base.getindex(po::$T{U}, i::Base.Integer) where U = po.p[1, i]::U function Base.setindex!(po::$T, val, i::Base.Integer) @boundscheck 1 <= length(po) <= i @@ -23,7 +23,7 @@ for (T, _t) in ((:PointVector, :point_vector), (:RayVector, :ray_vector)) Base.firstindex(::$T) = 1 Base.lastindex(iter::$T) = length(iter) - Base.size(po::$T) = (size(po.p, 2),) + Base.size(po::$T) = (size(po.p, 2)::Int,) coefficient_field(po::$T) = base_ring(po.p) @@ -237,7 +237,7 @@ Base.IndexStyle(::Type{<:SubObjectIterator}) = IndexLinear() function Base.getindex(iter::SubObjectIterator{T}, i::Base.Integer) where T @boundscheck 1 <= i && i <= iter.n - return iter.Acc(T, iter.Obj, i; iter.options...) + return iter.Acc(T, iter.Obj, i; iter.options...)::T end Base.firstindex(::SubObjectIterator) = 1 From 3938ffed18cdfef5f0aac9588313da52334b986a Mon Sep 17 00:00:00 2001 From: Thomas Breuer Date: Fri, 16 Feb 2024 15:09:24 +0100 Subject: [PATCH 04/29] rename and change some `*_reps` functions (#3291) --- docs/src/Groups/subgroups.md | 23 ++- src/Groups/GAPGroups.jl | 217 ++++++++++++++---------- src/Groups/GrpAb.jl | 67 +++----- src/Groups/cosets.jl | 2 +- src/Groups/gsets.jl | 2 +- src/Groups/sub.jl | 80 ++------- src/NumberTheory/GaloisGrp/GaloisGrp.jl | 8 +- src/NumberTheory/GaloisGrp/Group.jl | 2 +- src/deprecations.jl | 18 ++ src/exports.jl | 16 +- test/Groups/GrpAb.jl | 31 ++-- test/Groups/conjugation.jl | 16 +- test/Groups/elements.jl | 2 +- test/Groups/matrixgroups.jl | 4 +- test/Groups/subgroups_and_cosets.jl | 31 ++-- 15 files changed, 266 insertions(+), 253 deletions(-) diff --git a/docs/src/Groups/subgroups.md b/docs/src/Groups/subgroups.md index f132fa331c6e..b46096f38cba 100644 --- a/docs/src/Groups/subgroups.md +++ b/docs/src/Groups/subgroups.md @@ -43,17 +43,13 @@ intersect(::T, V::T...) where T<:GAPGroup The following functions return a vector of subgroups. ```@docs -subgroups(G::GAPGroup) normal_subgroups -maximal_subgroups maximal_normal_subgroups minimal_normal_subgroups characteristic_subgroups derived_series sylow_system -hall_subgroup_reps hall_system -complement_class_reps complement_system chief_series composition_series @@ -71,6 +67,18 @@ upper_central_series one can type `embedding(G,H)`. +The following functions return an iterator of subgroups. +Usually it is more efficient to work with (representatives of) the +underlying conjugacy classes of subgroups instead. + +```@docs +complements(G::T, N::T) where T <: GAPGroup +hall_subgroups +low_index_subgroups +maximal_subgroups +subgroups(G::GAPGroup) +``` + ## Conjugation action of elements and subgroups ```@docs @@ -94,8 +102,11 @@ number_of_conjugacy_classes(G::GAPGroup) conjugacy_class(G::GAPGroup, g::GAPGroupElem) conjugacy_class(G::T, g::T) where T<:GAPGroup conjugacy_classes(G::GAPGroup) -conjugacy_classes_subgroups(G::GAPGroup) -conjugacy_classes_maximal_subgroups(G::GAPGroup) +complement_classes +hall_subgroup_classes +low_index_subgroup_classes +maximal_subgroup_classes(G::GAPGroup) +subgroup_classes(G::GAPGroup) ``` diff --git a/src/Groups/GAPGroups.jl b/src/Groups/GAPGroups.jl index 7276ae2dca2c..f0c6ab20a73f 100644 --- a/src/Groups/GAPGroups.jl +++ b/src/Groups/GAPGroups.jl @@ -304,9 +304,11 @@ function Base.show(io::IO, G::PermGroup) # Treat groups specially which know that they are nat. symmetric/alternating. io = pretty(io) - if has_is_natural_symmetric_group(G) && is_natural_symmetric_group(G) + if has_is_natural_symmetric_group(G) && is_natural_symmetric_group(G) && + number_of_moved_points(G) == degree(G) print(io, LowercaseOff(), "Sym(", degree(G), ")") - elseif has_is_natural_alternating_group(G) && is_natural_alternating_group(G) + elseif has_is_natural_alternating_group(G) && is_natural_alternating_group(G) && + number_of_moved_points(G) == degree(G) print(io, LowercaseOff(), "Alt(", degree(G), ")") else print(io, "Permutation group") @@ -696,7 +698,7 @@ number_of_conjugacy_classes(::Type{T}, G::GAPGroup) where T <: IntegerUnion = T( """ conjugacy_classes(G::Group) -Return the vector of all conjugacy classes of elements in `G`. +Return a vector of all conjugacy classes of elements in `G`. It is guaranteed that the class of the identity is in the first position. """ function conjugacy_classes(G::GAPGroup) @@ -756,123 +758,131 @@ function Base.rand(rng::Random.AbstractRNG, C::GroupConjClass{S,T}) where S wher end """ - conjugacy_classes_subgroups(G::Group) + subgroup_classes(G::GAPGroup; order::T = ZZRingElem(-1)) where T <: IntegerUnion -Return the vector of all conjugacy classes of subgroups of G. +Return a vector of all conjugacy classes of subgroups of `G` or, +if `order` is positive, the classes of subgroups of this order. # Examples ```jldoctest julia> G = symmetric_group(3) Sym(3) -julia> conjugacy_classes_subgroups(G) +julia> subgroup_classes(G) 4-element Vector{GAPGroupConjClass{PermGroup, PermGroup}}: Conjugacy class of permutation group in G Conjugacy class of permutation group in G Conjugacy class of permutation group in G Conjugacy class of permutation group in G + +julia> subgroup_classes(G, order = ZZRingElem(2)) +1-element Vector{GAPGroupConjClass{PermGroup, PermGroup}}: + Conjugacy class of permutation group in G ``` """ -function conjugacy_classes_subgroups(G::GAPGroup) +function subgroup_classes(G::GAPGroup; order::T = ZZRingElem(-1)) where T <: IntegerUnion L = Vector{GapObj}(GAPWrap.ConjugacyClassesSubgroups(G.X)) - return [GAPGroupConjClass(G, _as_subgroup_bare(G, GAPWrap.Representative(cc)), cc) for cc in L] + res = [GAPGroupConjClass(G, _as_subgroup_bare(G, GAPWrap.Representative(cc)), cc) for cc in L] + if order != -1 + filter!(x -> AbstractAlgebra.order(representative(x)) == order, res) + end + return res end """ - subgroup_reps(G::GAPGroup; order::ZZRingElem = ZZRingElem(-1)) + subgroups(G::GAPGroup) -Return a vector of representatives (under conjugation) for all subgroups of `G`. -If given, only subgroups of a certain order are returned. +Return an iterator over all subgroups in `G`. +Very likely it is better to use [`subgroup_classes`](@ref) instead. # Examples ```jldoctest -julia> G = symmetric_group(3); - -julia> subgroup_reps(G) -4-element Vector{PermGroup}: - Permutation group of degree 3 and order 1 - Permutation group of degree 3 and order 2 - Permutation group of degree 3 and order 3 - Permutation group of degree 3 and order 6 - -julia> subgroup_reps(G, order = ZZRingElem(2)) -1-element Vector{PermGroup}: - Permutation group of degree 3 and order 2 +julia> println([order(H) for H in subgroups(symmetric_group(3))]) +ZZRingElem[1, 2, 2, 2, 3, 6] +julia> println([order(H) for H in subgroups(quaternion_group(8))]) +ZZRingElem[1, 2, 4, 4, 4, 8] ``` """ -function subgroup_reps(G::GAPGroup; order::ZZRingElem = ZZRingElem(-1)) - C = GAPWrap.ConjugacyClassesSubgroups(G.X) - C = map(GAPWrap.Representative, C) - if order != -1 - C = [x for x = C if GAPWrap.Order(x) == order] - end - return [Oscar._as_subgroup(G, x)[1] for x = C] -end +subgroups(G::GAPGroup) = Iterators.flatten(subgroup_classes(G)) """ - conjugacy_classes_maximal_subgroups(G::Group) + maximal_subgroup_classes(G::Group) -Return the vector of all conjugacy classes of maximal subgroups of G. +Return a vector of all conjugacy classes of maximal subgroups of `G`. # Examples ```jldoctest julia> G = symmetric_group(3); -julia> conjugacy_classes_maximal_subgroups(G) +julia> maximal_subgroup_classes(G) 2-element Vector{GAPGroupConjClass{PermGroup, PermGroup}}: Conjugacy class of permutation group in G Conjugacy class of permutation group in G ``` """ -function conjugacy_classes_maximal_subgroups(G::GAPGroup) - L = Vector{GapObj}(GAPWrap.ConjugacyClassesMaximalSubgroups(G.X)) - return [GAPGroupConjClass(G, _as_subgroup_bare(G, GAPWrap.Representative(cc)), cc) for cc in L] +@gapattribute function maximal_subgroup_classes(G::GAPGroup) + L = Vector{GapObj}(GAP.Globals.ConjugacyClassesMaximalSubgroups(G.X)::GapObj) + T = typeof(G) + LL = [GAPGroupConjClass(G, _as_subgroup_bare(G, GAPWrap.Representative(cc)), cc) for cc in L] + return Vector{GAPGroupConjClass{T, T}}(LL) end """ - maximal_subgroup_reps(G::GAPGroup) + maximal_subgroups(G::Group) -Return a vector of representatives (under conjugation) for all maximal -subgroups of `G`. +Return an iterator over the maximal subgroups in `G`. +Very likely it is better to use [`maximal_subgroup_classes`](@ref) instead. # Examples ```jldoctest -julia> maximal_subgroup_reps(symmetric_group(4)) -3-element Vector{PermGroup}: - Permutation group of degree 4 - Permutation group of degree 4 and order 8 - Permutation group of degree 4 and order 6 +julia> println([order(H) for H in maximal_subgroups(symmetric_group(3))]) +ZZRingElem[3, 2, 2, 2] +julia> println([order(H) for H in maximal_subgroups(quaternion_group(8))]) +ZZRingElem[4, 4, 4] ``` """ -function maximal_subgroup_reps(G::GAPGroup) - return Oscar._as_subgroups(G, GAP.Globals.MaximalSubgroupClassReps(G.X)) -end +maximal_subgroups(G::T) where T <: Union{GAPGroup, FinGenAbGroup} = Iterators.flatten(maximal_subgroup_classes(G)) """ - low_index_subgroup_reps(G::GAPGroup, n::Int) + low_index_subgroup_classes(G::GAPGroup, n::Int) -Return a vector of representatives (under conjugation) for all subgroups -of index at most `n` in `G`. +Return a vector of conjugacy classes of subgroups of index at most `n` in `G`. # Examples ```jldoctest julia> G = symmetric_group(5); -julia> low_index_subgroup_reps(G, 5) -3-element Vector{PermGroup}: - Sym(5) - Alt(5) - Sym(5) - +julia> low_index_subgroup_classes(G, 5) +3-element Vector{GAPGroupConjClass{PermGroup, PermGroup}}: + Conjugacy class of Sym(5) in G + Conjugacy class of Alt(5) in G + Conjugacy class of permutation group in G ``` """ -function low_index_subgroup_reps(G::GAPGroup, n::Int) - ll = GAP.Globals.LowIndexSubgroups(G.X, n) - return [Oscar._as_subgroup(G, x)[1] for x = ll] +function low_index_subgroup_classes(G::GAPGroup, n::Int) + @req (n > 0) "index must be positive" + ll = GAP.Globals.LowIndexSubgroups(G.X, n)::GapObj + return [conjugacy_class(G, H) for H in _as_subgroups(G, ll)] end +""" + low_index_subgroups(G::Group, n::Int) + +Return an iterator over the subgroups of index at most `n` in `G`. +Very likely it is better to use [`low_index_subgroup_classes`](@ref) instead. + +# Examples +```jldoctest +julia> G = alternating_group(6); + +julia> length(collect(low_index_subgroups(G, 6))) +13 +``` +""" +low_index_subgroups(G::T, n::Int) where T <: Union{GAPGroup, FinGenAbGroup} = Iterators.flatten(low_index_subgroup_classes(G, n)) + """ conjugate_group(G::T, x::GAPGroupElem) where T <: GAPGroup @@ -1248,18 +1258,10 @@ function sylow_subgroup(G::GAPGroup, p::IntegerUnion) return _as_subgroup(G, GAPWrap.SylowSubgroup(G.X, GAP.Obj(p))) end -# no longer documented, better use `hall_subgroup_reps` -function hall_subgroup(G::GAPGroup, P::AbstractVector{<:IntegerUnion}) - P = unique(P) - @req all(is_prime, P) "The integers must be prime" - @req is_solvable(G) "The group is not solvable" - return _as_subgroup(G,GAP.Globals.HallSubgroup(G.X,GAP.Obj(P, recursive=true))::GapObj) -end - """ - hall_subgroup_reps(G::Group, P::AbstractVector{<:IntegerUnion}) + hall_subgroup_classes(G::Group, P::AbstractVector{<:IntegerUnion}) -Return a vector that contains representatives of conjugacy classes of +Return a vector that contains the conjugacy classes of Hall `P`-subgroups of the finite group `G`, for a vector `P` of primes. A Hall `P`-subgroup of `G` is a subgroup the order of which is only divisible by primes in `P` and whose index in `G` is coprime to all primes in `P`. @@ -1272,37 +1274,53 @@ up to conjugacy. ```jldoctest julia> g = dihedral_group(30); -julia> h = hall_subgroup_reps(g, [2, 3]); +julia> h = hall_subgroup_classes(g, [2, 3]); -julia> (length(h), order(h[1])) +julia> (length(h), order(representative(h[1]))) (1, 6) julia> g = GL(3, 2) GL(3,2) -julia> h = hall_subgroup_reps(g, [2, 3]); +julia> h = hall_subgroup_classes(g, [2, 3]); -julia> (length(h), order(h[1])) +julia> (length(h), order(representative(h[1]))) (2, 24) -julia> h = hall_subgroup_reps(g, [2, 7]); length(h) +julia> h = hall_subgroup_classes(g, [2, 7]); length(h) 0 - ``` """ -function hall_subgroup_reps(G::GAPGroup, P::AbstractVector{<:IntegerUnion}) +function hall_subgroup_classes(G::GAPGroup, P::AbstractVector{<:IntegerUnion}) P = unique(P) @req all(is_prime, P) "The integers must be prime" res_gap = GAP.Globals.HallSubgroup(G.X, GAP.Obj(P, recursive = true))::GapObj if res_gap == GAP.Globals.fail - return typeof(G)[] + T = typeof(G) + return GAPGroupConjClass{T, T}[] elseif GAPWrap.IsList(res_gap) - return _as_subgroups(G, res_gap) + return [conjugacy_class(G, H) for H in _as_subgroups(G, res_gap)] else - return [_as_subgroup_bare(G, res_gap)] + return [conjugacy_class(G, _as_subgroup_bare(G, res_gap))] end end +""" + hall_subgroups(G::Group, P::AbstractVector{<:IntegerUnion}) + +Return an iterator over the Hall `P`-subgroups in `G`. +Very likely it is better to use [`hall_subgroup_classes`](@ref) instead. + +# Examples +```jldoctest +julia> g = GL(3, 2); + +julia> describe(first(hall_subgroups(g, [2, 3]))) +"S4" +``` +""" +hall_subgroups(G::T, P::AbstractVector{<:IntegerUnion}) where T <: Union{GAPGroup, FinGenAbGroup} = Iterators.flatten(hall_subgroup_classes(G, P)) + @doc raw""" sylow_system(G::Group) @@ -1319,9 +1337,9 @@ an exception is thrown if `G` is not solvable. end @doc raw""" - complement_class_reps(G::T, N::T) where T <: GAPGroup + complement_classes(G::T, N::T) where T <: GAPGroup -Return a vector of representatives of the conjugacy classes of complements +Return a vector of the conjugacy classes of complements of the normal subgroup `N` in `G`. This function may throw an error exception if both `N` and `G/N` are nonsolvable. @@ -1333,21 +1351,42 @@ together with `N` generates `G`. ```jldoctest julia> G = symmetric_group(3); -julia> complement_class_reps(G, derived_subgroup(G)[1]) -1-element Vector{PermGroup}: - Permutation group of degree 3 +julia> complement_classes(G, derived_subgroup(G)[1]) +1-element Vector{GAPGroupConjClass{PermGroup, PermGroup}}: + Conjugacy class of permutation group in G julia> G = dihedral_group(8) Pc group of order 8 -julia> complement_class_reps(G, center(G)[1]) -PcGroup[] +julia> complement_classes(G, center(G)[1]) +GAPGroupConjClass{PcGroup, PcGroup}[] ``` """ -function complement_class_reps(G::T, N::T) where T <: GAPGroup - return _as_subgroups(G, GAP.Globals.ComplementClassesRepresentatives(G.X, N.X)) +function complement_classes(G::T, N::T) where T <: GAPGroup + res_gap = GAP.Globals.ComplementClassesRepresentatives(G.X, N.X)::GapObj + if length(res_gap) == 0 + return GAPGroupConjClass{T, T}[] + else + return [conjugacy_class(G, H) for H in _as_subgroups(G, res_gap)] + end end +@doc raw""" + complements(G::T, N::T) where T <: GAPGroup + +Return an iterator over the complements of the normal subgroup `N` in `G`. +Very likely it is better to use [`complement_classes`](@ref) instead. + +# Examples +```jldoctest +julia> G = symmetric_group(3); + +julia> describe(first(complements(G, derived_subgroup(G)[1]))) +"C2" +``` +""" +complements(G::T, N::T) where T <: GAPGroup = Iterators.flatten(complement_classes(G, N)) + @doc raw""" complement_system(G::Group) diff --git a/src/Groups/GrpAb.jl b/src/Groups/GrpAb.jl index 9a3ed48fc759..2114a32a4f9d 100644 --- a/src/Groups/GrpAb.jl +++ b/src/Groups/GrpAb.jl @@ -71,24 +71,24 @@ end # ################################################################################ -struct GrpAbFinGenConjClass{T<:FinGenAbGroup, S<:Union{FinGenAbGroupElem,FinGenAbGroup}} <: GroupConjClass{T, S} +struct FinGenAbGroupConjClass{T<:FinGenAbGroup, S<:Union{FinGenAbGroupElem,FinGenAbGroup}} <: GroupConjClass{T, S} X::T repr::S end -function Base.hash(C::GrpAbFinGenConjClass, h::UInt) +function Base.hash(C::FinGenAbGroupConjClass, h::UInt) return Base.hash(Representative(C), h) end -function Base.show(io::IO, C::GrpAbFinGenConjClass) +function Base.show(io::IO, C::FinGenAbGroupConjClass) print(io, string(representative(C)), " ^ ", string(C.X)) end -==(a::GrpAbFinGenConjClass, b::GrpAbFinGenConjClass) = representative(a) == representative(b) +==(a::FinGenAbGroupConjClass, b::FinGenAbGroupConjClass) = representative(a) == representative(b) -Base.length(::Type{T}, C::GrpAbFinGenConjClass) where T <: IntegerUnion = T(1) +Base.length(::Type{T}, C::FinGenAbGroupConjClass) where T <: IntegerUnion = T(1) -Base.length(C::GrpAbFinGenConjClass) = ZZRingElem(1) +Base.length(C::FinGenAbGroupConjClass) = ZZRingElem(1) ################################################################################ @@ -97,19 +97,19 @@ Base.length(C::GrpAbFinGenConjClass) = ZZRingElem(1) # ################################################################################ -conjugacy_class(G::FinGenAbGroup, g::FinGenAbGroupElem) = GrpAbFinGenConjClass(G, g) +conjugacy_class(G::FinGenAbGroup, g::FinGenAbGroupElem) = FinGenAbGroupConjClass(G, g) -Base.eltype(::Type{GrpAbFinGenConjClass{T,S}}) where {T,S} = S +Base.eltype(::Type{FinGenAbGroupConjClass{T,S}}) where {T,S} = S -Base.rand(C::GrpAbFinGenConjClass) = representative(C) +Base.rand(C::FinGenAbGroupConjClass) = representative(C) -Base.rand(rng::Random.AbstractRNG, C::GrpAbFinGenConjClass) = representative(C) +Base.rand(rng::Random.AbstractRNG, C::FinGenAbGroupConjClass) = representative(C) number_of_conjugacy_classes(G::FinGenAbGroup) = order(ZZRingElem, G) number_of_conjugacy_classes(::Type{T}, G::FinGenAbGroup) where T <: IntegerUnion = order(T, G) -conjugacy_classes(G::FinGenAbGroup) = [GrpAbFinGenConjClass(G, x) for x in G] +conjugacy_classes(G::FinGenAbGroup) = [FinGenAbGroupConjClass(G, x) for x in G] is_conjugate(G::FinGenAbGroup, x::FinGenAbGroupElem, y::FinGenAbGroupElem) = (x == y) @@ -123,45 +123,37 @@ end # ################################################################################ -conjugacy_class(G::T, H::T) where T <: FinGenAbGroup = GrpAbFinGenConjClass(G, H) +conjugacy_class(G::T, H::T) where T <: FinGenAbGroup = FinGenAbGroupConjClass(G, H) -function conjugacy_classes_subgroups(G::FinGenAbGroup) +function subgroup_classes(G::FinGenAbGroup; order::T = ZZRingElem(-1)) where T <: IntegerUnion @req is_finite(G) "G is not finite" - return [conjugacy_class(G, H) for (H, mp) in subgroups(G)] -end - -function subgroup_reps(G::FinGenAbGroup; order::ZZRingElem = ZZRingElem(-1)) if order > 0 && mod(Hecke.order(G), order) != 0 # `subgroups` would throw an error - return FinGenAbGroup[] + return FinGenAbGroupConjClass{FinGenAbGroup, FinGenAbGroup}[] end - return [H for (H, mp) in subgroups(G, order = order)] + return [conjugacy_class(G, H) for (H, mp) in Hecke.subgroups(G, order = order)] end -function low_index_subgroup_reps(G::FinGenAbGroup, n::Int) +function low_index_subgroup_classes(G::FinGenAbGroup, n::Int) @req (n > 0) "index must be positive" - res = [G] + res = [conjugacy_class(G, G)] ord = order(G) for i in 2:n if mod(ord, i) == 0 - append!(res, [H for (H, mp) in subgroups(G, index = i)]) + append!(res, [conjugacy_class(G, H) for (H, mp) in Hecke.subgroups(G, index = i)]) end end return res end -function maximal_subgroup_reps(G::FinGenAbGroup) +function maximal_subgroup_classes(G::FinGenAbGroup) @req is_finite(G) "G is not finite" primes = [p for (p, e) in factor(order(G))] res = typeof(G)[] for p in primes - append!(res, [H for (H, mp) in subgroups(G, index = p)]) + append!(res, [H for (H, mp) in Hecke.subgroups(G, index = p)]) end - return res -end - -function conjugacy_classes_maximal_subgroups(G::FinGenAbGroup) - return [conjugacy_class(G, H) for H in maximal_subgroup_reps(G)] + return [conjugacy_class(G, H) for H in res] end conjugate_group(G::FinGenAbGroup, x::FinGenAbGroupElem) = G @@ -184,11 +176,11 @@ end is_conjugate_subgroup(G::T, U::T, V::T) where T <: FinGenAbGroup = is_subgroup(V, U)[1] is_conjugate_subgroup_with_data(G::T, U::T, V::T) where T <: FinGenAbGroup = is_subgroup(V, U)[1], zero(G) -Base.IteratorSize(::Type{<:GrpAbFinGenConjClass}) = Base.HasLength() +Base.IteratorSize(::Type{<:FinGenAbGroupConjClass}) = Base.HasLength() -Base.iterate(C::GrpAbFinGenConjClass) = iterate(C, 0) +Base.iterate(C::FinGenAbGroupConjClass) = iterate(C, 0) -function Base.iterate(C::GrpAbFinGenConjClass, state::Int) +function Base.iterate(C::FinGenAbGroupConjClass, state::Int) if state == 0 return representative(C), 1 else @@ -279,7 +271,7 @@ solvable_radical(G::FinGenAbGroup) = (G, identity_map(G)) ################################################################################ #TODO: how to compute complements? -# complement_class_reps(G::T, N::T) where T <: FinGenAbGroup +# complement_classes(G::T, N::T) where T <: FinGenAbGroup # complement_system(G::FinGenAbGroup) function sylow_system(G::FinGenAbGroup) @@ -291,10 +283,7 @@ function sylow_system(G::FinGenAbGroup) return result end -# no longer documented, better use `hall_subgroup_reps` -hall_subgroup(G::FinGenAbGroup, P::AbstractVector{<:IntegerUnion}) = hall_subgroup_reps(G, P)[1] - -function hall_subgroup_reps(G::FinGenAbGroup, P::AbstractVector{<:IntegerUnion}) +function hall_subgroup_classes(G::FinGenAbGroup, P::AbstractVector{<:IntegerUnion}) @req is_finite(G) "G is not finite" P = unique(P) @req all(is_prime, P) "The integers must be prime" @@ -312,7 +301,7 @@ function hall_subgroup_reps(G::FinGenAbGroup, P::AbstractVector{<:IntegerUnion}) end end end - return [sub(G, subgens)[1]] + return [conjugacy_class(G, sub(G, subgens)[1])] end function hall_system(G::FinGenAbGroup) @@ -320,7 +309,7 @@ function hall_system(G::FinGenAbGroup) primes = [p for (p, e) in factor(order(G))] result = FinGenAbGroup[] for P in subsets(Set(primes)) - push!(result, hall_subgroup_reps(G, collect(P))[1]) + push!(result, representative(hall_subgroup_classes(G, collect(P))[1])) end return result end diff --git a/src/Groups/cosets.jl b/src/Groups/cosets.jl index bee4731cfc9f..eb51fdddb554 100644 --- a/src/Groups/cosets.jl +++ b/src/Groups/cosets.jl @@ -525,7 +525,7 @@ Base.:*(H::GAPGroup, g::GAPGroupElem, K::GAPGroup) = double_coset(H,g,K) """ double_cosets(G::T, H::T, K::T; check::Bool=true) where T<: GAPGroup -Return the vector of all the double cosets `HxK` for `x` in `G`. +Return a vector of all the double cosets `HxK` for `x` in `G`. If `check == false`, do not check whether `H` and `K` are subgroups of `G`. # Examples diff --git a/src/Groups/gsets.jl b/src/Groups/gsets.jl index f1b9555bad43..4c67812fb99c 100644 --- a/src/Groups/gsets.jl +++ b/src/Groups/gsets.jl @@ -1016,7 +1016,7 @@ the action is transitive and the point stabilizers are maximal in `G`. ```jldoctest julia> G = alternating_group(6); -julia> mx = filter(is_transitive, maximal_subgroup_reps(G)) +julia> mx = filter(is_transitive, map(representative, maximal_subgroup_classes(G))) 3-element Vector{PermGroup}: Permutation group of degree 6 and order 24 Permutation group of degree 6 and order 36 diff --git a/src/Groups/sub.jl b/src/Groups/sub.jl index 2932195d1a50..bc05e667d226 100644 --- a/src/Groups/sub.jl +++ b/src/Groups/sub.jl @@ -187,62 +187,6 @@ julia> normal_subgroups(quaternion_group(8)) @gapattribute normal_subgroups(G::GAPGroup) = _as_subgroups(G, GAP.Globals.NormalSubgroups(G.X)) -""" - subgroups(G::Group) - -Return all subgroups of `G`. - -# Examples -```jldoctest -julia> subgroups(symmetric_group(3)) -6-element Vector{PermGroup}: - Permutation group of degree 3 and order 1 - Permutation group of degree 3 and order 2 - Permutation group of degree 3 and order 2 - Permutation group of degree 3 and order 2 - Permutation group of degree 3 and order 3 - Permutation group of degree 3 and order 6 - -julia> subgroups(quaternion_group(8)) -6-element Vector{PcGroup}: - Pc group of order 1 - Pc group of order 2 - Pc group of order 4 - Pc group of order 4 - Pc group of order 4 - Pc group of order 8 -``` -""" -function subgroups(G::GAPGroup) - # TODO: this is super inefficient. Slightly better would be to return an iterator - # which iterates over the (elements of) the conjugacy classes of subgroups - return _as_subgroups(G, GAP.Globals.AllSubgroups(G.X)) -end - -""" - maximal_subgroups(G::Group) - -Return all maximal subgroups of `G`. - -# Examples -```jldoctest -julia> maximal_subgroups(symmetric_group(3)) -4-element Vector{PermGroup}: - Permutation group of degree 3 and order 3 - Permutation group of degree 3 and order 2 - Permutation group of degree 3 and order 2 - Permutation group of degree 3 and order 2 - -julia> maximal_subgroups(quaternion_group(8)) -3-element Vector{PcGroup}: - Pc group of order 4 - Pc group of order 4 - Pc group of order 4 -``` -""" -@gapattribute maximal_subgroups(G::GAPGroup) = - _as_subgroups(G, GAP.Globals.MaximalSubgroups(G.X)) - """ maximal_normal_subgroups(G::Group) @@ -295,14 +239,11 @@ i.e., those subgroups that are invariant under all automorphisms of `G`. # Examples ```jldoctest -julia> subgroups(symmetric_group(3)) -6-element Vector{PermGroup}: - Permutation group of degree 3 and order 1 - Permutation group of degree 3 and order 2 - Permutation group of degree 3 and order 2 - Permutation group of degree 3 and order 2 +julia> characteristic_subgroups(symmetric_group(3)) +3-element Vector{PermGroup}: + Sym(3) Permutation group of degree 3 and order 3 - Permutation group of degree 3 and order 6 + Permutation group of degree 3 and order 1 julia> characteristic_subgroups(quaternion_group(8)) 3-element Vector{PcGroup}: @@ -512,7 +453,7 @@ julia> lower_central_series(symmetric_group(4)) upper_central_series(G::GAPGroup) Return the vector $[ G_1, G_2, \ldots ]$ where the last entry is the -trivial group, and $G_i$ is defined as the overgroup of $G_{i+1} +trivial group, and $G_i$ is defined as the overgroup of $G_{i+1}$ satisfying $G_i / G_{i+1} = Z(G/G_{i+1})$. The series ends as soon as it is repeating (e.g. when the whole group $G$ is reached, which happens if and only if $G$ is nilpotent). @@ -611,11 +552,14 @@ function is_maximal_subgroup(H::T, G::T; check::Bool = true) where T <: GAPGroup if check @req is_subset(H, G) "H is not a subgroup of G" end - if order(G) // order(H) < 100 - t = right_transversal(G, H)[2:end] #drop the identity - return all(x -> order(sub(G, vcat(gens(H), [x]))[1]) == order(G), t) + ind = index(G, H) + is_prime(ind) && return true + if ind < 100 + # Do not unpack the right transversal object. + t = right_transversal(G, H) + return all(i -> order(sub(G, vcat(gens(H), [t[i]]))[1]) == order(G), 2:Int(ind)) end - return any(M -> is_conjugate(G, M, H), maximal_subgroup_reps(G)) + return any(C -> H in C, maximal_subgroup_classes(G)) end """ diff --git a/src/NumberTheory/GaloisGrp/GaloisGrp.jl b/src/NumberTheory/GaloisGrp/GaloisGrp.jl index 6bdf9fcf5cb4..ffc3222cf3aa 100644 --- a/src/NumberTheory/GaloisGrp/GaloisGrp.jl +++ b/src/NumberTheory/GaloisGrp/GaloisGrp.jl @@ -894,7 +894,7 @@ function set_orbit(G::PermGroup, H::PermGroup) # http://dblp.uni-trier.de/db/journals/jsc/jsc79.html#Elsenhans17 # https://doi.org/10.1016/j.jsc.2016.02.005 - l = low_index_subgroup_reps(H, 2*degree(G)^2) + l = representative.(low_index_subgroup_classes(H, 2*degree(G)^2)) S, g = slpoly_ring(ZZ, degree(G), cached = false) sort!(l, lt = (a,b) -> isless(order(b), order(a))) @@ -1227,7 +1227,7 @@ mutable struct DescentEnv #a more select choice of group.... function DescentEnv(G::PermGroup, f::GroupFilter = GroupFilter()) - s = maximal_subgroup_reps(G) + s = map(representative, maximal_subgroup_classes(G)) r = new() r.G = G @vprint :GaloisGroup 1 "starting with $(length(s)) maximal subgroup classes\n" @@ -2374,7 +2374,7 @@ function galois_quotient(C::GaloisCtx, Q::PermGroup) if order(G) % degree(Q) != 0 return [] end - s = subgroup_reps(G, order = divexact(order(G), degree(Q))) + s = map(representative, subgroup_classes(G, order = divexact(order(G), degree(Q)))) res = [] for U = s phi = right_coset_action(G, U) @@ -2413,7 +2413,7 @@ function galois_quotient(C::GaloisCtx, d::Int) if order(G) % d != 0 return [] end - s = subgroup_reps(G, order = divexact(order(G), d)) + s = map(representative, subgroup_classes(G, order = divexact(order(G), d))) res = [] for U = s phi = right_coset_action(G, U) diff --git a/src/NumberTheory/GaloisGrp/Group.jl b/src/NumberTheory/GaloisGrp/Group.jl index dd50d7e76e9d..a441deac9639 100644 --- a/src/NumberTheory/GaloisGrp/Group.jl +++ b/src/NumberTheory/GaloisGrp/Group.jl @@ -7,7 +7,7 @@ minimal supergroups, ie. it fails in ``C_4``. function maximal_subgroup_chain(G::PermGroup, U::PermGroup) l = [G] while order(l[end]) > order(U) - m = maximal_subgroups(l[end]) + m = collect(maximal_subgroups(l[end])) push!(l, m[findfirst(x -> is_subset(U, x), m)]) end return reverse(l) diff --git a/src/deprecations.jl b/src/deprecations.jl index 9c7b6a37fbb1..eaaee4742b52 100644 --- a/src/deprecations.jl +++ b/src/deprecations.jl @@ -73,3 +73,21 @@ Base.@deprecate_binding jacobi_ideal jacobian_ideal @deprecate factorisations factorizations @deprecate centraliser centralizer + +@deprecate hall_subgroup_reps(G::T, P::AbstractVector{<:IntegerUnion}) where T <: Union{GAPGroup, FinGenAbGroup} map(representative, hall_subgroup_classes(G, P)) +@deprecate hall_subgroups_representatives(G::GAPGroup, P::AbstractVector{<:IntegerUnion}) map(representative, hall_subgroup_classes(G, P)) + +function hall_subgroup(G::T, P::AbstractVector{<:IntegerUnion}) where T <: Union{GAPGroup, FinGenAbGroup} + Base.depwarn("The function hall_subgroup is deprecated. Please use hall_subgroup_classes.", :hall_subgroup) + @req is_solvable(G) "The group is not solvable" + return representative(hall_subgroup_classes(G, P)[1]) +end + +@deprecate low_index_subgroup_reps(G::T, n::Int) where T <: Union{GAPGroup, FinGenAbGroup} map(representative, low_index_subgroup_classes(G, n)) + +@deprecate complement_class_reps(G::T, N::T) where T <: GAPGroup map(representative, complement_classes(G, N)) + +@deprecate maximal_subgroup_reps(G::T) where T <: Union{GAPGroup, FinGenAbGroup} map(representative, maximal_subgroup_classes(G)) +@deprecate subgroup_reps(G::T) where T <: Union{GAPGroup, FinGenAbGroup} map(representative, subgroup_classes(G)) +@deprecate conjugacy_classes_maximal_subgroups(G::T) where T <: Union{GAPGroup, FinGenAbGroup} maximal_subgroup_classes(G) +@deprecate conjugacy_classes_subgroups(G::T) where T <: Union{GAPGroup, FinGenAbGroup} subgroup_classes(G) diff --git a/src/exports.jl b/src/exports.jl index 00e174ec89f7..6c764fdbddb7 100644 --- a/src/exports.jl +++ b/src/exports.jl @@ -348,7 +348,7 @@ export comm! export common_components export common_refinement export complement -export complement_class_reps +export complement_classes export complement_equation export complement_equations export complement_ideal @@ -356,6 +356,7 @@ export complement_of_point_ideal export complement_of_prime_ideal export complement_scheme export complement_system, has_complement_system, set_complement_system +export complements export complete_bipartite_graph export complete_graph export complete_intersection_germ @@ -369,7 +370,6 @@ export cone_from_inequalities export cones export conjugacy_class export conjugacy_classes -export conjugacy_classes_maximal_subgroups export conjugacy_classes_subgroups export conjugate export conjugate_group @@ -608,7 +608,8 @@ export h_vector export halfspace export halfspace_matrix_pair export hall_subgroup -export hall_subgroup_reps +export hall_subgroup_classes +export hall_subgroups export hall_system, has_hall_system, set_hall_system export has_du_val_singularities export has_edge @@ -943,7 +944,8 @@ export load_mps export localization export localized_ring export loops -export low_index_subgroup_reps +export low_index_subgroup_classes +export low_index_subgroups export lower_central_series, has_lower_central_series, set_lower_central_series export lower_triangular_matrix export map @@ -981,8 +983,8 @@ export maximal_extension export maximal_groebner_cone export maximal_normal_subgroups, has_maximal_normal_subgroups, set_maximal_normal_subgroups export maximal_polyhedra, maximal_polyhedra_and_multiplicities -export maximal_subgroup_reps -export maximal_subgroups, has_maximal_subgroups, set_maximal_subgroups +export maximal_subgroup_classes, has_maximal_subgroup_classes, set_maximal_subgroup_classes +export maximal_subgroups export metadata export milnor_algebra export milnor_number @@ -1394,7 +1396,7 @@ export structure_sheaf export sub export subalgebra_membership export subalgebra_membership_homogeneous -export subgroup_reps +export subgroup_classes export subquo_type export subquotient export subscheme diff --git a/test/Groups/GrpAb.jl b/test/Groups/GrpAb.jl index 21566828931b..7e3d2b30cd1e 100644 --- a/test/Groups/GrpAb.jl +++ b/test/Groups/GrpAb.jl @@ -83,8 +83,9 @@ end end # conjugacy classes of subgroups - CC = conjugacy_classes_subgroups(G1) - @test length(CC) == length(conjugacy_classes_subgroups(G2)) + CC = subgroup_classes(G1) + @test length(CC) == length(subgroup_classes(G2)) + @test length(CC) == length(collect(subgroups(G1))) @test all(C -> length(C) == 1, CC) @test rand(CC[1]) == representative(CC[1]) @test acting_group(CC[1]) == G1 @@ -105,22 +106,24 @@ end for H in C @test H == representative(C) end - S1 = subgroup_reps(G1) - S2 = subgroup_reps(G2) - @test sort!([length(x) for x in S1]) == sort!([length(x) for x in S2]) + S1 = map(representative, subgroup_classes(G1)) + S2 = map(representative, subgroup_classes(G2)) + @test sort!([order(x) for x in S1]) == sort!([order(x) for x in S2]) for n in 2:4 - S1 = subgroup_reps(G1, order = ZZ(n)) - S2 = subgroup_reps(G2, order = ZZ(n)) + S1 = subgroup_classes(G1, order = n) + S2 = subgroup_classes(G2, order = n) @test length(S1) == length(S2) end for n in 1:4 - S1 = low_index_subgroup_reps(G1, n) - S2 = low_index_subgroup_reps(G2, n) + S1 = low_index_subgroup_classes(G1, n) + S2 = low_index_subgroup_classes(G2, n) @test length(S1) == length(S2) + @test length(S1) == length(collect(low_index_subgroups(G1, n))) end - S1 = conjugacy_classes_maximal_subgroups(G1) - S2 = conjugacy_classes_maximal_subgroups(G2) + S1 = maximal_subgroup_classes(G1) + S2 = maximal_subgroup_classes(G2) @test sort!([length(x) for x in S1]) == sort!([length(x) for x in S2]) + @test length(S1) == length(collect(maximal_subgroups(G1))) # operations x = representative(rand(cc)) @@ -138,8 +141,10 @@ end # operations depending on sets of primes for P in subsets(Set(primes)) - @test [images(iso, S)[1] for S in hall_subgroup_reps(G1, collect(P))] == - hall_subgroup_reps(G2, collect(P)) + @test [images(iso, representative(C))[1] for C in hall_subgroup_classes(G1, collect(P))] == + map(representative, hall_subgroup_classes(G2, collect(P))) + @test [images(iso, C)[1] for C in hall_subgroups(G1, collect(P))] == + collect(hall_subgroups(G2, collect(P))) end @test sort!([order(images(iso, S)[1]) for S in hall_system(G1)]) == sort!([order(S) for S in hall_system(G2)]) diff --git a/test/Groups/conjugation.jl b/test/Groups/conjugation.jl index a355849a804b..6b9e045e7228 100644 --- a/test/Groups/conjugation.jl +++ b/test/Groups/conjugation.jl @@ -70,7 +70,9 @@ @test !is_conjugate_with_data(G,x,y)[1] end - CC = @inferred conjugacy_classes_subgroups(G) + CC5 = @inferred subgroup_classes(G, order = 5) + @test length(CC5) == 0 + CC = @inferred subgroup_classes(G) @test length(CC)==11 @test all(cc -> acting_group(cc) === G, CC) @testset for C in CC @@ -78,8 +80,8 @@ @test length(C) == index(G, normalizer(G, representative(C))[1]) @test degree(representative(C)) == degree(G) end - H=rand(subgroups(G)) - @test sum([length(c) for c in CC]) == length(subgroups(G)) + H = rand(rand(CC)) + @test sum([length(c) for c in CC]) == length(collect(Iterators.flatten(CC))) @test count(c -> H in c, CC) == 1 # H belongs to a unique conjugacy class @testset for i in 1:length(CC) c = CC[i] @@ -98,7 +100,7 @@ @test !is_conjugate_with_data(G,x,y)[1] end - CC = @inferred conjugacy_classes_maximal_subgroups(G) + CC = @inferred maximal_subgroup_classes(G) @test length(CC)==3 @test Set([order(Int, representative(l)) for l in CC])==Set([6,8,12]) @@ -107,8 +109,10 @@ @test normalizer(G,H)==normalizer(G,x) G = symmetric_group(5) - CC = @inferred conjugacy_classes_maximal_subgroups(G) - all(H -> degree(H) == degree(G), map(representative, CC)) + CC = @inferred maximal_subgroup_classes(G) + @test all(H -> degree(H) == degree(G), map(representative, CC)) + @test all(H -> is_maximal_subgroup(H, G), map(representative, CC)) + @test !is_maximal_subgroup(trivial_subgroup(G)[1], G) G = symmetric_group(10) x = rand(G) diff --git a/test/Groups/elements.jl b/test/Groups/elements.jl index c08788d96fee..e72549e4bff0 100644 --- a/test/Groups/elements.jl +++ b/test/Groups/elements.jl @@ -80,7 +80,7 @@ end FPGroup(small_group(2, 1)) GL(2,2) ] - H = first(subgroups(G)) + H = rand(rand(subgroup_classes(G))) @test parent(one(H)) === H @test parent(G(one(H))) === G end diff --git a/test/Groups/matrixgroups.jl b/test/Groups/matrixgroups.jl index b35b6936de9b..1cae16db89dc 100644 --- a/test/Groups/matrixgroups.jl +++ b/test/Groups/matrixgroups.jl @@ -547,8 +547,8 @@ end G = GL(2,3) @test length(conjugacy_classes(G))==8 - @test length(@inferred conjugacy_classes_subgroups(G))==16 - @test length(@inferred conjugacy_classes_maximal_subgroups(G))==3 + @test length(@inferred subgroup_classes(G))==16 + @test length(@inferred maximal_subgroup_classes(G))==3 end @testset "Jordan structure" begin diff --git a/test/Groups/subgroups_and_cosets.jl b/test/Groups/subgroups_and_cosets.jl index be907ec70a18..9bd878678c68 100644 --- a/test/Groups/subgroups_and_cosets.jl +++ b/test/Groups/subgroups_and_cosets.jl @@ -35,7 +35,7 @@ G = symmetric_group(4) A = alternating_group(4) - L = subgroups(G) + L = collect(subgroups(G)) @test length(L)==30 @test L[1] isa PermGroup L1 = [x for x in L if is_normal_subgroup(x, G)] @@ -44,8 +44,9 @@ for H in L1 @test H in K end - @test length(maximal_subgroups(G))==8 - @test A in maximal_subgroups(G) + @test length(maximal_subgroup_classes(G)) == 3 + @test sum(map(length, maximal_subgroup_classes(G))) == 8 + @test any(C -> A in C, maximal_subgroup_classes(G)) @test maximal_normal_subgroups(G)==[A] H = sub(G,[G([3,4,1,2]), G([2,1,4,3])])[1] @test minimal_normal_subgroups(G)==[H] @@ -327,15 +328,15 @@ end end L = [[2],[3],[5],[7],[2,3],[2,5],[2,7],[3,5],[3,7],[5,7],[2,3,5],[2,3,7],[2,5,7],[3,5,7],[2,3,5,7]] @testset for l in L - h = hall_subgroup_reps(G, l) + h = hall_subgroup_classes(G, l) @test length(h) == 1 - @test h[1] == sub(G,[g^(210÷lcm(l))])[1] + @test representative(h[1]) == sub(G,[g^(210÷lcm(l))])[1] end - h = hall_subgroup_reps(G, Int64[]) + h = hall_subgroup_classes(G, Int64[]) @test length(h) == 1 - @test h[1] == sub(G, [one(G)])[1] - @test length(hall_subgroup_reps(symmetric_group(5), [2, 5])) == 0 - @test_throws ArgumentError hall_subgroup_reps(G, [4]) + @test representative(h[1]) == sub(G, [one(G)])[1] + @test length(hall_subgroup_classes(symmetric_group(5), [2, 5])) == 0 + @test_throws ArgumentError hall_subgroup_classes(G, [4]) L = sylow_system(G) Lo = [order(l) for l in L] @@ -359,26 +360,26 @@ end # solvable group G = symmetric_group(4) N = pcore(G, 2)[1] - @test length(complement_class_reps(G, N)) == 1 + @test length(complement_classes(G, N)) == 1 # nonsolvable factor group G = special_linear_group(2, 5) N = center(G)[1] - @test length(complement_class_reps(G, N)) == 0 + @test length(complement_classes(G, N)) == 0 # nonsolvable normal subgroup G = symmetric_group(6) N = derived_subgroup(G)[1] - @test length(complement_class_reps(G, N)) == 2 + @test length(complement_classes(G, N)) == 2 # both normal subgroup and factor group nonsolvable: # check that GAP throws an error # (if not then perhaps a statement in the documentation of - # `complement_class_reps` can be changed) + # `complement_classes` can be changed) G = alternating_group(5) W = wreath_product(G, G) N = kernel(canonical_projection(W))[1] - @test_throws ErrorException complement_class_reps(W, N) + @test_throws ErrorException complement_classes(W, N) end @testset "Some specific subgroups" begin @@ -388,7 +389,7 @@ end @test order(fitting_subgroup(G)[1])==8 @test fitting_subgroup(S)==sub(S,[S([3,4,1,2]), S([4,3,2,1])]) @test frattini_subgroup(S)==sub(S,[one(S)]) - @test frattini_subgroup(G)[1]==intersect(maximal_subgroups(G))[1] + @test frattini_subgroup(G)[1]==intersect(collect(maximal_subgroups(G)))[1] @test frattini_subgroup(G)==center(G) @test is_characteristic_subgroup(center(G)[1], G) @test socle(G)==frattini_subgroup(G) From e3f0177e9bd02174f55f91ba51681cd593686fbe Mon Sep 17 00:00:00 2001 From: antonydellavecchia Date: Fri, 16 Feb 2024 16:44:17 +0100 Subject: [PATCH 05/29] Adv/upgrade regression fix (#3325) * some debuggging * add fix to upgrade tests, and fix code regression * updates johnson matrices, and always adds the refs to s.refs --- data/JohnsonMatrices/j10.mat | 2 +- data/JohnsonMatrices/j13.mat | 2 +- data/JohnsonMatrices/j16.mat | 2 +- data/JohnsonMatrices/j17.mat | 2 +- data/JohnsonMatrices/j18.mat | 2 +- data/JohnsonMatrices/j20.mat | 2 +- data/JohnsonMatrices/j21.mat | 2 +- data/JohnsonMatrices/j22.mat | 2 +- data/JohnsonMatrices/j23.mat | 2 +- data/JohnsonMatrices/j24.mat | 2 +- data/JohnsonMatrices/j25.mat | 2 +- data/JohnsonMatrices/j30.mat | 2 +- data/JohnsonMatrices/j32.mat | 2 +- data/JohnsonMatrices/j33.mat | 2 +- data/JohnsonMatrices/j34.mat | 2 +- data/JohnsonMatrices/j35.mat | 2 +- data/JohnsonMatrices/j36.mat | 2 +- data/JohnsonMatrices/j38.mat | 2 +- data/JohnsonMatrices/j39.mat | 2 +- data/JohnsonMatrices/j40.mat | 2 +- data/JohnsonMatrices/j41.mat | 2 +- data/JohnsonMatrices/j42.mat | 2 +- data/JohnsonMatrices/j43.mat | 2 +- data/JohnsonMatrices/j44.mat | 2 +- data/JohnsonMatrices/j45.mat | 2 +- data/JohnsonMatrices/j46.mat | 2 +- data/JohnsonMatrices/j47.mat | 2 +- data/JohnsonMatrices/j48.mat | 2 +- data/JohnsonMatrices/j49.mat | 2 +- data/JohnsonMatrices/j50.mat | 2 +- data/JohnsonMatrices/j51.mat | 2 +- data/JohnsonMatrices/j52.mat | 2 +- data/JohnsonMatrices/j53.mat | 2 +- data/JohnsonMatrices/j54.mat | 2 +- data/JohnsonMatrices/j55.mat | 2 +- data/JohnsonMatrices/j56.mat | 2 +- data/JohnsonMatrices/j57.mat | 2 +- data/JohnsonMatrices/j58.mat | 2 +- data/JohnsonMatrices/j59.mat | 2 +- data/JohnsonMatrices/j60.mat | 2 +- data/JohnsonMatrices/j61.mat | 2 +- data/JohnsonMatrices/j64.mat | 2 +- data/JohnsonMatrices/j68.mat | 2 +- data/JohnsonMatrices/j69.mat | 2 +- data/JohnsonMatrices/j70.mat | 2 +- data/JohnsonMatrices/j71.mat | 2 +- data/JohnsonMatrices/j72.mat | 2 +- data/JohnsonMatrices/j73.mat | 2 +- data/JohnsonMatrices/j74.mat | 2 +- data/JohnsonMatrices/j75.mat | 2 +- data/JohnsonMatrices/j77.mat | 2 +- data/JohnsonMatrices/j78.mat | 2 +- data/JohnsonMatrices/j79.mat | 2 +- data/JohnsonMatrices/j82.mat | 2 +- data/JohnsonMatrices/j84.mat | 2 +- data/JohnsonMatrices/j85.mat | 2 +- data/JohnsonMatrices/j86.mat | 2 +- data/JohnsonMatrices/j87.mat | 2 +- data/JohnsonMatrices/j88.mat | 2 +- data/JohnsonMatrices/j89.mat | 2 +- data/JohnsonMatrices/j9.mat | 2 +- data/JohnsonMatrices/j90.mat | 2 +- data/JohnsonMatrices/j92.mat | 2 +- src/Serialization/Upgrades/0.11.3.jl | 2 +- src/Serialization/Upgrades/0.13.0.jl | 23 +++++++++++++++-------- src/Serialization/main.jl | 13 +++++++------ src/Serialization/serializers.jl | 3 +-- test/Serialization/upgrades/runtests.jl | 6 ++++++ 68 files changed, 93 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b/src/Serialization/Upgrades/0.13.0.jl @@ -45,11 +45,14 @@ push!(upgrade_scripts_set, UpgradeScript( if haskey(dict, :base_ring) && dict[:base_ring] isa Dict if dict[:base_ring][:type] == "#backref" upgraded_dict[:base_ring] = dict[:base_ring][:id] - elseif haskey(dict[:base_ring], :data) - # should have only one key, since any base_ring that - # doesn't use an id has one parameter - key = first(keys(dict[:base_ring][:data])) - upgraded_dict[:base_ring][:data] = string(dict[:base_ring][:data][key]) + else + if haskey(dict[:base_ring], :data) + # should have only one key, since any base_ring that + # doesn't use an id has one parameter + key = first(keys(dict[:base_ring][:data])) + upgraded_dict[:base_ring][:data] = string(dict[:base_ring][:data][key]) + end + upgraded_dict[:base_ring][:_type] = dict[:base_ring][:type] end if haskey(dict, :symbols) if dict[:symbols] isa Dict @@ -85,8 +88,9 @@ push!(upgrade_scripts_set, UpgradeScript( error("The upgrade script needs an update") elseif contains(type_string, "PolyRingElem") if dict[:data] isa Dict && haskey(dict[:data], :parents) - upgraded_parents = dict[:data][:parents][end] - params = upgraded_parents + # this currently only handles one parent + upgraded_parent = dict[:data][:parents][end] + params = upgraded_parent[:id] upgraded_dict[:data] = upgrade_terms(dict[:data][:terms]) else # this section wasn't necessary for upgrading the folder of surfaces @@ -162,7 +166,6 @@ push!(upgrade_scripts_set, UpgradeScript( upgraded_dict[:data] = matrix_data end - if contains(type_string, "Field") if dict[:data] isa Dict &&haskey(dict[:data], :def_pol) upgraded_dict[:data][:def_pol] = upgrade_0_13_0(s, dict[:data][:def_pol]) @@ -176,6 +179,10 @@ push!(upgrade_scripts_set, UpgradeScript( end upgraded_dict[:_refs] = upgraded_refs end + + if haskey(upgraded_dict, :type) && !haskey(upgraded_dict, :_type) + upgraded_dict[:_type] = upgraded_dict[:type] + end return upgraded_dict end )) diff --git a/src/Serialization/main.jl b/src/Serialization/main.jl index 8e1063abd304..6abfe7d2dd25 100644 --- a/src/Serialization/main.jl +++ b/src/Serialization/main.jl @@ -74,15 +74,15 @@ end const reverse_type_map = Dict{String, Type}() function encode_type(::Type{T}) where T - error("unsupported type '$T' for encoding") + error("Unsupported type '$T' for encoding. to add support see + https://docs.oscar-system.org/stable/DeveloperDocumentation/serialization/ \n") end function decode_type(s::DeserializerState) if s.obj isa String if !isnothing(tryparse(UUID, s.obj)) id = s.obj - obj = deepcopy(s.obj) - + obj = s.obj if isnothing(s.refs) return typeof(global_serializer_state.id_to_obj[UUID(id)]) end @@ -206,8 +206,8 @@ function load_typed_object(s::DeserializerState; override_params::Any = nothing) else # depending on the type, :params is either an object to be loaded or a # dict with keys and object values to be loaded - load_node(s, type_key) do _ - params = load_params_node(s) + params = load_node(s, type_key) do _ + load_params_node(s) end end load_node(s, :data) do _ @@ -551,7 +551,8 @@ function load(io::IO; params::Any = nothing, type::Any = nothing, jsondict = JSON.parse(json(s.obj), dicttype=Dict{Symbol, Any}) jsondict = upgrade(file_version, jsondict) s.obj = JSON3.read(json(jsondict)) - if !isnothing(s.refs) && haskey(s.obj, refs_key) + + if haskey(s.obj, refs_key) s.refs = s.obj[refs_key] end end diff --git a/src/Serialization/serializers.jl b/src/Serialization/serializers.jl index d0ec1ea1b758..62e6d446d90e 100644 --- a/src/Serialization/serializers.jl +++ b/src/Serialization/serializers.jl @@ -193,10 +193,9 @@ end function load_params_node(s::DeserializerState) T = decode_type(s) - params = load_node(s, :params) do _ + load_node(s, :params) do _ return load_type_params(s, T) end - return params end ################################################################################ diff --git a/test/Serialization/upgrades/runtests.jl b/test/Serialization/upgrades/runtests.jl index 41e7a27780de..a66641b0d2c3 100644 --- a/test/Serialization/upgrades/runtests.jl +++ b/test/Serialization/upgrades/runtests.jl @@ -1,5 +1,8 @@ @testset "Serialization.Upgrades" begin @testset "< 0.11.3 Upgrade" begin + # test loading + load(joinpath(@__DIR__, "file_version_less_than_0.11.2.json")) + L = ones(QQFieldElem, 15) R, x = QQ["x"] p = R(L) @@ -8,6 +11,9 @@ end @testset "< 0.12.0 Upgrade" begin + # test loading + load(joinpath(@__DIR__, "file_version_less_than_0.12.0.json")); + Zt, t = polynomial_ring(residue_ring(ZZ, 2)[1], "t") Fin, d = Nemo.Native.finite_field(t^2 + t + 1) Rx, x = Fin["x"] From 9e8b2250464ecc31e4ebd6720bfdbc325dbc0d69 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Lars=20G=C3=B6ttgens?= Date: Fri, 16 Feb 2024 15:24:19 +0100 Subject: [PATCH 06/29] Overhaul root system type detection (#3351) --- .../LieAlgebras/src/AbstractLieAlgebra.jl | 15 - experimental/LieAlgebras/src/CartanMatrix.jl | 280 ++++++++++-------- experimental/LieAlgebras/src/DynkinDiagram.jl | 58 +++- experimental/LieAlgebras/src/LieAlgebras.jl | 6 +- experimental/LieAlgebras/src/RootSystem.jl | 64 ++-- experimental/LieAlgebras/src/WeylGroup.jl | 19 +- .../LieAlgebras/test/CartanMatrix-test.jl | 215 ++++++++------ .../LieAlgebras/test/DynkinDiagram-test.jl | 149 ++++++++++ .../LieAlgebras/test/WeylGroup-test.jl | 1 + 9 files changed, 546 insertions(+), 261 deletions(-) diff --git a/experimental/LieAlgebras/src/AbstractLieAlgebra.jl b/experimental/LieAlgebras/src/AbstractLieAlgebra.jl index e49e3c7e44c8..52ea93c7e50a 100644 --- a/experimental/LieAlgebras/src/AbstractLieAlgebra.jl +++ b/experimental/LieAlgebras/src/AbstractLieAlgebra.jl @@ -85,19 +85,6 @@ function root_system(L::LieAlgebra) return L.root_system end -has_root_system_type(L::AbstractLieAlgebra) = - has_root_system(L) && has_root_system_type(L.root_system) - -function root_system_type(L::AbstractLieAlgebra) - @req has_root_system_type(L) "No root system type known." - return root_system_type(root_system(L)) -end - -function root_system_type_string(L::AbstractLieAlgebra) - @req has_root_system_type(L) "No root system type known." - return root_system_type_string(root_system(L)) -end - @doc raw""" chevalley_basis(L::AbstractLieAlgebra{C}) -> NTuple{3,Vector{AbstractLieAlgebraElem{C}}} @@ -128,8 +115,6 @@ function Base.show(io::IO, ::MIME"text/plain", L::AbstractLieAlgebra) io = pretty(io) println(io, "Abstract Lie algebra") println(io, Indent(), "of dimension $(dim(L))", Dedent()) - has_root_system_type(L) && - println(io, Indent(), "of type $(root_system_type_string(L))", Dedent()) print(io, "over ") print(io, Lowercase(), coefficient_ring(L)) end diff --git a/experimental/LieAlgebras/src/CartanMatrix.jl b/experimental/LieAlgebras/src/CartanMatrix.jl index 0858454b9611..fbce231ae372 100644 --- a/experimental/LieAlgebras/src/CartanMatrix.jl +++ b/experimental/LieAlgebras/src/CartanMatrix.jl @@ -79,6 +79,28 @@ function cartan_matrix(fam::Symbol, rk::Int) return mat end +@doc raw""" + cartan_matrix(type::Vector{Tuple{Symbol,Int}}) -> ZZMatrix + +Returns a block diagonal matrix of indecomposable Cartan matrices as defined by type. +For allowed values see `cartan_matrix(fam::Symbol, rk::Int)`. + +# Example +```jldoctest +julia> cartan_matrix([(:A, 2), (:B, 2)]) +[ 2 -1 0 0] +[-1 2 0 0] +[ 0 0 2 -1] +[ 0 0 -2 2] +``` +""" +function cartan_matrix(type::Vector{Tuple{Symbol,Int}}) + @req length(type) > 0 "At least one type is required" + + blocks = [cartan_matrix(t...) for t in type] + return block_diagonal_matrix(blocks) +end + @doc raw""" cartan_matrix(type::Tuple{Symbol,Int}...) -> ZZMatrix @@ -97,8 +119,7 @@ julia> cartan_matrix((:A, 2), (:B, 2)) function cartan_matrix(type::Tuple{Symbol,Int}...) @req length(type) > 0 "At least one type is required" - blocks = [cartan_matrix(t...) for t in type] - return block_diagonal_matrix(blocks) + return cartan_matrix(collect(type)) end @doc raw""" @@ -257,6 +278,9 @@ This function is left inverse to `cartan_matrix`, i.e. in the case of isomorphic the ordering of the roots does matter (see the example below). The keyword argument `check` can be set to `false` to skip verification whether `gcm` is indeed a Cartan matrix of finite type. +The order of returned components is, in general, not unique and might change between versions. +If this function is called with the output of `cartan_matrix(type)`, it will keep the order of `type`. + # Example ```jldoctest julia> cartan_type(ZZ[2 -1; -2 2]) @@ -278,19 +302,17 @@ end Returns the Cartan type of a Cartan matrix `gcm` together with a vector indicating a canonical ordering of the roots in the Dynkin diagram (currently only Cartan matrices of finite type are supported). -The keyword argument `check` can be set to `false` to skip verification whether `gcm` is indeed a Cartan matrix of finite type. +The keyword argument `check` can be set to `false` to skip verification whether `gcm` is indeed a +Cartan matrix of finite type. + +The order of returned components and the ordering is, in general, not unique and might change between versions. +If this function is called with the output of `cartan_matrix(type)`, it will keep the order of `type` and the +returned ordering will be the identity. + # Example ```jldoctest -julia> cartan_matrix(:E, 6) -[ 2 0 -1 0 0 0] -[ 0 2 0 -1 0 0] -[-1 0 2 -1 0 0] -[ 0 -1 -1 2 -1 0] -[ 0 0 0 -1 2 -1] -[ 0 0 0 0 -1 2] - julia> cartan_type_with_ordering(cartan_matrix(:E, 6)) -([(:E, 6)], [1, 3, 4, 2, 5, 6]) +([(:E, 6)], [1, 2, 3, 4, 5, 6]) julia> cartan_type_with_ordering(ZZ[2 0 -1 0; 0 2 0 -2; -2 0 2 0; 0 -1 0 2]) ([(:B, 2), (:C, 2)], [1, 3, 2, 4]) @@ -304,135 +326,133 @@ function cartan_type_with_ordering(gcm::ZZMatrix; check::Bool=true) # global information ord = sizehint!(Int[], rk) # ordering of the roots - adj = [sizehint!(Int[], 3) for _ in 1:rk] # store adjacent roots, adj[i] is ordered asc + adj = [[j for j in 1:rk if i != j && !is_zero_entry(gcm, i, j)] for i in 1:rk] # adjacency list + done = falses(rk) # whether a root is already in a component - # information about current type - num = 0 # number of roots - roots = sizehint!(Int[], rk) + for v0 in 1:rk + done[v0] && continue - # used for traversal - undone = trues(rk) - plan = zeros(Int, 3) # a root is connected to up to 3 others - head = 0 # index up to which we planned (cyclic) - tail = 0 # index of plan which will be done next - - i, j = 1, 2 - while true - while i == j || (j <= rk && is_zero_entry(gcm, i, j)) - j += 1 + # rank 1 + if length(adj[v0]) == 0 + push!(type, (:A, 1)) + push!(ord, v0) + done[v0] = true + continue end - if j == rk + 1 - num += 1 - undone[i] = false - push!(roots, i) - - if tail != head - tail += 1 - if tail == 4 - tail = 1 - end - i = plan[tail] - else # nothing further is planned - offset = length(ord) + 1 - if num == 1 # rank 1 - push!(type, (:A, 1)) - push!(ord, i) - elseif num == 2 # rank 2 - i, j = roots[1], roots[2] - if gcm[i, j] * gcm[j, i] == 1 - push!(type, (:A, 2)) - push!(ord, i, j) - elseif gcm[i, j] == -2 - push!(type, (:C, 2)) - push!(ord, i, j) - elseif gcm[j, i] == -2 - push!(type, (:B, 2)) - push!(ord, i, j) - elseif gcm[i, j] == -3 - push!(type, (:G, 2)) - push!(ord, i, j) - else - push!(type, (:G, 2)) - push!(ord, j, i) - end - else # rank > 2 - # find start of the Dynkin graph - v = 0 - for i in roots - j = adj[i][1] - if length(adj[i]) == 1 && gcm[i, j] * gcm[j, i] == 1 - if length(adj[j]) == 1 || (length(adj[j]) == 2 && gcm[j, adj[j][2]] == -1) - v = i - break - elseif v == 0 - v = i - end - end - end - push!(ord, v) - - n = 1 - adj3 = false # true if found a root with 3 adjacents - while n < num - nv = v - for vv in adj[v] - filter!(x -> x != v, adj[vv]) - push!(ord, vv) - n += 1 - if length(adj[vv]) > 0 - nv = vv - if length(adj[vv]) == 2 # +1 for the predecessor - adj3 = true - end - end - end - v = nv - end - - if adj3 - if isempty(adj[ord[end]]) && isempty(adj[ord[end - 1]]) - push!(type, (:D, num)) - else - push!(type, (:E, num)) - end - elseif num == 4 && - gcm[ord[end - 2], ord[end - 1]] * gcm[ord[end - 1], ord[end - 2]] > 1 - push!(type, (:F, 4)) - elseif gcm[ord[end - 1], ord[end]] * gcm[ord[end], ord[end - 1]] == 1 - push!(type, (:A, num)) - elseif gcm[ord[end - 1], ord[end]] == -1 - push!(type, (:B, num)) - else - push!(type, (:C, num)) - end - end - - # find next component - i = findfirst(undone) - if isnothing(i) - break - end - # reset number of roots - num = 0 - empty!(roots) + # rank 2 + if length(adj[v0]) == 1 && length(adj[only(adj[v0])]) == 1 + v1 = only(adj[v0]) + if gcm[v0, v1] * gcm[v1, v0] == 1 + push!(type, (:A, 2)) + push!(ord, v0, v1) + elseif gcm[v0, v1] == -2 + push!(type, (:C, 2)) + push!(ord, v0, v1) + elseif gcm[v1, v0] == -2 + push!(type, (:B, 2)) + push!(ord, v0, v1) + elseif gcm[v0, v1] == -3 + push!(type, (:G, 2)) + push!(ord, v0, v1) + elseif gcm[v1, v0] == -3 + push!(type, (:G, 2)) + push!(ord, v1, v0) + else + error("unreachable") end - - j = 1 + done[v0] = true + done[v1] = true continue end - # plan to visit j if undone - if undone[j] - head += 1 - if head == 4 - head = 1 + # rank > 2 + # do a DFS to find the whole component + comp = [v0] + todo = [v0] + done[v0] = true + while !isempty(todo) + v = pop!(todo) + for w in adj[v] + if !done[w] + push!(comp, w) + push!(todo, w) + done[w] = true + end end - plan[head] = j end + sort!(comp) + len_comp = length(comp) + + deg3 = findfirst(v -> length(adj[v]) == 3, comp) + if isnothing(deg3) + # case A, B, C, F + + # find start of the Dynkin graph + start = 0 + for v1 in filter(v -> length(adj[v]) == 1, comp) + v2 = only(adj[v1]) + gcm[v1, v2] * gcm[v2, v1] == 1 || continue # discard right end of B and C + if len_comp == 4 + v3 = only(filter(!=(v1), adj[v2])) + gcm[v2, v3] == -1 || continue # discard right end of F + end - push!(adj[i], j) - j += 1 + # found start + start = v1 + break + end + @assert start != 0 + + # find the path + path = [start, only(adj[start])] + for _ in 1:(len_comp - 2) + push!(path, only(filter(!=(path[end - 1]), adj[path[end]]))) + end + # determine type + if len_comp == 4 && gcm[path[3], path[2]] == -2 + push!(type, (:F, 4)) + elseif gcm[path[end - 1], path[end]] == -2 + push!(type, (:C, len_comp)) + elseif gcm[path[end], path[end - 1]] == -2 + push!(type, (:B, len_comp)) + else + push!(type, (:A, len_comp)) + end + append!(ord, path) + else + # case D or E + + # find the three paths + v_deg3 = comp[deg3] + paths = [[v_deg3, v_n] for v_n in adj[v_deg3]] + for path in paths + while length(adj[path[end]]) == 2 + push!(path, only(filter(!=(path[end - 1]), adj[path[end]]))) + end + popfirst!(path) + end + sort!(paths; by=length) + @assert sum(length, paths) + 1 == len_comp + # determine type + if length(paths[2]) == 1 + # case D + push!(type, (:D, len_comp)) + if len_comp == 4 + push!(ord, only(paths[1]), v_deg3, only(paths[2]), only(paths[3])) + else + append!(ord, reverse!(paths[3])) + push!(ord, v_deg3, only(paths[1]), only(paths[2])) + end + elseif length(paths[2]) == 2 + # case E + push!(type, (:E, len_comp)) + push!(ord, paths[2][2], only(paths[1]), paths[2][1], v_deg3) + append!(ord, paths[3]) + else + error("unreachable") + end + end end return type, ord diff --git a/experimental/LieAlgebras/src/DynkinDiagram.jl b/experimental/LieAlgebras/src/DynkinDiagram.jl index 6dc07b6fd6c6..5aea2acc34be 100644 --- a/experimental/LieAlgebras/src/DynkinDiagram.jl +++ b/experimental/LieAlgebras/src/DynkinDiagram.jl @@ -1,3 +1,58 @@ +@doc raw""" + show_dynkin_diagram(cartan_matrix::ZZMatrix) -> Nothing + +Prints a string representation of the Dynkin diagram of the root system +with the given cartan matrix. +The labels of the nodes are the indices of the simple roots. + +Currently, only cartan matrices of finite type are supported. +""" +function show_dynkin_diagram(cartan_matrix::ZZMatrix) + type, label = cartan_type_with_ordering(cartan_matrix) + return show_dynkin_diagram(type, label) +end + +@doc raw""" + show_dynkin_diagram(rs::RootSystem) -> Nothing + +Prints a string representation of the Dynkin diagram of the given root system. +The labels of the nodes are the indices of the simple roots. + +Currently, only root systems of finite type are supported. +""" +function show_dynkin_diagram(rs::RootSystem) + type, label = root_system_type_with_ordering(rs) + return show_dynkin_diagram(type, label) +end + +@doc raw""" + show_dynkin_diagram(type::Vector{Tuple{Symbol,Int}}) -> Nothing + +Prints a string representation of the Dynkin diagram of the root system of +the given cartan type. +""" +function show_dynkin_diagram(type::Vector{Tuple{Symbol,Int}}) + return show_dynkin_diagram(type, 1:sum(t[2] for t in type; init=0)) +end + +@doc raw""" + show_dynkin_diagram(type::Vector{Tuple{Symbol,Int}}, labels::AbstractVector{Int}) -> Nothing + +Prints a string representation of the Dynkin diagram of the root system of +the given cartan type. +""" +function show_dynkin_diagram(type::Vector{Tuple{Symbol,Int}}, labels::AbstractVector{Int}) + @req length(labels) == sum(t[2] for t in type; init=0) "Invalid number of labels" + offset = 0 + for (fam, rk) in type + show_dynkin_diagram(fam, rk, labels[(offset + 1):(offset + rk)]) + offset += rk + println() + println() + end + return nothing +end + @doc raw""" show_dynkin_diagram(fam::Symbol, rk::Int) -> Nothing @@ -5,7 +60,7 @@ Prints a string representation of the Dynkin diagram of the root system of the given cartan type. """ function show_dynkin_diagram(fam::Symbol, rk::Int) - show_dynkin_diagram(fam, rk, 1:rk) + return show_dynkin_diagram(fam, rk, 1:rk) end @doc raw""" @@ -49,4 +104,5 @@ function show_dynkin_diagram(fam::Symbol, rk::Int, labels::AbstractVector{Int}) end isempty(D) && error("Unreachable") print(D) + return nothing end diff --git a/experimental/LieAlgebras/src/LieAlgebras.jl b/experimental/LieAlgebras/src/LieAlgebras.jl index 75f69a1f8d3c..ab537ded7a28 100644 --- a/experimental/LieAlgebras/src/LieAlgebras.jl +++ b/experimental/LieAlgebras/src/LieAlgebras.jl @@ -167,8 +167,9 @@ export positive_root export positive_roots export reduced_expressions export reflect, reflect! -export root_system_type, has_root_system_type export root_system, has_root_system +export root_system_type, has_root_system_type +export root_system_type_with_ordering export show_dynkin_diagram export simple_coroot export simple_coroots @@ -290,8 +291,9 @@ export positive_roots export reduced_expressions export reflect, reflect! export root -export root_system_type, has_root_system_type export root_system, has_root_system +export root_system_type, has_root_system_type +export root_system_type_with_ordering export roots export show_dynkin_diagram export simple_coroot diff --git a/experimental/LieAlgebras/src/RootSystem.jl b/experimental/LieAlgebras/src/RootSystem.jl index ab7ad21ddebe..640b9f3c8739 100644 --- a/experimental/LieAlgebras/src/RootSystem.jl +++ b/experimental/LieAlgebras/src/RootSystem.jl @@ -13,6 +13,7 @@ mutable struct RootSystem # optional: type::Vector{Tuple{Symbol,Int}} + type_ordering::Vector{Int} function RootSystem(mat::ZZMatrix) pos_roots, pos_coroots, refl = positive_roots_and_reflections(mat) @@ -28,19 +29,22 @@ mutable struct RootSystem end @doc raw""" - root_system(cartan_matrix::ZZMatrix; check::Bool=true) -> RootSystem - root_system(cartan_matrix::Matrix{Int}; check::Bool=true) -> RootSystem + root_system(cartan_matrix::ZZMatrix; check::Bool=true, detect_type::Bool=true) -> RootSystem + root_system(cartan_matrix::Matrix{Int}; check::Bool=true, detect_type::Bool=true) -> RootSystem Constructs the root system defined by the Cartan matrix. If `check` is `true`, checks that `cartan_matrix` is a generalized Cartan matrix. +Passing `detect_type=false` will skip the detection of the root system type. """ -function root_system(cartan_matrix::ZZMatrix; check::Bool=true) +function root_system(cartan_matrix::ZZMatrix; check::Bool=true, detect_type::Bool=true) @req !check || is_cartan_matrix(cartan_matrix) "Requires a generalized Cartan matrix" - return RootSystem(cartan_matrix) + R = RootSystem(cartan_matrix) + detect_type && is_finite(weyl_group(R)) && set_root_system_type(R, cartan_type_with_ordering(cartan_matrix)...) + return R end -function root_system(cartan_matrix::Matrix{<:Integer}; check::Bool=true) - return root_system(matrix(ZZ, cartan_matrix); check) +function root_system(cartan_matrix::Matrix{<:Integer}; kwargs...) + return root_system(matrix(ZZ, cartan_matrix); kwargs...) end @doc raw""" @@ -50,18 +54,22 @@ Constructs the root system of the given type. See `cartan_matrix(fam::Symbol, rk """ function root_system(fam::Symbol, rk::Int) cartan = cartan_matrix(fam, rk) - R = root_system(cartan; check=false) - R.type = [(fam, rk)] + R = root_system(cartan; check=false, detect_type=false) + set_root_system_type(R, [(fam, rk)]) return R end -function root_system(types::Tuple{Symbol,Int}...) - cartan = cartan_matrix(types...) - R = root_system(cartan; check=false) - R.type = collect(types) +function root_system(type::Vector{Tuple{Symbol,Int}}) + cartan = cartan_matrix(type) + R = root_system(cartan; check=false, detect_type=false) + set_root_system_type(R, type) return R end +function root_system(type::Tuple{Symbol,Int}...) + return root_system(collect(type)) +end + function Base.show(io::IO, ::MIME"text/plain", R::RootSystem) io = pretty(io) println(io, "Root system defined by Cartan matrix") @@ -133,12 +141,8 @@ function fundamental_weights(R::RootSystem) return [fundamental_weight(R, i) for i in 1:rank(R)] end -function has_root_system_type(R::RootSystem) - return isdefined(R, :type) -end - function is_simple(R::RootSystem) - if has_root_system_type(R) + if is_finite(weyl_group(R)) return length(root_system_type(R)) == 1 end error("Not implemented") # TODO: implement is_simple @@ -280,10 +284,30 @@ function rank(R::RootSystem) end function root_system_type(R::RootSystem) - @req has_root_system_type(R) "root system type not defined" + has_root_system_type(R) || error("Root system type not known and cannot be determined") return R.type end +function root_system_type_with_ordering(R::RootSystem) + return R.type, R.type_ordering +end + +function has_root_system_type(R::RootSystem) + return isdefined(R, :type) && isdefined(R, :type_ordering) +end + +function set_root_system_type(R::RootSystem, type::Vector{Tuple{Symbol,Int}}) + return set_root_system_type(R, type, 1:sum(t[2] for t in type; init=0)) +end + +function set_root_system_type( + R::RootSystem, type::Vector{Tuple{Symbol,Int}}, ordering::AbstractVector{Int} +) + R.type = type + R.type_ordering = collect(ordering) + return nothing +end + function root_system_type_string(R::RootSystem) return join([string(t[1]) * string(t[2]) for t in root_system_type(R)], " x ") end @@ -340,10 +364,6 @@ function simple_roots(R::RootSystem) return positive_roots(R)[1:rank(R)] end -function type(R::RootSystem) - return R.type -end - @doc raw""" simple_coroot(R::RootSystem, i::Int) -> RootSpaceElem diff --git a/experimental/LieAlgebras/src/WeylGroup.jl b/experimental/LieAlgebras/src/WeylGroup.jl index 2b0188d5aa7b..e8c6a2a1a058 100644 --- a/experimental/LieAlgebras/src/WeylGroup.jl +++ b/experimental/LieAlgebras/src/WeylGroup.jl @@ -54,19 +54,28 @@ end @doc raw""" weyl_group(fam::Symbol, rk::Int) -> WeylGroup -Returns the Weyl group defined by . +Returns the Weyl group of the given type. See `cartan_matrix(fam::Symbol, rk::Int)` for allowed combinations. """ function weyl_group(fam::Symbol, rk::Int) return weyl_group(root_system(fam, rk)) end @doc raw""" - weyl_group(type::Tuple{Symbol, Int}...) -> WeylGroup + weyl_group(type::Vector{Tuple{Symbol,Int}}) -> WeylGroup -Returns the Weyl group defined by . +Returns the Weyl group of the given type. See `cartan_matrix(fam::Symbol, rk::Int)` for allowed combinations. +""" +function weyl_group(type::Vector{Tuple{Symbol,Int}}) + return weyl_group(root_system(type)) +end + +@doc raw""" + weyl_group(type::Tuple{Symbol,Int}...) -> WeylGroup + +Returns the Weyl group of the given type. See `cartan_matrix(fam::Symbol, rk::Int)` for allowed combinations. """ function weyl_group(type::Tuple{Symbol,Int}...) - return weyl_group(root_system(type...)) + return weyl_group(root_system(collect(type))) end @doc raw""" @@ -175,7 +184,7 @@ function order(::Type{T}, W::WeylGroup) where {T} end ord = T(1) - for (fam, rk) in type(root_system(W)) + for (fam, rk) in root_system_type(root_system(W)) if fam == :A ord *= T(factorial(rk + 1)) elseif fam == :B || fam == :C diff --git a/experimental/LieAlgebras/test/CartanMatrix-test.jl b/experimental/LieAlgebras/test/CartanMatrix-test.jl index 8d53a14c0159..a03474f0a56f 100644 --- a/experimental/LieAlgebras/test/CartanMatrix-test.jl +++ b/experimental/LieAlgebras/test/CartanMatrix-test.jl @@ -121,100 +121,143 @@ @test cartan_bilinear_form(ZZ[2 -4; -1 2]) == ZZ[2 -4; -4 8] end - @testset "cartan_type(gcm::ZZMatrix; check::Bool)" begin - # test if we follow our own conventions - @test cartan_type(cartan_matrix(:A, 3); check=false) == [(:A, 3)] - @test cartan_type(cartan_matrix(:B, 2); check=false) == [(:B, 2)] - @test cartan_type(cartan_matrix(:C, 2); check=false) == [(:C, 2)] - - # tests for irreducibles - @test cartan_type(cartan_matrix(:A, 1); check=false) == [(:A, 1)] - @test cartan_type(cartan_matrix(:A, 2); check=false) == [(:A, 2)] - - @test cartan_type(cartan_matrix(:B, 3); check=false) == [(:B, 3)] - @test cartan_type(ZZ[2 -2 0; -1 2 -1; 0 -1 2]; check=false) == [(:B, 3)] - - # Cn - @test cartan_type(cartan_matrix(:C, 3); check=false) == [(:C, 3)] - @test cartan_type(ZZ[2 -1 0; -2 2 -1; 0 -1 2]; check=false) == [(:C, 3)] - - # Dn - @test cartan_type(cartan_matrix(:D, 4); check=false) == [(:D, 4)] - @test cartan_type(ZZ[2 -1 -1 -1; -1 2 0 0; -1 0 2 0; -1 0 0 2]) == [(:D, 4)] - @test cartan_type(cartan_matrix(:D, 6); check=false) == [(:D, 6)] - - @test cartan_type(cartan_matrix(:E, 6); check=false) == [(:E, 6)] - @test cartan_type(cartan_matrix(:E, 7); check=false) == [(:E, 7)] - @test cartan_type(cartan_matrix(:E, 8); check=false) == [(:E, 8)] - @test cartan_type(cartan_matrix(:F, 4); check=false) == [(:F, 4)] - @test cartan_type(cartan_matrix(:G, 2); check=false) == [(:G, 2)] - - # for F4 and G2 we also allow the transposed Cartan matrix - @test cartan_type(transpose(cartan_matrix(:F, 4))) == [(:F, 4)] - @test cartan_type(transpose(cartan_matrix(:G, 2))) == [(:G, 2)] - - # test decomposable Cartan matrices - @test cartan_type(cartan_matrix((:A, 1), (:A, 2)); check=false) == [(:A, 1), (:A, 2)] - @test cartan_type(cartan_matrix((:A, 1), (:B, 2)); check=false) == [(:A, 1), (:B, 2)] - @test cartan_type(cartan_matrix((:C, 2), (:B, 2)); check=false) == [(:C, 2), (:B, 2)] - @test cartan_type(ZZ[2 0 -1 0; 0 2 0 -2; -2 0 2 0; 0 -1 0 2]; check=false) == - [(:B, 2), (:C, 2)] - end - - @testset "cartan_type_with_ordering(gcm::ZZMatrix; check::Bool)" begin - # we only test the ordering here the type detection is tested in "cartan_type(gcm::ZZMatrix; check::Bool)" - - # An - _, ord = cartan_type_with_ordering(cartan_matrix(:A, 1)) - @test ord == [1] - - _, ord = cartan_type_with_ordering(cartan_matrix(:A, 2)) - @test ord == [1, 2] - - # Bn - _, ord = cartan_type_with_ordering(cartan_matrix(:B, 2)) - @test ord == [1, 2] - - _, ord = cartan_type_with_ordering(cartan_matrix(:B, 3)) - @test ord == [1, 2, 3] - - # Cn - _, ord = cartan_type_with_ordering(cartan_matrix(:C, 2)) - @test ord == [1, 2] - - _, ord = cartan_type_with_ordering(cartan_matrix(:C, 3)) - @test ord == [1, 2, 3] - - # Dn - _, ord = cartan_type_with_ordering(cartan_matrix(:D, 4)) - @test ord == [1, 2, 3, 4] + @testset "cartan_type_with_ordering" begin + function test_cartan_type_with_ordering( + fam::Symbol, n::Int; autos::Vector{PermGroupElem}=[one(symmetric_group(n))] + ) + @req all(aut -> parent(aut) == symmetric_group(n), autos) "Incompatible permutation parent" + cm = cartan_matrix(fam, n) + for perm in symmetric_group(n) + type, ord = cartan_type_with_ordering( + permutation_matrix(ZZ, inv(perm)) * cm * permutation_matrix(ZZ, perm); check=false + ) + @test type == [(fam, n)] + @test ord in [Vector{Int}(aut * perm) for aut in autos] + @test !is_one(perm) || ord == 1:n + end + end - _, ord = cartan_type_with_ordering(ZZ[2 -1 -1 -1; -1 2 0 0; -1 0 2 0; -1 0 0 2]) - @test ord == [2, 1, 3, 4] + @testset "A_n" begin + @testset "A_$n" for n in 1:8 + # automorphism group of Dynkin diagram ≅ S_2 (horizontal reflection) + test_cartan_type_with_ordering( + :A, + n; + autos=[ + cperm(symmetric_group(n), Int[]), + cperm(symmetric_group(n), Vector{Int}[[i, n + 1 - i] for i in 1:div(n, 2)]), + ], + ) + end + end - # En - _, ord = cartan_type_with_ordering(cartan_matrix(:E, 6)) - @test ord == [1, 3, 4, 2, 5, 6] + @testset "B_n" begin + @testset "B_2" begin + n = 2 + # B_2 is isomorphic to C_2; we decide based on the ordering + cm = cartan_matrix(:B, n) + # identity permutation + type, ord = cartan_type_with_ordering(cm; check=false) + @test type == [(:B, n)] + @test ord == [1, 2] + # non-identity permutation + type, ord = cartan_type_with_ordering(transpose(cm); check=false) + @test type == [(:C, 2)] + @test ord == [1, 2] + end + @testset "B_$n" for n in 3:8 + # no automorphisms of Dynkin diagram + test_cartan_type_with_ordering(:B, n) + end + end - _, ord = cartan_type_with_ordering(cartan_matrix(:E, 7)) - @test ord == [1, 3, 4, 2, 5, 6, 7] + @testset "C_n" begin + @testset "C_2" begin + n = 2 + # C_2 is isomorphic to B_2; we decide based on the ordering + cm = cartan_matrix(:C, n) + # identity permutation + type, ord = cartan_type_with_ordering(cm; check=false) + @test type == [(:C, n)] + @test ord == [1, 2] + # non-identity permutation + type, ord = cartan_type_with_ordering(transpose(cm); check=false) + @test type == [(:B, 2)] + @test ord == [1, 2] + end + @testset "C_$n" for n in 3:8 + # no automorphisms of Dynkin diagram + test_cartan_type_with_ordering(:C, n) + end + end - _, ord = cartan_type_with_ordering(cartan_matrix(:E, 8)) - @test ord == [1, 3, 4, 2, 5, 6, 7, 8] + @testset "D_n" begin + @testset "D_$n" for n in 4:8 + if n == 4 + # automorphism group of Dynkin diagram ≅ S_3 + test_cartan_type_with_ordering( + :D, n; autos=(@perm 4 [(), (1, 3), (1, 4), (3, 4), (1, 3, 4), (1, 4, 3)]) + ) + else + # automorphism group of Dynkin diagram ≅ S_2 (vertical reflection) + test_cartan_type_with_ordering( + :D, + n; + autos=[ + cperm(symmetric_group(n), Int[]), cperm(symmetric_group(n), Int[n - 1, n]) + ], + ) + end + end + end - # F4 - _, ord = cartan_type_with_ordering(cartan_matrix(:F, 4)) - @test ord == [1, 2, 3, 4] + @testset "E_n" begin + @testset "E_$n" for n in 6:8 + if n == 6 + # automorphism group of Dynkin diagram ≅ S_2 (horizontal reflection) + test_cartan_type_with_ordering(:E, n; autos=(@perm 6 [(), (1, 6)(3, 5)])) + else + # no automorphisms of Dynkin diagram + test_cartan_type_with_ordering(:E, n) + end + end + end - _, ord = cartan_type_with_ordering(ZZ[2 -1 0 0; -1 2 -2 0; 0 -1 2 -1; 0 0 -1 2]) - @test ord == [4, 3, 2, 1] + @testset "F_4" begin + # no automorphisms of Dynkin diagram + test_cartan_type_with_ordering(:F, 4) + end - # G2 - _, ord = cartan_type_with_ordering(cartan_matrix(:G, 2)) - @test ord == [1, 2] + @testset "G_2" begin + # no automorphisms of Dynkin diagram + test_cartan_type_with_ordering(:G, 2) + end - _, ord = cartan_type_with_ordering(transpose(cartan_matrix(:G, 2))) - @test ord == [2, 1] + @testset "non-simple cases" begin + type, ord = cartan_type_with_ordering(cartan_matrix((:A, 1), (:A, 2)); check=false) + @test type == [(:A, 1), (:A, 2)] + @test ord == 1:3 + + type, ord = cartan_type_with_ordering(cartan_matrix((:A, 1), (:B, 2)); check=false) + @test type == [(:A, 1), (:B, 2)] + @test ord == 1:3 + + type, ord = cartan_type_with_ordering(cartan_matrix((:C, 2), (:B, 2)); check=false) + @test type == [(:C, 2), (:B, 2)] + @test ord == 1:4 + + type, ord = cartan_type_with_ordering( + cartan_matrix((:E, 8), (:A, 5), (:D, 4), (:F, 4), (:B, 8)); check=false + ) + @test type == [(:E, 8), (:A, 5), (:D, 4), (:F, 4), (:B, 8)] + @test ord == 1:(8 + 5 + 4 + 4 + 8) + + type, ord = cartan_type_with_ordering( + ZZ[2 0 -1 0; 0 2 0 -2; -2 0 2 0; 0 -1 0 2]; check=false + ) + @test type == [(:B, 2), (:C, 2)] + @test ord == [1, 3, 2, 4] + end end @testset "is_cartan_type" begin diff --git a/experimental/LieAlgebras/test/DynkinDiagram-test.jl b/experimental/LieAlgebras/test/DynkinDiagram-test.jl index 1f13ccd76e79..d7c899013f65 100644 --- a/experimental/LieAlgebras/test/DynkinDiagram-test.jl +++ b/experimental/LieAlgebras/test/DynkinDiagram-test.jl @@ -231,6 +231,155 @@ julia> show_dynkin_diagram(:F, 4, [105, 2, 99, 300]) julia> show_dynkin_diagram(:G, 2, [412, 5]) 412 <<< 5 ``` + +non-simple diagram with canonical labels + +```jldoctest show_ns_dynkin_diagram.test +julia> using Oscar + +julia> show_dynkin_diagram([(:B, 5), (:B, 5)]) +1 - 2 - 3 - 4 >=> 5 + +6 - 7 - 8 - 9 >=> 10 + +julia> show_dynkin_diagram([(:A, 2), (:B, 3), (:C, 4), (:D, 5), (:E, 6), (:F, 4), (:G, 2)]) +1 - 2 + +3 - 4 >=> 5 + +6 - 7 - 8 <=< 9 + +. 13 + / +10 - 11 - 12 + \ + 14 + +15 - 17 - 18 - 19 - 20 + | + 16 + +21 - 22 >=> 23 - 24 + +25 <<< 26 +``` + +non-simple diagram with non-canonical labels + +```jldoctest show_ns_dynkin_diagram_with_labels.test +julia> using Oscar + +julia> show_dynkin_diagram([(:B, 5), (:B, 5)], [15,3,6,0,1000,23,8,22,65,1]) +15 - 3 - 6 - 0 >=> 1000 + +23 - 8 - 22 - 65 >=> 1 + +julia> show_dynkin_diagram([(:A, 2), (:B, 3), (:C, 4), (:D, 5), (:E, 6), (:F, 4), (:G, 2)], 2*(2+3+4+5+6+4+2):-2:2) +52 - 50 + +48 - 46 >=> 44 + +42 - 40 - 38 <=< 36 + +. 28 + / +34 - 32 - 30 + \ + 26 + +24 - 20 - 18 - 16 - 14 + | + 22 + +12 - 10 >=> 8 - 6 + +4 <<< 2 +``` + +Dynkin diagram from cartan matrix + +```jldoctest show_dynkin_diagram_cartan_matrix.test +julia> using Oscar + +julia> show_dynkin_diagram(cartan_matrix(:A, 3)) +1 - 2 - 3 + +julia> show_dynkin_diagram(cartan_matrix(:B, 4)) +1 - 2 - 3 >=> 4 + +julia> show_dynkin_diagram(cartan_matrix(:C, 5)) +1 - 2 - 3 - 4 <=< 5 + +julia> show_dynkin_diagram(cartan_matrix(:D, 6)) +. 5 + / +1 - 2 - 3 - 4 + \ + 6 + +julia> show_dynkin_diagram(cartan_matrix(:E, 7)) +1 - 3 - 4 - 5 - 6 - 7 + | + 2 + +julia> show_dynkin_diagram(cartan_matrix(:F, 4)) +1 - 2 >=> 3 - 4 + +julia> show_dynkin_diagram(cartan_matrix(:G, 2)) +1 <<< 2 + +julia> show_dynkin_diagram(ZZ[2 0 -1 0; 0 2 0 -2; -2 0 2 0; 0 -1 0 2]) +1 >=> 3 + +2 <=< 4 + +julia> show_dynkin_diagram(transpose(cartan_matrix(:F, 4))) +4 - 3 >=> 2 - 1 + +julia> show_dynkin_diagram(transpose(cartan_matrix(:G, 2))) +2 <<< 1 +``` + +Dynkin diagram from root system + +```jldoctest show_dynkin_diagram_cartan_matrix.test +julia> using Oscar + +julia> show_dynkin_diagram(root_system(:A, 3)) +1 - 2 - 3 + +julia> show_dynkin_diagram(root_system([(:B, 4)])) +1 - 2 - 3 >=> 4 + +julia> show_dynkin_diagram(root_system(cartan_matrix(:C, 5))) +1 - 2 - 3 - 4 <=< 5 + +julia> show_dynkin_diagram(root_system([(:D, 8), (:E, 6), (:F, 4), (:G, 2)])) +. 7 + / +1 - 2 - 3 - 4 - 5 - 6 + \ + 8 + +9 - 11 - 12 - 13 - 14 + | + 10 + +15 - 16 >=> 17 - 18 + +19 <<< 20 + +julia> show_dynkin_diagram(root_system(ZZ[2 0 -1 0; 0 2 0 -2; -2 0 2 0; 0 -1 0 2])) +1 >=> 3 + +2 <=< 4 + +julia> show_dynkin_diagram(root_system(transpose(cartan_matrix(:F, 4)))) +4 - 3 >=> 2 - 1 + +julia> show_dynkin_diagram(root_system(transpose(cartan_matrix(:G, 2)))) +2 <<< 1 +``` """ function dummy_placeholder end diff --git a/experimental/LieAlgebras/test/WeylGroup-test.jl b/experimental/LieAlgebras/test/WeylGroup-test.jl index de2a23738ec5..9ffa1f51dde6 100644 --- a/experimental/LieAlgebras/test/WeylGroup-test.jl +++ b/experimental/LieAlgebras/test/WeylGroup-test.jl @@ -55,6 +55,7 @@ include( ("B4", weyl_group(root_system(:B, 4))), ("D5", weyl_group(cartan_matrix(:D, 5))), ("F4+G2", weyl_group((:F, 4), (:G, 2))), + ("E6+C3", weyl_group([(:E, 6), (:C, 3)])), ("A_1^(1)", weyl_group(ZZ[2 -2; -2 2])), # TODO: replace with cartan_matrix(A_1^(1)), once functionality for affine type is added ( "complicated case 1", From fe3521c934451a19988f2aa211ba0981fea78708 Mon Sep 17 00:00:00 2001 From: Johannes Schmitt Date: Fri, 16 Feb 2024 16:08:10 +0100 Subject: [PATCH 07/29] Make `partitions` and `(semi)standard_tableaux` return iterators (#3365) ... the quick and dirty way to have a stable API --- .../EnumerativeCombinatorics/partitions.md | 2 +- experimental/LieAlgebras/src/Combinatorics.jl | 2 +- .../EnumerativeCombinatorics/partitions.jl | 84 +++++++++++-------- .../EnumerativeCombinatorics/tableaux.jl | 37 ++++---- .../EnumerativeCombinatorics/partitions.jl | 48 +++++------ .../EnumerativeCombinatorics/tableaux.jl | 16 ++-- 6 files changed, 99 insertions(+), 90 deletions(-) diff --git a/docs/src/Combinatorics/EnumerativeCombinatorics/partitions.md b/docs/src/Combinatorics/EnumerativeCombinatorics/partitions.md index 29be7f4e7e23..70a8b9d8404d 100644 --- a/docs/src/Combinatorics/EnumerativeCombinatorics/partitions.md +++ b/docs/src/Combinatorics/EnumerativeCombinatorics/partitions.md @@ -75,7 +75,7 @@ one can also handle more general types of restrictions. For example, there are precisely six ways for the second question in the exercise quoted above: ```jldoctest -julia> partitions(100, [1, 2, 5, 10, 20, 50], [2, 2, 2, 2, 2, 2]) +julia> collect(partitions(100, [1, 2, 5, 10, 20, 50], [2, 2, 2, 2, 2, 2])) 6-element Vector{Partition{Int64}}: [50, 50] [50, 20, 20, 10] diff --git a/experimental/LieAlgebras/src/Combinatorics.jl b/experimental/LieAlgebras/src/Combinatorics.jl index 6706f32adb54..ff40eba35bae 100644 --- a/experimental/LieAlgebras/src/Combinatorics.jl +++ b/experimental/LieAlgebras/src/Combinatorics.jl @@ -33,7 +33,7 @@ function multicombinations(n::Integer, k::Integer) return sort( map( reverse ∘ Vector, - reduce(vcat, partitions(i, k, 1, n) for i in 0:(k * n); init=Vector{Int}[]), + reduce(vcat, collect(partitions(i, k, 1, n)) for i in 0:(k * n); init=Vector{Int}[]), ), ) end diff --git a/src/Combinatorics/EnumerativeCombinatorics/partitions.jl b/src/Combinatorics/EnumerativeCombinatorics/partitions.jl index efe54ad568c3..7c0acfd5c238 100644 --- a/src/Combinatorics/EnumerativeCombinatorics/partitions.jl +++ b/src/Combinatorics/EnumerativeCombinatorics/partitions.jl @@ -151,8 +151,8 @@ end @doc raw""" partitions(n::IntegerUnion) -Return a list of all partitions of a non-negative integer `n`, produced in -lexicographically *descending* order. +Return an iterator over all partitions of a non-negative integer `n`, produced +in lexicographically *descending* order. Using a smaller integer type for `n` (e.g. `Int8`) may increase performance. The algorithm used is "Algorithm ZS1" by [ZS98](@cite). This algorithm is also @@ -160,7 +160,12 @@ discussed in [Knu11](@cite), Algorithm P (page 392). # Examples ```jldoctest -julia> partitions(4) +julia> p = partitions(4); + +julia> first(p) +[4] + +julia> collect(p) 5-element Vector{Partition{Int64}}: [4] [3, 1] @@ -168,7 +173,7 @@ julia> partitions(4) [2, 1, 1] [1, 1, 1, 1] -julia> partitions(Int8(4)) # using less memory +julia> collect(partitions(Int8(4))) # using less memory 5-element Vector{Partition{Int8}}: Int8[4] Int8[3, 1] @@ -184,9 +189,9 @@ function partitions(n::T) where T <: IntegerUnion # Some trivial cases if n == 0 - return Partition{T}[ partition(T[], check = false) ] + return (p for p in Partition{T}[ partition(T[], check = false) ]) elseif n == 1 - return Partition{T}[ partition(T[1], check = false) ] + return (p for p in Partition{T}[ partition(T[1], check = false) ]) end # Now, the algorithm starts @@ -222,7 +227,7 @@ function partitions(n::T) where T <: IntegerUnion end push!(P, partition(d[1:k], check = false)) end - return P + return (p for p in P) end ################################################################################ @@ -287,9 +292,10 @@ end partitions(m::IntegerUnion, n::IntegerUnion; only_distinct_parts::Bool = false) partitions(m::IntegerUnion, n::IntegerUnion, l1::IntegerUnion, l2::IntegerUnion; only_distinct_parts::Bool = false) -Return all partitions of a non-negative integer `m` into `n >= 0` parts. -Optionally, a lower bound `l1 >= 0` and an upper bound `l2` for the parts can be -supplied. In this case, the partitions are produced in *decreasing* order. +Return an iterator over all partitions of a non-negative integer `m` into +`n >= 0` parts. Optionally, a lower bound `l1 >= 0` and an upper bound `l2` for +the parts can be supplied. In this case, the partitions are produced in +*decreasing* order. There are two choices for the parameter `only_distinct_parts`: * `false`: no further restriction (*default*); @@ -300,7 +306,7 @@ The implemented algorithm is "parta" in [RJ76](@cite). # Examples All partitions of 7 into 3 parts: ```jldoctest -julia> partitions(7, 3) +julia> collect(partitions(7, 3)) 4-element Vector{Partition{Int64}}: [5, 1, 1] [4, 2, 1] @@ -309,7 +315,7 @@ julia> partitions(7, 3) ``` All partitions of 7 into 3 parts where all parts are between 1 and 4: ```jldoctest -julia> partitions(7, 3, 1, 4) +julia> collect(partitions(7, 3, 1, 4)) 3-element Vector{Partition{Int64}}: [4, 2, 1] [3, 3, 1] @@ -317,7 +323,7 @@ julia> partitions(7, 3, 1, 4) ``` Same as above but requiring all parts to be distinct: ```jldoctest -julia> partitions(7, 3, 1, 4; only_distinct_parts = true) +julia> collect(partitions(7, 3, 1, 4; only_distinct_parts = true)) 1-element Vector{Partition{Int64}}: [4, 2, 1] ``` @@ -339,15 +345,15 @@ function partitions(m::T, n::IntegerUnion, l1::IntegerUnion, l2::IntegerUnion; o # Some trivial cases if m == 0 && n == 0 - return Partition{T}[ partition(T[], check = false) ] + return (p for p in Partition{T}[ partition(T[], check = false) ]) end if n == 0 || n > m - return Partition{T}[] + return (p for p in Partition{T}[]) end if l2 < l1 - return Partition{T}[] + return (p for p in Partition{T}[]) end # If l1 == 0 the algorithm parta will actually create lists containing the @@ -411,7 +417,7 @@ function partitions(m::T, n::IntegerUnion, l1::IntegerUnion, l2::IntegerUnion; o end end - return P + return (p for p in P) end function partitions(m::T, n::IntegerUnion; only_distinct_parts::Bool = false) where T <: IntegerUnion @@ -420,14 +426,14 @@ function partitions(m::T, n::IntegerUnion; only_distinct_parts::Bool = false) wh # Special cases if m == n - return [ partition(T[ 1 for i in 1:m], check = false) ] + return (p for p in [ partition(T[ 1 for i in 1:m], check = false) ]) elseif m < n || n == 0 - return Partition{T}[] + return (p for p in Partition{T}[]) elseif n == 1 - return [ partition(T[m], check = false) ] + return (p for p in [ partition(T[m], check = false) ]) end - return partitions(m, n, 1, m; only_distinct_parts = only_distinct_parts) + return (p for p in partitions(m, n, 1, m; only_distinct_parts = only_distinct_parts)) end function partitions(m::T, n::IntegerUnion, v::Vector{T}, mu::Vector{S}) where {T <: IntegerUnion, S <: IntegerUnion} @@ -451,15 +457,17 @@ function partitions(m::T, n::IntegerUnion, v::Vector{T}, mu::Vector{S}) where {T # Special cases if n == 0 + # TODO: I don't understand this distinction here + # (it also makes the function tabe instable) if m == 0 - return [ Partition{T}[] ] + return (p for p in [ Partition{T}[] ]) else - return Partition{T}[] + return (p for p in Partition{T}[]) end end if isempty(mu) - return Partition{T}[] + return (p for p in Partition{T}[]) end #This will be the list of all partitions found. @@ -523,7 +531,7 @@ function partitions(m::T, n::IntegerUnion, v::Vector{T}, mu::Vector{S}) where {T # This is a necessary condition for existence of a partition if m < 0 || m > n * (lr - ll) - return P #goto b3 + return (p for p in P) #goto b3 end # The following is a condition for when only a single partition @@ -534,7 +542,7 @@ function partitions(m::T, n::IntegerUnion, v::Vector{T}, mu::Vector{S}) where {T # Noticed on Mar 23, 2023. if m == 0 && x[1] != 0 push!(P, partition(copy(x), check = false)) - return P + return (p for p in P) end # Now, the actual algorithm starts @@ -625,7 +633,7 @@ function partitions(m::T, n::IntegerUnion, v::Vector{T}, mu::Vector{S}) where {T end #if gotob2 end #while - return P + return (p for p in P) end function partitions(m::T, v::Vector{T}, mu::Vector{S}) where {T <: IntegerUnion, S <: IntegerUnion} @@ -645,11 +653,12 @@ function partitions(m::T, v::Vector{T}, mu::Vector{S}) where {T <: IntegerUnion, res = Partition{T}[] if isempty(v) - return res + return (p for p in res) end if m == 0 - return [ Partition{T}[] ] + # TODO: I don't understand this return (and it is type instable) + return (p for p in [ Partition{T}[] ]) end # We will loop over the number of parts. @@ -680,7 +689,7 @@ function partitions(m::T, v::Vector{T}, mu::Vector{S}) where {T <: IntegerUnion, append!(res, partitions(m, n, v, mu)) end - return res + return (p for p in res) end @doc raw""" @@ -688,8 +697,8 @@ end partitions(m::T, v::Vector{T}, mu::Vector{<:IntegerUnion}) where T <: IntegerUnion partitions(m::T, n::IntegerUnion, v::Vector{T}, mu::Vector{<:IntegerUnion}) where T <: IntegerUnion -Return all partitions of a non-negative integer `m` where each part is an element -in the vector `v` of positive integers. +Return an iterator over all partitions of a non-negative integer `m` where each +part is an element in the vector `v` of positive integers. It is assumed that the entries in `v` are strictly increasing. If the optional vector `mu` is supplied, then each `v[i]` occurs a maximum of @@ -710,7 +719,7 @@ julia> length(partitions(100, [1, 2, 5, 10, 20, 50])) All partitions of 100 where the parts are from {1, 2, 5, 10, 20, 50} and each part is allowed to occur at most twice: ```jldoctest -julia> partitions(100, [1, 2, 5, 10, 20, 50], [2, 2, 2, 2, 2, 2]) +julia> collect(partitions(100, [1, 2, 5, 10, 20, 50], [2, 2, 2, 2, 2, 2])) 6-element Vector{Partition{Int64}}: [50, 50] [50, 20, 20, 10] @@ -722,7 +731,7 @@ julia> partitions(100, [1, 2, 5, 10, 20, 50], [2, 2, 2, 2, 2, 2]) The partitions of 100 into seven parts, where the parts are required to be elements from {1, 2, 5, 10, 20, 50} and each part is allowed to occur at most twice. ```jldoctest -julia> partitions(100, 7, [1, 2, 5, 10, 20, 50], [2, 2, 2, 2, 2, 2]) +julia> collect(partitions(100, 7, [1, 2, 5, 10, 20, 50], [2, 2, 2, 2, 2, 2])) 1-element Vector{Partition{Int64}}: [50, 20, 20, 5, 2, 2, 1] ``` @@ -735,11 +744,12 @@ function partitions(m::T, v::Vector{T}) where T <: IntegerUnion res = Partition{T}[] if isempty(v) - return res + return (p for p in res) end if m == 0 - return [ Partition{T}[] ] + # TODO: I don't understand this return (and it is type instable) + return (p for p in [ Partition{T}[] ]) end # We will loop over the number of parts. @@ -755,7 +765,7 @@ function partitions(m::T, v::Vector{T}) where T <: IntegerUnion append!(res, partitions(m, n, v, mu)) end - return res + return (p for p in res) end ################################################################################ diff --git a/src/Combinatorics/EnumerativeCombinatorics/tableaux.jl b/src/Combinatorics/EnumerativeCombinatorics/tableaux.jl index 74502cc37881..65af5b0e59e1 100644 --- a/src/Combinatorics/EnumerativeCombinatorics/tableaux.jl +++ b/src/Combinatorics/EnumerativeCombinatorics/tableaux.jl @@ -342,8 +342,8 @@ end semistandard_tableaux(shape::Partition{T}, max_val::T = sum(shape)) where T <: Integer semistandard_tableaux(shape::Vector{T}, max_val::T = sum(shape)) where T <: Integer -Return all semistandard Young tableaux of given shape `shape` and filling elements -bounded by `max_val`. +Return an iterator over all semistandard Young tableaux of given shape `shape` +and filling elements bounded by `max_val`. By default, `max_val` is equal to the sum of the shape partition (the number of boxes in the Young diagram). @@ -355,10 +355,10 @@ function semistandard_tableaux(shape::Partition{T}, max_val::T = sum(shape)) whe SST = Vector{YoungTableau{T}}() len = length(shape) if max_val < len - return SST + return (t for t in SST) elseif len == 0 push!(SST, young_tableau(Vector{T}[], check = false)) - return SST + return (t for t in SST) end tab = [Array{T}(fill(i, shape[i])) for i = 1:len] m = len @@ -377,7 +377,7 @@ function semistandard_tableaux(shape::Partition{T}, max_val::T = sum(shape)) whe m -= 1 n = shape[m] else - return SST + return (t for t in SST) end end @@ -418,14 +418,14 @@ end @doc raw""" semistandard_tableaux(box_num::T, max_val::T = box_num) where T <: Integer -Return all semistandard Young tableaux consisting of `box_num` boxes and -filling elements bounded by `max_val`. +Return an iterator over all semistandard Young tableaux consisting of `box_num` +boxes and filling elements bounded by `max_val`. """ function semistandard_tableaux(box_num::T, max_val::T = box_num) where T <: Integer @req box_num >= 0 "box_num >= 0 required" SST = Vector{YoungTableau{T}}() if max_val <= 0 - return SST + return (t for t in SST) end shapes = partitions(box_num) @@ -435,16 +435,15 @@ function semistandard_tableaux(box_num::T, max_val::T = box_num) where T <: Inte end end - return SST + return (t for t in SST) end - @doc raw""" semistandard_tableaux(s::Partition{T}, weight::Vector{T}) where T <: Integer semistandard_tableaux(s::Vector{T}, weight::Vector{T}) where T <: Integer -Return all semistandard Young tableaux with shape `s` and given weight. This -requires that `sum(s) = sum(weight)`. +Return an iterator over all semistandard Young tableaux with shape `s` and given +weight. This requires that `sum(s) = sum(weight)`. """ function semistandard_tableaux(s::Vector{T}, weight::Vector{T}) where T <: Integer n_max = sum(s) @@ -453,7 +452,7 @@ function semistandard_tableaux(s::Vector{T}, weight::Vector{T}) where T <: Integ tabs = Vector{YoungTableau}() if isempty(s) push!(tabs, young_tableau(Vector{Int}[], check = false)) - return tabs + return (t for t in tabs) end ls = length(s) @@ -540,7 +539,7 @@ function semistandard_tableaux(s::Vector{T}, weight::Vector{T}) where T <: Integ end #rec_sst!() rec_sst!(1) - return tabs + return (t for t in tabs) end function semistandard_tableaux(s::Partition{T}, weight::Partition{T}) where T <: Integer @@ -620,13 +619,13 @@ end standard_tableaux(s::Partition) standard_tableaux(s::Vector{Integer}) -Return all standard Young tableaux of a given shape `s`. +Return an iterator over all standard Young tableaux of a given shape `s`. """ function standard_tableaux(s::Partition) tabs = Vector{YoungTableau}() if isempty(s) push!(tabs, young_tableau(Vector{Int}[], check = false)) - return tabs + return (t for t in tabs) end n_max = sum(s) ls = length(s) @@ -669,7 +668,7 @@ function standard_tableaux(s::Partition) end end - return tabs + return (t for t in tabs) end function standard_tableaux(s::Vector{T}) where T <: Integer @@ -679,7 +678,7 @@ end @doc raw""" standard_tableaux(n::Integer) -Return all standard Young tableaux with `n` boxes. +Return an iterator over all standard Young tableaux with `n` boxes. """ function standard_tableaux(n::Integer) @req n >= 0 "n >= 0 required" @@ -687,7 +686,7 @@ function standard_tableaux(n::Integer) for s in partitions(n) append!(ST, standard_tableaux(s)) end - return ST + return (t for t in ST) end ################################################################################ diff --git a/test/Combinatorics/EnumerativeCombinatorics/partitions.jl b/test/Combinatorics/EnumerativeCombinatorics/partitions.jl index 8ab5a370d086..a0424d398558 100644 --- a/test/Combinatorics/EnumerativeCombinatorics/partitions.jl +++ b/test/Combinatorics/EnumerativeCombinatorics/partitions.jl @@ -32,7 +32,7 @@ # partitions(n) ############################################################################ for n = 0:20 - P = partitions(n) + P = collect(partitions(n)) # Check that the number of partitions is correct # Note that number_of_partitions(n) is computed independently of partitions(n) @@ -76,10 +76,10 @@ ############################################################################ for n in 0:20 for k = 0:n+1 - P = partitions(n,k) + P = collect(partitions(n,k)) # Create the same by filtering all partitions - Q = partitions(n) + Q = collect(partitions(n)) filter!( Q->length(Q) == k, Q) # Check that P and Q coincide (up to reordering) @@ -98,10 +98,10 @@ for k = 0:n+1 for l1 = 0:n for l2 = l1:n - P = partitions(n,k,l1,l2) + P = collect(partitions(n,k,l1,l2)) # Create the same by filtering all partitions - Q = partitions(n,k) + Q = collect(partitions(n,k)) filter!( Q->all(>=(l1),Q), Q) filter!( Q->all(<=(l2),Q), Q) @@ -120,10 +120,10 @@ for k = 0:n+1 for l1 = 0:n for l2 = l1:n - P = partitions(n,k,l1,l2; only_distinct_parts=true) + P = collect(partitions(n, k, l1, l2; only_distinct_parts=true)) # Create the same by filtering all partitions - Q = partitions(n,k, l1, l2) + Q = collect(partitions(n, k, l1, l2)) filter!( Q->Q==unique(Q), Q ) # Check that P and Q coincide (up to reordering) @@ -147,40 +147,40 @@ @test_throws ArgumentError partitions(6,3,[0,2,1],[1,2,3]) #v > 0 # Issues from https://github.com/oscar-system/Oscar.jl/issues/2043 - @test length(partitions(17, 3, [1,4], [1,4])) == 0 - @test partitions(17, 5, [1,4], [1,4]) == [ partition(4,4,4,4,1) ] - @test length(partitions(17,6,[1,2], [1,7])) == 0 - @test length(partitions(20,5,[1,2,3],[1,3,6])) == 0 + @test length(collect(partitions(17, 3, [1, 4], [1,4]))) == 0 + @test collect(partitions(17, 5, [1, 4], [1, 4])) == [ partition(4, 4, 4, 4, 1) ] + @test length(collect(partitions(17, 6, [1, 2], [1, 7]))) == 0 + @test length(collect(partitions(20, 5, [1, 2, 3], [1, 3, 6]))) == 0 # Issues UT found - @test length(partitions(1,1,[1],[1])) == 1 - @test length(partitions(100, 7, [1,2,5,10,20,50], [2,2,2,2,2,2])) == 1 + @test length(collect(partitions(1, 1, [1], [1]))) == 1 + @test length(collect(partitions(100, 7, [1, 2, 5, 10, 20, 50], [2, 2, 2, 2, 2, 2]))) == 1 # Special cases - for n=0:20 - for k=0:n+1 - P = partitions(n,k, [i for i in 1:n], [n for i in 1:n]) - Q = partitions(n,k) + for n in 0:20 + for k in 0:n + 1 + P = collect(partitions(n, k, [i for i in 1:n], [n for i in 1:n])) + Q = collect(partitions(n, k)) @test length(P) == length(Q) @test Set(P) == Set(Q) - P = partitions(n,k, [i for i in 1:n], [1 for i in 1:n]) - Q = partitions(n,k,1,n;only_distinct_parts=true) + P = collect(partitions(n, k, [i for i in 1:n], [1 for i in 1:n])) + Q = collect(partitions(n, k, 1, n; only_distinct_parts=true)) @test length(P) == length(Q) @test Set(P) == Set(Q) end end # From https://www.maa.org/frank-morgans-math-chat-293-ways-to-make-change-for-a-dollar - @test length(partitions(100, [1,5,10,25,50])) == 292 - @test length(partitions(200, [1,5,10,25,50,100])) == 2728 + @test length(collect(partitions(100, [1, 5, 10, 25, 50]))) == 292 + @test length(collect(partitions(200, [1, 5, 10, 25, 50, 100]))) == 2728 # From Knu11, Exercise 11 on page 408 - @test length(partitions(100, [1,2,5,10,20,50], [2,2,2,2,2,2])) == 6 - @test length(partitions(100, [1,2,5,10,20,50])) == 4562 + @test length(collect(partitions(100, [1, 2, 5, 10, 20, 50], [2, 2, 2, 2, 2, 2]))) == 6 + @test length(collect(partitions(100, [1, 2, 5, 10, 20, 50]))) == 4562 # From https://oeis.org/A000008 - @test [ length(partitions(n, [1,2,5,10])) for n in 0:60 ] == + @test [ length(collect(partitions(n, [1,2,5,10]))) for n in 0:60 ] == [ 1, 1, 2, 2, 3, 4, 5, 6, 7, 8, 11, 12, 15, 16, 19, 22, 25, 28, 31, 34, 40, 43, 49, 52, 58, 64, 70, 76, 82, 88, 98, 104, 114, 120, 130, 140, 150, 160, 170, 180, 195, 205, 220, 230, 245, 260, 275, 290, 305, 320, diff --git a/test/Combinatorics/EnumerativeCombinatorics/tableaux.jl b/test/Combinatorics/EnumerativeCombinatorics/tableaux.jl index 4e8cacce3fd5..aa87c5fc9ba3 100644 --- a/test/Combinatorics/EnumerativeCombinatorics/tableaux.jl +++ b/test/Combinatorics/EnumerativeCombinatorics/tableaux.jl @@ -32,7 +32,7 @@ # semistandard_tableaux(shape::Array{T,1}, max_val=sum(shape)::Integer) shapes = [[3,2,1],[3,3,1],[2,2,2]] for s in shapes - SST = semistandard_tableaux(s) + SST = collect(semistandard_tableaux(s)) #check that all tableaux are distinct @test SST == unique(SST) @@ -48,7 +48,7 @@ weights = [[1,1,1,1,1,1,1,1,1,1],[3,0,2,0,0,5],[4,3,2,1]] for s in shapes for w in weights - SST = semistandard_tableaux(s,w) + SST = collect(semistandard_tableaux(s, w)) #check that all tableaux are distinct @test SST == unique(SST) #check that all tableaux are semistandard_tableaux @@ -65,14 +65,14 @@ end end end - @test semistandard_tableaux(Int[], Int[]) == [young_tableau(Array{Int,1}[])] + @test collect(semistandard_tableaux(Int[], Int[])) == [young_tableau(Array{Int,1}[])] #semistandard_tableaux(box_num, max_val) BoxNum = 0:5 MaxVal = 1:6 for box_num in BoxNum for max_val in MaxVal - SST = semistandard_tableaux(box_num, max_val) + SST = collect(semistandard_tableaux(box_num, max_val)) #check that all tableaux are distinct @test SST == unique(SST) #check that all tableaux are semistandard_tableaux @@ -96,7 +96,7 @@ # standard_tableaux(s::Partition) for i = 1:10 for s in partitions(i) - ST = standard_tableaux(s) + ST = collect(standard_tableaux(s)) #check that all tableaux are distinct @test ST == unique(ST) #check that all tableaux are standard_tableaux @@ -107,12 +107,12 @@ @test length(ST) == number_of_standard_tableaux(s) end end - @test standard_tableaux(partition(Int[])) == [young_tableau(Array{Int,1}[])] - @test standard_tableaux([3,2,1]) == standard_tableaux(partition([3,2,1])) + @test collect(standard_tableaux(partition(Int[]))) == [young_tableau(Array{Int,1}[])] + @test collect(standard_tableaux([3, 2, 1])) == collect(standard_tableaux(partition([3, 2, 1]))) # standard_tableaux(n::Integer) for n = 0:10 - ST = standard_tableaux(n) + ST = collect(standard_tableaux(n)) #check that all tableaux are distinct @test ST == unique(ST) #check that all tableaux are standard_tableaux From 09f72f12944df21787856b95cf9ed935d62628fc Mon Sep 17 00:00:00 2001 From: HechtiDerLachs Date: Fri, 16 Feb 2024 13:53:05 +0100 Subject: [PATCH 08/29] Bugfix from running book code run. (cherry picked from commit d0aad4ef183b6b1d5d96e0de65d6a7a30fa0f800) from PR #3298 --- src/Modules/UngradedModules/FreeResolutions.jl | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/Modules/UngradedModules/FreeResolutions.jl b/src/Modules/UngradedModules/FreeResolutions.jl index e593d702c654..17f0a2530951 100644 --- a/src/Modules/UngradedModules/FreeResolutions.jl +++ b/src/Modules/UngradedModules/FreeResolutions.jl @@ -519,7 +519,7 @@ function free_resolution(Q::MPolyQuoRing; q = quotient_ring_as_module(Q) n = AbstractAlgebra.get_name(Q) if n !== nothing - AbstractAlgebra.set_name!(S, n) + AbstractAlgebra.set_name!(q, n) end return free_resolution(q, length = length, algorithm = algorithm) end From edbf62a93aa405f57fcd67f5d5f20013df5c3fdd Mon Sep 17 00:00:00 2001 From: Johannes Schmitt Date: Fri, 16 Feb 2024 13:37:41 +0100 Subject: [PATCH 09/29] Remove deprecated functions (#3366) * Remove deprecated use of `Frac` * Remove deprecated use of `chi` * Remove deprecated use of `MPolyElem` --- .../src/LiteratureModels/constructors.jl | 4 ++-- .../FTheoryTools/src/TateModels/attributes.jl | 2 +- .../src/TateModels/constructors.jl | 2 +- .../src/WeierstrassModels/constructors.jl | 2 +- .../src/IntersectionTheory.jl | 2 +- experimental/ModStd/ModStdQt.jl | 14 +++++++------- experimental/Schemes/FunctionFields.jl | 6 +++--- experimental/Schemes/Types.jl | 4 ++-- experimental/Schemes/elliptic_surface.jl | 12 ++++++------ .../Schemes/SpecOpen/Morphisms/Constructors.jl | 4 ++-- .../Schemes/SpecOpen/Rings/Constructors.jl | 18 +++++++++--------- src/InvariantTheory/types.jl | 2 +- src/Rings/FunctionField.jl | 10 +++++----- src/Rings/MPolyQuo.jl | 2 +- src/Rings/localization_interface.jl | 4 ++-- src/Rings/mpoly-graded.jl | 4 ++-- src/Rings/mpoly-ideals.jl | 2 +- src/Rings/mpoly-local.jl | 10 +++++----- src/Rings/mpoly-localizations.jl | 6 +++--- src/Rings/mpolyquo-localizations.jl | 8 ++++---- 20 files changed, 59 insertions(+), 59 deletions(-) diff --git a/experimental/FTheoryTools/src/LiteratureModels/constructors.jl b/experimental/FTheoryTools/src/LiteratureModels/constructors.jl index 00d46b9344d8..87646075844e 100644 --- a/experimental/FTheoryTools/src/LiteratureModels/constructors.jl +++ b/experimental/FTheoryTools/src/LiteratureModels/constructors.jl @@ -297,7 +297,7 @@ function _construct_literature_model_over_concrete_base(model_dict::Dict{String, explicit_model_sections["a6"] = map(a6) # Find defining_section_parametrization - defining_section_parametrization = Dict{String, MPolyElem}() + defining_section_parametrization = Dict{String, MPolyRingElem}() if !("a1" in vars) || (a1 != eval_poly("a1", parent(a1))) defining_section_parametrization["a1"] = a1 end @@ -328,7 +328,7 @@ function _construct_literature_model_over_concrete_base(model_dict::Dict{String, explicit_model_sections["g"] = map(g) # Find defining_section_parametrization - defining_section_parametrization = Dict{String, MPolyElem}() + defining_section_parametrization = Dict{String, MPolyRingElem}() if !("f" in vars) || (f != eval_poly("f", parent(f))) defining_section_parametrization["f"] = f end diff --git a/experimental/FTheoryTools/src/TateModels/attributes.jl b/experimental/FTheoryTools/src/TateModels/attributes.jl index aa56c4712a40..ba8d67c22771 100644 --- a/experimental/FTheoryTools/src/TateModels/attributes.jl +++ b/experimental/FTheoryTools/src/TateModels/attributes.jl @@ -202,7 +202,7 @@ Weierstrass model over a not fully specified base -- SU(5)xU(1) restricted Tate # Compute parametrization of Weierstrass sections parametrization = defining_section_parametrization(t) param_keys = collect(keys(parametrization)) - new_defining_section_parametrization = Dict{String, MPolyElem}() + new_defining_section_parametrization = Dict{String, MPolyRingElem}() if length(param_keys) > 0 # Find ring to evaluate polynomials into R = parent(parametrization[param_keys[1]]) diff --git a/experimental/FTheoryTools/src/TateModels/constructors.jl b/experimental/FTheoryTools/src/TateModels/constructors.jl index 128123c114f9..7c46ae037f2b 100644 --- a/experimental/FTheoryTools/src/TateModels/constructors.jl +++ b/experimental/FTheoryTools/src/TateModels/constructors.jl @@ -168,7 +168,7 @@ function global_tate_model(auxiliary_base_ring::MPolyRing, auxiliary_base_gradin end # Compute defining_section_parametrization - defining_section_parametrization = Dict{String, MPolyElem}() + defining_section_parametrization = Dict{String, MPolyRingElem}() vars_S = [string(k) for k in gens(S)] if !("a1" in vars_S) || (a1 != eval_poly("a1", parent(a1))) defining_section_parametrization["a1"] = a1 diff --git a/experimental/FTheoryTools/src/WeierstrassModels/constructors.jl b/experimental/FTheoryTools/src/WeierstrassModels/constructors.jl index ee0867bad7f6..efa9d92f81c5 100644 --- a/experimental/FTheoryTools/src/WeierstrassModels/constructors.jl +++ b/experimental/FTheoryTools/src/WeierstrassModels/constructors.jl @@ -148,7 +148,7 @@ function weierstrass_model(auxiliary_base_ring::MPolyRing, auxiliary_base_gradin end # Compute defining_section_parametrization - defining_section_parametrization = Dict{String, MPolyElem}() + defining_section_parametrization = Dict{String, MPolyRingElem}() vars_S = [string(k) for k in gens(S)] if !("f" in vars_S) || (f != eval_poly("f", parent(f))) defining_section_parametrization["f"] = f diff --git a/experimental/IntersectionTheory/src/IntersectionTheory.jl b/experimental/IntersectionTheory/src/IntersectionTheory.jl index 3627885cd3f7..562acf03edf3 100644 --- a/experimental/IntersectionTheory/src/IntersectionTheory.jl +++ b/experimental/IntersectionTheory/src/IntersectionTheory.jl @@ -3,7 +3,7 @@ using ..Oscar import Base: +, -, *, ^, ==, div, zero, one, parent import ..Oscar: AffAlgHom, Ring, MPolyDecRingElem, symmetric_power, exterior_power, pullback, canonical_bundle, graph, euler_characteristic, pullback -import ..Oscar: basis, betti, chi, codomain, degree, det, dim, domain, dual, gens, hilbert_polynomial, hom, integral, rank, signature +import ..Oscar: basis, betti, codomain, degree, det, dim, domain, dual, gens, hilbert_polynomial, hom, integral, rank, signature import ..Oscar.AbstractAlgebra: combinations import ..Oscar.AbstractAlgebra.Generic: FunctionalMap diff --git a/experimental/ModStd/ModStdQt.jl b/experimental/ModStd/ModStdQt.jl index d5e71977c2fe..983c9eb0f229 100644 --- a/experimental/ModStd/ModStdQt.jl +++ b/experimental/ModStd/ModStdQt.jl @@ -161,7 +161,7 @@ end mutable struct Vals{T} v::Vector{Vector{T}} nd::Vector{Tuple{<:PolyRingElem{T}, <:PolyRingElem{T}}} - G::RingElem # can be Generic.Frac{<:MPolyRingElem{T}} or PolyRingElem + G::RingElem # can be Generic.FracFieldElem{<:MPolyRingElem{T}} or PolyRingElem function Vals(v::Vector{Vector{S}}) where {S} r = new{S}() r.v = v @@ -275,11 +275,11 @@ function Base.setindex!(v::Vals{T}, c::T, i::Int, j::Int) where {T} v.v[i][j] = c end -function exp_groebner_basis(I::Oscar.MPolyIdeal{<:Generic.MPoly{<:Generic.Frac{QQMPolyRingElem}}}; ord::Symbol = :degrevlex, complete_reduction::Bool = true) +function exp_groebner_basis(I::Oscar.MPolyIdeal{<:Generic.MPoly{<:Generic.FracFieldElem{QQMPolyRingElem}}}; ord::Symbol = :degrevlex, complete_reduction::Bool = true) Oscar.exp_groebner_assure(I, ord, complete_reduction = complete_reduction) end -function exp_groebner_assure(I::Oscar.MPolyIdeal{<:Generic.MPoly{<:Generic.Frac{QQMPolyRingElem}}}, ord::Symbol = :degrevlex; complete_reduction::Bool = true) +function exp_groebner_assure(I::Oscar.MPolyIdeal{<:Generic.MPoly{<:Generic.FracFieldElem{QQMPolyRingElem}}}, ord::Symbol = :degrevlex; complete_reduction::Bool = true) T = QQFieldElem if ord == :degrevlex && isdefined(I, :gb) return I.gb @@ -559,7 +559,7 @@ function _cmp(f::MPolyRingElem, g::MPolyRingElem) end @doc raw""" - factor_absolute(f::MPolyRingElem{Generic.Frac{QQMPolyRingElem}}) + factor_absolute(f::MPolyRingElem{Generic.FracFieldElem{QQMPolyRingElem}}) For an irreducible polynomial in Q[A][X], perform an absolute factorisation, ie. a factorisation in K[X] where K is the @@ -599,7 +599,7 @@ Multivariate polynomial ring in 2 variables X[1], X[2] over residue field of univariate polynomial ring modulo t^2 + a[1] ``` """ -function Oscar.factor_absolute(f::MPolyRingElem{Generic.Frac{QQMPolyRingElem}}) +function Oscar.factor_absolute(f::MPolyRingElem{Generic.FracFieldElem{QQMPolyRingElem}}) Qtx = parent(f) # Q[t1,t2][x1,x2] Qt = base_ring(base_ring(Qtx)) # Q[t1,t2] Rx, x = polynomial_ring(QQ, ngens(Qtx) + ngens(Qt)) # Q[x1,x2,t1,t2] @@ -639,7 +639,7 @@ function Oscar.factor_absolute(f::MPolyRingElem{Generic.Frac{QQMPolyRingElem}}) return an end -function Oscar.is_absolutely_irreducible(f::MPolyRingElem{Generic.Frac{QQMPolyRingElem}}) +function Oscar.is_absolutely_irreducible(f::MPolyRingElem{Generic.FracFieldElem{QQMPolyRingElem}}) lf = factor_absolute(f) @assert length(lf) > 1 return length(lf) == 2 && lf[2][end] == 1 && is_one(lf[2][2]) @@ -852,7 +852,7 @@ function my_reduce(A, d) end function Oscar.lift(f::PolyRingElem, g::PolyRingElem, a::AbsSimpleNumFieldElem, b::AbsSimpleNumFieldElem, V::Vector{QQFieldElem}) - S = base_ring(f) # should be a Frac{MPoly} + S = base_ring(f) # should be a FracFieldElem{MPoly} R = base_ring(S) d_a = reduce(lcm, map(denominator, coefficients(f))) diff --git a/experimental/Schemes/FunctionFields.jl b/experimental/Schemes/FunctionFields.jl index 30917adbb133..4010e36d1171 100644 --- a/experimental/Schemes/FunctionFields.jl +++ b/experimental/Schemes/FunctionFields.jl @@ -290,7 +290,7 @@ function move_representative( return h_generic end -function (KK::VarietyFunctionField)(h::AbstractAlgebra.Generic.Frac; check::Bool=true) +function (KK::VarietyFunctionField)(h::AbstractAlgebra.Generic.FracFieldElem; check::Bool=true) return KK(numerator(h), denominator(h), check=check) end @@ -451,7 +451,7 @@ inv(f::VarietyFunctionFieldElem) = parent(f)(denominator(representative(f)), ) AbstractAlgebra.promote_rule(::Type{T}, ::Type{S}) where {T<:VarietyFunctionFieldElem, S<:Integer} = T -AbstractAlgebra.promote_rule(::Type{T}, ::Type{S}) where {T<:VarietyFunctionFieldElem, S<:AbstractAlgebra.Generic.Frac} = T +AbstractAlgebra.promote_rule(::Type{T}, ::Type{S}) where {T<:VarietyFunctionFieldElem, S<:AbstractAlgebra.Generic.FracFieldElem} = T AbstractAlgebra.promote_rule(::Type{T}, ::Type{T}) where {T<:VarietyFunctionFieldElem} = T @@ -459,7 +459,7 @@ function AbstractAlgebra.promote_rule(::Type{FFET}, ::Type{U}) where {T, FFET<:V promote_rule(T, U) == T ? FFET : Union{} end -function AbstractAlgebra.promote_rule(::Type{FFET}, ::Type{U}) where {T, FFET<:VarietyFunctionFieldElem{AbstractAlgebra.Generic.Frac{T}}, U<:RingElement} +function AbstractAlgebra.promote_rule(::Type{FFET}, ::Type{U}) where {T, FFET<:VarietyFunctionFieldElem{AbstractAlgebra.Generic.FracFieldElem{T}}, U<:RingElement} promote_rule(T, U) == T ? FFET : Union{} end diff --git a/experimental/Schemes/Types.jl b/experimental/Schemes/Types.jl index 18070be54a64..632284775f9d 100644 --- a/experimental/Schemes/Types.jl +++ b/experimental/Schemes/Types.jl @@ -38,7 +38,7 @@ end ######################################################################## # Elements of VarietyFunctionFields # ######################################################################## -mutable struct VarietyFunctionFieldElem{FracType<:AbstractAlgebra.Generic.Frac, +mutable struct VarietyFunctionFieldElem{FracType<:AbstractAlgebra.Generic.FracFieldElem, ParentType<:VarietyFunctionField } KK::ParentType @@ -46,7 +46,7 @@ mutable struct VarietyFunctionFieldElem{FracType<:AbstractAlgebra.Generic.Frac, function VarietyFunctionFieldElem( KK::VarietyFunctionField, - f::AbstractAlgebra.Generic.Frac; + f::AbstractAlgebra.Generic.FracFieldElem; check::Bool=true ) representative_field(KK) == parent(f) || error("element does not have the correct parent") diff --git a/experimental/Schemes/elliptic_surface.jl b/experimental/Schemes/elliptic_surface.jl index fe2c64a2444b..c03058036eb2 100644 --- a/experimental/Schemes/elliptic_surface.jl +++ b/experimental/Schemes/elliptic_surface.jl @@ -96,7 +96,7 @@ Elliptic surface with generic fiber -x^3 + y^2 - t^7 + 2*t^6 - t^5 """ function elliptic_surface(generic_fiber::EllipticCurve{BaseField}, euler_characteristic::Int, mwl_basis::Vector{<:EllipticCurvePoint}=EllipticCurvePoint[]) where { - BaseField <: Frac{<:PolyRingElem{<:FieldElem}}} + BaseField <: FracFieldElem{<:PolyRingElem{<:FieldElem}}} @req all(parent(i)==generic_fiber for i in mwl_basis) "not a vector of points on $(generic_fiber)" S = EllipticSurface(generic_fiber, euler_characteristic, mwl_basis) return S @@ -1154,7 +1154,7 @@ function two_neighbor_step(X::EllipticSurface, F::Vector{QQFieldElem}) # Make sure the coefficient of y² is one (or a square) so that # completing the square works. - c = my_const(coeff(eqn1, [x2, y2], [0, 2]))::AbstractAlgebra.Generic.Frac + c = my_const(coeff(eqn1, [x2, y2], [0, 2]))::AbstractAlgebra.Generic.FracFieldElem eqn1 = inv(unit(factor(c)))*eqn1 eqn2, phi2 = _normalize_hyperelliptic_curve(eqn1) @@ -1166,7 +1166,7 @@ function two_neighbor_step(X::EllipticSurface, F::Vector{QQFieldElem}) # Make sure the coefficient of y² is one (or a square) so that # completing the square works. - c = my_const(coeff(eqn1, [x2, y2], [0, 2]))::AbstractAlgebra.Generic.Frac + c = my_const(coeff(eqn1, [x2, y2], [0, 2]))::AbstractAlgebra.Generic.FracFieldElem eqn1 = inv(unit(factor(c)))*eqn1 eqn2, phi2 = _normalize_hyperelliptic_curve(eqn1) @@ -1593,11 +1593,11 @@ function _is_in_weierstrass_form(f::MPolyRingElem) return f == (-(y^2 + a1*x*y + a3*y) + (x^3 + a2*x^2 + a4*x + a6)) end -function evaluate(f::AbstractAlgebra.Generic.Frac{<:MPolyRingElem}, a::Vector{T}) where {T<:RingElem} +function evaluate(f::AbstractAlgebra.Generic.FracFieldElem{<:MPolyRingElem}, a::Vector{T}) where {T<:RingElem} return evaluate(numerator(f), a)//evaluate(denominator(f), a) end -function evaluate(f::AbstractAlgebra.Generic.Frac{<:PolyRingElem}, a::RingElem) +function evaluate(f::AbstractAlgebra.Generic.FracFieldElem{<:PolyRingElem}, a::RingElem) return evaluate(numerator(f), a)//evaluate(denominator(f), a) end @@ -1640,7 +1640,7 @@ function _elliptic_parameter_conversion(X::EllipticSurface, u::VarietyFunctionFi @assert f == R_to_kkt_frac_XY(f_loc) && _is_in_weierstrass_form(f) "local equation is not in Weierstrass form" a = a_invars(E) - u_loc = u[U]::AbstractAlgebra.Generic.Frac # the representative on the Weierstrass chart + u_loc = u[U]::AbstractAlgebra.Generic.FracFieldElem # the representative on the Weierstrass chart # Set up the ambient_coordinate_ring of the new Weierstrass-chart kkt2, t2 = polynomial_ring(kk, names[3], cached=false) diff --git a/src/AlgebraicGeometry/Schemes/SpecOpen/Morphisms/Constructors.jl b/src/AlgebraicGeometry/Schemes/SpecOpen/Morphisms/Constructors.jl index 752b796d0d15..c97f3311ce03 100644 --- a/src/AlgebraicGeometry/Schemes/SpecOpen/Morphisms/Constructors.jl +++ b/src/AlgebraicGeometry/Schemes/SpecOpen/Morphisms/Constructors.jl @@ -104,7 +104,7 @@ end # functions on the affine patches. # ######################################################################## @doc raw""" - maximal_extension(X::AbsSpec, Y::AbsSpec, f::AbstractAlgebra.Generic.Frac) + maximal_extension(X::AbsSpec, Y::AbsSpec, f::AbstractAlgebra.Generic.FracFieldElem) Given a rational map ``ϕ : X ---> Y ⊂ Spec 𝕜[y₁,…,yₙ]`` of affine schemes determined by ``ϕ*(yⱼ) = fⱼ = aⱼ/bⱼ``, find the maximal open subset ``U⊂ X`` @@ -113,7 +113,7 @@ to which ``ϕ`` can be extended to a regular map ``g : U → Y`` and return ``g` function maximal_extension( X::AbsSpec, Y::AbsSpec, - f::Vector{AbstractAlgebra.Generic.Frac{RET}} + f::Vector{AbstractAlgebra.Generic.FracFieldElem{RET}} ) where {RET<:RingElem} U, g = maximal_extension(X, f) n = length(affine_patches(U)) diff --git a/src/AlgebraicGeometry/Schemes/SpecOpen/Rings/Constructors.jl b/src/AlgebraicGeometry/Schemes/SpecOpen/Rings/Constructors.jl index 8d0ccd373901..c8a6932c4a73 100644 --- a/src/AlgebraicGeometry/Schemes/SpecOpen/Rings/Constructors.jl +++ b/src/AlgebraicGeometry/Schemes/SpecOpen/Rings/Constructors.jl @@ -94,7 +94,7 @@ end # Maximal extensions of rational functions on affine schemes # ######################################################################## @doc raw""" - maximal_extension(X::Spec, f::AbstractAlgebra.Generic.Frac) + maximal_extension(X::Spec, f::AbstractAlgebra.Generic.FracFieldElem) Return the maximal extension of the restriction of ``f`` to a rational function on ``X`` on a maximal domain of @@ -106,7 +106,7 @@ the ring ``𝕜[x₁,…,xₙ]``. """ function maximal_extension( X::AbsSpec{<:Ring, <:MPolyLocRing}, - f::AbstractAlgebra.Generic.Frac{RET} + f::AbstractAlgebra.Generic.FracFieldElem{RET} ) where {RET<:MPolyRingElem} a = numerator(f) @@ -126,7 +126,7 @@ end function maximal_extension( X::AbsSpec{<:Ring, <:MPolyQuoLocRing}, - f::AbstractAlgebra.Generic.Frac{RET} + f::AbstractAlgebra.Generic.FracFieldElem{RET} ) where {RET<:RingElem} a = numerator(f) @@ -141,7 +141,7 @@ end function maximal_extension( X::AbsSpec{<:Ring, <:MPolyQuoRing}, - f::AbstractAlgebra.Generic.Frac{RET} + f::AbstractAlgebra.Generic.FracFieldElem{RET} ) where {RET<:RingElem} a = numerator(f) b = denominator(f) @@ -155,7 +155,7 @@ end function maximal_extension( X::AbsSpec{<:Ring, <:MPolyRing}, - f::AbstractAlgebra.Generic.Frac{RET} + f::AbstractAlgebra.Generic.FracFieldElem{RET} ) where {RET<:RingElem} a = numerator(f) b = denominator(f) @@ -168,7 +168,7 @@ function maximal_extension( end @doc raw""" - maximal_extension(X::Spec, f::Vector{AbstractAlgebra.Generic.Frac}) + maximal_extension(X::Spec, f::Vector{AbstractAlgebra.Generic.FracFieldElem}) Return the extension of the restriction of the ``fᵢ`` as a set of rational functions on ``X`` as *regular* functions to a @@ -180,7 +180,7 @@ be elements of the ring ``𝕜[x₁,…,xₙ]``. """ function maximal_extension( X::AbsSpec{<:Ring, <:AbsLocalizedRing}, - f::Vector{AbstractAlgebra.Generic.Frac{RET}} + f::Vector{AbstractAlgebra.Generic.FracFieldElem{RET}} ) where {RET<:RingElem} if length(f) == 0 return SpecOpen(X), Vector{structure_sheaf_elem_type(X)}() @@ -206,7 +206,7 @@ end function maximal_extension( X::AbsSpec{<:Ring, <:MPolyRing}, - f::Vector{AbstractAlgebra.Generic.Frac{RET}} + f::Vector{AbstractAlgebra.Generic.FracFieldElem{RET}} ) where {RET<:RingElem} if length(f) == 0 return SpecOpen(X), Vector{structure_sheaf_elem_type(X)}() @@ -230,7 +230,7 @@ end function maximal_extension( X::AbsSpec{<:Ring, <:MPolyQuoRing}, - f::Vector{AbstractAlgebra.Generic.Frac{RET}} + f::Vector{AbstractAlgebra.Generic.FracFieldElem{RET}} ) where {RET<:RingElem} if length(f) == 0 return SpecOpen(X), Vector{structure_sheaf_elem_type(X)}() diff --git a/src/InvariantTheory/types.jl b/src/InvariantTheory/types.jl index 157d439dcbf1..299a63eff4a7 100644 --- a/src/InvariantTheory/types.jl +++ b/src/InvariantTheory/types.jl @@ -72,7 +72,7 @@ mutable struct InvRing{FldT, GrpT, PolyRingElemT, PolyRingT, ActionT} reynolds_operator::MapFromFunc{PolyRingT, PolyRingT} - molien_series::Generic.Frac{QQPolyRingElem} + molien_series::Generic.FracFieldElem{QQPolyRingElem} function InvRing(K::FldT, G::GrpT, action::Vector{ActionT}) where {FldT <: Field, GrpT <: AbstractAlgebra.Group, ActionT} n = degree(G) diff --git a/src/Rings/FunctionField.jl b/src/Rings/FunctionField.jl index 17aa3d22e52e..97ea0bc9b1bd 100644 --- a/src/Rings/FunctionField.jl +++ b/src/Rings/FunctionField.jl @@ -9,7 +9,7 @@ function Oscar.singular_coeff_ring(F::AbstractAlgebra.Generic.FracField{T}) wher return Singular.FunctionField(singular_coeff_ring(base_ring(R)), [string(R.S)])[1] end -function (F::Singular.N_FField)(x::AbstractAlgebra.Generic.Frac{T}) where T <: Union{QQPolyRingElem, fpPolyRingElem, FqPolyRingElem} +function (F::Singular.N_FField)(x::AbstractAlgebra.Generic.FracFieldElem{T}) where T <: Union{QQPolyRingElem, fpPolyRingElem, FqPolyRingElem} check_char(F, parent(x)) @req Singular.transcendence_degree(F) == 1 "wrong number of generators" a = Singular.transcendence_basis(F)[1] @@ -29,7 +29,7 @@ function Oscar.singular_coeff_ring(F::AbstractAlgebra.Generic.FracField{T}) wher return Singular.FunctionField(singular_coeff_ring(base_ring(R)), _variables_for_singular(symbols(R)))[1] end -function (F::Singular.N_FField)(x::AbstractAlgebra.Generic.Frac{T}) where T <: Union{QQMPolyRingElem, fpMPolyRingElem, FqMPolyRingElem} +function (F::Singular.N_FField)(x::AbstractAlgebra.Generic.FracFieldElem{T}) where T <: Union{QQMPolyRingElem, fpMPolyRingElem, FqMPolyRingElem} check_char(F, parent(x)) @req Singular.transcendence_degree(F) == ngens(base_ring(parent(x))) "wrong number of generators" a = Singular.transcendence_basis(F) @@ -63,7 +63,7 @@ function (Ox::PolyRing)(f::Singular.spoly) end # coercion -function (F::QQField)(x::AbstractAlgebra.Generic.Frac{T}) where T <: Union{QQPolyRingElem, QQMPolyRingElem} +function (F::QQField)(x::AbstractAlgebra.Generic.FracFieldElem{T}) where T <: Union{QQPolyRingElem, QQMPolyRingElem} num = numerator(x) cst_num = constant_coefficient(num) denom = denominator(x) @@ -76,7 +76,7 @@ function (F::QQField)(x::AbstractAlgebra.Generic.RationalFunctionFieldElem{QQFie return F(x.d) end -function (F::Nemo.fpField)(x::AbstractAlgebra.Generic.Frac{T}) where T <: Union{fpPolyRingElem, fpMPolyRingElem} +function (F::Nemo.fpField)(x::AbstractAlgebra.Generic.FracFieldElem{T}) where T <: Union{fpPolyRingElem, fpMPolyRingElem} num = numerator(x) cst_num = constant_coefficient(num) denom = denominator(x) @@ -85,7 +85,7 @@ function (F::Nemo.fpField)(x::AbstractAlgebra.Generic.Frac{T}) where T <: Union{ F(cst_num) // F(cst_denom) end -function (F::Nemo.FqField)(x::AbstractAlgebra.Generic.Frac{T}) where T <: Union{FqPolyRingElem, FqMPolyRingElem} +function (F::Nemo.FqField)(x::AbstractAlgebra.Generic.FracFieldElem{T}) where T <: Union{FqPolyRingElem, FqMPolyRingElem} num = numerator(x) cst_num = constant_coefficient(num) denom = denominator(x) diff --git a/src/Rings/MPolyQuo.jl b/src/Rings/MPolyQuo.jl index fd27ce7b376f..55f0b89e70e5 100644 --- a/src/Rings/MPolyQuo.jl +++ b/src/Rings/MPolyQuo.jl @@ -1269,7 +1269,7 @@ function vector_space(K::AbstractAlgebra.Field, Q::MPolyQuoRing) end # To fix printing of fraction fields of MPolyQuoRing -function AbstractAlgebra.expressify(a::AbstractAlgebra.Generic.Frac{T}; +function AbstractAlgebra.expressify(a::AbstractAlgebra.Generic.FracFieldElem{T}; context = nothing) where {T <: MPolyQuoRingElem} n = numerator(a, false) d = denominator(a, false) diff --git a/src/Rings/localization_interface.jl b/src/Rings/localization_interface.jl index a09a1e511646..0d3bff66f4aa 100644 --- a/src/Rings/localization_interface.jl +++ b/src/Rings/localization_interface.jl @@ -200,11 +200,11 @@ function localization(R::Ring, U::AbsMultSet) end @doc raw""" - (W::AbsLocalizedRing{RingType, RingElemType, MultSetType})(f::AbstractAlgebra.Generic.Frac{RingElemType}) where {RingType, RingElemType, MultSetType} + (W::AbsLocalizedRing{RingType, RingElemType, MultSetType})(f::AbstractAlgebra.Generic.FracFieldElem{RingElemType}) where {RingType, RingElemType, MultSetType} Converts a fraction f = a//b to an element of the localized ring W. """ -function (W::AbsLocalizedRing{RingType, RingElemType, MultSetType})(f::AbstractAlgebra.Generic.Frac{RingElemType}) where {RingType, RingElemType, MultSetType} +function (W::AbsLocalizedRing{RingType, RingElemType, MultSetType})(f::AbstractAlgebra.Generic.FracFieldElem{RingElemType}) where {RingType, RingElemType, MultSetType} error("conversion for fractions to elements of type $(typeof(W)) is not implemented") end diff --git a/src/Rings/mpoly-graded.jl b/src/Rings/mpoly-graded.jl index 1adbcf1d193f..7eae9699e350 100644 --- a/src/Rings/mpoly-graded.jl +++ b/src/Rings/mpoly-graded.jl @@ -1521,7 +1521,7 @@ function _rational_function_to_power_series(P::QQRelPowerSeriesRing, f) end @doc raw""" - expand(f::Frac{QQPolyRingElem}, d::Int) -> RelPowerSeries + expand(f::FracFieldElem{QQPolyRingElem}, d::Int) -> RelPowerSeries Given a rational function $f$ over the rationals, expand $f$ as a power series up to terms of degree $d$. @@ -1533,7 +1533,7 @@ julia> expand(1//(1 - x^2), 5) 1 + t^2 + t^4 + O(t^6) ``` """ -function expand(f::Generic.Frac{QQPolyRingElem}, d::Int) +function expand(f::Generic.FracFieldElem{QQPolyRingElem}, d::Int) T, t = power_series_ring(QQ, d+1, "t") return _rational_function_to_power_series(T, f) end diff --git a/src/Rings/mpoly-ideals.jl b/src/Rings/mpoly-ideals.jl index 1e8b1ff7bfac..20c1307ad44c 100644 --- a/src/Rings/mpoly-ideals.jl +++ b/src/Rings/mpoly-ideals.jl @@ -2053,7 +2053,7 @@ function flag_pluecker_ideal(F::Field, dimensions::Vector{Int}, n::Int) L2 = reduce(vcat, [subsets(n, d + 1) for d in dimensions]) R, x = polynomial_ring(F, "x" => L; cached=false) - xdict = Dict{Vector{Int},MPolyElem}([L[i] => x[i] for i in 1:length(L)]) + xdict = Dict{Vector{Int},MPolyRingElem}([L[i] => x[i] for i in 1:length(L)]) X = [(a, b) for a in L1, b in L2 if length(b) - length(a) >= 2] diff --git a/src/Rings/mpoly-local.jl b/src/Rings/mpoly-local.jl index f7f2d2639ffd..d6127e138252 100644 --- a/src/Rings/mpoly-local.jl +++ b/src/Rings/mpoly-local.jl @@ -41,15 +41,15 @@ end An element f/g in an instance of `MPolyRingLoc{T}`. The data being stored consists of - * the fraction f/g as an instance of `AbstractAlgebra.Generic.Frac`; + * the fraction f/g as an instance of `AbstractAlgebra.Generic.FracFieldElem`; * the parent instance of `MPolyRingLoc{T}`. """ struct MPolyRingElemLoc{T} <: AbstractAlgebra.RingElem where {T} - frac::AbstractAlgebra.Generic.Frac + frac::AbstractAlgebra.Generic.FracFieldElem parent::MPolyRingLoc{T} # pass with checked = false to skip the non-trivial denominator check - function MPolyRingElemLoc{T}(f::AbstractAlgebra.Generic.Frac, + function MPolyRingElemLoc{T}(f::AbstractAlgebra.Generic.FracFieldElem, p::MPolyRingLoc{T}, checked = true) where {T} R = base_ring(p) B = base_ring(R) @@ -73,7 +73,7 @@ function MPolyRingElemLoc(f::MPolyRingElem{T}, m::Oscar.MPolyIdeal) where {T} return MPolyRingElemLoc{T}(f//R(1), localization(R, m), false) end -function MPolyRingElemLoc(f::AbstractAlgebra.Generic.Frac, m::Oscar.MPolyIdeal) +function MPolyRingElemLoc(f::AbstractAlgebra.Generic.FracFieldElem, m::Oscar.MPolyIdeal) R = parent(numerator(f)) B = base_ring(R) return MPolyRingElemLoc{elem_type(B)}(f, localization(R, m)) @@ -128,7 +128,7 @@ function (W::MPolyRingLoc{T})(f::MPolyRingElem) where {T} return MPolyRingElemLoc{T}(f//one(parent(f)), W) end -function (W::MPolyRingLoc{T})(g::AbstractAlgebra.Generic.Frac) where {T} +function (W::MPolyRingLoc{T})(g::AbstractAlgebra.Generic.FracFieldElem) where {T} return MPolyRingElemLoc{T}(g, W) end diff --git a/src/Rings/mpoly-localizations.jl b/src/Rings/mpoly-localizations.jl index e486f8502322..0f53b1b8a5a3 100644 --- a/src/Rings/mpoly-localizations.jl +++ b/src/Rings/mpoly-localizations.jl @@ -1282,11 +1282,11 @@ mutable struct MPolyLocRingElem{ } W::MPolyLocRing{BaseRingType, BaseRingElemType, RingType, RingElemType, MultSetType} - frac::AbstractAlgebra.Generic.Frac{RingElemType} + frac::AbstractAlgebra.Generic.FracFieldElem{RingElemType} function MPolyLocRingElem( W::MPolyLocRing{BaseRingType, BaseRingElemType, RingType, RingElemType, MultSetType}, - f::AbstractAlgebra.Generic.Frac{RingElemType}; + f::AbstractAlgebra.Generic.FracFieldElem{RingElemType}; check::Bool=true ) where {BaseRingType, BaseRingElemType, RingType, RingElemType, MultSetType} base_ring(parent(f)) == base_ring(W) || error( @@ -1383,7 +1383,7 @@ end RingType, RingElemType, MultSetType - })(f::AbstractAlgebra.Generic.Frac{RingElemType}; check::Bool=true) where { + })(f::AbstractAlgebra.Generic.FracFieldElem{RingElemType}; check::Bool=true) where { BaseRingType, BaseRingElemType, RingType, diff --git a/src/Rings/mpolyquo-localizations.jl b/src/Rings/mpolyquo-localizations.jl index 5b18423b69bf..644e276ad09a 100644 --- a/src/Rings/mpolyquo-localizations.jl +++ b/src/Rings/mpolyquo-localizations.jl @@ -1,4 +1,4 @@ -import AbstractAlgebra: Ring, RingElem, Generic.Frac +import AbstractAlgebra: Ring, RingElem, Generic.FracFieldElem import Base: issubset @@ -363,7 +363,7 @@ function MPolyQuoLocRing(W::MPolyLocRing) return MPolyQuoLocRing(R, I, U, Q, W) end -function Base.in(f::AbstractAlgebra.Generic.Frac{RET}, L::MPolyQuoLocRing{BRT, BRET, RT, RET, MST}) where {BRT, BRET, RT, RET, MST} +function Base.in(f::AbstractAlgebra.Generic.FracFieldElem{RET}, L::MPolyQuoLocRing{BRT, BRET, RT, RET, MST}) where {BRT, BRET, RT, RET, MST} R = base_ring(L) R === parent(numerator(f)) || error("element does not belong to the correct ring") denominator(f) in inverted_set(L) && return true @@ -513,7 +513,7 @@ function (L::MPolyQuoLocRing{ end ### additional conversions -function (L::MPolyQuoLocRing{BRT, BRET, RT, RET, MST})(f::Frac{RET}; check::Bool=true, is_reduced::Bool=false) where {BRT, BRET, RT, RET, MST} +function (L::MPolyQuoLocRing{BRT, BRET, RT, RET, MST})(f::FracFieldElem{RET}; check::Bool=true, is_reduced::Bool=false) where {BRT, BRET, RT, RET, MST} R = base_ring(L) return L(R(numerator(f)), R(denominator(f)), check=check, is_reduced=is_reduced) end @@ -680,7 +680,7 @@ end # to the form [f] = [c]//[dᵏ] with d∈ S. function convert( L::MPolyQuoLocRing{BRT, BRET, RT, RET, MPolyPowersOfElement{BRT, BRET, RT, RET}}, - f::AbstractAlgebra.Generic.Frac{RET} + f::AbstractAlgebra.Generic.FracFieldElem{RET} ) where {BRT, BRET, RT, RET} a = numerator(f) b = denominator(f) From 2e9cebc754b0ebe0a401f8b8866725092aff650c Mon Sep 17 00:00:00 2001 From: Johannes Schmitt Date: Fri, 16 Feb 2024 15:22:27 +0100 Subject: [PATCH 10/29] New linear solving interface + bump dependencies (#3350) * feat: Use new linear algebra functionality * Adjust to deleted deprecations/aliases Hecke edition --- Project.toml | 6 +- docs/src/NumberTheory/galois.md | 6 +- examples/BinomIdeal.jl | 2 +- examples/BinomIdeal2.jl | 2 +- .../src/FamilyOfSpaces/attributes.jl | 2 +- experimental/FTheoryTools/src/auxiliary.jl | 2 +- experimental/GITFans/src/GITFans.jl | 2 +- experimental/GModule/Brueckner.jl | 2 +- experimental/GModule/Cohomology.jl | 8 +-- experimental/GModule/GModule.jl | 20 +++---- experimental/GModule/GaloisCohomology.jl | 6 +- experimental/GaloisGrp/src/Solve.jl | 10 ++-- experimental/LieAlgebras/src/LieAlgebra.jl | 6 +- experimental/LieAlgebras/src/LieAlgebraHom.jl | 4 +- experimental/LieAlgebras/src/LieSubalgebra.jl | 3 +- experimental/LieAlgebras/src/Util.jl | 3 +- .../LieAlgebras/test/LieAlgebraModule-test.jl | 2 +- experimental/LinearQuotients/src/cox_rings.jl | 6 +- experimental/ModStd/ModStdNF.jl | 2 +- experimental/ModStd/ModStdQ.jl | 2 +- experimental/ModStd/ModStdQt.jl | 4 +- .../QuadFormAndIsom/src/embeddings.jl | 15 ++--- .../src/hermitian_miranda_morrison.jl | 2 +- .../src/lattices_with_isometry.jl | 8 +-- experimental/Rings/QQAbAndPChars.jl | 5 +- experimental/Schemes/DerivedPushforward.jl | 2 +- experimental/Schemes/WeilDivisor.jl | 3 +- experimental/Schemes/elliptic_surface.jl | 5 +- .../src/representations.jl | 7 +-- .../src/symmetric_grassmannians.jl | 2 +- src/AlgebraicGeometry/Surfaces/K3Auto.jl | 56 ++++++++++--------- .../NormalToricVarieties/toric_ideal.jl | 1 - .../ToricMorphisms/attributes.jl | 4 +- src/InvariantTheory/affine_algebra.jl | 6 +- src/InvariantTheory/iterators.jl | 4 +- src/NumberTheory/GaloisGrp/GaloisGrp.jl | 14 ++--- src/Oscar.jl | 38 ++++++------- .../Polyhedron/constructors.jl | 2 +- src/Rings/AbelianClosure.jl | 2 +- src/Rings/FinField.jl | 2 +- src/Rings/groebner.jl | 2 +- src/TropicalGeometry/intersection.jl | 8 +-- src/TropicalGeometry/linear_space.jl | 2 +- src/TropicalGeometry/variety.jl | 8 +-- test/AlgebraicGeometry/Surfaces/K3Auto.jl | 4 +- test/Groups/gsets.jl | 6 +- test/PolyhedralGeometry/polyhedron.jl | 2 +- 47 files changed, 156 insertions(+), 154 deletions(-) diff --git a/Project.toml b/Project.toml index 3a395a7caca9..cc876615086e 100644 --- a/Project.toml +++ b/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" diff --git a/docs/src/NumberTheory/galois.md b/docs/src/NumberTheory/galois.md index df8a02f60dd9..9294ab41c1b8 100644 --- a/docs/src/NumberTheory/galois.md +++ b/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) diff --git a/examples/BinomIdeal.jl b/examples/BinomIdeal.jl index ed32191347d7..8e0f5333bde6 100644 --- a/examples/BinomIdeal.jl +++ b/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 diff --git a/examples/BinomIdeal2.jl b/examples/BinomIdeal2.jl index f73a7a640c01..18b3100d1fad 100644 --- a/examples/BinomIdeal2.jl +++ b/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 diff --git a/experimental/FTheoryTools/src/FamilyOfSpaces/attributes.jl b/experimental/FTheoryTools/src/FamilyOfSpaces/attributes.jl index 8899600b7db2..d2a1b5c636c0 100644 --- a/experimental/FTheoryTools/src/FamilyOfSpaces/attributes.jl +++ b/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 diff --git a/experimental/FTheoryTools/src/auxiliary.jl b/experimental/FTheoryTools/src/auxiliary.jl index 1df22edcefbb..a11ee072b3a9 100644 --- a/experimental/FTheoryTools/src/auxiliary.jl +++ b/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)) diff --git a/experimental/GITFans/src/GITFans.jl b/experimental/GITFans/src/GITFans.jl index de785ee52473..0ee1544ec412 100644 --- a/experimental/GITFans/src/GITFans.jl +++ b/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. diff --git a/experimental/GModule/Brueckner.jl b/experimental/GModule/Brueckner.jl index 052108ee1d56..159cb9b33a0f 100644 --- a/experimental/GModule/Brueckner.jl +++ b/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 diff --git a/experimental/GModule/Cohomology.jl b/experimental/GModule/Cohomology.jl index 6762947010f4..183f4d1b6707 100644 --- a/experimental/GModule/Cohomology.jl +++ b/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 ###################################################################### diff --git a/experimental/GModule/GModule.jl b/experimental/GModule/GModule.jl index 11dfc8eaff02..de3937ba028c 100644 --- a/experimental/GModule/GModule.jl +++ b/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) diff --git a/experimental/GModule/GaloisCohomology.jl b/experimental/GModule/GaloisCohomology.jl index bead762397c7..a12c0f65aa3b 100644 --- a/experimental/GModule/GaloisCohomology.jl +++ b/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 diff --git a/experimental/GaloisGrp/src/Solve.jl b/experimental/GaloisGrp/src/Solve.jl index 5dee7706b180..537506a661a9 100644 --- a/experimental/GaloisGrp/src/Solve.jl +++ b/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] diff --git a/experimental/LieAlgebras/src/LieAlgebra.jl b/experimental/LieAlgebras/src/LieAlgebra.jl index 5270d8e69083..d9353762a705 100644 --- a/experimental/LieAlgebras/src/LieAlgebra.jl +++ b/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 diff --git a/experimental/LieAlgebras/src/LieAlgebraHom.jl b/experimental/LieAlgebras/src/LieAlgebraHom.jl index dad0ec23fc74..2a4d8d3b8d88 100644 --- a/experimental/LieAlgebras/src/LieAlgebraHom.jl +++ b/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 diff --git a/experimental/LieAlgebras/src/LieSubalgebra.jl b/experimental/LieAlgebras/src/LieSubalgebra.jl index 09a9ebd68637..712e632b3d7c 100644 --- a/experimental/LieAlgebras/src/LieSubalgebra.jl +++ b/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) diff --git a/experimental/LieAlgebras/src/Util.jl b/experimental/LieAlgebras/src/Util.jl index b6a7aff337ca..65fb4355b0e0 100644 --- a/experimental/LieAlgebras/src/Util.jl +++ b/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 diff --git a/experimental/LieAlgebras/test/LieAlgebraModule-test.jl b/experimental/LieAlgebras/test/LieAlgebraModule-test.jl index e581c1968467..bf696e2ab194 100644 --- a/experimental/LieAlgebras/test/LieAlgebraModule-test.jl +++ b/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, diff --git a/experimental/LinearQuotients/src/cox_rings.jl b/experimental/LinearQuotients/src/cox_rings.jl index 0f1ef2128fff..e92e09690d7f 100644 --- a/experimental/LinearQuotients/src/cox_rings.jl +++ b/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. diff --git a/experimental/ModStd/ModStdNF.jl b/experimental/ModStd/ModStdNF.jl index c6149b310237..328e1a2aa46e 100644 --- a/experimental/ModStd/ModStdNF.jl +++ b/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 diff --git a/experimental/ModStd/ModStdQ.jl b/experimental/ModStd/ModStdQ.jl index b97af8ff4bbc..7c22bae45c09 100644 --- a/experimental/ModStd/ModStdQ.jl +++ b/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) diff --git a/experimental/ModStd/ModStdQt.jl b/experimental/ModStd/ModStdQt.jl index 983c9eb0f229..2f86499b666b 100644 --- a/experimental/ModStd/ModStdQt.jl +++ b/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))) diff --git a/experimental/QuadFormAndIsom/src/embeddings.jl b/experimental/QuadFormAndIsom/src/embeddings.jl index a0468f772937..dd10d558fdff 100644 --- a/experimental/QuadFormAndIsom/src/embeddings.jl +++ 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) diff --git a/experimental/QuadFormAndIsom/src/hermitian_miranda_morrison.jl b/experimental/QuadFormAndIsom/src/hermitian_miranda_morrison.jl index ab9000a3ff13..6a51c1c18f40 100644 --- a/experimental/QuadFormAndIsom/src/hermitian_miranda_morrison.jl +++ b/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 diff --git a/experimental/QuadFormAndIsom/src/lattices_with_isometry.jl b/experimental/QuadFormAndIsom/src/lattices_with_isometry.jl index 34b34d41607b..1a3ef6f886a6 100644 --- a/experimental/QuadFormAndIsom/src/lattices_with_isometry.jl +++ b/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 = 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 = 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(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(basis_matrix(C), basis_matrix(C)*g_ambient; side = :left) push!(gene, m) else push!(gene, matrix(g)) diff --git a/experimental/Rings/QQAbAndPChars.jl b/experimental/Rings/QQAbAndPChars.jl index 862472b70ca8..2e6d7237c3fc 100644 --- a/experimental/Rings/QQAbAndPChars.jl +++ b/experimental/Rings/QQAbAndPChars.jl @@ -42,9 +42,8 @@ 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) - @assert s[1] - return evaluate(FacElem(Dict([(Chi.b[i], s[2][1, i]) for i = 1:length(Chi.b)]))) + s = solve(Chi.A, b, side = :left) + return evaluate(FacElem(Dict([(Chi.b[i], s[1, i]) for i = 1:length(Chi.b)]))) end function (Chi::PartialCharacter)(b::Vector{ZZRingElem}) diff --git a/experimental/Schemes/DerivedPushforward.jl b/experimental/Schemes/DerivedPushforward.jl index e92d0d724db7..e6604acf1aa5 100644 --- a/experimental/Schemes/DerivedPushforward.jl +++ b/experimental/Schemes/DerivedPushforward.jl @@ -75,7 +75,7 @@ end =# function rank(phi::FreeModuleHom{FreeMod{T}, FreeMod{T}, Nothing}) where {T<:FieldElem} - return ngens(domain(phi)) - left_kernel(sparse_matrix(phi))[1] + return ngens(domain(phi)) - nrows(kernel(sparse_matrix(phi), side = :left)) end diff --git a/experimental/Schemes/WeilDivisor.jl b/experimental/Schemes/WeilDivisor.jl index 9e4c95115128..eed77eab164f 100644 --- a/experimental/Schemes/WeilDivisor.jl +++ b/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 = 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) diff --git a/experimental/Schemes/elliptic_surface.jl b/experimental/Schemes/elliptic_surface.jl index c03058036eb2..7d6e9cc1f5bb 100644 --- a/experimental/Schemes/elliptic_surface.jl +++ b/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 = 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, kernel(G; side = :left) end function basis_representation(X::EllipticSurface, D::WeilDivisor) diff --git a/experimental/SymmetricIntersections/src/representations.jl b/experimental/SymmetricIntersections/src/representations.jl index e5ca6e2bedba..10615d90451a 100644 --- a/experimental/SymmetricIntersections/src/representations.jl +++ b/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(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 = kernel(_K; side = :left) Borth = K2*reduce(vcat, B1) @assert is_submodule(rep, Borth) bas = vcat(bas, Borth) @@ -1316,8 +1316,7 @@ function quotient_representation(rep::LinRep{S, T, U}, M::W) where {S, T, U, W < mr = matrix_representation(rep) coll = eltype(mr)[] for m in mr - ok, mm = can_solve_with_solution(proj, m*proj; side=:right) - @assert ok + mm = solve(proj, m*proj; side=:right) push!(coll, mm) end repQ = _linear_representation(representation_ring(rep), coll) diff --git a/experimental/SymmetricIntersections/src/symmetric_grassmannians.jl b/experimental/SymmetricIntersections/src/symmetric_grassmannians.jl index cc751ab60856..f528f6961747 100644 --- a/experimental/SymmetricIntersections/src/symmetric_grassmannians.jl +++ b/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 = kernel(B; side = :right) if ncols(K) == 0 return ideal_Gr diff --git a/src/AlgebraicGeometry/Surfaces/K3Auto.jl b/src/AlgebraicGeometry/Surfaces/K3Auto.jl index 4c470f074255..ee5f88013354 100644 --- a/src/AlgebraicGeometry/Surfaces/K3Auto.jl +++ b/src/AlgebraicGeometry/Surfaces/K3Auto.jl @@ -92,7 +92,7 @@ function BorcherdsCtx(L::ZZLat, S::ZZLat, weyl::ZZMatrix; compute_OR::Bool=true) R = lll(Hecke.orthogonal_submodule(L, S)) # the following completes the basis of R to a basis of L - basisRL = solve_left(basis_matrix(L),basis_matrix(R)) + basisRL = solve(basis_matrix(L),basis_matrix(R); side = :left) basisRL = change_base_ring(ZZ, basisRL) A, j = snf(abelian_group(basisRL)) @@ -101,9 +101,9 @@ function BorcherdsCtx(L::ZZLat, S::ZZLat, weyl::ZZMatrix; compute_OR::Bool=true) # carry the Weyl vector along L1 = lattice(ambient_space(L), basisL1) - weyl = change_base_ring(ZZ, solve_left(basisL1, weyl*basis_matrix(L))) - basisSL1 = solve_left(basis_matrix(L1), basis_matrix(S)) - basisRL1 = solve_left(basis_matrix(L1), basis_matrix(R)) + weyl = change_base_ring(ZZ, solve(basisL1, weyl*basis_matrix(L); side = :left)) + basisSL1 = solve(basis_matrix(L1), basis_matrix(S); side = :left) + basisRL1 = solve(basis_matrix(L1), basis_matrix(R); side = :left) # Assure that L has the standard basis. L = integer_lattice(gram=gram_matrix(L1)) @@ -552,7 +552,7 @@ function short_vectors_affine(S::ZZLat, v::MatrixElem, alpha, d) alpha = QQ(alpha) gram = gram_matrix(S) tmp = v*gram_matrix(ambient_space(S))*transpose(basis_matrix(S)) - v_S = solve_left(gram_matrix(S),tmp) + v_S = solve(gram_matrix(S),tmp; side = :left) sol = short_vectors_affine(gram, v_S, alpha, d) B = basis_matrix(S) return [s*B for s in sol] @@ -564,11 +564,11 @@ function short_vectors_affine(gram::MatrixElem, v::MatrixElem, alpha::QQFieldEle tmp = FakeFmpqMat(w) wn = numerator(tmp) wd = denominator(tmp) - b, x = can_solve_with_solution(transpose(wn), matrix(ZZ, 1, 1, [alpha*wd])) + b, x = can_solve_with_solution(transpose(wn), matrix(ZZ, 1, 1, [alpha*wd]); side = :right) if !b return QQMatrix[] end - _, K = left_kernel(wn) + K = kernel(wn; side = :left) # (x + y*K)*gram*(x + y*K) = x gram x + 2xGKy + y K G K y # now I want to formulate this as a cvp @@ -606,8 +606,8 @@ function separating_hyperplanes(S::ZZLat, v::QQMatrix, h::QQMatrix, d) @hassert :K3Auto 1 inner_product(V,h,h)[1,1]>0 gram = gram_matrix(S) B = basis_matrix(S) - vS = solve_left(B,v) - hS = solve_left(B,h) + vS = solve(B,v; side = :left) + hS = solve(B,h; side = :left) return [a*B for a in separating_hyperplanes(gram,vS,hS,d)] end @@ -622,7 +622,7 @@ function separating_hyperplanes(gram::QQMatrix, v::QQMatrix, h::QQMatrix, d) bW = basis_matrix(W) # set up the quadratic triple for SW gramW = gram_matrix(W) - s = solve_left(bW, v*prW) * gramW + s = solve(bW, v*prW; side = :left) * gramW Q = gramW + transpose(s)*s*ch*cv^-2 @vprint :K3Auto 5 Q @@ -1032,7 +1032,7 @@ function _alg58_close_vector(data::BorcherdsCtx, w::ZZMatrix) SSdual = dual(data.SS) delta_w = QQMatrix[] wS = w*data.prS - #wS = solve_left(gram_matrix(S),w*gram_matrix(V)*transpose(basis_matrix(S))) + #wS = solve(gram_matrix(S),w*gram_matrix(V)*transpose(basis_matrix(S)); side = :left) Vw = data.gramL*transpose(w) # since we do repeated cvp in the same lattice # we do the preprocessing here @@ -1077,7 +1077,7 @@ function _alg58_close_vector(data::BorcherdsCtx, w::ZZMatrix) tmp = FakeFmpqMat(ww) wn = numerator(tmp) wd = denominator(tmp) - _, K = left_kernel(wn) + K = kernel(wn; side = :left) K = lll!(K) # perhaps doing this has no gain? # (x + y*K)*gram*(x + y*K) = x gram x + 2xGKy + y K G K y @@ -1096,7 +1096,7 @@ function _alg58_close_vector(data::BorcherdsCtx, w::ZZMatrix) B = basis_matrix(SSdual) KB = K*B for (alpha, d) in keys(cvp_inputs) - can_solve_i, x = can_solve_with_solution(transpose(wn), matrix(ZZ, 1, 1, [alpha*wd])) + can_solve_i, x = can_solve_with_solution(transpose(wn), matrix(ZZ, 1, 1, [alpha*wd]); side = :right) if !can_solve_i continue end @@ -1389,7 +1389,7 @@ and it is equal to $2$ if and only if $S$ is $2$-elementary. If an ample class is given, then the generators returned preserve it. This kind of computation can be very expensive. To print progress information -use `set_verbose_level(:K3Auto, 2)` or higher. +use `set_verbosity_level(:K3Auto, 2)` or higher. # Input - `S`: a hyperbolic lattice @@ -1401,7 +1401,7 @@ function K3_surface_automorphism_group(S::ZZLat) end function K3_surface_automorphism_group(S::ZZLat, ample_class::QQMatrix, n::Int=26) - ample_classS = solve_left(basis_matrix(S), ample_class) + ample_classS = solve(basis_matrix(S), ample_class; side = :left) L, S, weyl = borcherds_method_preprocessing(S, n, ample=ample_class) return borcherds_method(L, S, weyl, compute_OR=false)[2:end] end @@ -1598,8 +1598,8 @@ function span_in_S(L, S, weyl) else M = linear_equation_matrix(spanC) end - k, K = kernel(M) - gensN = transpose(K)[1:k,:] + K = kernel(M; side = :right) + gensN = transpose(K) return gensN end @@ -1620,9 +1620,9 @@ function weyl_vector_non_degenerate(L::ZZLat, S::ZZLat, u0::QQMatrix, weyl::QQMa @vprint :K3Auto 2 "calculating separating hyperplanes\n" separating_walls = separating_hyperplanes(L, u, ample, -2) - @vprint :K3Auto 2 "moving Weyl vector $(solve_left(basis_matrix(L),weyl)) towards the ample class\n" + @vprint :K3Auto 2 "moving Weyl vector $(solve(basis_matrix(L),weyl; side = :left)) towards the ample class\n" u, weyl = chain_reflect(V, ample, u, weyl, separating_walls) - @vprint :K3Auto "new weyl: $(solve_left(basis_matrix(L),weyl)) \n" + @vprint :K3Auto "new weyl: $(solve(basis_matrix(L),weyl; side = :left)) \n" if is_S_nondegenerate(L,S,weyl) return weyl, u, ample end @@ -1728,7 +1728,7 @@ function weyl_vector(L::ZZLat, U0::ZZLat) A = change_base_ring(ZZ, gram_matrix(R)*transpose(v)) b = change_base_ring(GF(2), b) A = change_base_ring(GF(2), A) - x = lift(solve_left(A, b)) + x = lift(solve(A, b; side = :left)) v = (v + 2*x)*basis_matrix(R) @hassert :K3Auto 1 mod(inner_product(V,v,v)[1,1], 8)==0 u = basis_matrix(U) @@ -1843,7 +1843,7 @@ function borcherds_method_preprocessing(S::ZZLat, n::Integer; ample=nothing) if ample isa Nothing @vprint :K3Auto 1 "searching a random ample vector in S\n" h = ample_class(S) - hS = solve_left(basis_matrix(S),h) + hS = solve(basis_matrix(S),h; side = :left) @vprint :K3Auto 1 "ample vector: $hS \n" else h = ample*basis_matrix(S) @@ -1858,7 +1858,7 @@ function borcherds_method_preprocessing(S::ZZLat, n::Integer; ample=nothing) weyl1, u, hh = weyl_vector_non_degenerate(L, S, u0, weyl, h) - weyl2 = change_base_ring(ZZ, solve_left(basis_matrix(L), weyl1)) + weyl2 = change_base_ring(ZZ, solve(basis_matrix(L), weyl1; side = :left)) return L, S, weyl2 end @@ -1990,7 +1990,7 @@ function fibration_type(NS::ZZLat, f::QQMatrix) V = ambient_space(NS) # compute f^\perp / ZZf K = orthogonal_submodule(NS, lattice(V, f)) - fK = change_base_ring(ZZ, solve_left(basis_matrix(K), f)) + fK = change_base_ring(ZZ, solve(basis_matrix(K), f; side = :left)) g = gcd(vec(collect(fK))) fK = divexact(fK, g) A, j = snf(abelian_group(fK)) @@ -2001,7 +2001,7 @@ function fibration_type(NS::ZZLat, f::QQMatrix) mwl_rank = rank(NS) - 2 - rank(R) ade_type = root_lattice_recognition(R)[1] barR = primitive_closure(Frame, R) - torsion = abelian_group(change_base_ring(ZZ,solve_left(basis_matrix(barR), basis_matrix(R)))) + torsion = abelian_group(change_base_ring(ZZ,solve(basis_matrix(barR), basis_matrix(R); side = :left))) return mwl_rank, snf(torsion)[1], ade_type end @@ -2025,9 +2025,10 @@ function find_section(L::ZZLat, f::QQMatrix) else # search a smallish section using a cvp A = change_base_ring(ZZ,basis_matrix(L)*gram_matrix(V)*transpose(f)) - ss = solve_left(A,identity_matrix(ZZ,1)) + ss = solve(A,identity_matrix(ZZ,1); side = :left) s = ss*basis_matrix(L) - k, K = left_kernel(A) + K = kernel(A; side = :left) + k = nrows(K) Kl = integer_lattice(gram=K*transpose(K)) # project ss to K sK = solve(change_base_ring(QQ,K*transpose(K)),change_base_ring(QQ,K*transpose(ss))) @@ -2070,7 +2071,8 @@ fibration_type(NS::ZZLat, f::Vector) = fibration_type(NS, matrix(QQ, 1, degree(N ################################################################################ function _common_invariant(Gamma) - return left_kernel(reduce(hcat,[g-1 for g in Gamma])) + K = kernel(reduce(hcat,[g-1 for g in Gamma]); side = :left) + return nrows(K), K end @doc raw""" diff --git a/src/AlgebraicGeometry/ToricVarieties/NormalToricVarieties/toric_ideal.jl b/src/AlgebraicGeometry/ToricVarieties/NormalToricVarieties/toric_ideal.jl index b879ec44ba9d..0b6327433a09 100644 --- a/src/AlgebraicGeometry/ToricVarieties/NormalToricVarieties/toric_ideal.jl +++ b/src/AlgebraicGeometry/ToricVarieties/NormalToricVarieties/toric_ideal.jl @@ -107,7 +107,6 @@ Ideal generated by """ function toric_ideal(R::MPolyRing, pts::ZZMatrix) intkernel = kernel(pts, side=:left) - intkernel = intkernel[2] presat = binomial_exponents_to_ideal(R, intkernel) J = ideal([prod(gens(base_ring(presat)))]) return saturation(presat, J) diff --git a/src/AlgebraicGeometry/ToricVarieties/ToricMorphisms/attributes.jl b/src/AlgebraicGeometry/ToricVarieties/ToricMorphisms/attributes.jl index 4dc3d9a22e68..787e5ce82c32 100644 --- a/src/AlgebraicGeometry/ToricVarieties/ToricMorphisms/attributes.jl +++ b/src/AlgebraicGeometry/ToricVarieties/ToricMorphisms/attributes.jl @@ -78,7 +78,7 @@ Map v = [images[i,k] for k in 1:ncols(images)] j = findfirst(x -> x == true, [(v in maximal_cones(cod)[j]) for j in 1:n_maximal_cones(cod)]) m = reduce(vcat, [Int(ray_indices(maximal_cones(cod))[j, k]) * cod_rays[k:k, :] for k in 1:n_rays(cod)]) - mapping_matrix = hcat(mapping_matrix, solve(transpose(m), transpose(images[i:i, :]))) + mapping_matrix = hcat(mapping_matrix, solve(transpose(m), transpose(images[i:i, :]); side = :right)) end return hom(torusinvariant_weil_divisor_group(d), torusinvariant_weil_divisor_group(cod), transpose(mapping_matrix)) end @@ -240,7 +240,7 @@ Covering hb_V_mat = matrix(ZZ, hb_V) hb_V_img = hb_V_mat * At hb_U_mat = matrix(ZZ, hb_U) - sol = solve_left(hb_U_mat, hb_V_img) + sol = solve(hb_U_mat, hb_V_img; side = :left) @assert sol*hb_U_mat == hb_V_img @assert all(x->x>=0, sol) diff --git a/src/InvariantTheory/affine_algebra.jl b/src/InvariantTheory/affine_algebra.jl index 0bd6e7984956..354a30cf9c48 100644 --- a/src/InvariantTheory/affine_algebra.jl +++ b/src/InvariantTheory/affine_algebra.jl @@ -203,8 +203,7 @@ function relations_primary_and_irreducible_secondary(RG::InvRing) # Write the products (in N) in the basis of K[V]^G_d given by the secondary # invariants (in M) - fl, x = can_solve_with_solution(M, N, side = :left) - @assert fl + x = solve(M, N, side = :left) # Translate the relations to the free algebra S for i = 1:nrows(x) @@ -308,8 +307,7 @@ function module_syzygies(RG::InvRing) monomial_to_column = enumerate_monomials(gens_d) M = polys_to_smat(gens_d, monomial_to_column) N = polys_to_smat(s_invars_d, monomial_to_column) - fl, sol = can_solve_with_solution(M, N, side = :left) - @assert fl + sol = solve(M, N, side = :left) for i in 1:length(s_invars_d) a = F() diff --git a/src/InvariantTheory/iterators.jl b/src/InvariantTheory/iterators.jl index 0097896ba363..a85cd51d9df5 100644 --- a/src/InvariantTheory/iterators.jl +++ b/src/InvariantTheory/iterators.jl @@ -410,9 +410,9 @@ function iterate_basis_linear_algebra(IR::InvRing, d::Int) end end end - n, N = right_kernel(M) + N = kernel(M, side = :right) - return InvRingBasisIterator{typeof(IR), Nothing, typeof(mons_iterator), eltype(mons), typeof(N)}(IR, d, n, false, nothing, mons_iterator, mons, N) + return InvRingBasisIterator{typeof(IR), Nothing, typeof(mons_iterator), eltype(mons), typeof(N)}(IR, d, ncols(N), false, nothing, mons_iterator, mons, N) end Base.eltype(BI::InvRingBasisIterator) = elem_type(polynomial_ring(BI.R)) diff --git a/src/NumberTheory/GaloisGrp/GaloisGrp.jl b/src/NumberTheory/GaloisGrp/GaloisGrp.jl index ffc3222cf3aa..06bd3b68a9a3 100644 --- a/src/NumberTheory/GaloisGrp/GaloisGrp.jl +++ b/src/NumberTheory/GaloisGrp/GaloisGrp.jl @@ -2,8 +2,7 @@ module GaloisGrp using Oscar, Random import Base: ^, +, -, *, == -import Oscar: Hecke, AbstractAlgebra, GAP, extension_field, isinteger, - upper_bound +import Oscar: Hecke, AbstractAlgebra, GAP, extension_field, isinteger using Oscar: SLPolyRing, SLPoly, SLPolynomialRing, CycleType import Oscar: pretty, LowercaseOff @@ -17,6 +16,7 @@ export galois_quotient export power_sum export slpoly_ring export to_elementary_symmetric +export upper_bound export valuation_of_roots import Hecke: orbit, fixed_field, extension_field @@ -24,9 +24,9 @@ import Hecke: orbit, fixed_field, extension_field function __init__() GAP.Packages.load("ferret"; install=true) - Hecke.add_verbose_scope(:GaloisGroup) - Hecke.add_verbose_scope(:GaloisInvariant) - Hecke.add_assert_scope(:GaloisInvariant) + Hecke.add_verbosity_scope(:GaloisGroup) + Hecke.add_verbosity_scope(:GaloisInvariant) + Hecke.add_assertion_scope(:GaloisInvariant) end """ @@ -1171,8 +1171,8 @@ end #TODO: Max: rank the filter function by cost, cheapest first... # possibly needs a third field in the structure function (F::GroupFilter)(G::PermGroup) - do_print = Hecke.get_verbose_level(:GaloisGroup) >= 1 - do_all = Hecke.get_verbose_level(:GaloisGroup) >= 2 + do_print = Hecke.get_verbosity_level(:GaloisGroup) >= 1 + do_all = Hecke.get_verbosity_level(:GaloisGroup) >= 2 res = true for (x, s) = F.f diff --git a/src/Oscar.jl b/src/Oscar.jl index 4299b018d472..dfd0737ab8e6 100644 --- a/src/Oscar.jl +++ b/src/Oscar.jl @@ -112,34 +112,34 @@ function __init__() end __init_group_libraries() - add_verbose_scope(:K3Auto) - add_assert_scope(:K3Auto) + add_verbosity_scope(:K3Auto) + add_assertion_scope(:K3Auto) - add_verbose_scope(:EllipticSurface) - add_assert_scope(:EllipticSurface) + add_verbosity_scope(:EllipticSurface) + add_assertion_scope(:EllipticSurface) - add_verbose_scope(:MorphismFromRationalFunctions) - add_assert_scope(:MorphismFromRationalFunctions) + add_verbosity_scope(:MorphismFromRationalFunctions) + add_assertion_scope(:MorphismFromRationalFunctions) - add_verbose_scope(:Gluing) - add_assert_scope(:Gluing) + add_verbosity_scope(:Gluing) + add_assertion_scope(:Gluing) - add_verbose_scope(:Intersections) - add_assert_scope(:Intersections) + add_verbosity_scope(:Intersections) + add_assertion_scope(:Intersections) - add_verbose_scope(:MaximalAssociatedPoints) - add_assert_scope(:MaximalAssociatedPoints) + add_verbosity_scope(:MaximalAssociatedPoints) + add_assertion_scope(:MaximalAssociatedPoints) - add_verbose_scope(:Divisors) - add_assert_scope(:Divisors) + add_verbosity_scope(:Divisors) + add_assertion_scope(:Divisors) - add_verbose_scope(:Blowup) - add_assert_scope(:Blowup) + add_verbosity_scope(:Blowup) + add_assertion_scope(:Blowup) - add_verbose_scope(:hilbert) - add_assert_scope(:hilbert) + add_verbosity_scope(:hilbert) + add_assertion_scope(:hilbert) - add_verbose_scope(:FTheoryModelPrinter) + add_verbosity_scope(:FTheoryModelPrinter) add_verbosity_scope(:LinearQuotients) diff --git a/src/PolyhedralGeometry/Polyhedron/constructors.jl b/src/PolyhedralGeometry/Polyhedron/constructors.jl index 9e404d2f3193..25c7effb3a90 100644 --- a/src/PolyhedralGeometry/Polyhedron/constructors.jl +++ b/src/PolyhedralGeometry/Polyhedron/constructors.jl @@ -31,7 +31,7 @@ Construct a `Polyhedron` corresponding to a `Polymake.BigObject` of type `Polyto """ function polyhedron(p::Polymake.BigObject) T, f = _detect_scalar_and_field(Polyhedron, p) - if T == EmbeddedNumFieldElem{AbsSimpleNumFieldElem} && Hecke.isquadratic_type(number_field(f))[1] && Polymake.bigobject_eltype(p) == "QuadraticExtension" + if T == EmbeddedNumFieldElem{AbsSimpleNumFieldElem} && Hecke.is_quadratic_type(number_field(f))[1] && Polymake.bigobject_eltype(p) == "QuadraticExtension" p = _polyhedron_qe_to_on(p, f) end return Polyhedron{T}(p, f) diff --git a/src/Rings/AbelianClosure.jl b/src/Rings/AbelianClosure.jl index 9496cef12842..c75b28e03c6b 100644 --- a/src/Rings/AbelianClosure.jl +++ b/src/Rings/AbelianClosure.jl @@ -923,7 +923,7 @@ function _embedding(F::AbsSimpleNumField, K::QQAbField{AbsSimpleNumField}, x = Hecke.force_coerce_cyclo(Kn, x) # ... and then w.r.t. `F` a = Hecke.coefficients(x) - fl, sol = can_solve_with_solution(c, matrix(QQ, length(a), 1, a)) + fl, sol = can_solve_with_solution(c, matrix(QQ, length(a), 1, a); side = :right) if fl b = transpose(sol) b = [b[i] for i in 1:length(b)] diff --git a/src/Rings/FinField.jl b/src/Rings/FinField.jl index 1346ed99aa71..3ef85d240d4b 100644 --- a/src/Rings/FinField.jl +++ b/src/Rings/FinField.jl @@ -5,7 +5,7 @@ import Oscar.Nemo import Oscar.Hecke function __init__() - Hecke.add_verbose_scope(:DiscLog) + Hecke.add_verbosity_scope(:DiscLog) end ############################################################### diff --git a/src/Rings/groebner.jl b/src/Rings/groebner.jl index bee553f888e3..8e197377a66c 100644 --- a/src/Rings/groebner.jl +++ b/src/Rings/groebner.jl @@ -1565,7 +1565,7 @@ function _find_weights(F::Vector{P}) where {P <: MPolyRingElem} exp_diffs = permutedims(reduce(hcat, [e[i] - e[1] for e in (collect).((exponents).(F)) for i in 2:length(e)])) - K = kernel(matrix(QQ, nrows, ncols, exp_diffs))[2] + K = kernel(matrix(QQ, nrows, ncols, exp_diffs); side = :right) isempty(K) && return zeros(Int, ncols) # Here we try to find a vector with strictly positive entries in K # this method to find such a vector is taken from diff --git a/src/TropicalGeometry/intersection.jl b/src/TropicalGeometry/intersection.jl index f9ea0eeded7a..5ac2cb75de41 100644 --- a/src/TropicalGeometry/intersection.jl +++ b/src/TropicalGeometry/intersection.jl @@ -82,12 +82,12 @@ end # Output: the tropical intersection number as defined in [Maclagan-Sturmfels, Definition 3.6.5] # todo: rewrite function below so that it takes polyhedra as input function tropical_intersection_multiplicity(sigma1::Polyhedron,sigma2::Polyhedron) - B1 = kernel_basis(affine_equation_matrix(affine_hull(sigma1))[:,2:end]) - B1 = matrix(ZZ,[ numerator.(b .* lcm(denominator.(b))) for b in B1 ]) + B1 = kernel(affine_equation_matrix(affine_hull(sigma1))[:,2:end], side = :right) + B1 = matrix(ZZ,[ numerator.(B1[:, i] .* lcm(denominator.(B1[:, i]))) for i in 1:ncols(B1) ]) B1 = saturate(B1) - B2 = kernel_basis(affine_equation_matrix(affine_hull(sigma2))[:,2:end]) - B2 = matrix(ZZ,[ numerator.(b .* lcm(denominator.(b))) for b in B2 ]) + B2 = kernel(affine_equation_matrix(affine_hull(sigma2))[:,2:end], side = :right) + B2 = matrix(ZZ,[ numerator.(B2[:, i] .* lcm(denominator.(B2[:, i]))) for i in 1:ncols(B2) ]) B2 = saturate(B2) @req ncols(B1) == ncols(B2) && nrows(B1)+nrows(B2) >= ncols(B1) "polyhedra do not span ambient space" diff --git a/src/TropicalGeometry/linear_space.jl b/src/TropicalGeometry/linear_space.jl index 295d120f7a55..e8883a6faeef 100644 --- a/src/TropicalGeometry/linear_space.jl +++ b/src/TropicalGeometry/linear_space.jl @@ -308,7 +308,7 @@ function tropical_linear_space(I::MPolyIdeal, nu::Union{Nothing,TropicalSemiring x = gens(base_ring(I)) G = gens(I) macaulayMatrix = matrix([[coeff(g,xi) for xi in x] for g in G]) - A = matrix(kernel_basis(macaulayMatrix)) + A = transpose(kernel(macaulayMatrix, side = :right)) TropL = tropical_linear_space(A,nu, weighted_polyhedral_complex_only=weighted_polyhedral_complex_only) if !weighted_polyhedral_complex_only diff --git a/src/TropicalGeometry/variety.jl b/src/TropicalGeometry/variety.jl index 81f9be02a4e7..9bf08072344b 100644 --- a/src/TropicalGeometry/variety.jl +++ b/src/TropicalGeometry/variety.jl @@ -260,7 +260,7 @@ function tropical_variety_binomial(I::MPolyIdeal,nu::TropicalSemiringMap; weight # Constructing tropical variety set-theoretically ### A = QQMatrix(A) - L = matrix(QQ,kernel_basis(A)) + L = transpose(kernel(A, side = :right)) can_solve, V = can_solve_with_solution(transpose(A),matrix(QQ,[b]),side=:left) @req can_solve "tropical variety cannot be empty" SigmaV = polyhedral_complex(IncidenceMatrix([[1]]), V, nothing, L) @@ -456,7 +456,7 @@ function slope_eigenspace(M::MatElem{T}) where T <: Hecke.NonArchLocalFieldElem zk = maximal_order(k) for f = keys(lf) - se[f] = kernel(f(M))[2] #hopefully, this is in rref + se[f] = kernel(f(M), side = :right) #hopefully, this is in rref end @assert sum(ncols(x) for x = values(se)) == nrows(M) return se @@ -473,8 +473,8 @@ function _intersect(M::MatElem{T}, N::MatElem{T}) where T <: Hecke.FieldElem end end - r, v = kernel(I) #precision issues... - l = M*v[1:ncols(M), 1:r] + v = kernel(I, side = :right) #precision issues... + l = M*v[1:ncols(M), 1:ncols(v)] return transpose(rref(transpose(l))[2]) end diff --git a/test/AlgebraicGeometry/Surfaces/K3Auto.jl b/test/AlgebraicGeometry/Surfaces/K3Auto.jl index f61abfe36079..05f1ebc395a3 100644 --- a/test/AlgebraicGeometry/Surfaces/K3Auto.jl +++ b/test/AlgebraicGeometry/Surfaces/K3Auto.jl @@ -32,7 +32,7 @@ end S = integer_lattice(B, gram = G); weyl = QQ[31 61 52 71 5 -6 5 -2 -7 8] - weylk3 = change_base_ring(ZZ,solve_left(basis_matrix(L), weyl)) + weylk3 = change_base_ring(ZZ,Oscar.solve(basis_matrix(L), weyl; side = :left)) k3,_ = BorcherdsCtx(L, S, weylk3; compute_OR=false) walls = Oscar._walls_of_chamber(k3, weylk3) @test length(walls)==4 @@ -107,7 +107,7 @@ end # This is the a little expensive bit ... we leave it to the lower dimensional tests # weyl1, u, hh = Oscar.weyl_vector_non_degenerate(L, S, u0, weyl, h) weyl1 = QQ[80 30 -4 -14 -27 11 2 -12 -14 1 9 7 -1 -2 16 -12 4 7 11 6 -1 1 0 3 1 0] - weyl2 = change_base_ring(ZZ, solve_left(basis_matrix(L), weyl1)) + weyl2 = change_base_ring(ZZ, Oscar.solve(basis_matrix(L), weyl1; side = :left)) _, k3aut, chambers, rational_mod_aut =borcherds_method(L, S, weyl2, compute_OR=true) @test order(matrix_group(k3aut))==6 diff --git a/test/Groups/gsets.jl b/test/Groups/gsets.jl index 2fbd1e53871d..d10ca853c1fd 100644 --- a/test/Groups/gsets.jl +++ b/test/Groups/gsets.jl @@ -262,10 +262,10 @@ end @test has_preimage_with_preimage(acthom, pi)[1] @test order(image(acthom)[1]) == 48 - # isconjugate + # is_conjugate Omega = gset(G) - @test isconjugate(Omega, gen(V, 1), gen(V, 2)) - @test ! isconjugate(Omega, zero(V), gen(V, 1)) + @test is_conjugate(Omega, gen(V, 1), gen(V, 2)) + @test ! is_conjugate(Omega, zero(V), gen(V, 1)) # is_conjugate_with_data Omega = gset(G) diff --git a/test/PolyhedralGeometry/polyhedron.jl b/test/PolyhedralGeometry/polyhedron.jl index 62842a832215..18e41a83a6be 100644 --- a/test/PolyhedralGeometry/polyhedron.jl +++ b/test/PolyhedralGeometry/polyhedron.jl @@ -498,7 +498,7 @@ D = polyhedron(Polymake.polytope.dodecahedron()) R = coefficient_field(D) NF = number_field(R) - let isq = Hecke.isquadratic_type(NF) + let isq = Hecke.is_quadratic_type(NF) @test isq[1] @test isq[2] == 5 end From a7b4ceb3a9d975c952c6edd18f2331955f2a07da Mon Sep 17 00:00:00 2001 From: antonydellavecchia Date: Mon, 19 Feb 2024 10:12:38 +0100 Subject: [PATCH 11/29] Fix Grassmann Pluecker (#3382) * fixed * fix for symmetric intersections test * back to the roots * revert * Apply suggestions from code review Co-authored-by: Benjamin Lorenz --------- Co-authored-by: Tommy Hofmann Co-authored-by: Benjamin Lorenz (cherry picked from commit 74335480f99c8390f239437e5fdcbcb3e49a090d) --- src/Rings/mpoly-ideals.jl | 42 ++++++++++++++++++++++----------------- 1 file changed, 24 insertions(+), 18 deletions(-) diff --git a/src/Rings/mpoly-ideals.jl b/src/Rings/mpoly-ideals.jl index 20c1307ad44c..2e9b7d7a9281 100644 --- a/src/Rings/mpoly-ideals.jl +++ b/src/Rings/mpoly-ideals.jl @@ -1922,7 +1922,15 @@ small_generating_set(I::MPolyIdeal{<:MPolyDecRingElem}) = minimal_generating_set # ################################################################################ function grassmann_pluecker_ideal(subspace_dimension::Int, ambient_dimension::Int) - return convert(MPolyIdeal{QQMPolyRingElem}, Polymake.ideal.pluecker_ideal(subspace_dimension, ambient_dimension)) + I = convert(MPolyIdeal{QQMPolyRingElem}, + Polymake.ideal.pluecker_ideal(subspace_dimension, ambient_dimension)) + base = base_ring(I) + o = degrevlex(base) + + return ideal(IdealGens(base, gens(I), o; + keep_ordering=true, + isReduced=true, + isGB=true)) end @doc raw""" @@ -1944,33 +1952,31 @@ julia> grassmann_pluecker_ideal(2, 4) Ideal generated by x[1]*x[6] - x[2]*x[5] + x[3]*x[4] -julia> R, x = polynomial_ring(residue_ring(ZZ, 7)[1], "x" => (1:2, 1:3), ordering=:degrevlex) +julia> R, x = polynomial_ring(residue_ring(ZZ, 7)[1], "x" => (1:2, 1:3)) (Multivariate polynomial ring in 6 variables over ZZ/(7), zzModMPolyRingElem[x[1, 1] x[1, 2] x[1, 3]; x[2, 1] x[2, 2] x[2, 3]]) julia> grassmann_pluecker_ideal(R, 2, 4) Ideal generated by - x[1, 2]*x[2, 2] + 6*x[2, 1]*x[1, 3] + x[1, 1]*x[2, 3] + x[1, 1]*x[2, 3] + 6*x[2, 1]*x[1, 3] + x[1, 2]*x[2, 2] ``` """ function grassmann_pluecker_ideal(ring::MPolyRing, subspace_dimension::Int, ambient_dimension::Int) - pluecker_ideal = grassmann_pluecker_ideal(subspace_dimension, ambient_dimension) - converted_generators = elem_type(ring)[] - coeff_ring = base_ring(ring) - for g in gens(pluecker_ideal) - converted_coeffs = [coeff_ring(numerator(c)) for c in AbstractAlgebra.coefficients(g)] - polynomial = MPolyBuildCtx(ring) - - for (i, exponent) in enumerate(AbstractAlgebra.exponent_vectors(g)) - c = converted_coeffs[i] - push_term!(polynomial, c, exponent) - end - converted_g = finish(polynomial) - push!(converted_generators, converted_g) - end - return ideal(ring, converted_generators) + I = grassmann_pluecker_ideal(subspace_dimension, ambient_dimension) + coeff_ring = base_ring(ring) + o = degrevlex(ring) + coeffmap = c -> begin + @assert is_integral(c) + return coeff_ring(numerator(c)) + end + h = hom(base_ring(I), ring, coeffmap, gens(ring)) + converted_generators = elem_type(ring)[h(g) for g in groebner_basis(I; ordering = degrevlex(base_ring(I)))] + ideal(IdealGens(ring, converted_generators, o; + keep_ordering=true, + isReduced=true, + isGB=true)) end ################################################################################ From 684aadfba5d49c036ac70dfa1809cbc6b892f398 Mon Sep 17 00:00:00 2001 From: Max Horn Date: Mon, 19 Feb 2024 11:23:14 +0100 Subject: [PATCH 12/29] Fix show for RelativeBrauerGroupElem (#3373) - fix error because `Indent` was undefined - remove extra newline at end - add a missing `Lowercase` - simplify the code - make output order less random (cherry picked from commit aefcd0a7f265fd0c3d29df935df999391453c26b) --- experimental/GModule/GaloisCohomology.jl | 38 +++++++++++++++++++----- 1 file changed, 30 insertions(+), 8 deletions(-) diff --git a/experimental/GModule/GaloisCohomology.jl b/experimental/GModule/GaloisCohomology.jl index a12c0f65aa3b..c610f5c32505 100644 --- a/experimental/GModule/GaloisCohomology.jl +++ b/experimental/GModule/GaloisCohomology.jl @@ -6,7 +6,7 @@ import Oscar.GrpCoh: CoChain, MultGrpElem, MultGrp, GModule, is_consistent, Group import Base: parent import Oscar: direct_sum -import Oscar: pretty, Lowercase +import Oscar: pretty, Lowercase, Indent, Dedent export is_coboundary, idel_class_gmodule, relative_brauer_group export local_invariants, global_fundamental_class, shrink @@ -1398,14 +1398,12 @@ end function Base.show(io::IO, m::MIME"text/plain", a::RelativeBrauerGroupElem) io = pretty(io) - print(io, "Element of relative Brauer group of $(parent(a).k)\n") - ioC = IOContext(io, :supercompact => true, :compact => true) + print(io, "Element of relative Brauer group of ", Lowercase(), parent(a).k) + io = IOContext(io, :supercompact => true, :compact => true) print(io, Indent()) - for (p,v) = a.data - show(ioC, p) - print(io, " -> ") - show(ioC, v) - print(io, "\n") + data = sort(collect(a.data); by =(x -> first(x) isa AbsSimpleNumFieldEmbedding ? Inf : minimum(first(x)))) + for (p,v) in data + print(io, "\n", p, " -> ", v) end print(io, Dedent()) end @@ -1514,6 +1512,30 @@ an infinite direct sum of the local Brauer groups. The second return value is a map translating between the local data and explicit 2-cochains. + +```jldoctest +julia> G = SL(2,5) +SL(2,5) + +julia> T = character_table(G); + +julia> R = gmodule(T[9]) +G-module for G acting on vector space of dimension 6 over abelian closure of Q + +julia> S = gmodule(CyclotomicField, R) +G-module for G acting on vector space of dimension 6 over cyclotomic field of order 5 + +julia> B, mB = relative_brauer_group(base_ring(S), character_field(S)); + +julia> B +Relative Brauer group for cyclotomic field of order 5 over number field of degree 1 over QQ + +julia> b = B(S) +Element of relative Brauer group of number field of degree 1 over QQ + <2, 2> -> 1//2 + Z + <5, 5> -> 0 + Z + Complex embedding of number field -> 1//2 + Z +``` """ function relative_brauer_group(K::AbsSimpleNumField, k::Union{QQField, AbsSimpleNumField} = QQ) G, mG = automorphism_group(PermGroup, K) From eccd795050fe9f5c1f0b625387dc2f863e982fe7 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Lars=20G=C3=B6ttgens?= Date: Mon, 19 Feb 2024 12:48:03 +0100 Subject: [PATCH 13/29] Enable edit and show source buttons in docs (#3381) * Typos * Make the "show source" buttons in the docs work again * Enable the "Edit page on GitHub" buttons (cherry picked from commit 56b8182168f2d6535e718b3405892408c0b35278) --- docs/make_work.jl | 31 +++++++++++++++++++++++++++---- src/utils/utils.jl | 1 + 2 files changed, 28 insertions(+), 4 deletions(-) diff --git a/docs/make_work.jl b/docs/make_work.jl index 8a5ee65d35f4..ac86a8cd5a89 100644 --- a/docs/make_work.jl +++ b/docs/make_work.jl @@ -1,6 +1,6 @@ # # This file is included by docs/make.jl and by a helper function -# in src/Oscar.jl +# in src/utils/docs.jl # module BuildDoc @@ -139,7 +139,7 @@ function doit( joinpath(Oscar.oscardir, "docs", "oscar_references.bib"); style=oscar_style ) - # Copy documentation from Hecke, Nemo, AnstratAlgebra + # Copy documentation from Hecke, Nemo, AbstractAlgebra other_packages = [ (Oscar.Hecke, Oscar.heckedir), (Oscar.Nemo, Oscar.nemodir), @@ -166,12 +166,30 @@ function doit( end src = normpath(root, file) dst = normpath(dstbase, relpath(root, srcbase), file) - cp(src, dst; force=true) + if endswith(file, ".md") + symlink(src, dst) + else + cp(src, dst; force=true) + end chmod(dst, 0o644) end end end + function get_rev(uuid::Base.UUID) + deps = Documenter.Pkg.dependencies() + @assert haskey(deps, uuid) + if !isnothing(deps[uuid].git_revision) + return deps[uuid].git_revision + else + return "v$(deps[uuid].version)" + end + end + aarev = get_rev(Base.PkgId(Oscar.AbstractAlgebra).uuid) + nemorev = get_rev(Base.PkgId(Oscar.Nemo).uuid) + heckerev = get_rev(Base.PkgId(Oscar.Hecke).uuid) + singularrev = get_rev(Base.PkgId(Oscar.Singular).uuid) + cd(joinpath(Oscar.oscardir, "docs")) do DocMeta.setdocmeta!(Oscar, :DocTestSetup, Oscar.doctestsetup(); recursive=true) DocMeta.setdocmeta!(Oscar.Hecke, :DocTestSetup, :(using Hecke); recursive=true) @@ -197,7 +215,12 @@ function doit( warnonly=warnonly, checkdocs=:none, pages=doc, - remotes=nothing, # TODO: make work with Hecke, Nemo, AbstractAlgebra, see https://github.com/oscar-system/Oscar.jl/issues/588 + remotes=Dict( + Oscar.aadir => (Remotes.GitHub("Nemocas", "AbstractAlgebra.jl"), aarev), + Oscar.nemodir => (Remotes.GitHub("Nemocas", "Nemo.jl"), nemorev), + Oscar.heckedir => (Remotes.GitHub("thofma", "Hecke.jl"), heckerev), + Oscar.singulardir => (Remotes.GitHub("oscar-system", "Singular.jl"), singularrev), + ), plugins=[bib], ) end diff --git a/src/utils/utils.jl b/src/utils/utils.jl index 1d3d07cd7241..942aa935bb9c 100644 --- a/src/utils/utils.jl +++ b/src/utils/utils.jl @@ -5,6 +5,7 @@ const jll_deps = String["Antic_jll", "Arb_jll", "Calcium_jll", "FLINT_jll", "GAP const aadir = Base.pkgdir(AbstractAlgebra) const nemodir = Base.pkgdir(Nemo) const heckedir = Base.pkgdir(Hecke) +const singulardir = Base.pkgdir(Singular) include("versioninfo.jl") include("docs.jl") From 1a2a05081eb5e3c4f6e334eb1787b9773436bd4f Mon Sep 17 00:00:00 2001 From: Benjamin Lorenz Date: Tue, 20 Feb 2024 01:49:32 +0100 Subject: [PATCH 14/29] galois_group: fix is_normal call after removed deprecations (#3385) * fix is_normal call after removed deprecations * galois_group: add test from the book (cherry picked from commit a73b844f0b2d32180c5ff84ed6555a3439706a18) --- src/NumberTheory/GaloisGrp/GaloisGrp.jl | 2 +- test/NumberTheory/galthy.jl | 6 ++++++ 2 files changed, 7 insertions(+), 1 deletion(-) diff --git a/src/NumberTheory/GaloisGrp/GaloisGrp.jl b/src/NumberTheory/GaloisGrp/GaloisGrp.jl index 06bd3b68a9a3..385b60638459 100644 --- a/src/NumberTheory/GaloisGrp/GaloisGrp.jl +++ b/src/NumberTheory/GaloisGrp/GaloisGrp.jl @@ -2091,7 +2091,7 @@ function descent(GC::GaloisCtx, G::PermGroup, F::GroupFilter, si::PermGroupElem; local lt if index(G, s) < 100 @vtime :GaloisGroup 2 lt = right_transversal(G, s) - elseif is_normal(G, s) + elseif is_normalized_by(s, G) lt = [one(G)] # I don't know how to get the identity else @vtime :GaloisGroup 2 lt = short_right_transversal(G, s, si) diff --git a/test/NumberTheory/galthy.jl b/test/NumberTheory/galthy.jl index a480d9a838e1..3910a12d8ae4 100644 --- a/test/NumberTheory/galthy.jl +++ b/test/NumberTheory/galthy.jl @@ -30,6 +30,12 @@ Gs, Cs = galois_group(K, algorithm = :Symbolic) @test is_isomorphic(G, Gc) @test is_isomorphic(G, Gs) + + # from the book + K, a = number_field(x^9 - 3*x^8 + x^6 + 15*x^5 - 13*x^4 - + 3*x^3 + 4*x - 1, "a") + G, C = galois_group(K) + @test order(G) == 216 end import Oscar.GaloisGrp: primitive_by_shape, an_sn_by_shape, cycle_structures From bac429aed969b8ebc11e4d72205910c0264a8884 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Lars=20G=C3=B6ttgens?= Date: Tue, 20 Feb 2024 15:46:30 +0100 Subject: [PATCH 15/29] Rename `vec` for AbstractAlgebra matrices to `_vec` (#3387) * Rename `vec` for AbstractAlgebra matrices to `_vec` * Move `_vec` to src * Adapt callsites (cherry picked from commit 0b282fbd8fe07b00a6dbfc4fc077193ab29f55b3) --- experimental/GModule/GModule.jl | 20 ++----------------- experimental/Schemes/elliptic_surface.jl | 2 +- src/AlgebraicGeometry/Surfaces/K3Auto.jl | 20 +++++++++---------- .../ToricLineBundles/constructors.jl | 2 +- src/Modules/missing_functionality.jl | 15 ++++++++++++++ src/Modules/mpoly-localizations.jl | 2 +- .../PolyhedralFan/standard_constructions.jl | 2 +- src/PolyhedralGeometry/solving_integrally.jl | 2 +- src/Rings/mpolyquo-localizations.jl | 2 +- 9 files changed, 33 insertions(+), 34 deletions(-) diff --git a/experimental/GModule/GModule.jl b/experimental/GModule/GModule.jl index de3937ba028c..b88b11dfe823 100644 --- a/experimental/GModule/GModule.jl +++ b/experimental/GModule/GModule.jl @@ -8,7 +8,7 @@ import Hecke: data # first does a "restriction of scalars" or blow up with the rep mat # second tries to conjugate down to k -import Oscar: gmodule, GAPWrap +import Oscar: _vec, gmodule, GAPWrap import Oscar.GrpCoh: MultGrp, MultGrpElem import AbstractAlgebra: Group, Module @@ -1351,7 +1351,7 @@ end function invariant_forms(C::GModule{<:Any, <:AbstractAlgebra.FPModule}) D = Oscar.dual(C) h = hom_base(C, D) - r, k = kernel(transpose(reduce(vcat, [matrix(base_ring(C), 1, dim(C)^2, vec(x-transpose(x))) for x = h]))) + r, k = kernel(transpose(reduce(vcat, [matrix(base_ring(C), 1, dim(C)^2, _vec(x-transpose(x))) for x = h]))) return [sum(h[i]*k[i, j] for i=1:length(h)) for j=1:r] end @@ -1443,22 +1443,6 @@ end #TODO: cover all finite fields # make the Modules work -#to bypass the vec(collect(M)) which copies twice -function Base.vec(M::Generic.Mat) - return vec(M.entries) -end - -function Base.vec(M::MatElem) - r = elem_type(base_ring(M))[] - sizehint!(r, nrows(M) * ncols(M)) - for j=1:ncols(M) - for i=1:nrows(M) - push!(r, M[i, j]) - end - end - return r -end - function Oscar.simplify(C::GModule{<:Any, <:AbstractAlgebra.FPModule{QQFieldElem}}) return gmodule(QQ, Oscar.simplify(gmodule(ZZ, C))[1]) end diff --git a/experimental/Schemes/elliptic_surface.jl b/experimental/Schemes/elliptic_surface.jl index 7d6e9cc1f5bb..57ff77e54e91 100644 --- a/experimental/Schemes/elliptic_surface.jl +++ b/experimental/Schemes/elliptic_surface.jl @@ -1215,7 +1215,7 @@ function horizontal_decomposition(X::EllipticSurface, F::Vector{QQFieldElem}) else found = false for (i,(T, tor)) in enumerate(tors) - d = F2-vec(tor) + d = F2 - _vec(tor) if all(isone(denominator(i)) for i in d) found = true T0 = mordell_weil_torsion(X)[i] diff --git a/src/AlgebraicGeometry/Surfaces/K3Auto.jl b/src/AlgebraicGeometry/Surfaces/K3Auto.jl index ee5f88013354..ce64ad6677b8 100644 --- a/src/AlgebraicGeometry/Surfaces/K3Auto.jl +++ b/src/AlgebraicGeometry/Surfaces/K3Auto.jl @@ -147,7 +147,7 @@ function BorcherdsCtx(L::ZZLat, S::ZZLat, weyl::ZZMatrix; compute_OR::Bool=true) phi = phiSS_S*inv(i)*phi*j img,_ = sub(ODSS,[ODSS(phi*hom(g)*inv(phi)) for g in imOR]) ds = degree(SS) - membership_test = (g->ODSS(hom(DSS,DSS,[DSS(vec(matrix(QQ, 1, ds, lift(x))*g)) for x in gens(DSS)])) in img) + membership_test = (g->ODSS(hom(DSS,DSS,[DSS(_vec(matrix(QQ, 1, ds, lift(x))*g)) for x in gens(DSS)])) in img) end else membership_test(g) = is_pm1_on_discr(SS,g) @@ -311,8 +311,8 @@ function rays(D::K3Chamber) # clear denominators Lz = ZZMatrix[change_base_ring(ZZ,i*denominator(i)) for i in Lq] # primitive in S - Lz = ZZMatrix[divexact(i,gcd(vec(i))) for i in Lz] - @hassert :K3Auto 2 all(all(x>=0 for x in vec(r*gram_matrix(D.data.SS)*transpose(i))) for i in Lz) + Lz = ZZMatrix[divexact(i,gcd(_vec(i))) for i in Lz] + @hassert :K3Auto 2 all(all(x>=0 for x in _vec(r*gram_matrix(D.data.SS)*transpose(i))) for i in Lz) return Lz end @@ -521,9 +521,9 @@ function enumerate_quadratic_triple(Q, b, c; algorithm=:short_vectors, equal=fal L, p, dist = Hecke._convert_type(Q, b, QQ(c)) #@vprint :K3Auto 1 ambient_space(L), basis_matrix(L), p, dist if equal - cv = Hecke.close_vectors(L, vec(p), dist, dist, check=false) + cv = Hecke.close_vectors(L, _vec(p), dist, dist, check=false) else - cv = Hecke.close_vectors(L, vec(p), dist, check=false) + cv = Hecke.close_vectors(L, _vec(p), dist, check=false) end end return cv @@ -696,7 +696,7 @@ Return whether the isometry `g` of `S` acts as `+-1` on the discriminant group. """ function is_pm1_on_discr(S::ZZLat, g::ZZMatrix) D = discriminant_group(S) - imgs = [D(vec(matrix(QQ,1,rank(S),lift(d))*g)) for d in gens(D)] + imgs = [D(_vec(matrix(QQ,1,rank(S),lift(d))*g)) for d in gens(D)] return all(imgs[i] == gen(D, i) for i in 1:ngens(D)) || all(imgs[i] == -gen(D, i) for i in 1:ngens(D)) # OD = orthogonal_group(D) # g1 = hom(D,D,[D(lift(d)*g) for d in gens(D)]) @@ -1109,7 +1109,7 @@ function _alg58_close_vector(data::BorcherdsCtx, w::ZZMatrix) #cv = enumerate_quadratic_triple(Q,-b,-c,equal=true) mul!(b, Qi, b) #b = Qi*b - v = vec(b) + v = _vec(b) upperbound = inner_product(V,v,v) + c # solve the quadratic triple cv = close_vectors(N, v, upperbound, upperbound, check=false) @@ -1157,7 +1157,7 @@ function _walls_of_chamber(data::BorcherdsCtx, weyl_vector, algorithm::Symbol=:s walls = Vector{ZZMatrix}(undef,d) for i in 1:d vs = numerator(FakeFmpqMat(walls1[i])) - g = gcd(vec(vs)) + g = gcd(_vec(vs)) if g != 1 vs = divexact(vs, g) end @@ -1175,7 +1175,7 @@ function _walls_of_chamber(data::BorcherdsCtx, weyl_vector, algorithm::Symbol=:s v = matrix(QQ, 1, degree(data.SS), r[i]) # rescale v to be primitive in S vs = numerator(FakeFmpqMat(v)) - g = gcd(vec(vs)) + g = gcd(_vec(vs)) if g!=1 vs = divexact(vs, g) end @@ -1262,7 +1262,7 @@ Based on Algorithm 5.13 in [Shi15](@cite) - `vS`: Given with respect to the basis of `S`. """ function unproject_wall(data::BorcherdsCtx, vS::ZZMatrix) - d = gcd(vec(vS*data.gramS)) + d = gcd(_vec(vS*data.gramS)) v = QQ(1,d)*(vS*basis_matrix(data.S)) # primitive in Sdual vsq = QQ((vS*data.gramS*transpose(vS))[1,1],d^2) diff --git a/src/AlgebraicGeometry/ToricVarieties/ToricLineBundles/constructors.jl b/src/AlgebraicGeometry/ToricVarieties/ToricLineBundles/constructors.jl index b616d17c097d..60bc39b42e47 100644 --- a/src/AlgebraicGeometry/ToricVarieties/ToricLineBundles/constructors.jl +++ b/src/AlgebraicGeometry/ToricVarieties/ToricLineBundles/constructors.jl @@ -129,7 +129,7 @@ function toric_line_bundle(v::NormalToricVarietyType, dc::ToricDivisorClass) g = map_from_torusinvariant_cartier_divisor_group_to_torusinvariant_weil_divisor_group(v) h = map_from_torusinvariant_cartier_divisor_group_to_picard_group(v) cartier_class = preimage(g*f, divisor_class(dc)) - td = toric_divisor(v, vec(g(cartier_class).coeff)) + td = toric_divisor(v, _vec(g(cartier_class).coeff)) l = ToricLineBundle(v, h(cartier_class)) set_attribute!(td, :is_cartier, true) set_attribute!(l, :toric_divisor, td) diff --git a/src/Modules/missing_functionality.jl b/src/Modules/missing_functionality.jl index 9e96c88f4a18..164928c479a3 100644 --- a/src/Modules/missing_functionality.jl +++ b/src/Modules/missing_functionality.jl @@ -84,3 +84,18 @@ function (==)(M1::SubquoModule{T}, M2::SubquoModule{T}) where {T<:AbsLocalizedRi end +#to bypass the vec(collect(M)) which copies twice +function _vec(M::Generic.Mat) + return vec(M.entries) +end + +function _vec(M::MatElem) + r = elem_type(base_ring(M))[] + sizehint!(r, nrows(M) * ncols(M)) + for j=1:ncols(M) + for i=1:nrows(M) + push!(r, M[i, j]) + end + end + return r +end diff --git a/src/Modules/mpoly-localizations.jl b/src/Modules/mpoly-localizations.jl index 644aeaaa88f0..1ae10fdb66c0 100644 --- a/src/Modules/mpoly-localizations.jl +++ b/src/Modules/mpoly-localizations.jl @@ -77,7 +77,7 @@ function has_nonempty_intersection(U::MPolyProductOfMultSets, I::MPolyIdeal; che T = pre_saturation_data(Iloc) Bext = transpose(T * transpose(A)) #Bext = A*T - u = lcm(vec(denominator.(Bext))) + u = lcm(_vec(denominator.(Bext))) B = map_entries(x->preimage(map_from_base_ring(Iloc), x), u*Bext) return true, u*g, B end diff --git a/src/PolyhedralGeometry/PolyhedralFan/standard_constructions.jl b/src/PolyhedralGeometry/PolyhedralFan/standard_constructions.jl index f3f824dd2da5..398f4d313249 100644 --- a/src/PolyhedralGeometry/PolyhedralFan/standard_constructions.jl +++ b/src/PolyhedralGeometry/PolyhedralFan/standard_constructions.jl @@ -106,7 +106,7 @@ function star_subdivision(Sigma::_FanLikeType, new_ray::AbstractVector{<:Integer old_rays = matrix(ZZ, rays(Sigma)) # In case the new ray is an old ray. - new_ray_index = findfirst(i->vec(old_rays[i:i,:])==new_ray, 1:nrows(old_rays)) + new_ray_index = findfirst(i->vec(old_rays[i,:])==new_ray, 1:nrows(old_rays)) new_rays = old_rays if isnothing(new_ray_index) new_rays = vcat(old_rays, matrix(ZZ, [new_ray])) diff --git a/src/PolyhedralGeometry/solving_integrally.jl b/src/PolyhedralGeometry/solving_integrally.jl index 09c86b0eaae9..50230fdf74a6 100644 --- a/src/PolyhedralGeometry/solving_integrally.jl +++ b/src/PolyhedralGeometry/solving_integrally.jl @@ -4,7 +4,7 @@ function solve_mixed(as::Type{SubObjectIterator{PointVector{ZZRingElem}}}, A::ZZ @req nrows(C) == nrows(d) "solve_mixed(A,b,C,d): C and d must have the same number of rows." @req ncols(b) == 1 "solve_mixed(A,b,C,d): b must be a matrix with a single column." @req ncols(d) == 1 "solve_mixed(A,b,C,d): d must be a matrix with a single column." - P = polyhedron((-C, vec(-d)), (A, vec(b))) + P = polyhedron((-C, _vec(-d)), (A, _vec(b))) if !permit_unbounded return lattice_points(P) else diff --git a/src/Rings/mpolyquo-localizations.jl b/src/Rings/mpolyquo-localizations.jl index 644e276ad09a..e5b88af17666 100644 --- a/src/Rings/mpolyquo-localizations.jl +++ b/src/Rings/mpolyquo-localizations.jl @@ -921,7 +921,7 @@ function write_as_linear_combination( for a in g parent(a) === L || error("elements do not belong to the same ring") end - return L.(vec(coordinates(lift(f), ideal(L, g)))[1:length(g)]) # temporary hack; to be replaced. + return L.(_vec(coordinates(lift(f), ideal(L, g)))[1:length(g)]) # temporary hack; to be replaced. end write_as_linear_combination(f::MPolyQuoLocRingElem, g::Vector) = write_as_linear_combination(f, parent(f).(g)) From c5389ae1eb9cd4f37fd6e91a059f682d44b15a26 Mon Sep 17 00:00:00 2001 From: Thomas Breuer Date: Fri, 16 Feb 2024 14:56:03 +0100 Subject: [PATCH 16/29] add `map_entries` for matrix groups (#3341) (cherry picked from commit eb7bbdf0abf368e476845ae9d5d43f6aa97fbace) --- docs/src/Groups/matgroup.md | 3 +- src/Groups/matrices/MatGrp.jl | 55 ++++++++++++++++++++++++++++++----- test/Groups/matrixgroups.jl | 32 ++++++++++++++++++++ 3 files changed, 82 insertions(+), 8 deletions(-) diff --git a/docs/src/Groups/matgroup.md b/docs/src/Groups/matgroup.md index 17ab0aa3e385..df733faa6e50 100644 --- a/docs/src/Groups/matgroup.md +++ b/docs/src/Groups/matgroup.md @@ -11,9 +11,10 @@ end matrix_group(R::Ring, m::Int, V::AbstractVector{T}; check::Bool=true) where T<:Union{MatElem,MatrixGroupElem} MatrixGroup{RE<:RingElem, T<:MatElem{RE}} MatrixGroupElem{RE<:RingElem, T<:MatElem{RE}} -base_ring(G::MatrixGroup) +base_ring(G::MatrixGroup{RE}) where RE <: RingElem degree(G::MatrixGroup) centralizer(G::MatrixGroup{T}, x::MatrixGroupElem{T}) where T <: FinFieldElem +map_entries(f, G::MatrixGroup) ``` ## Elements of matrix groups diff --git a/src/Groups/matrices/MatGrp.jl b/src/Groups/matrices/MatGrp.jl index 3e3ed7196569..92896f6d0339 100644 --- a/src/Groups/matrices/MatGrp.jl +++ b/src/Groups/matrices/MatGrp.jl @@ -102,13 +102,7 @@ function Base.deepcopy_internal(x::MatrixGroupElem, dict::IdDict) error("$x has neither :X nor :elm") end -function change_base_ring(R::Ring, G::MatrixGroup) - g = dense_matrix_type(R)[] - for h in gens(G) - push!(g, map_entries(R, h.elm)) - end - return matrix_group(g) -end +change_base_ring(R::Ring, G::MatrixGroup) = map_entries(R, G) ######################################################################## # @@ -547,6 +541,53 @@ function order(::Type{T}, G::MatrixGroup) where T <: IntegerUnion return T(res)::T end +""" + map_entries(f, G::MatrixGroup) + +Return the matrix group obtained by applying `f` element-wise to +each generator of `G`. + +`f` can be a ring or a field, a suitable map, or a Julia function. + +# Examples +```jldoctest +julia> mat = matrix(ZZ, 2, 2, [1, 1, 0, 1]); + +julia> G = matrix_group(mat); + +julia> G2 = map_entries(x -> -x, G) +Matrix group of degree 2 + over integer ring + +julia> is_finite(G2) +false + +julia> order(map_entries(GF(3), G)) +3 +``` +""" +function map_entries(f, G::MatrixGroup) + Ggens = gens(G) + if length(Ggens) == 0 + z = f(zero(base_ring(G))) + return matrix_group(parent(z), degree(G), MatrixGroupElem[]) + else + imgs = [map_entries(f, matrix(x)) for x in gens(G)] + return matrix_group(imgs) + end +end + +function map_entries(R::Ring, G::MatrixGroup) + imgs = [map_entries(R, matrix(x)) for x in gens(G)] + return matrix_group(R, degree(G), imgs) +end + +function map_entries(mp::Map, G::MatrixGroup) + imgs = [map_entries(mp, matrix(x)) for x in gens(G)] + return matrix_group(codomain(mp), degree(G), imgs) +end + + ######################################################################## # # Constructors diff --git a/test/Groups/matrixgroups.jl b/test/Groups/matrixgroups.jl index 1cae16db89dc..320606ddc62d 100644 --- a/test/Groups/matrixgroups.jl +++ b/test/Groups/matrixgroups.jl @@ -379,6 +379,38 @@ end @test_throws ArgumentError matrix_group([x1,x3]) end +@testset "map_entries for matrix groups" begin + mat = matrix(ZZ, 2, 2, [1, 1, 0, 1]) + G = matrix_group(mat) + T = trivial_subgroup(G)[1] + @test length(gens(T)) == 0 + for R in [GF(2), GF(3, 2), residue_ring(ZZ, 6)[1]] + red = map_entries(R, G) + @test matrix(gen(red, 1)) == map_entries(R, mat) + red = map_entries(R, T) + @test matrix(one(red)) == map_entries(R, one(mat)) + end + + F = GF(2) + mp = MapFromFunc(ZZ, F, x -> F(x)) + red = map_entries(mp, G) + @test red == map_entries(F, G) + red = map_entries(mp, T) + @test red == map_entries(F, T) + + G1 = special_linear_group(2, 9) + G2 = map_entries(x -> x^3, G1) + @test gens(G1) != gens(G2) + @test G1 == G2 + T = trivial_subgroup(G1)[1] + @test length(gens(T)) == 0 + @test map_entries(x -> x^3, T) == trivial_subgroup(G2)[1] + + mat = matrix(QQ, 2, 2, [2, 1, 0, 1]) + G = matrix_group(mat) + @test_throws ArgumentError map_entries(GF(2), G) +end + @testset "Iterator" begin G = SL(2,3) N = 0 From d8697bc142b9f5504d9ef72a093222de93cb77be Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Lars=20G=C3=B6ttgens?= Date: Tue, 20 Feb 2024 21:03:46 +0100 Subject: [PATCH 17/29] Remove unneeded GAP package `sla` (#3398) (cherry picked from commit 0bc8558fdff26f74b01f959e8f78494fa2d016fb) --- src/Oscar.jl | 1 - 1 file changed, 1 deletion(-) diff --git a/src/Oscar.jl b/src/Oscar.jl index dfd0737ab8e6..ee88287a68fe 100644 --- a/src/Oscar.jl +++ b/src/Oscar.jl @@ -103,7 +103,6 @@ function __init__() "forms", # bilinear/sesquilinear/quadratic forms "primgrp", # primitive groups library "repsn", # constructing representations of finite groups - "sla", # computing with simple Lie algebras "smallgrp", # small groups library "transgrp", # transitive groups library "wedderga", # provides a function to compute Schur indices From 72c5ca3067f1d73815f630be535a25bad91773c8 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Lars=20G=C3=B6ttgens?= Date: Tue, 20 Feb 2024 23:04:33 +0100 Subject: [PATCH 18/29] Make `is_exterior_power` (and friends) internal (#3346) * Rename `is_exterior_power` to `is_exterior_power_with_data` (and friends) * Revert "Rename `is_exterior_power` to `is_exterior_power_with_data` (and friends)" This reverts commit b19369b6f8eba00b59cb359858956a163180bcf8. * Make `is_exterior_power` internal * the same for similar functions (cherry picked from commit 9d88a8f55625d8aff7ccf65f1a76f48ec186ec70) --- experimental/LieAlgebras/docs/src/modules.md | 12 --- .../LieAlgebras/src/LieAlgebraModule.jl | 102 +++++++++--------- .../LieAlgebras/src/LieAlgebraModuleHom.jl | 42 ++++---- experimental/LieAlgebras/src/LieAlgebras.jl | 23 ++-- .../LieAlgebras/test/LieAlgebraModule-test.jl | 34 +++--- src/Modules/ExteriorPowers/FreeModules.jl | 4 +- src/Modules/ExteriorPowers/Generic.jl | 26 ++--- src/Modules/UngradedModules/Methods.jl | 6 +- src/Modules/deRhamComplexes.jl | 4 +- src/exports.jl | 1 - test/Modules/ExteriorPowers.jl | 2 +- 11 files changed, 119 insertions(+), 137 deletions(-) diff --git a/experimental/LieAlgebras/docs/src/modules.md b/experimental/LieAlgebras/docs/src/modules.md index a646d517f5d2..1c0dc6ecf63b 100644 --- a/experimental/LieAlgebras/docs/src/modules.md +++ b/experimental/LieAlgebras/docs/src/modules.md @@ -63,15 +63,3 @@ tensor_power(::LieAlgebraModule{C}, ::Int) where {C<:FieldElem} abstract_module(::LieAlgebra{C}, ::Int, ::Vector{<:MatElem{C}}, ::Vector{<:VarName}; ::Bool) where {C<:FieldElem} abstract_module(::LieAlgebra{C}, ::Int, ::Matrix{SRow{C}}, ::Vector{<:VarName}; ::Bool) where {C<:FieldElem} ``` - -# Type-dependent getters - -```@docs -is_standard_module(::LieAlgebraModule) -is_dual(::LieAlgebraModule) -is_direct_sum(::LieAlgebraModule) -is_tensor_product(::LieAlgebraModule) -is_exterior_power(::LieAlgebraModule) -is_symmetric_power(::LieAlgebraModule) -is_tensor_power(::LieAlgebraModule) -``` diff --git a/experimental/LieAlgebras/src/LieAlgebraModule.jl b/experimental/LieAlgebras/src/LieAlgebraModule.jl index 6c4c680048fc..9d03f57ad385 100644 --- a/experimental/LieAlgebras/src/LieAlgebraModule.jl +++ b/experimental/LieAlgebras/src/LieAlgebraModule.jl @@ -155,12 +155,12 @@ function Base.show(io::IO, ::MIME"text/plain", V::LieAlgebraModule) io = pretty(io) println(io, _module_type_to_string(V)) println(io, Indent(), "of dimension $(dim(V))") - if is_dual(V)[1] || - is_direct_sum(V)[1] || - is_tensor_product(V)[1] || - is_exterior_power(V)[1] || - is_symmetric_power(V)[1] || - is_tensor_power(V)[1] + if _is_dual(V)[1] || + _is_direct_sum(V)[1] || + _is_tensor_product(V)[1] || + _is_exterior_power(V)[1] || + _is_symmetric_power(V)[1] || + _is_tensor_power(V)[1] _show_inner(io, V) end print(io, Dedent()) @@ -169,38 +169,38 @@ function Base.show(io::IO, ::MIME"text/plain", V::LieAlgebraModule) end function _show_inner(io::IO, V::LieAlgebraModule) - if is_standard_module(V) + if _is_standard_module(V) println(io, "standard module") - elseif ((fl, W) = is_dual(V); fl) + elseif ((fl, W) = _is_dual(V); fl) println(io, "dual of ", Lowercase()) print(io, Indent()) _show_inner(io, W) print(io, Dedent()) - elseif ((fl, Ws) = is_direct_sum(V); fl) + elseif ((fl, Ws) = _is_direct_sum(V); fl) println(io, "direct sum with direct summands") print(io, Indent()) for W in Ws _show_inner(io, W) end print(io, Dedent()) - elseif ((fl, Ws) = is_tensor_product(V); fl) + elseif ((fl, Ws) = _is_tensor_product(V); fl) println(io, "tensor product with tensor factors") print(io, Indent()) for W in Ws _show_inner(io, W) end print(io, Dedent()) - elseif ((fl, W, k) = is_exterior_power(V); fl) + elseif ((fl, W, k) = _is_exterior_power(V); fl) println(io, "$(ordinal_number_string(k)) exterior power of") print(io, Indent()) _show_inner(io, W) print(io, Dedent()) - elseif ((fl, W, k) = is_symmetric_power(V); fl) + elseif ((fl, W, k) = _is_symmetric_power(V); fl) println(io, "$(ordinal_number_string(k)) symmetric power of") print(io, Indent()) _show_inner(io, W) print(io, Dedent()) - elseif ((fl, W, k) = is_tensor_power(V); fl) + elseif ((fl, W, k) = _is_tensor_power(V); fl) println(io, "$(ordinal_number_string(k)) tensor power of") print(io, Indent()) _show_inner(io, W) @@ -221,19 +221,19 @@ function Base.show(io::IO, V::LieAlgebraModule) end function _module_type_to_string(V::LieAlgebraModule) - if is_standard_module(V) + if _is_standard_module(V) return "Standard module" - elseif is_dual(V)[1] + elseif _is_dual(V)[1] return "Dual module" - elseif is_direct_sum(V)[1] + elseif _is_direct_sum(V)[1] return "Direct sum module" - elseif is_tensor_product(V)[1] + elseif _is_tensor_product(V)[1] return "Tensor product module" - elseif is_exterior_power(V)[1] + elseif _is_exterior_power(V)[1] return "Exterior power module" - elseif is_symmetric_power(V)[1] + elseif _is_symmetric_power(V)[1] return "Symmetric power module" - elseif is_tensor_power(V)[1] + elseif _is_tensor_power(V)[1] return "Tensor power module" else return "Abstract Lie algebra module" @@ -354,24 +354,24 @@ function (V::LieAlgebraModule{C})( ) where {C<:FieldElem} if length(a) == 1 && V === parent(a[1]) return a[1] - elseif ((fl, W) = is_dual(V); fl) + elseif ((fl, W) = _is_dual(V); fl) @req length(a) == 1 "Invalid input length." @req W === parent(v) "Incompatible modules." return V(coefficients(v)) - elseif ((fl, Vs) = is_direct_sum(V); fl) + elseif ((fl, Vs) = _is_direct_sum(V); fl) @req length(a) == length(Vs) "Invalid input length." @req all(i -> parent(a[i]) === Vs[i], 1:length(a)) "Incompatible modules." return sum(inji(ai) for (ai, inji) in zip(a, canonical_injections(V)); init=zero(V)) - elseif is_tensor_product(V)[1] + elseif _is_tensor_product(V)[1] pure = get_attribute(V, :tensor_pure_function) return pure(a)::elem_type(V) - elseif is_exterior_power(V)[1] + elseif _is_exterior_power(V)[1] pure = get_attribute(V, :wedge_pure_function) return pure(a)::elem_type(V) - elseif is_symmetric_power(V)[1] + elseif _is_symmetric_power(V)[1] pure = get_attribute(V, :mult_pure_function) return pure(a)::elem_type(V) - elseif is_tensor_power(V)[1] + elseif _is_tensor_power(V)[1] pure = get_attribute(V, :tensor_pure_function) return pure(a)::elem_type(V) else @@ -384,15 +384,15 @@ function (V::LieAlgebraModule{C})(a::LieAlgebraModuleElem{C}...) where {C<:Field end function _is_allowed_input_length(V::LieAlgebraModule, a::Int) - if ((fl, Vs) = is_direct_sum(V); fl) + if ((fl, Vs) = _is_direct_sum(V); fl) return a == length(Vs) - elseif ((fl, Vs) = is_tensor_product(V); fl) + elseif ((fl, Vs) = _is_tensor_product(V); fl) return a == length(Vs) - elseif ((fl, W, k) = is_exterior_power(V); fl) + elseif ((fl, W, k) = _is_exterior_power(V); fl) return a == k - elseif ((fl, W, k) = is_symmetric_power(V); fl) + elseif ((fl, W, k) = _is_symmetric_power(V); fl) return a == k - elseif ((fl, W, k) = is_tensor_power(V); fl) + elseif ((fl, W, k) = _is_tensor_power(V); fl) return a == k else throw(ArgumentError("Invalid input.")) @@ -518,11 +518,11 @@ end ############################################################################### @doc raw""" - is_standard_module(V::LieAlgebraModule{C}) -> Bool + _is_standard_module(V::LieAlgebraModule{C}) -> Bool Check whether `V` has been constructed as a standard module. """ -function is_standard_module(V::LieAlgebraModule) +function _is_standard_module(V::LieAlgebraModule) if has_attribute(V, :is_standard_module) @assert get_attribute(V, :is_standard_module)::Bool === true return true @@ -531,13 +531,13 @@ function is_standard_module(V::LieAlgebraModule) end @doc raw""" - is_dual(V::LieAlgebraModule{C}) -> Bool, LieAlgebraModule{C} + _is_dual(V::LieAlgebraModule{C}) -> Bool, LieAlgebraModule{C} Check whether `V` has been constructed as a dual module. If it has, return `true` and the base module. If not, return `false` as the first return value, and an arbitrary value for the second. """ -function is_dual(V::LieAlgebraModule) +function _is_dual(V::LieAlgebraModule) if has_attribute(V, :is_dual) W = get_attribute(V, :is_dual)::typeof(V) return (true, W) @@ -546,13 +546,13 @@ function is_dual(V::LieAlgebraModule) end @doc raw""" - is_direct_sum(V::LieAlgebraModule{C}) -> Bool, Vector{LieAlgebraModule{C}} + _is_direct_sum(V::LieAlgebraModule{C}) -> Bool, Vector{LieAlgebraModule{C}} Check whether `V` has been constructed as a direct sum of modules. If it has, return `true` and the summands. If not, return `false` as the first return value, and an empty vector for the second. """ -function is_direct_sum(V::LieAlgebraModule) +function _is_direct_sum(V::LieAlgebraModule) if has_attribute(V, :is_direct_sum) summands = get_attribute(V, :is_direct_sum)::Vector{typeof(V)} return (true, summands) @@ -561,13 +561,13 @@ function is_direct_sum(V::LieAlgebraModule) end @doc raw""" - is_tensor_product(V::LieAlgebraModule{C}) -> Bool, Vector{LieAlgebraModule{C}} + _is_tensor_product(V::LieAlgebraModule{C}) -> Bool, Vector{LieAlgebraModule{C}} Check whether `V` has been constructed as a tensor product of modules. If it has, return `true` and the tensor factors. If not, return `false` as the first return value, and an empty vector for the second. """ -function is_tensor_product(V::LieAlgebraModule) +function _is_tensor_product(V::LieAlgebraModule) if has_attribute(V, :is_tensor_product) factors = get_attribute(V, :is_tensor_product)::Vector{typeof(V)} return (true, factors) @@ -576,13 +576,13 @@ function is_tensor_product(V::LieAlgebraModule) end @doc raw""" - is_exterior_power(V::LieAlgebraModule{C}) -> Bool, LieAlgebraModule{C}, Int + _is_exterior_power(V::LieAlgebraModule{C}) -> Bool, LieAlgebraModule{C}, Int Check whether `V` has been constructed as an exterior power of a module. If it has, return `true`, the base module, and the power. If not, return `false` as the first return value, and arbitrary values for the other two. """ -function is_exterior_power(V::LieAlgebraModule) +function _is_exterior_power(V::LieAlgebraModule) if has_attribute(V, :is_exterior_power) W, k = get_attribute(V, :is_exterior_power)::Tuple{typeof(V),Int} return (true, W, k) @@ -591,13 +591,13 @@ function is_exterior_power(V::LieAlgebraModule) end @doc raw""" - is_symmetric_power(V::LieAlgebraModule{C}) -> Bool, LieAlgebraModule{C}, Int + _is_symmetric_power(V::LieAlgebraModule{C}) -> Bool, LieAlgebraModule{C}, Int Check whether `V` has been constructed as an symmetric power of a module. If it has, return `true`, the base module, and the power. If not, return `false` as the first return value, and arbitrary values for the other two. """ -function is_symmetric_power(V::LieAlgebraModule) +function _is_symmetric_power(V::LieAlgebraModule) if has_attribute(V, :is_symmetric_power) W, k = get_attribute(V, :is_symmetric_power)::Tuple{typeof(V),Int} return (true, W, k) @@ -606,13 +606,13 @@ function is_symmetric_power(V::LieAlgebraModule) end @doc raw""" - is_tensor_power(V::LieAlgebraModule{C}) -> Bool, LieAlgebraModule{C}, Int + _is_tensor_power(V::LieAlgebraModule{C}) -> Bool, LieAlgebraModule{C}, Int Check whether `V` has been constructed as a tensor power of a module. If it has, return `true`, the base module, and the power. If not, return `false` as the first return value, and arbitrary values for the other two. """ -function is_tensor_power(V::LieAlgebraModule) +function _is_tensor_power(V::LieAlgebraModule) if has_attribute(V, :is_tensor_power) W, k = get_attribute(V, :is_tensor_power)::Tuple{typeof(V),Int} return (true, W, k) @@ -797,7 +797,7 @@ function dual(V::LieAlgebraModule{C}; cached::Bool=true) where {C<:FieldElem} -transpose(transformation_matrix(V, i)) end - s = if is_standard_module(V) + s = if _is_standard_module(V) [Symbol("$(s)*") for s in symbols(V)] else [Symbol("($(s))*") for s in symbols(V)] @@ -855,7 +855,7 @@ function direct_sum(V::LieAlgebraModule{C}, Vs::LieAlgebraModule{C}...) where {C else [ Symbol("$s^($j)") for (j, Vj) in enumerate(Vs) for - s in (is_standard_module(Vj) ? symbols(Vj) : (x -> "($x)").(symbols(Vj))) + s in (_is_standard_module(Vj) ? symbols(Vj) : (x -> "($x)").(symbols(Vj))) ] end @@ -926,7 +926,7 @@ function tensor_product( Symbol(join(s, (is_unicode_allowed() ? "⊗" : "(x)"))) for s in reverse.( ProductIterator([ - is_standard_module(Vi) ? symbols(Vi) : (x -> "($x)").(symbols(Vi)) for + _is_standard_module(Vi) ? symbols(Vi) : (x -> "($x)").(symbols(Vi)) for Vi in reverse(Vs) ]) ) @@ -1049,7 +1049,7 @@ function exterior_power( [Symbol("1")] elseif k == 1 symbols(V) - elseif is_standard_module(V) + elseif _is_standard_module(V) [Symbol(join(s, (is_unicode_allowed() ? "∧" : "^"))) for s in combinations(symbols(V), k)] else [ @@ -1185,7 +1185,7 @@ function symmetric_power( [Symbol("1")] elseif k == 1 symbols(V) - elseif is_standard_module(V) + elseif _is_standard_module(V) [ Symbol( join( @@ -1336,7 +1336,7 @@ function tensor_power( [Symbol("1")] elseif k == 1 symbols(V) - elseif is_standard_module(V) + elseif _is_standard_module(V) [ Symbol(join(s, (is_unicode_allowed() ? "⊗" : "(x)"))) for s in reverse.(ProductIterator(symbols(V), k)) diff --git a/experimental/LieAlgebras/src/LieAlgebraModuleHom.jl b/experimental/LieAlgebras/src/LieAlgebraModuleHom.jl index 4854e418e600..f544f7a07fd2 100644 --- a/experimental/LieAlgebras/src/LieAlgebraModuleHom.jl +++ b/experimental/LieAlgebras/src/LieAlgebraModuleHom.jl @@ -360,7 +360,7 @@ Return the canonical injections from all components into $V$ where $V$ has been constructed as $V_1 \oplus \cdot \oplus V_n$. """ function canonical_injections(V::LieAlgebraModule) - fl, Vs = is_direct_sum(V) + fl, Vs = Oscar._is_direct_sum(V) @req fl "Module must be a direct sum" return [canonical_injection(V, i) for i in 1:length(Vs)] end @@ -372,7 +372,7 @@ Return the canonical injection $V_i \to V$ where $V$ has been constructed as $V_1 \oplus \cdot \oplus V_n$. """ function canonical_injection(V::LieAlgebraModule, i::Int) - fl, Vs = is_direct_sum(V) + fl, Vs = Oscar._is_direct_sum(V) @req fl "Module must be a direct sum" @req 1 <= i <= length(Vs) "Index out of bound" j = sum(dim(Vs[l]) for l in 1:(i - 1); init=0) @@ -387,7 +387,7 @@ Return the canonical projections from $V$ to all components where $V$ has been constructed as $V_1 \oplus \cdot \oplus V_n$. """ function canonical_projections(V::LieAlgebraModule) - fl, Vs = is_direct_sum(V) + fl, Vs = Oscar._is_direct_sum(V) @req fl "Module must be a direct sum" return [canonical_projection(V, i) for i in 1:length(Vs)] end @@ -399,7 +399,7 @@ Return the canonical projection $V \to V_i$ where $V$ has been constructed as $V_1 \oplus \cdot \oplus V_n$. """ function canonical_projection(V::LieAlgebraModule, i::Int) - fl, Vs = is_direct_sum(V) + fl, Vs = Oscar._is_direct_sum(V) @req fl "Module must be a direct sum" @req 1 <= i <= length(Vs) "Index out of bound" j = sum(dim(Vs[l]) for l in 1:(i - 1); init=0) @@ -430,9 +430,9 @@ If `hs` is a vector, then it is interpreted as a diagonal matrix. function hom_direct_sum( V::LieAlgebraModule{C}, W::LieAlgebraModule{C}, hs::Matrix{<:LieAlgebraModuleHom} ) where {C<:FieldElem} - fl, Vs = is_direct_sum(V) + fl, Vs = Oscar._is_direct_sum(V) @req fl "First module must be a direct sum" - fl, Ws = is_direct_sum(W) + fl, Ws = Oscar._is_direct_sum(W) @req fl "Second module must be a direct sum" @req length(Vs) == size(hs, 1) "Length mismatch" @req length(Ws) == size(hs, 2) "Length mismatch" @@ -456,9 +456,9 @@ end function hom_direct_sum( V::LieAlgebraModule{C}, W::LieAlgebraModule{C}, hs::Vector{<:LieAlgebraModuleHom} ) where {C<:FieldElem} - fl, Vs = is_direct_sum(V) + fl, Vs = Oscar._is_direct_sum(V) @req fl "First module must be a direct sum" - fl, Ws = is_direct_sum(W) + fl, Ws = Oscar._is_direct_sum(W) @req fl "Second module must be a direct sum" @req length(Vs) == length(Ws) == length(hs) "Length mismatch" @req all(i -> domain(hs[i]) === Vs[i] && codomain(hs[i]) === Ws[i], 1:length(hs)) "Domain/codomain mismatch" @@ -479,16 +479,16 @@ This works for $r$th tensor powers as well. function hom_tensor( V::LieAlgebraModule{C}, W::LieAlgebraModule{C}, hs::Vector{<:LieAlgebraModuleHom} ) where {C<:FieldElem} # TODO: cleanup after refactoring tensor_product - if ((fl, Vs) = is_tensor_product(V); fl) + if ((fl, Vs) = _is_tensor_product(V); fl) # nothing to do - elseif ((fl, Vb, k) = is_tensor_power(V); fl) + elseif ((fl, Vb, k) = _is_tensor_power(V); fl) Vs = [Vb for _ in 1:k] else throw(ArgumentError("First module must be a tensor product or power")) end - if ((fl, Ws) = is_tensor_product(W); fl) + if ((fl, Ws) = _is_tensor_product(W); fl) # nothing to do - elseif ((fl, Wb, k) = is_tensor_power(W); fl) + elseif ((fl, Wb, k) = _is_tensor_power(W); fl) Ws = [Wb for _ in 1:k] else throw(ArgumentError("Second module must be a tensor product or power")) @@ -515,11 +515,11 @@ $S^k h: V \to W$ (analogous for other types of powers). function hom( V::LieAlgebraModule{C}, W::LieAlgebraModule{C}, h::LieAlgebraModuleHom ) where {C<:FieldElem} - if is_exterior_power(V)[1] + if _is_exterior_power(V)[1] return induced_map_on_exterior_power(h; domain=V, codomain=W) - elseif is_symmetric_power(V)[1] + elseif _is_symmetric_power(V)[1] return induced_map_on_symmetric_power(h; domain=V, codomain=W) - elseif is_tensor_power(V)[1] + elseif _is_tensor_power(V)[1] return induced_map_on_tensor_power(h; domain=V, codomain=W) else throw(ArgumentError("First module must be a power module")) @@ -553,8 +553,8 @@ function induced_map_on_exterior_power( domain::LieAlgebraModule{C}=exterior_power(Oscar.domain(phi), p)[1], codomain::LieAlgebraModule{C}=exterior_power(Oscar.codomain(phi), p)[1], ) where {C<:FieldElem} - (domain_fl, domain_base, domain_k) = is_exterior_power(domain) - (codomain_fl, codomain_base, codomain_k) = is_exterior_power(codomain) + (domain_fl, domain_base, domain_k) = _is_exterior_power(domain) + (codomain_fl, codomain_base, codomain_k) = _is_exterior_power(codomain) @req domain_fl "Domain must be an exterior power" @req codomain_fl "Codomain must be an exterior power" @req domain_k == codomain_k "Exponent mismatch" @@ -569,8 +569,8 @@ function induced_map_on_symmetric_power( domain::LieAlgebraModule{C}=symmetric_power(Oscar.domain(phi), p)[1], codomain::LieAlgebraModule{C}=symmetric_power(Oscar.codomain(phi), p)[1], ) where {C<:FieldElem} - (domain_fl, domain_base, domain_k) = is_symmetric_power(domain) - (codomain_fl, codomain_base, codomain_k) = is_symmetric_power(codomain) + (domain_fl, domain_base, domain_k) = _is_symmetric_power(domain) + (codomain_fl, codomain_base, codomain_k) = _is_symmetric_power(codomain) @req domain_fl "Domain must be an symmetric power" @req codomain_fl "Codomain must be an symmetric power" @req domain_k == codomain_k "Exponent mismatch" @@ -585,8 +585,8 @@ function induced_map_on_tensor_power( domain::LieAlgebraModule{C}=tensor_power(Oscar.domain(phi), p)[1], codomain::LieAlgebraModule{C}=tensor_power(Oscar.codomain(phi), p)[1], ) where {C<:FieldElem} - (domain_fl, domain_base, domain_k) = is_tensor_power(domain) - (codomain_fl, codomain_base, codomain_k) = is_tensor_power(codomain) + (domain_fl, domain_base, domain_k) = _is_tensor_power(domain) + (codomain_fl, codomain_base, codomain_k) = _is_tensor_power(codomain) @req domain_fl "Domain must be an tensor power" @req codomain_fl "Codomain must be an tensor power" @req domain_k == codomain_k "Exponent mismatch" diff --git a/experimental/LieAlgebras/src/LieAlgebras.jl b/experimental/LieAlgebras/src/LieAlgebras.jl index ab537ded7a28..cd183c16fbc8 100644 --- a/experimental/LieAlgebras/src/LieAlgebras.jl +++ b/experimental/LieAlgebras/src/LieAlgebras.jl @@ -15,6 +15,8 @@ using AbstractAlgebra.PrettyPrinting # functions with new methods import ..Oscar: + _is_exterior_power, + _is_tensor_product, _iso_oscar_gap, action, basis_matrix, @@ -50,14 +52,12 @@ import ..Oscar: induced_map_on_exterior_power, inv, is_abelian, - is_exterior_power, is_finite, is_isomorphism, is_nilpotent, is_perfect, is_simple, is_solvable, - is_tensor_product, is_welldefined, kernel, lower_central_series, @@ -99,6 +99,13 @@ export WeightLatticeElem export WeylGroup, WeylGroupElem export WeylOrbitIterator +export _is_direct_sum +export _is_dual +export _is_exterior_power +export _is_standard_module +export _is_symmetric_power +export _is_tensor_power +export _is_tensor_product export abelian_lie_algebra export abstract_module export base_lie_algebra @@ -131,9 +138,7 @@ export induced_map_on_tensor_power export is_cartan_matrix export is_cartan_type export is_coroot_with_index -export is_direct_sum export is_dominant -export is_dual export is_negative_coroot_with_index export is_negative_root_with_index export is_positive_coroot_with_index @@ -142,10 +147,6 @@ export is_root_with_index export is_self_normalizing export is_simple_coroot_with_index export is_simple_root_with_index -export is_standard_module -export is_symmetric_power -export is_tensor_power -export is_tensor_product export lie_algebra export lmul, lmul! export longest_element @@ -257,9 +258,7 @@ export induced_map_on_tensor_power export is_cartan_matrix export is_cartan_type export is_coroot_with_index -export is_direct_sum export is_dominant -export is_dual export is_negative_coroot_with_index export is_negative_root_with_index export is_positive_coroot_with_index @@ -268,10 +267,6 @@ export is_root_with_index export is_self_normalizing export is_simple_coroot_with_index export is_simple_root_with_index -export is_standard_module -export is_symmetric_power -export is_tensor_power -export is_tensor_product export lie_algebra export lmul, lmul! export longest_element diff --git a/experimental/LieAlgebras/test/LieAlgebraModule-test.jl b/experimental/LieAlgebras/test/LieAlgebraModule-test.jl index bf696e2ab194..77701add151d 100644 --- a/experimental/LieAlgebras/test/LieAlgebraModule-test.jl +++ b/experimental/LieAlgebras/test/LieAlgebraModule-test.jl @@ -181,13 +181,13 @@ end module_type_bools(V) = ( - is_standard_module(V), - is_dual(V)[1], - is_direct_sum(V)[1], - is_tensor_product(V)[1], - is_exterior_power(V)[1], - is_symmetric_power(V)[1], - is_tensor_power(V)[1], + Oscar._is_standard_module(V), + Oscar._is_dual(V)[1], + Oscar._is_direct_sum(V)[1], + Oscar._is_tensor_product(V)[1], + Oscar._is_exterior_power(V)[1], + Oscar._is_symmetric_power(V)[1], + Oscar._is_tensor_power(V)[1], ) @testset "module constructions" begin @@ -215,7 +215,7 @@ @test dual_V === dual(V) @test dual_V !== dual(V; cached=false) @test type_V == module_type_bools(V) # construction of dual_V should not change type of V - @test is_dual(dual_V) === (true, V) + @test Oscar._is_dual(dual_V) === (true, V) @test dim(dual_V) == dim(V) @test length(repr(dual_V)) < 10^4 # outputs tend to be excessively long due to recursion @@ -241,8 +241,8 @@ @test_broken ds_V === direct_sum([V for _ in 1:k]...) @test_broken ds_V !== direct_sum([V for _ in 1:k]...; cached=false) @test type_V == module_type_bools(V) # construction of ds_V should not change type of V - @test is_direct_sum(ds_V) == (true, [V for _ in 1:k]) - @test all(x -> x[1] === x[2], zip(is_direct_sum(ds_V)[2], [V for _ in 1:k])) + @test Oscar._is_direct_sum(ds_V) == (true, [V for _ in 1:k]) + @test all(x -> x[1] === x[2], zip(Oscar._is_direct_sum(ds_V)[2], [V for _ in 1:k])) @test dim(ds_V) == k * dim(V) @test length(repr(ds_V)) < 10^4 # outputs tend to be excessively long due to recursion @@ -262,7 +262,7 @@ ds_V = direct_sum(V1, V2) @test type_V1 == module_type_bools(V1) # construction of ds_V should not change type of V1 @test type_V2 == module_type_bools(V2) # construction of ds_V should not change type of V2 - @test is_direct_sum(ds_V) == (true, [V1, V2]) + @test Oscar._is_direct_sum(ds_V) == (true, [V1, V2]) @test dim(ds_V) == dim(V1) + dim(V2) @test length(repr(ds_V)) < 10^4 # outputs tend to be excessively long due to recursion @@ -282,8 +282,8 @@ @test_broken tp_V === tensor_product([V for _ in 1:k]...) @test_broken tp_V !== tensor_product([V for _ in 1:k]...; cached=false) @test type_V == module_type_bools(V) # construction of tp_V should not change type of V - @test is_tensor_product(tp_V) == (true, [V for _ in 1:k]) - @test all(x -> x[1] === x[2], zip(is_tensor_product(tp_V)[2], [V for _ in 1:k])) + @test Oscar._is_tensor_product(tp_V) == (true, [V for _ in 1:k]) + @test all(x -> x[1] === x[2], zip(Oscar._is_tensor_product(tp_V)[2], [V for _ in 1:k])) @test dim(tp_V) == dim(V)^k @test length(repr(tp_V)) < 10^4 # outputs tend to be excessively long due to recursion @@ -305,7 +305,7 @@ tp_V = tensor_product(V1, V2) @test type_V1 == module_type_bools(V1) # construction of tp_V should not change type of V1 @test type_V2 == module_type_bools(V2) # construction of tp_V should not change type of V2 - @test is_tensor_product(tp_V) == (true, [V1, V2]) + @test Oscar._is_tensor_product(tp_V) == (true, [V1, V2]) @test dim(tp_V) == dim(V1) * dim(V2) @test length(repr(tp_V)) < 10^4 # outputs tend to be excessively long due to recursion @@ -328,7 +328,7 @@ @test E === exterior_power(V, k)[1] @test E !== exterior_power(V, k; cached=false)[1] @test type_V == module_type_bools(V) # construction of E should not change type of V - @test is_exterior_power(E) === (true, V, k) + @test Oscar._is_exterior_power(E) === (true, V, k) @test dim(E) == binomial(dim(V), k) @test length(repr(E)) < 10^4 # outputs tend to be excessively long due to recursion @@ -386,7 +386,7 @@ @test S === symmetric_power(V, k)[1] @test S !== symmetric_power(V, k; cached=false)[1] @test type_V == module_type_bools(V) # construction of S should not change type of V - @test is_symmetric_power(S) === (true, V, k) + @test Oscar._is_symmetric_power(S) === (true, V, k) @test dim(S) == binomial(dim(V) + k - 1, k) @test length(repr(S)) < 10^4 # outputs tend to be excessively long due to recursion @@ -441,7 +441,7 @@ @test T === tensor_power(V, k)[1] @test T !== tensor_power(V, k; cached=false)[1] @test type_V == module_type_bools(V) # construction of T should not change type of V - @test is_tensor_power(T) === (true, V, k) + @test Oscar._is_tensor_power(T) === (true, V, k) @test dim(T) == dim(V)^k @test length(repr(T)) < 10^4 # outputs tend to be excessively long due to recursion diff --git a/src/Modules/ExteriorPowers/FreeModules.jl b/src/Modules/ExteriorPowers/FreeModules.jl index dc7bf8241eeb..ff653591bc79 100644 --- a/src/Modules/ExteriorPowers/FreeModules.jl +++ b/src/Modules/ExteriorPowers/FreeModules.jl @@ -160,7 +160,7 @@ function koszul_homology(v::FreeModElem, M::ModuleFP, i::Int; cached::Bool=true) end function koszul_dual(F::FreeMod; cached::Bool=true) - success, M, p = is_exterior_power(F) + success, M, p = _is_exterior_power(F) !success && error("module must be an exterior power of some other module") return exterior_power(M, rank(M) - p, cached=cached)[1] end @@ -170,7 +170,7 @@ function koszul_duals(v::Vector{T}; cached::Bool=true) where {T<:FreeModElem} all(u->parent(u) === parent(first(v)), v[2:end]) || error("parent mismatch") F = parent(first(v)) - success, M, p = is_exterior_power(F) + success, M, p = _is_exterior_power(F) n = rank(M) success || error("element must be an exterior product") k = [findfirst(x->x==u, gens(F)) for u in v] diff --git a/src/Modules/ExteriorPowers/Generic.jl b/src/Modules/ExteriorPowers/Generic.jl index a1adcc46aa6b..b9f48389d557 100644 --- a/src/Modules/ExteriorPowers/Generic.jl +++ b/src/Modules/ExteriorPowers/Generic.jl @@ -6,7 +6,7 @@ end # User facing method to ask whether F = ⋀ ᵖ M for some M. # This returns a triple `(true, M, p)` in the affirmative case # and `(false, F, 0)` otherwise. -function is_exterior_power(M::ModuleFP) +function _is_exterior_power(M::ModuleFP) if has_attribute(M, :is_exterior_power) MM, p = get_attribute(M, :is_exterior_power)::Tuple{typeof(M), Int} return (true, MM, p) @@ -16,7 +16,7 @@ end # Printing of exterior powers function show_exterior_product(io::IO, M::ModuleFP) - success, F, p = is_exterior_power(M) + success, F, p = _is_exterior_power(M) success || error("module is not an exterior power") if is_unicode_allowed() print(io, "⋀^$p($F)") @@ -26,7 +26,7 @@ function show_exterior_product(io::IO, M::ModuleFP) end function show_exterior_product(io::IO, ::MIME"text/html", M::ModuleFP) - success, F, p = is_exterior_power(M) + success, F, p = _is_exterior_power(M) success || error("module is not an exterior power") io = IOContext(io, :compact => true) if is_unicode_allowed() @@ -60,7 +60,7 @@ end # We also allow v ∈ M considered as ⋀ ¹M and the same holds in # the cases p = 1 and r = 1. function wedge_multiplication_map(F::ModuleFP, G::ModuleFP, v::ModuleFPElem) - success, orig_mod, p = is_exterior_power(F) + success, orig_mod, p = _is_exterior_power(F) if !success Fwedge1, _ = exterior_power(F, 1) id = hom(F, Fwedge1, gens(Fwedge1)) @@ -68,7 +68,7 @@ function wedge_multiplication_map(F::ModuleFP, G::ModuleFP, v::ModuleFPElem) return compose(id, tmp) end - success, orig_mod_2, q = is_exterior_power(G) + success, orig_mod_2, q = _is_exterior_power(G) if !success Gwedge1, _ = exterior_power(G, 1) id = hom(Gwedge1, G, gens(G)) @@ -86,7 +86,7 @@ function wedge_multiplication_map(F::ModuleFP, G::ModuleFP, v::ModuleFPElem) return wedge_multiplication_map(F, G, w) end - success, orig_mod_2, r = is_exterior_power(H) + success, orig_mod_2, r = _is_exterior_power(H) success || error("element is not an exterior product") orig_mod_2 === orig_mod || error("element is not an exterior product for the correct module") p + r == q || error("powers are incompatible") @@ -99,24 +99,24 @@ end # The wedge product of two or more elements. function wedge(u::ModuleFPElem, v::ModuleFPElem; parent::ModuleFP=begin - success, F, p = is_exterior_power(Oscar.parent(u)) + success, F, p = _is_exterior_power(Oscar.parent(u)) if !success F = Oscar.parent(u) p = 1 end - success, _, q = is_exterior_power(Oscar.parent(v)) + success, _, q = _is_exterior_power(Oscar.parent(v)) !success && (q = 1) exterior_power(F, p + q)[1] end ) - success1, F1, p = is_exterior_power(Oscar.parent(u)) + success1, F1, p = _is_exterior_power(Oscar.parent(u)) if !success1 F = Oscar.parent(u) Fwedge1, _ = exterior_power(F1, 1) return wedge(Fwedge1(coordinates(u)), v, parent=parent) end - success2, F2, q = is_exterior_power(Oscar.parent(v)) + success2, F2, q = _is_exterior_power(Oscar.parent(v)) if !success2 F = Oscar.parent(v) Fwedge1, _ = exterior_power(F1, 1) @@ -145,7 +145,7 @@ function wedge(u::Vector{T}; isempty(u) && error("list must not be empty") F = Oscar.parent(first(u)) # initialize variable for v in u - success, F, p = is_exterior_power(Oscar.parent(v)) + success, F, p = _is_exterior_power(Oscar.parent(v)) if !success F = Oscar.parent(v) p = 1 @@ -182,9 +182,9 @@ end # The induced map on exterior powers function hom(M::FreeMod, N::FreeMod, phi::FreeModuleHom) - success, F, p = is_exterior_power(M) + success, F, p = _is_exterior_power(M) @req success "module is not an exterior power" - success, FF, q = is_exterior_power(N) + success, FF, q = _is_exterior_power(N) @req success "module is not an exterior power" @req F === domain(phi) "map not compatible" @req FF === codomain(phi) "map not compatible" diff --git a/src/Modules/UngradedModules/Methods.jl b/src/Modules/UngradedModules/Methods.jl index 48bbdd6ee98a..d0250dc6e6eb 100644 --- a/src/Modules/UngradedModules/Methods.jl +++ b/src/Modules/UngradedModules/Methods.jl @@ -791,19 +791,19 @@ function Base.:*(k::Int, f::ModuleFPHom) return base_ring(codomain(f))(k)*f end -function is_tensor_product(M::ModuleFP) +function _is_tensor_product(M::ModuleFP) !has_attribute(M, :tensor_product) && return false, [M] return true, get_attribute(M, :tensor_product)::Tuple end function tensor_pure_function(M::ModuleFP) - success, facs = is_tensor_product(M) + success, facs = _is_tensor_product(M) success || error("not a tensor product") return get_attribute(M, :tensor_pure_function) end function tensor_generator_decompose_function(M::ModuleFP) - success, facs = is_tensor_product(M) + success, facs = _is_tensor_product(M) success || error("not a tensor product") return get_attribute(M, :tensor_generator_decompose_function) end diff --git a/src/Modules/deRhamComplexes.jl b/src/Modules/deRhamComplexes.jl index b344c99c7533..146bb4609f9f 100644 --- a/src/Modules/deRhamComplexes.jl +++ b/src/Modules/deRhamComplexes.jl @@ -150,7 +150,7 @@ end # printing of kaehler differentials function show_kaehler_differentials(io::IO, M::ModuleFP) - success, F, p = is_exterior_power(M) + success, F, p = _is_exterior_power(M) R = base_ring(F) if success if is_unicode_allowed() @@ -168,7 +168,7 @@ function show_kaehler_differentials(io::IO, M::ModuleFP) end function show_kaehler_differentials(io::IO, ::MIME"text/html", M::ModuleFP) - success, F, p = is_exterior_power(M) + success, F, p = _is_exterior_power(M) R = base_ring(F) io = IOContext(io, :compact => true) if success diff --git a/src/exports.jl b/src/exports.jl index 6c764fdbddb7..74c4da894801 100644 --- a/src/exports.jl +++ b/src/exports.jl @@ -763,7 +763,6 @@ export is_embedded export is_empty export is_equal_with_morphism export is_equidimensional -export is_exterior_power export is_faithful export is_fano export is_feasible diff --git a/test/Modules/ExteriorPowers.jl b/test/Modules/ExteriorPowers.jl index c3749f8b0392..fb7320952215 100644 --- a/test/Modules/ExteriorPowers.jl +++ b/test/Modules/ExteriorPowers.jl @@ -8,7 +8,7 @@ Fwedge1, _ = Oscar.exterior_power(F, 1) Fwedge2, _ = Oscar.exterior_power(F, 2) - success, orig_mod, q = Oscar.is_exterior_power(Fwedge3) + success, orig_mod, q = Oscar._is_exterior_power(Fwedge3) @test success @test orig_mod === F @test q == 3 From 4fcb43ff09359a683e662105ef5d7b182d5f0bcb Mon Sep 17 00:00:00 2001 From: Johannes Schmitt Date: Tue, 20 Feb 2024 19:16:35 +0100 Subject: [PATCH 19/29] Make equality check less expensive (#3399) (cherry picked from commit 6408748a4bcee53b4fbdad5eab2609eb21995e16) --- src/Rings/MPolyQuo.jl | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/Rings/MPolyQuo.jl b/src/Rings/MPolyQuo.jl index 55f0b89e70e5..926e475b024e 100644 --- a/src/Rings/MPolyQuo.jl +++ b/src/Rings/MPolyQuo.jl @@ -1234,7 +1234,7 @@ function vector_space(K::AbstractAlgebra.Field, Q::MPolyQuoRing) l = _kbase(Q) V = free_module(K, length(l)) function im(a::Generic.FreeModuleElem) - @assert parent(a) == V + @assert parent(a) === V b = R(0) for k=1:length(l) c = a[k] From 739f80270e3c88ca97b01e1e6425557b753a64c8 Mon Sep 17 00:00:00 2001 From: antonydellavecchia Date: Thu, 22 Feb 2024 10:31:41 +0100 Subject: [PATCH 20/29] Fixes for phylogenetic adjacency tree (#3406) * fixers for phylogenetic adjacency tree * get rid of whitespace * fix for tests (cherry picked from commit c65cb77505d3d402d2b7355df2e5fba343bf61e2) --- src/Combinatorics/PhylogeneticTrees.jl | 36 ++++++++++++++++++------- test/Combinatorics/PhylogeneticTrees.jl | 2 +- 2 files changed, 28 insertions(+), 10 deletions(-) diff --git a/src/Combinatorics/PhylogeneticTrees.jl b/src/Combinatorics/PhylogeneticTrees.jl index 5a5a17a9e08a..f667b9674a98 100644 --- a/src/Combinatorics/PhylogeneticTrees.jl +++ b/src/Combinatorics/PhylogeneticTrees.jl @@ -9,11 +9,11 @@ end @doc raw""" phylogenetic_tree(T::Type{<:Union{Float64, QQFieldElem}}, newick::String) -Constructs a phylogenetic tree with Newick representation `newick`. `T` indicates +Constructs a phylogenetic tree with Newick representation `newick`. `T` indicates the numerical type of the edge lengths. # Examples -Make a phylogenetic tree with 4 leaves from its Newick representation and print +Make a phylogenetic tree with 4 leaves from its Newick representation and print its taxa and cophenetic matrix. ```jldoctest julia> phylo_t = phylogenetic_tree(Float64, "((H:3,(C:1,B:1):2):1,G:4);"); @@ -38,7 +38,7 @@ function phylogenetic_tree(T::Type{<:Union{Float64, QQFieldElem}}, newick::Strin # load graph properties pm_ptree.ADJACENCY - + return PhylogeneticTree{T}(pm_ptree) end @@ -92,7 +92,6 @@ end adjacency_tree(ptree::PhylogeneticTree) Returns the underlying graph of the phylogenetic tree `ptree`. - # Examples Make a phylogenetic tree with given Newick format and print its underlying graph. @@ -100,12 +99,31 @@ Make a phylogenetic tree with given Newick format and print its underlying graph julia> ptree = phylogenetic_tree(Float64, "((H:3,(C:1,B:1):2):1,G:4);"); julia> adjacency_tree(ptree) -Undirected graph with 7 nodes and the following edges: -(2, 1)(3, 2)(4, 2)(5, 4)(6, 4)(7, 1) +Directed graph with 7 nodes and the following edges: +(1, 2)(1, 7)(2, 3)(2, 4)(4, 5)(4, 6) ``` """ function adjacency_tree(ptree::PhylogeneticTree) - return Graph{Undirected}(pm_object(ptree).ADJACENCY) + udir_tree = Graph{Undirected}(ptree.pm_ptree.ADJACENCY) + n = nv(udir_tree) + + dir_tree = Graph{Directed}(n) + + queue = [1] + visited = fill(false, n) + visited[1] = true + while length(queue) > 0 + x = popfirst!(queue) + for y in neighbors(udir_tree, x) + if visited[y] == false + add_edge!(dir_tree, x, y) + push!(queue, y) + visited[y] = true + end + end + end + + return dir_tree end function Base.show(io::IO, ptree::PhylogeneticTree{T}) where T @@ -248,9 +266,9 @@ function tropical_median_consensus(arr::Vector{PhylogeneticTree{T}}) where {T <: phylo_type = Polymake.bigobject_type(pm_object(first(arr))) pm_arr = Polymake.Array{Polymake.BigObject}(phylo_type, n) - + pm_arr .= pm_object.(arr) - + pm_cons_tree = Polymake.tropical.tropical_median_consensus(pm_arr) return PhylogeneticTree{T}(pm_cons_tree) end diff --git a/test/Combinatorics/PhylogeneticTrees.jl b/test/Combinatorics/PhylogeneticTrees.jl index e0221dc814ea..636ebb4a214a 100644 --- a/test/Combinatorics/PhylogeneticTrees.jl +++ b/test/Combinatorics/PhylogeneticTrees.jl @@ -1,6 +1,6 @@ @testset "Phylogenetic Trees" begin ptree1 = phylogenetic_tree(Float64, "((A:4,B:4):5,C:9);") - test_tree = graph_from_edges([[2, 1], [3, 2], [4, 2], [5, 1]]) + test_tree = graph_from_edges(Directed, [[1, 2], [2, 3], [2, 4], [1, 5]]) @test is_isomorphic(adjacency_tree(ptree1), test_tree) @test equidistant(ptree1) == true From 30df842738099b5336a7f4ecc781bfd3c981929c Mon Sep 17 00:00:00 2001 From: Lax202 <115473549+Lax202@users.noreply.github.com> Date: Wed, 21 Feb 2024 17:45:32 +0100 Subject: [PATCH 21/29] Draft - InvRing for SLn (#2823) * added cayley-omega.jl * made omegap a separate function * updates reynolds__ - need to fix det denominator * First attempt for SLn * fixed the bug * Added direct product and tensor * removed a loop from generators * small fix - reduce_gens_ * deleted cayley omega * coefficient bug fixed * Created object Reductive Groups in file InvariantRings_ReductiveGroups * small fixes in InvariantRings_ReductiveGroups.jl * callable derksen_ideal and hilbert_ideal in InvariantRings_ReductiveGroups * export functions in InvariantRings_ReductiveGroups * printing of direct sum of vector stpaces in InvariantRings_ReductiveGroups * mu_star, reynolds_operator added to Inv Rings Red Grps * added file InvariantRings_ReductiveGroups * deleted redundant folder * Some tweaks * edits to make the code more efficient in InvariantTheory.jl * minor edits in InvariantTheory.jl * fixed coefficient problem in InvariantTheory.jl * added comments and minor edits. Lazy computation of InvariantRing in InvariantTheory.jl * minor edits to InvariantTheory.jl * added export functions in InvariantTheory.jl * typo in InvariantTheory.jl * minor edits in InvaraintTheory.jl, few tests in tests.jl * finished tests.jl for invariant theory of SLm * removed factorise in InvariantTheory.jl * more efficient rep_mat_ function in InvariantTheory.jl * chenged degree_basis function * pretty(io) in InvariantTheory.jl * minor change in reductive group constructor * evaluate func in generators func in InvariantTheory.jl * started with adding Torus to reductive groups * incorporating tori with fast algorithm to InvariantTheory.jl * removed show functions, added test in invariant theory * field error for reductive groups * minor type changes * added test for invariants of tori * direct product and tensor for representations * tests for direct sum, tensor of representaions, minor fix in construction function of reductive groups * minor modification * minor edits in InvariantTheory.jl * Update experimental/InvariantTheory/src/InvariantTheory.jl Co-authored-by: Max Horn * Update experimental/InvariantTheory/src/InvariantTheory.jl Co-authored-by: Max Horn * minor changes discussed in pull request * removed goto in torus invariants function * removed import statement * changed name of representation_from_forms * torus of rank * minor changes from pull request * minor edits from pr comments * minor changes in show commands * started file for torus fast * shifted torus to new file TorusInvariantsFast * minor change in fundtion degree basis * fixed typo * added comments, removed extra output of generators(..) * renamed InvariantRing to RedGrpInvRing * minor changes * fixed all texts except torus * no internal constructor needed * fixed tests, changed names * print field for LinearlyReductiveGroup * changed RedGrpInvRing to attributes. Other minor changes * added error messages for @req, fixed typo * added export functions to torus groups * fixed export functions in InvariantTheory.jl * minor changes suggested in pr implemented * fixed test * exported direct_sum, tensor * included file TorusInvariantsFast.jl --------- Co-authored-by: Max Horn (cherry picked from commit 7da422475b91503d23c1eaeb8b78e9f4e1804f7b) --- .../InvariantTheory/src/InvariantTheory.jl | 497 ++++++++++++++++++ .../src/TorusInvariantsFast.jl | 208 ++++++++ experimental/InvariantTheory/test/runtests.jl | 60 +++ 3 files changed, 765 insertions(+) create mode 100644 experimental/InvariantTheory/src/InvariantTheory.jl create mode 100644 experimental/InvariantTheory/src/TorusInvariantsFast.jl create mode 100644 experimental/InvariantTheory/test/runtests.jl diff --git a/experimental/InvariantTheory/src/InvariantTheory.jl b/experimental/InvariantTheory/src/InvariantTheory.jl new file mode 100644 index 000000000000..a5b895f6d20f --- /dev/null +++ b/experimental/InvariantTheory/src/InvariantTheory.jl @@ -0,0 +1,497 @@ +#This code uses Derksen's algorithm to compute fundamental invariants of linearly reductive group. +#We first set up LinearlyReductiveGroup , then we set up a representation via which the group acts on a vector space (RepresentationLinearlyReductiveGroup) +#Then we set up the invariant ring of the group. The fundamental invariants are computed using Derksen's alg. +#As of now, the only reynolds operator that is implemented is the one for SLm, using Cayley's Omega process. + +export LinearlyReductiveGroup, linearly_reductive_group, representation_matrix, group, reynolds_operator, group_ideal, canonical_representation, natural_representation +export RepresentationLinearlyReductiveGroup, representation_reductive_group, representation_on_forms, representation_matrix, direct_sum, tensor +export RedGrpInvRing, invariant_ring, fundamental_invariants, NullConeIdeal, poly_ring, representation +########################## +#Setting up Reductive Groups +########################## +#These are objects that carry information about a linearly reductive group. +#As of now it is only implemented for SLn, its direct products and tensors. + +mutable struct LinearlyReductiveGroup + field::Field #characteristic zero. implement check? + group::Tuple{Symbol, Int} + group_ideal::MPolyIdeal + reynolds_operator::Function + canonical_representation::MatElem + + function LinearlyReductiveGroup(sym::Symbol, m::Int, fld::Field) #have not decided the representation yet + #check char(fld) + @assert sym == :SL + R, _ = polynomial_ring(fld, :z => (1:m,1:m)) + return LinearlyReductiveGroup(sym, m, R) + end + + function LinearlyReductiveGroup(sym::Symbol, m::Int, pring::MPolyRing) #the ring input is the group ring + #check char(field) + G = new() + @assert sym == :SL + fld = base_ring(pring) + characteristic(fld) == 0 || error("Characteristic should be 0 for linearly reductive groups") + G.field = fld + @req m^2 == ngens(pring) "ring not compatible" + G.group = (sym,m) + G.reynolds_operator = reynolds_slm + M = matrix(pring, m, m, gens(pring)) + G.canonical_representation = M + G.group_ideal = ideal([det(M) - 1]) + #base ring of M has to be the same as the representation matrix when that is created later. + return G + end +end + +function Base.show(io::IO, G::LinearlyReductiveGroup) + io = pretty(io) + if G.group[1] == :SL + println(io, "Reductive group ", G.group[1], G.group[2]) + print(IOContext(io, :supercompact => true), Indent(), "over ", Lowercase(), field(G)) + print(io, Dedent()) + end +end + +#getter functions +linearly_reductive_group(sym::Symbol, m::Int, R::MPolyRing) = LinearlyReductiveGroup(sym,m,R) +linearly_reductive_group(sym::Symbol, m::Int, F::Field) = LinearlyReductiveGroup(sym,m,F) +group(G::LinearlyReductiveGroup) = G.group +field(G::LinearlyReductiveGroup) = G.field +reynolds_operator(G::LinearlyReductiveGroup) = G.reynolds_operator +group_ideal(G::LinearlyReductiveGroup) = G.group_ideal +canonical_representation(G::LinearlyReductiveGroup) = G.canonical_representation +natural_representation(G::LinearlyReductiveGroup) = G.canonical_representation + +##################### +#Setting up Representation objects +##################### +#Objects of type LinearlyReductiveGroup can be embedded in GLn (for some n) via a representation. This defines the action on a vector space. +#We set up an object RepresentationLinearlyReductiveGroup that carries information about this representation. + +mutable struct RepresentationLinearlyReductiveGroup + group::LinearlyReductiveGroup + rep_mat::MatElem + reynolds_v::Function + + #stores if the representation is on symmetric forms, and of which degree. + sym_deg::Tuple{Bool, Int} + + + #representation of group G over symmetric degree d + function RepresentationLinearlyReductiveGroup(G::LinearlyReductiveGroup, d::Int) + R = new() + R.group = G + R.rep_mat = rep_mat_(G, d) + R.sym_deg = (true, d) + R.reynolds_v = reynolds_v_slm + return R + end + + #matrix M is the representation matrix. does not check M. + function RepresentationLinearlyReductiveGroup(G::LinearlyReductiveGroup, M::MatElem) + @req base_ring(M) == base_ring(G.group_ideal) "Group ideal and representation matrix must have same parent ring" + R = new() + R.group = G + R.rep_mat = M + R.sym_deg = (false, 0) + R.reynolds_v = reynolds_v_slm + return R + end +end + +representation_reductive_group(G::LinearlyReductiveGroup, M::MatElem) = RepresentationLinearlyReductiveGroup(G,M) +group(R::RepresentationLinearlyReductiveGroup) = R.group +representation_matrix(R::RepresentationLinearlyReductiveGroup) = R.rep_mat +vector_space_dimension(R::RepresentationLinearlyReductiveGroup) = ncols(R.rep_mat) + +function representation_on_forms(G::LinearlyReductiveGroup, d::Int) + @assert G.group[1] == :SL + return RepresentationLinearlyReductiveGroup(G, d) +end + +function representation_reductive_group(G::LinearlyReductiveGroup) + @assert G.group[1] == :SL + M = canonical_representation(G) + return RepresentationLinearlyReductiveGroup(G,M) +end + +function Base.show(io::IO, R::RepresentationLinearlyReductiveGroup) + io = pretty(io) + @assert group(group(R))[1] == :SL + println(io, "Representation of ", group(group(R))[1], group(group(R))[2]) + if R.sym_deg[1] + print(io, Indent(), "on symmetric forms of degree ", R.sym_deg[2]) + print(io, Dedent()) + else + println(io, Indent(), "with representation matrix") + show(io, R.rep_mat) + print(io, Dedent()) + end +end + +function direct_sum(X::RepresentationLinearlyReductiveGroup, Y::RepresentationLinearlyReductiveGroup) + @req group(X) == group(Y) "not compatible" + G = group(X) + R = base_ring(group_ideal(G)) + Mat = block_diagonal_matrix(R, [Matrix(representation_matrix(X)), Matrix(representation_matrix(Y))]) + return RepresentationLinearlyReductiveGroup(G, Mat) +end + +function direct_sum(V::Vector{RepresentationLinearlyReductiveGroup}) + n = length(V) + G = group(V[1]) + for i in 2:n + @req G == group(V[i]) "not compatible" + end + R = base_ring(group_ideal(G)) + Mat = block_diagonal_matrix(R, [Matrix(representation_matrix(V[i])) for i in 1:n]) + return RepresentationLinearlyReductiveGroup(G, Mat) +end + +function tensor(X::RepresentationLinearlyReductiveGroup, Y::RepresentationLinearlyReductiveGroup) + @req group(X) == group(Y) "not compatible" + Mat = kronecker_product(representation_matrix(X), representation_matrix(Y)) + return RepresentationLinearlyReductiveGroup(group(X), Mat) +end + +function tensor(V::Vector{RepresentationLinearlyReductiveGroup}) + n = length(V) + for i in 2:n + @req group(V[1]) == group(V[i]) "not compatible" + end + Mat = representation_matrix(V[1]) + for i in 2:n + Mat = kronecker_product(Mat,representation_matrix(V[i])) + end + return RepresentationLinearlyReductiveGroup(group(V[1]), Mat) +end + +############### + +#computes the representation matrices of SL_m acting over m-forms of symmetric degree sym_deg +function rep_mat_(G::LinearlyReductiveGroup, sym_deg::Int) + G.group[1] == :SL || error("Only implemented for SLm") + m = G.group[2] + R = base_ring(G.group_ideal) # TODO: probably should have a getter function for this + mixed_ring, t = polynomial_ring(R, "t" => 1:m) + group_mat = natural_representation(G) + new_vars = group_mat*t + + b = degree_basis(mixed_ring,sym_deg) + n = length(b) + + # transform the b elements + images_of_b = [evaluate(f, new_vars) for f in b] + + mat = zero_matrix(R, n, n) + for j in 1:n + f = images_of_b[j] + x = mixed_ring() + # express f as a linear combination of degree_basis + for i in 1:n + c = coeff(f, leading_exponent(b[i])) + mat[i,j] = c / leading_coefficient(b[i]) + end + end + return mat +end + +#computes symmetric degree basis (of the first m variables) WITH multinomial coefficients! +function degree_basis(R::MPolyRing, t::Int) + m = ngens(R) + C = zero_matrix(ZZ, m, m) + for i in 1:m + C[i,i] = -1 + end + d = zeros(Int, m) + A = ones(Int, m) + b = [t] + P = polyhedron((C, d), (A, b)) + L = lattice_points(P) + W = Vector{MPolyRingElem}(undef,0) + for l in L + v = R(1) + for i in 1:m + v = v*gen(R,i)^l[i] + end + v = v*multinomial(t,l) + push!(W,v) + end + #we reverse here to get the natural order of a degree basis, eg x^2, 2xy, y^2. + return reverse(W) +end + +#used to compute multinomial expansion coefficients (used in degree_basis) +function multinomial(n::Int, v::Union{Vector{T},PointVector{T}}) where T <: IntegerUnion + x = prod(factorial, v) + return Int(factorial(n)/x) +end + +########################## +#Invariant Rings of Reductive groups +########################## +@attributes mutable struct RedGrpInvRing + field::Field + poly_ring::MPolyDecRing #graded + + group::LinearlyReductiveGroup + representation::RepresentationLinearlyReductiveGroup + + reynolds_operator::Function + + #Invariant ring of reductive group G (in representation R), no other input. + function RedGrpInvRing(R::RepresentationLinearlyReductiveGroup) #here G already contains information n and rep_mat + z = new() + n = ncols(R.rep_mat) + z.representation = R + z.group = R.group + G = z.group + z.field = G.field + z.poly_ring, __ = graded_polynomial_ring(G.field, "X" => 1:n) + z.reynolds_operator = reynolds_v_slm + return z + end + + #to compute invariant ring ring^G where G is the reductive group of R. + function RedGrpInvRing(R::RepresentationLinearlyReductiveGroup, ring::MPolyDecRing) + n = ncols(R.rep_mat) + n == ngens(ring) || error("The given polynomial ring is not compatible.") + z = new() + if isdefined(R, :weights) + #dosomething + end + z.representation = R + z.group = R.group + G = R.group + z.field = G.field + z.poly_ring = ring + z.reynolds_operator = reynolds_v_slm + return z + end +end + +invariant_ring(R::RepresentationLinearlyReductiveGroup) = RedGrpInvRing(R) +invariant_ring(ring::MPolyDecRing, R::RepresentationLinearlyReductiveGroup) = RedGrpInvRing(R, ring) + +@attr MPolyIdeal function NullConeIdeal(R::RedGrpInvRing) + Z = R.representation + I, _ = proj_of_image_ideal(group(Z), Z.rep_mat) + return ideal(generators(Z.group, I, Z.rep_mat)) +end + +poly_ring(R::RedGrpInvRing) = R.poly_ring +group(R::RedGrpInvRing) = R.group +representation(R::RedGrpInvRing) = R.representation + +@attr function fundamental_invariants(z::RedGrpInvRing) #unable to use abstract type + R = z.representation + I, M = proj_of_image_ideal(R.group, R.rep_mat) + NullConeIdeal(z) = ideal(generators(R.group, I, R.rep_mat)) + return inv_generators(NullConeIdeal(z), R.group, z.poly_ring, M, z.reynolds_operator) +end + +function Base.show(io::IO, R::RedGrpInvRing) + io = pretty(io) + println(io, "Invariant Ring of") + println(io, Lowercase(), R.poly_ring) + print(io, Indent(), "under group action of ", R.group.group[1], R.group.group[2]) + print(io, Dedent()) +end + +#computing the graph Gamma from Derksens paper +function image_ideal(G::LinearlyReductiveGroup, rep_mat::MatElem) + R = base_ring(rep_mat) + n = ncols(rep_mat) + m = G.group[2] + mixed_ring_xy, x, y, zz = polynomial_ring(G.field, "x"=>1:n, "y"=>1:n, "zz"=>1:m^2) + ztozz = hom(R,mixed_ring_xy, gens(mixed_ring_xy)[(2*n)+1:(2*n)+(m^2)]) + genss = [ztozz(f) for f in gens(G.group_ideal)] + #rep_mat in the new ring + new_rep_mat = matrix(mixed_ring_xy,n,n,[ztozz(rep_mat[i,j]) for i in 1:n, j in 1:n]) + new_vars = new_rep_mat*x + ideal_vect = y - new_vars + ideal_vect = vcat(ideal_vect,genss) + return ideal(mixed_ring_xy, ideal_vect), new_rep_mat +end + +#computing I_{\Bar{B}} +function proj_of_image_ideal(G::LinearlyReductiveGroup, rep_mat::MatElem) + W = image_ideal(G, rep_mat) + mixed_ring_xy = base_ring(W[2]) + n = ncols(rep_mat) + m = G.group[2] + #use parallelised groebner bases here. This is the bottleneck! + return eliminate(W[1], gens(mixed_ring_xy)[(2*n)+1:(2*n)+(m^2)]), W[2] +end + +#this function gets the generators of the null cone. they may or may not be invariant. +#to do this we evaluate what is returned from proj_of_image_ideal at y = 0 +#ie at gens(basering)[n+1:2*n] = [0 for i in 1:n] +function generators(G::LinearlyReductiveGroup, X::MPolyIdeal, rep_mat::MatElem) + n = ncols(rep_mat) + m = G.group[2] + gbasis = gens(X) + length(gbasis) == 0 && return gbasis + mixed_ring_xy = parent(gbasis[1]) + #evaluate at gens(mixed_ring_xy)[n+1:2*n] = 0 + V = vcat(gens(mixed_ring_xy)[1:n], [0 for i in 1:n], gens(mixed_ring_xy)[2*n+1:2*n+m^2]) + ev_gbasis = [evaluate(f,V) for f in gbasis] + #grading starts here. In the end, our invariant ring is graded. + mixed_ring_graded, _ = grade(mixed_ring_xy) + mapp = hom(mixed_ring_xy, mixed_ring_graded, gens(mixed_ring_graded)) + ev_gbasis_new = [mapp(ev_gbasis[i]) for i in 1:length(ev_gbasis)] + if length(ev_gbasis_new) == 0 + return [mixed_ring_graded()] + end + return minimal_generating_set(ideal(ev_gbasis_new)) +end + +#computing the invariant generators of the null cone by applying reynolds operator to gens(I). This is done in K[X,Y] (basering(I)). +#the elements returned will be in the polynomial K[X] (ringg). +function inv_generators(I::MPolyIdeal, G::LinearlyReductiveGroup, ringg::MPolyRing, M::MatElem, reynolds_function::Function) + genss = gens(I) + if length(genss) == 0 + return Vector{elem_type(ringg)}() + end + + #we need the representation matrix and determinant of group matrix to be in basering(I) + mixed_ring_xy = parent(genss[1]) + R = base_ring(M) + m = G.group[2] + n = ncols(M) + mapp = hom(R, mixed_ring_xy, gens(mixed_ring_xy)) + new_rep_mat = matrix(mixed_ring_xy,n,n,[mapp(M[i,j]) for i in 1:n, j in 1:n]) + det_ = det(G.canonical_representation) + mapp_ = hom(parent(det_), mixed_ring_xy, gens(mixed_ring_xy)[(2*n)+1:(2*n)+(m^2)]) + new_det = mapp_(det_) + + #now we apply reynolds operator to genss + if G.group[1] == :SL #TODO other types of reductive groups + new_gens_wrong_ring = [reynolds_function(genss[i], new_rep_mat, new_det, m) for i in 1:length(genss)] + else + return nothing + end + + #map them to the required ring, ringg. + img_genss = vcat(gens(ringg), zeros(ringg, n+m^2)) + mixed_to_ring = hom(mixed_ring_xy, ringg, img_genss) + new_gens = Vector{elem_type(ringg)}() + for elemm in new_gens_wrong_ring + if elemm != 0 + push!(new_gens, mixed_to_ring(elemm)) + end + end + if length(new_gens) == 0 + return [ringg()] + end + + #remove ugly coefficients: + V= Vector{FieldElem}[] + new_gens_ = Vector{elem_type(ringg)}() + for elem in new_gens + V = vcat(V,collect(coefficients(elem))) + maxx = maximum([abs(denominator(V[i])) for i in 1:length(V)]) + minn = minimum([abs(numerator(V[i])) for i in 1:length(V)]) + if denominator((maxx*elem)//minn) != 1 + error("den not 1") + end + push!(new_gens_, numerator((maxx*elem)//minn)) + V= Vector{FieldElem}[] + end + return new_gens_ +end + +#the reynolds operator for SLm acting via new_rep_mat. +function reynolds_v_slm(elem::MPolyDecRingElem, new_rep_mat::MatElem, new_det::MPolyDecRingElem, m::Int) + mixed_ring_xy = parent(elem) + n = ncols(new_rep_mat) + new_vars = new_rep_mat*gens(mixed_ring_xy)[1:n] + sum_ = mixed_ring_xy() + phi = hom(mixed_ring_xy, mixed_ring_xy, vcat(new_vars, [0 for i in 1:ncols(new_rep_mat)+m^2])) + sum_ = phi(elem) + t = needed_degree(sum_, m) + if !is_divisible_by(t, m) + return parent(elem)() + else + p = divexact(t, m) + end + #num = omegap_(p, new_det, sum_) + #den = omegap_(p, new_det, (new_det)^p) + #if !(denominator(num//den)==1) + # error("denominator of reynolds not rational") + #end + #return numerator(num//den) + return reynolds_slm(sum_, new_det, p) +end + +#reynolds operator for SLm using Cayleys Omega process +function reynolds_slm(elem::MPolyRingElem, det_::MPolyRingElem, p::Int) + num = omegap_(p,det_, elem) + den = omegap_(p,det_,det_^p) + if !(denominator(num//den)==1) + error("denominator of reynolds not rational") + end + return numerator(num//den) +end + +#used to compute the degree p of omega_p +#computes the degree of the z_ij variables of the leading term of elem. +function needed_degree(elem_::MPolyDecRingElem, m::Int) + elem = leading_monomial(elem_) + R = parent(elem) + n = ngens(R) - m^2 + extra_ring, _= polynomial_ring(base_ring(R), "z"=>1:m^2) + mapp = hom(R,extra_ring, vcat([1 for i in 1:n], gens(extra_ring))) + return total_degree(mapp(elem)) +end + +function omegap_(p::Int, det_::MPolyDecRingElem, f::MPolyDecRingElem) + parent(det_) == parent(f) || error("Omega process ring error") + action_ring = parent(det_) + monos = collect(monomials(det_)) + coeffs = collect(coefficients(det_)) + for i in 1:p + h = action_ring() + for i in 1:length(monos) + exp_vect = exponent_vector(monos[i], 1) + x = f + for i in 1:length(exp_vect), j in 1:exp_vect[i] + x = derivative(x, i) + iszero(x) && break + end + h += coeffs[i]*x + end + f = h + end + return f +end + +#####################callable reynold's operator + +#this function returns the image of elem under the reynolds operator of group with representation X +function reynolds_operator(X::RepresentationLinearlyReductiveGroup, elem::MPolyRingElem) + X.group.group[1] == :SL || error("Only implemented for SLm") + vector_ring = parent(elem) + G = X.group + n = ngens(vector_ring) + n == ncols(X.rep_mat) || error("group not compatible with element") + m = G.group[2] + R, _ = graded_polynomial_ring(G.field,"x"=>1:n, "y"=>1:n, "z"=>(1:m, 1:m)) + map1 = hom(vector_ring, R, gens(R)[1:n]) + new_elem = map1(elem) + group_ring = base_ring(X.rep_mat) + map2 = hom(group_ring, R, gens(R)[2*n+1:2*n+m^2]) + new_rep_mat = map_entries(map2, X.rep_mat) + new_det = map2(det(G.canonical_representation)) + f = X.reynolds_v(new_elem, new_rep_mat, new_det, m) + reverse_map = hom(R, vector_ring, vcat(gens(vector_ring), [0 for i in 1:n+m^2])) + return reverse_map(f) +end + +function reynolds_operator(R::RedGrpInvRing, elem::MPolyRingElem) + X = R.representation + return reynolds_operator(X, elem) +end + +include("TorusInvariantsFast.jl") diff --git a/experimental/InvariantTheory/src/TorusInvariantsFast.jl b/experimental/InvariantTheory/src/TorusInvariantsFast.jl new file mode 100644 index 000000000000..f778f19f2549 --- /dev/null +++ b/experimental/InvariantTheory/src/TorusInvariantsFast.jl @@ -0,0 +1,208 @@ +export torus_group, rank, field, representation_from_weights, weights, group, invariant_ring, poly_ring, representation, fundamental_invariants + +##################### +#Setting up reductive groups for fast torus algorithm +##################### + +struct ReductiveGroupFastTorus + field::Field + rank::Int + #weights::Vector{Vector{ZZRingElem}} +end + +torus_group(F::Field, n::Int) = ReductiveGroupFastTorus(F,n) +rank(G::ReductiveGroupFastTorus) = G.rank +field(G::ReductiveGroupFastTorus) = G.field + +function Base.show(io::IO, G::ReductiveGroupFastTorus) + io = pretty(io) + println(io, "Torus of rank ", rank(G)) + print(IOContext(io, :supercompact => true), Indent(), "over ", Lowercase(), field(G)) + print(io, Dedent()) +end + +##################### +#Setting up weights for fast torus algorithm +##################### + +struct RepresentationReductiveGroupFastTorus + group::ReductiveGroupFastTorus + weights::Vector{Vector{ZZRingElem}} +end + +function representation_from_weights(G::ReductiveGroupFastTorus, W::Union{ZZMatrix, Matrix{<:Integer}, Vector{<:Int}}) + n = rank(G) + V = weights_from_matrix(n,W) + return RepresentationReductiveGroupFastTorus(G,V) +end + +function weights_from_matrix(n::Int, W::Union{ZZMatrix, Matrix{<:Integer}, Vector{<:Int}}) + V = Vector{Vector{ZZRingElem}}() + if W isa Vector + n == 1 || error("Incompatible weights") + for i in 1:length(W) + push!(V, [ZZRingElem(W[i])]) + end + else + n == ncols(W) || error("Incompatible weights") + #assume columns = G.group[2] + for i in 1:nrows(W) + push!(V, [ZZRingElem(W[i,j]) for j in 1:ncols(W)]) + end + end + return V +end + +weights(R::RepresentationReductiveGroupFastTorus) = R.weights +group(R::RepresentationReductiveGroupFastTorus) = R.group + +function Base.show(io::IO, R::RepresentationReductiveGroupFastTorus) + io = pretty(io) + println(io, "Representation of torus of rank ", rank(group(R))) + println(IOContext(io, :supercompact => true), Indent(), "over ", Lowercase(), field(group(R)), " and weights ") + print(io, R.weights) + print(io, Dedent()) +end + +##################### +#Setting up invariant ring for fast torus algorithm. +##################### + +mutable struct InvariantRingFastTorus + field::Field + poly_ring::MPolyDecRing #graded + + group::ReductiveGroupFastTorus + representation::RepresentationReductiveGroupFastTorus + + fundamental::Vector{MPolyDecRingElem} + + #Invariant ring of reductive group G (in representation R), no other input. + function InvariantRingFastTorus(R::RepresentationReductiveGroupFastTorus) #here G already contains information n and rep_mat + n = length(weights(R)) + super_ring, __ = graded_polynomial_ring(field(group(R)), "X"=>1:n) + return InvariantRingFastTorus(R, super_ring) + end + + #to compute invariant ring ring^G where G is the reductive group of R. + function InvariantRingFastTorus(R::RepresentationReductiveGroupFastTorus, ring_::MPolyDecRing) + z = new() + n = length(weights(R)) + z.field = field(group(R)) + z.poly_ring = ring_ + z.representation = R + z.group = group(R) + return z + end +end + +invariant_ring(R::RepresentationReductiveGroupFastTorus) = InvariantRingFastTorus(R) +poly_ring(R::InvariantRingFastTorus) = R.poly_ring +group(R::InvariantRingFastTorus) = R.group +representation(R::InvariantRingFastTorus) = R.representation + +function fundamental_invariants(z::InvariantRingFastTorus) + if isdefined(z, :fundamental) + return z.fundamental + else + R = z.representation + z.fundamental = torus_invariants_fast(weights(R), poly_ring(z)) + return z.fundamental + end +end + +function Base.show(io::IO, R::InvariantRingFastTorus) + io = pretty(io) + println(io, "Invariant Ring of") + print(io, Lowercase(), R.poly_ring) + print(io, Indent(), " under group action of torus of rank", rank(group(R))) + print(io, Dedent()) +end + +########################## +#fast algorithm for invariants of tori +########################## +#Algorithm 4.3.1 from Derksen and Kemper. Computes Torus invariants without Reynolds operator. +function torus_invariants_fast(W::Vector{Vector{ZZRingElem}}, R::MPolyRing) + #no check that length(W[i]) for all i is the same + length(W) == ngens(R) || error("number of weights must be equal to the number of generators of the polynomial ring") + n = length(W) + r = length(W[1]) + #step 2 + if length(W[1]) == 1 + M = zero_matrix(ZZ, n, 1) + for i in 1:n + M[i,1] = W[i][1] + end + C1 = lattice_points(convex_hull(M)) + else + M = zero_matrix(ZZ, 2*n, r) + for i in 1:n + M[i, 1:r] = 2*r*W[i] + M[n + i, 1:r] = -2*r*W[i] + end + C1 = lattice_points(convex_hull(M)) + end + + #get a Vector{Vector{ZZRingElem}} from Vector{PontVector{ZZRingElem}} + C = map(Vector{ZZRingElem}, C1) + #step 3 + S = Vector{Vector{elem_type(R)}}() + U = Vector{Vector{elem_type(R)}}() + index_0 = 0 + for point in C + if is_zero(point) + index_0 = findfirst(item -> item == point, C) + end + c = true + for i in 1:n + if point == W[i] + push!(S, [gen(R,i)]) + push!(U, [gen(R,i)]) + c = false + break + end + end + if c == true + push!(S, elem_type(R)[]) + push!(U, elem_type(R)[]) + end + end + #step 4 + count = 0 + while true + for j in 1:length(U) + if length(U[j]) != 0 + m = U[j][1] + w = C[j] #weight_of_monomial(m, W) + #step 5 - 7 + for i in 1:n + u = m*gen(R,i) + v = w + W[i] + if v in C + index = findfirst(item -> item == v, C) + c = true + for elem in S[index] + if is_divisible_by(u, elem) + c = false + break + end + end + if c == true + push!(S[index], u) + push!(U[index], u) + end + end + end + deleteat!(U[j], findall(item -> item == m, U[j])) + else + count += 1 + end + end + if count == length(U) + return S[index_0] + else + count = 0 + end + end +end diff --git a/experimental/InvariantTheory/test/runtests.jl b/experimental/InvariantTheory/test/runtests.jl new file mode 100644 index 000000000000..3de3a24b3bde --- /dev/null +++ b/experimental/InvariantTheory/test/runtests.jl @@ -0,0 +1,60 @@ +@testset "Invariant Theory of SL_m" begin + S, z = polynomial_ring(QQ, "z"=> (1:2, 1:2)) + G = linearly_reductive_group(:SL,2,S) + @test group(G)[1] == :SL + @test group(G)[2] == 2 + @test group_ideal(G) == ideal([z[1, 1]*z[2, 2] - z[2, 1]*z[1, 2] - 1]) + @test ncols(canonical_representation(G)) == 2 + @test natural_representation(G) == canonical_representation(G) + + rep1 = representation_on_forms(G,2) + @test ncols(representation_matrix(rep1)) == 3 + @test group(rep1) == G + @test vector_space_dimension(rep1) == 3 + + R_rep1 = invariant_ring(rep1) + FI_rep1 = fundamental_invariants(R_rep1) + @test length(FI_rep1) == 1 + + #same rep mat as in rep1, only without multinomial coefficients. + M = matrix(S,3,3,[z[1,1]^2 z[1,1]*z[2,1] z[2,1]^2 ; 2*z[1,1]*z[1,2] z[1,1]*z[2,2] + z[2,1]*z[1,2] 2*z[2,1]*z[2,2]; z[1,2]^2 z[1,2]*z[2,2] z[2,2]^2]) + rep2 = representation_reductive_group(G, M) + R_rep2 = invariant_ring(R_rep1.poly_ring, rep2) + FI_rep2 = fundamental_invariants(R_rep2) + x = gens(R_rep1.poly_ring) + @test FI_rep2 == [-4*x[1]*x[3] + x[2]^2] + + #direct sum of representation_linearly_reductive_group + D = direct_sum(rep1, rep2) + @test ncols(representation_matrix(D)) == 6 + T1 = tensor([rep1, rep2]) + T2 = tensor(rep1, rep2) + @test representation_matrix(T1) == representation_matrix(T2) + @test ncols(representation_matrix(T1)) == 9 + + #ternary cubics + T, X = graded_polynomial_ring(QQ, "X"=>1:10) + g = linearly_reductive_group(:SL, 3, QQ) + rep3 = representation_on_forms(g, 3) + R_rep3 = invariant_ring(T, rep3) + f = X[1]*X[4]*X[8]*X[10] - X[1]*X[4]*X[9]^2 - X[1]*X[5]*X[7]*X[10] + X[1]*X[5]*X[8]*X[9] + X[1]*X[6]*X[7]*X[9] - X[1]*X[6]*X[8]^2 - X[2]^2*X[8]*X[10] + X[2]^2*X[9]^2 + X[2]*X[3]*X[7]*X[10] - X[2]*X[3]*X[8]*X[9] + X[2]*X[4]*X[5]*X[10] - X[2]*X[4]*X[6]*X[9] - 2*X[2]*X[5]^2*X[9] + 3*X[2]*X[5]*X[6]*X[8] - X[2]*X[6]^2*X[7] - X[3]^2*X[7]*X[9] + X[3]^2*X[8]^2 - X[3]*X[4]^2*X[10] + 3*X[3]*X[4]*X[5]*X[9] - X[3]*X[4]*X[6]*X[8] - 2*X[3]*X[5]^2*X[8] + X[3]*X[5]*X[6]*X[7] + X[4]^2*X[6]^2 - 2*X[4]*X[5]^2*X[6] + X[5]^4 + @test reynolds_operator(R_rep3, f) == f + + #tori + #example in the derksen book + T = torus_group(QQ,1) + r = representation_from_weights(T, [-3, -1, 1, 2]) + I = invariant_ring(r) + f = fundamental_invariants(I) + @test length(f) == 6 + + #example from Macaulay2 + T = torus_group(QQ,2) + r = representation_from_weights(T, [1 0; 0 1; -1 -1; -1 1]) + I = invariant_ring(r) + R = poly_ring(I) + X = gens(R) + f = fundamental_invariants(I) + @test f == [X[1]*X[2]*X[3], X[1]^2*X[3]*X[4]] + +end From f1abad7935e5272277fe3206d87de02d31dacc5d Mon Sep 17 00:00:00 2001 From: Matthias Zach <85350711+HechtiDerLachs@users.noreply.github.com> Date: Wed, 21 Feb 2024 10:32:24 +0100 Subject: [PATCH 22/29] Fixes for the degree function (#3298) MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit * Remove :task from sub methods for modules. * Introduce new function submodule. * Remove all deprecated uses of sub. * Export submodule. * Fix tests. * Fix tests again. * Register morphisms in general. * Rebase network of natural maps on WeakKeyIdDicts. * Clean up the morphisms network and dont store the actual morphisms. * Some small fix for Wolfram. * Some fixes and marking the test as broken again. * Fix documentation. * Another small fix for Wolfram. * Fix the fix. * Fix method selection. * Introduce kw argument for caching morphisms. * Redirect previous usages. * Adjust tests. * submodule -> sub_object. * Fix docstrings and signatures for quo. * Fix methods for quo. * Adjust documentation. * Fix up usages of quo. * Export new functions. * Some fixes. * Fix tests. * Fix tests. * Fix tests. * Fix tests. * Fix tests. * Fix tests. * Squashed changes. * Fix tests. * Fix up the truncation. * New rebase. * Fix tests. * WIP with debug messages. * Progress in debugging. * WIP on debugging. * Write truely generic presentation and kernel methods [no ci]. * Repair graded_map to accept zero entries. * Add tensor decomposition function to return value. * Add some assertions. * Repair kernel routine. * Rewrite hom methods for modules. * Add generic method for simplification of SubquoModuleElems. * Add missing check argument. * Fix or disable brittle tests. * Fix faulty merge. * Go back to old hom. * Switch tests to old hom. * Clean up some deprecated assertions. * Repair truncate. * Disable internal checks. * Update docs/src/CommutativeAlgebra/ModulesOverMultivariateRings/free_modules.md * Revert "Go back to old hom." This reverts commit a6b7c153f3f9de9b851f53533687a4c84d4f2c2b. * Revert "Switch tests to old hom." This reverts commit 178eaf3286fa3f377b2959645b326a1f3ba8ba62. * Disable duplicate method. * Adjust printing. * Fix tests. * Fix keyword argument for duals. * Fix doctests. * Fix tests. * Fix doctests. * Delete some falsely added files. * Remove deprecated code. * Another round of disabling internal checks. * Disable various internal checks. * Disable further internal checks. * Set random seeds in tests. * Adjust use of keyword argument. * Fix more random seeds. * Fix the generic simplify method for SubquoModuleElems. * Revert "Remove deprecated code." This reverts commit 190256bc9d0998caab99b76555991c0e91e573a1. * Repair revert to old hom. * Repair preimage function. * Repair degree function. * Adjust tests to use of repaired old hom. * Add dummy simplify function for FreeModuleElems. * Fix doctests. * Repair simplify. * Fix documentation. * Fix doctests. * Some tuning. * Fix tests. * Bugfix from running book code run. * Remove some debugging artifacts. * Fix faulty merge. * Restrict signature. * Update flattenings of modules over towers of polynomial rings to make the tests run again. * Small fix. * Disable the superfluous kernel routine. * Restrict some further signatures to cases Singular can handle. * Add tests for flattenings of modules. * Readd methods which are not superfluous, yet. --------- Co-authored-by: Lars Göttgens Co-authored-by: Lars Göttgens (cherry picked from commit cfb3413f0615394fa1f9c2bbbe0a9329d4c32cc7) --- .../free_modules.md | 2 +- .../module_operations.md | 2 +- .../subquotients.md | 4 +- .../CommutativeAlgebra/homological_algebra.md | 2 +- .../src/Morphisms/ext.jl | 10 +- .../src/Morphisms/free_resolutions.jl | 14 +- .../src/Morphisms/simplified_complexes.jl | 22 +- .../src/Objects/koszul_complexes.jl | 2 +- .../src/Objects/total_complexes.jl | 2 +- experimental/Schemes/DerivedPushforward.jl | 2 +- .../Morphisms/Constructors.jl | 2 +- .../ProjectiveSchemes/Morphisms/Methods.jl | 9 +- .../ProjectiveSchemes/Objects/Attributes.jl | 8 +- src/Modules/ExteriorPowers/FreeModules.jl | 2 +- src/Modules/ExteriorPowers/Generic.jl | 8 +- src/Modules/FreeModules-graded.jl | 2 +- src/Modules/Iterators.jl | 20 +- src/Modules/ModuleTypes.jl | 117 +++-- src/Modules/ModulesGraded.jl | 446 ++++++++++------- src/Modules/UngradedModules/DirectSum.jl | 20 +- src/Modules/UngradedModules/FreeModElem.jl | 2 + src/Modules/UngradedModules/FreeModuleHom.jl | 116 +++-- .../UngradedModules/FreeResolutions.jl | 34 +- src/Modules/UngradedModules/Hom_and_ext.jl | 284 ++++++++++- .../UngradedModules/HomologicalAlgebra.jl | 34 +- src/Modules/UngradedModules/Methods.jl | 138 ++--- src/Modules/UngradedModules/Presentation.jl | 112 ++++- src/Modules/UngradedModules/SubQuoHom.jl | 65 ++- src/Modules/UngradedModules/SubquoModule.jl | 12 +- .../UngradedModules/SubquoModuleElem.jl | 471 +++++++++++------- src/Modules/UngradedModules/Tensor.jl | 6 +- src/Modules/UngradedModules/flattenings.jl | 17 + src/Modules/flattenings.jl | 164 +++++- src/Modules/hilbert.jl | 6 +- src/Modules/homological-algebra.jl | 6 +- src/Modules/local_rings.jl | 2 +- src/Modules/mpoly-localizations.jl | 2 +- src/Modules/mpolyquo.jl | 2 + src/Rings/MPolyQuo.jl | 17 +- src/Rings/ReesAlgebra.jl | 4 +- src/Rings/mpoly-graded.jl | 40 +- src/Rings/mpoly-localizations.jl | 16 +- src/Rings/mpolyquo-localizations.jl | 16 +- src/exports.jl | 2 + test/Modules/ModulesGraded.jl | 44 +- test/Modules/UngradedModules.jl | 136 +++-- test/Modules/flattenings.jl | 42 ++ 47 files changed, 1738 insertions(+), 748 deletions(-) create mode 100644 src/Modules/UngradedModules/flattenings.jl create mode 100644 test/Modules/flattenings.jl diff --git a/docs/src/CommutativeAlgebra/ModulesOverMultivariateRings/free_modules.md b/docs/src/CommutativeAlgebra/ModulesOverMultivariateRings/free_modules.md index eae0b6552eee..2a2d7ea64b57 100644 --- a/docs/src/CommutativeAlgebra/ModulesOverMultivariateRings/free_modules.md +++ b/docs/src/CommutativeAlgebra/ModulesOverMultivariateRings/free_modules.md @@ -174,7 +174,7 @@ is_homogeneous(f::FreeModElem) ``` ```@docs -degree(f::FreeModElem) +degree(f::FreeModElem{T}) where {T<:Union{<:MPolyDecRingElem, <:MPolyQuoRingElem{<:MPolyDecRingElem}}} ``` diff --git a/docs/src/CommutativeAlgebra/ModulesOverMultivariateRings/module_operations.md b/docs/src/CommutativeAlgebra/ModulesOverMultivariateRings/module_operations.md index e0dc724cb705..2d5ef1ce33a1 100644 --- a/docs/src/CommutativeAlgebra/ModulesOverMultivariateRings/module_operations.md +++ b/docs/src/CommutativeAlgebra/ModulesOverMultivariateRings/module_operations.md @@ -37,7 +37,7 @@ direct_product(M::ModuleFP{T}...; task::Symbol = :prod) where T ## Truncation ```@docs -truncate(M::ModuleFP, g::FinGenAbGroupElem, task::Symbol = :with_morphism) +truncate(M::ModuleFP, g::FinGenAbGroupElem, task::Symbol=:with_morphism) ``` ## Twists diff --git a/docs/src/CommutativeAlgebra/ModulesOverMultivariateRings/subquotients.md b/docs/src/CommutativeAlgebra/ModulesOverMultivariateRings/subquotients.md index 1e4f0e0a2c67..6a35e3462e41 100644 --- a/docs/src/CommutativeAlgebra/ModulesOverMultivariateRings/subquotients.md +++ b/docs/src/CommutativeAlgebra/ModulesOverMultivariateRings/subquotients.md @@ -359,11 +359,11 @@ intersect(M::SubquoModule{T}, N::SubquoModule{T}) where T ## Submodules and Quotients ```@docs -sub(M::ModuleFP{T}, V::Vector{<:ModuleFPElem{T}}, task::Symbol = :with_morphism) where T +sub(M::ModuleFP{T}, V::Vector{<:ModuleFPElem{T}}) where T ``` ```@docs -quo(M::ModuleFP{T}, V::Vector{<:ModuleFPElem{T}}, task::Symbol = :with_morphism) where T +quo(M::ModuleFP{T}, V::Vector{<:ModuleFPElem{T}}; cache_morphism::Bool=false) where T ``` ## Homomorphisms From Subqotients diff --git a/docs/src/CommutativeAlgebra/homological_algebra.md b/docs/src/CommutativeAlgebra/homological_algebra.md index 793e39641e4e..fc25f5605bb9 100644 --- a/docs/src/CommutativeAlgebra/homological_algebra.md +++ b/docs/src/CommutativeAlgebra/homological_algebra.md @@ -104,7 +104,7 @@ homology(C::ComplexOfMorphisms{<:ModuleFP}, i::Int) ## Hom and Ext ```@docs -hom(M::ModuleFP, N::ModuleFP, algorithm::Symbol=:maps) +hom(M::ModuleFP, N::ModuleFP; algorithm::Symbol=:maps) ``` ```@docs diff --git a/experimental/DoubleAndHyperComplexes/src/Morphisms/ext.jl b/experimental/DoubleAndHyperComplexes/src/Morphisms/ext.jl index a948573a8ffe..c169365c0e8c 100644 --- a/experimental/DoubleAndHyperComplexes/src/Morphisms/ext.jl +++ b/experimental/DoubleAndHyperComplexes/src/Morphisms/ext.jl @@ -56,18 +56,18 @@ function (fac::HomMapFactory)(hc::AbsHyperComplex, p::Int, i::Tuple) cod = hc[i_inc] if iszero(dom) || iszero(cod) - return hom(dom, cod, elem_type(cod)[zero(cod) for i in 1:ngens(dom)]) + return hom(dom, cod, elem_type(cod)[zero(cod) for i in 1:ngens(dom)]; check=false) end if p <= dim(d) # contravariant induced map on first argument i1_inc = Tuple(-i1 - [k == p ? inc : 0 for k in 1:dim(d)]) img_gens = [homomorphism_to_element(cod, compose(map(d, p, i1_inc), element_to_homomorphism(g))) for g in gens(dom)] - return hom(dom, cod, img_gens) + return hom(dom, cod, img_gens; check=false) else # covariant induced map on second argument img_gens = [homomorphism_to_element(cod, compose(element_to_homomorphism(g), map(c, p - dim(d), Tuple(i2)))) for g in gens(dom)] - return hom(dom, cod, img_gens) + return hom(dom, cod, img_gens; check=false) end end @@ -214,7 +214,7 @@ function (fac::InterpretationMorphismFactory)(self::AbsHyperComplexMorphism, I:: projections_tot = projections_for_summand(tot, offset) M = dom[i] N = cod[j] - result = hom(M, N, elem_type(N)[zero(N) for i in 1:ngens(M)]) + result = hom(M, N, elem_type(N)[zero(N) for i in 1:ngens(M)]; check=false) for (k, K) in enumerate(indices_dom) pr = projections_dom[k] for (l, L) in enumerate(indices_cod) @@ -341,7 +341,7 @@ function (fac::HomComplexMorphismFactory)(self::AbsHyperComplexMorphism, I::Tupl img_gens = elem_type(cod_mod)[homomorphism_to_element(cod_mod, compose(element_to_homomorphism(v), fac.codomain_morphism[I_out])) for v in g] end - return hom(dom_mod, cod_mod, img_gens) # Set to false eventually + return hom(dom_mod, cod_mod, img_gens; check=false) # Set to false eventually end function can_compute(fac::HomComplexMorphismFactory, self::AbsHyperComplexMorphism, I::Tuple) diff --git a/experimental/DoubleAndHyperComplexes/src/Morphisms/free_resolutions.jl b/experimental/DoubleAndHyperComplexes/src/Morphisms/free_resolutions.jl index 92a6dc54cb3f..b48d2df67863 100644 --- a/experimental/DoubleAndHyperComplexes/src/Morphisms/free_resolutions.jl +++ b/experimental/DoubleAndHyperComplexes/src/Morphisms/free_resolutions.jl @@ -22,10 +22,11 @@ function (fac::ResolutionModuleFactory{ChainType})(c::AbsHyperComplex, I::Tuple) end if isone(i) - aug = hom(c[0], fac.orig_mod, gens(fac.orig_mod)) + aug = hom(c[0], fac.orig_mod, gens(fac.orig_mod); check=false) + aug.generators_map_to_generators = true K, inc = kernel(aug) next = _make_free_module(K, gens(K)) - phi = hom(next, c[0], ambient_representatives_generators(K)) + phi = hom(next, c[0], ambient_representatives_generators(K); check=false) push!(fac.map_cache, phi) return next end @@ -45,7 +46,7 @@ function (fac::ResolutionModuleFactory{ChainType})(c::AbsHyperComplex, I::Tuple) return next end next = _make_free_module(K, gens(K)) - phi = hom(next, c[i-1], ambient_representatives_generators(K)) + phi = hom(next, c[i-1], ambient_representatives_generators(K); check=false) push!(fac.map_cache, phi) return next @@ -54,10 +55,10 @@ end function zero_object(M::ModuleFP) if is_graded(M) result = graded_free_module(base_ring(M), []) - return result, hom(result, M, elem_type(M)[]) + return result, hom(result, M, elem_type(M)[]; check=false) else result = FreeMod(base_ring(M), 0) - return result, hom(result, M, elem_type(M)[]) + return result, hom(result, M, elem_type(M)[]; check=false) end end @@ -99,7 +100,8 @@ function free_resolution(::Type{T}, M::SubquoModule{RET}) where {T<:SimpleFreeRe ) result = SimpleFreeResolution(M, internal_complex) MC = ZeroDimensionalComplex(M)[0:0] # Wrap MC as a 1-dimensional complex concentrated in degree 0 - aug_map = hom(result[(0,)], M, gens(M)) # The actual augmentation map + aug_map = hom(result[(0,)], M, gens(M); check=false) # The actual augmentation map + aug_map.generators_map_to_generators = true aug_map_comp = MorphismFromDict(result, MC, Dict{Tuple, typeof(aug_map)}([(0,)=>aug_map])) result.augmentation_map = aug_map_comp return result, aug_map_comp diff --git a/experimental/DoubleAndHyperComplexes/src/Morphisms/simplified_complexes.jl b/experimental/DoubleAndHyperComplexes/src/Morphisms/simplified_complexes.jl index e8926c533152..7a248e74d7a7 100644 --- a/experimental/DoubleAndHyperComplexes/src/Morphisms/simplified_complexes.jl +++ b/experimental/DoubleAndHyperComplexes/src/Morphisms/simplified_complexes.jl @@ -80,7 +80,7 @@ function (fac::SimplifiedChainFactory)(d::AbsHyperComplex, Ind::Tuple) # Create the maps to the old complex img_gens_dom = elem_type(M)[sum(c*M[j] for (j, c) in S[i]; init=zero(M)) for i in I] new_dom = _make_free_module(M, img_gens_dom) - dom_map = hom(new_dom, M, img_gens_dom) + dom_map = hom(new_dom, M, img_gens_dom; check=false) if haskey(fac.maps_to_original, i) # This means that for the next map a partial or @@ -93,7 +93,7 @@ function (fac::SimplifiedChainFactory)(d::AbsHyperComplex, Ind::Tuple) img_gens_cod = elem_type(N)[sum(c*N[i] for (i, c) in T[j]; init=zero(N)) for j in J] new_cod = _make_free_module(N, img_gens_cod) - cod_map = hom(new_cod, N, img_gens_cod) + cod_map = hom(new_cod, N, img_gens_cod; check=false) if haskey(fac.maps_to_original, next) fac.maps_to_original[next] = compose(cod_map, fac.maps_to_original[next]) @@ -122,7 +122,7 @@ function (fac::SimplifiedChainFactory)(d::AbsHyperComplex, Ind::Tuple) # end push!(img_gens_dom, v) end - dom_map_inv = hom(M, new_dom, img_gens_dom) + dom_map_inv = hom(M, new_dom, img_gens_dom; check=false) if haskey(fac.maps_from_original, i) fac.maps_from_original[i] = compose(fac.maps_from_original[i], dom_map_inv) @@ -144,7 +144,7 @@ function (fac::SimplifiedChainFactory)(d::AbsHyperComplex, Ind::Tuple) w_new = sparse_row(base_ring(w), new_entries) push!(img_gens_cod, FreeModElem(w_new, new_cod)) end - cod_map_inv = hom(N, new_cod, img_gens_cod) + cod_map_inv = hom(N, new_cod, img_gens_cod; check=false) if haskey(fac.maps_from_original, next) fac.maps_from_original[next] = compose(fac.maps_from_original[next], cod_map_inv) @@ -184,7 +184,7 @@ function (fac::SimplifiedChainFactory)(d::AbsHyperComplex, Ind::Tuple) # Create the maps to the old complex img_gens_dom = elem_type(M)[sum(c*M[j] for (j, c) in S[i]; init=zero(M)) for i in I] new_dom = _make_free_module(M, img_gens_dom) - dom_map = hom(new_dom, M, img_gens_dom) + dom_map = hom(new_dom, M, img_gens_dom; check=false) if haskey(fac.maps_to_original, prev) fac.maps_to_original[prev] = compose(dom_map, fac.maps_to_original[prev]) @@ -195,7 +195,7 @@ function (fac::SimplifiedChainFactory)(d::AbsHyperComplex, Ind::Tuple) img_gens_cod = elem_type(N)[sum(c*N[i] for (i, c) in T[j]; init=zero(N)) for j in J] new_cod = _make_free_module(N, img_gens_cod) - cod_map = hom(new_cod, N, img_gens_cod) + cod_map = hom(new_cod, N, img_gens_cod; check=false) if haskey(fac.maps_to_original, i) fac.maps_to_original[i] = compose(cod_map, fac.maps_to_original[i]) @@ -214,7 +214,7 @@ function (fac::SimplifiedChainFactory)(d::AbsHyperComplex, Ind::Tuple) end push!(img_gens_dom, v) end - dom_map_inv = hom(M, new_dom, img_gens_dom) + dom_map_inv = hom(M, new_dom, img_gens_dom; check=false) if haskey(fac.maps_from_original, prev) fac.maps_from_original[prev] = compose(fac.maps_from_original[prev], dom_map_inv) @@ -235,7 +235,7 @@ function (fac::SimplifiedChainFactory)(d::AbsHyperComplex, Ind::Tuple) w_new = sparse_row(base_ring(w), new_entries) push!(img_gens_cod, FreeModElem(w_new, new_cod)) end - cod_map_inv = hom(N, new_cod, img_gens_cod) + cod_map_inv = hom(N, new_cod, img_gens_cod; check=false) if haskey(fac.maps_from_original, i) fac.maps_from_original[i] = compose(fac.maps_from_original[i], cod_map_inv) @@ -357,7 +357,7 @@ end ### Helper functions function _make_free_module(M::ModuleFP, g::Vector{T}) where {T<:ModuleFPElem} if is_graded(M) - w = degree.(g) + w = _degree_fast.(g) return graded_free_module(base_ring(M), w) else return FreeMod(base_ring(M), length(g)) @@ -598,9 +598,9 @@ function _alt_simplify(M::SubquoModule) Z0, inc_Z0 = kernel(simp, 0) result_to_M = hom(result, M, - elem_type(M)[aug[0](simp_to_orig[0](inc_Z0(preimage(Z0_to_result, x)))) for x in gens(result)]) + elem_type(M)[aug[0](simp_to_orig[0](inc_Z0(preimage(Z0_to_result, x)))) for x in gens(result)]; check=false) M_to_result = hom(M, result, - elem_type(result)[Z0_to_result(preimage(inc_Z0, orig_to_simp[0](preimage(aug[0], y)))) for y in gens(M)]) + elem_type(result)[Z0_to_result(preimage(inc_Z0, orig_to_simp[0](preimage(aug[0], y)))) for y in gens(M)]; check=false) return result, M_to_result, result_to_M end diff --git a/experimental/DoubleAndHyperComplexes/src/Objects/koszul_complexes.jl b/experimental/DoubleAndHyperComplexes/src/Objects/koszul_complexes.jl index 7e78d231669d..7be85996dd58 100644 --- a/experimental/DoubleAndHyperComplexes/src/Objects/koszul_complexes.jl +++ b/experimental/DoubleAndHyperComplexes/src/Objects/koszul_complexes.jl @@ -36,7 +36,7 @@ function (fac::KoszulMorphismFactory)(c::AbsHyperComplex, p::Int, i::Tuple) dom = c[i] cod = c[first(i) - 1] if first(i) == 0 || first(i) == r + 1 - return hom(dom, cod, elem_type(cod)[zero(cod) for i in 1:ngens(dom)]) + return hom(dom, cod, elem_type(cod)[zero(cod) for i in 1:ngens(dom)]; check=false) end return wedge_multiplication_map(dom, cod, fac.v) end diff --git a/experimental/DoubleAndHyperComplexes/src/Objects/total_complexes.jl b/experimental/DoubleAndHyperComplexes/src/Objects/total_complexes.jl index 4e4e0c188812..bca48c719159 100644 --- a/experimental/DoubleAndHyperComplexes/src/Objects/total_complexes.jl +++ b/experimental/DoubleAndHyperComplexes/src/Objects/total_complexes.jl @@ -119,7 +119,7 @@ function (fac::TotalComplexMapFactory)(c::AbsHyperComplex, p::Int, I::Tuple) next = d + inc dom = c[d] cod = c[next] - result = hom(dom, cod, elem_type(cod)[zero(cod) for i in 1:ngens(dom)]) + result = hom(dom, cod, elem_type(cod)[zero(cod) for i in 1:ngens(dom)]; check=false) for (ind, J) in enumerate(index_cache(chain_fac)[d]) for k in 1:dim(orig) target = collect(J) + (direction(orig, k) == :chain ? -1 : 1)*[(l == k ? 1 : 0) for l in 1:dim(orig)] diff --git a/experimental/Schemes/DerivedPushforward.jl b/experimental/Schemes/DerivedPushforward.jl index e6604acf1aa5..2351d283430f 100644 --- a/experimental/Schemes/DerivedPushforward.jl +++ b/experimental/Schemes/DerivedPushforward.jl @@ -79,7 +79,7 @@ function rank(phi::FreeModuleHom{FreeMod{T}, FreeMod{T}, Nothing}) where {T<:Fie end -_regularity_bound(F::FreeMod) = maximum(Int(degree(a)[1]) for a in gens(F)) +_regularity_bound(F::FreeMod) = maximum(Int(degree(a; check=false)[1]) for a in gens(F)) @doc raw""" simplify(c::ComplexOfMorphisms{ChainType}) where {ChainType<:ModuleFP} diff --git a/src/AlgebraicGeometry/Schemes/ProjectiveSchemes/Morphisms/Constructors.jl b/src/AlgebraicGeometry/Schemes/ProjectiveSchemes/Morphisms/Constructors.jl index 8fbb1d946d02..793bbeaf835c 100644 --- a/src/AlgebraicGeometry/Schemes/ProjectiveSchemes/Morphisms/Constructors.jl +++ b/src/AlgebraicGeometry/Schemes/ProjectiveSchemes/Morphisms/Constructors.jl @@ -186,7 +186,7 @@ function ambient_embedding(X::AbsProjectiveScheme) S = homogeneous_coordinate_ring(IP) T = homogeneous_coordinate_ring(X) I = defining_ideal(X) - pb = hom(S, T, gens(T)) + pb = hom(S, T, gens(T); check=false) inc_sub = ProjectiveSchemeMor(X, IP, pb, check=false) return ProjectiveClosedEmbedding(inc_sub, I, check=false) end diff --git a/src/AlgebraicGeometry/Schemes/ProjectiveSchemes/Morphisms/Methods.jl b/src/AlgebraicGeometry/Schemes/ProjectiveSchemes/Morphisms/Methods.jl index 1fc0f9ce4fa3..cc6b157c843d 100644 --- a/src/AlgebraicGeometry/Schemes/ProjectiveSchemes/Morphisms/Methods.jl +++ b/src/AlgebraicGeometry/Schemes/ProjectiveSchemes/Morphisms/Methods.jl @@ -74,7 +74,8 @@ with default covering u = inv(OO(U_ij)(denom)) mor_dict[U_ij] = morphism(U_ij, V_j, hom(OO(V_j), OO(U_ij), - [OO(U_ij)(dehom(pbf(gen(SY, k))))*u for k in 1:ngens(SY) if k != j] + [OO(U_ij)(dehom(pbf(gen(SY, k))))*u for k in 1:ngens(SY) if k != j]; + check=false ) ) end @@ -120,11 +121,11 @@ function pushforward(inc::ProjectiveClosedEmbedding, M::FreeMod) S = codomain(f) T = domain(f) S === base_ring(M) || error("rings do not match") - FT = graded_free_module(T, [degree(a) for a in gens(M)]) + FT = graded_free_module(T, [_degree_fast(a) for a in gens(M)]) I = image_ideal(inc) IFT, inc_IFT = I*FT MT = cokernel(inc_IFT) - id = hom(MT, M, gens(M), f) + id = hom(MT, M, gens(M), f; check=false) return MT, id end @@ -141,7 +142,7 @@ function pushforward(inc::ProjectiveClosedEmbedding, M::SubquoModule) G, inc_G = sub(FT, vcat(gT, relT)) Q, inc_Q = sub(G, gens(G)[length(gT)+1:end]) MT = cokernel(inc_Q) - id = hom(MT, M, vcat(gens(M), elem_type(M)[zero(M) for i in 1:length(relT)])) + id = hom(MT, M, vcat(gens(M), elem_type(M)[zero(M) for i in 1:length(relT)]); check=false) return MT, id end diff --git a/src/AlgebraicGeometry/Schemes/ProjectiveSchemes/Objects/Attributes.jl b/src/AlgebraicGeometry/Schemes/ProjectiveSchemes/Objects/Attributes.jl index 0ecd3371b18a..95149ca46017 100644 --- a/src/AlgebraicGeometry/Schemes/ProjectiveSchemes/Objects/Attributes.jl +++ b/src/AlgebraicGeometry/Schemes/ProjectiveSchemes/Objects/Attributes.jl @@ -533,10 +533,10 @@ function relative_euler_sequence(X::AbsProjectiveScheme{<:Ring, <:MPolyRing}) S = homogeneous_coordinate_ring(X)::MPolyDecRing W1 = kaehler_differentials(S) W0 = kaehler_differentials(S, 0) - theta = hom(W1, W0, [x*W0[1] for x in gens(S)]) + theta = hom(W1, W0, [x*W0[1] for x in gens(S)]; check=false) W, inc = kernel(theta) Z = graded_free_module(S, 0) - inc_Z = hom(Z, W, elem_type(W)[]) + inc_Z = hom(Z, W, elem_type(W)[]; check=false) comp = ComplexOfMorphisms(ModuleFP, [inc_Z, inc, theta], typ=:cochain, seed = -1) return comp end @@ -578,10 +578,10 @@ function relative_cotangent_module(X::AbsProjectiveScheme{<:Ring, <:MPolyQuoRing SP = homogeneous_coordinate_ring(P) F = graded_free_module(SP, degree.(f)) - jac = hom(F, eu[1], df) + jac = hom(F, eu[1], df; check=false) jac_res = _change_base_ring_and_preserve_gradings(phi, jac, codomain_change = res_Omega1) img_gens = [preimage(inc_W1X, jac_res(x)) for x in gens(domain(jac_res))] - psi = hom(domain(jac_res), W1X, img_gens) + psi = hom(domain(jac_res), W1X, img_gens; check=false) return cokernel(psi) end diff --git a/src/Modules/ExteriorPowers/FreeModules.jl b/src/Modules/ExteriorPowers/FreeModules.jl index ff653591bc79..48d39ae79e02 100644 --- a/src/Modules/ExteriorPowers/FreeModules.jl +++ b/src/Modules/ExteriorPowers/FreeModules.jl @@ -25,7 +25,7 @@ function exterior_power(F::FreeMod, p::Int; cached::Bool=true) G = grading_group(F) weights = elem_type(G)[] for ind in OrderedMultiIndexSet(p, n) - push!(weights, sum(degree(F[i]) for i in indices(ind); init=zero(G))) + push!(weights, sum(_degree_fast(F[i]) for i in indices(ind); init=zero(G))) end grade(result_, weights) else diff --git a/src/Modules/ExteriorPowers/Generic.jl b/src/Modules/ExteriorPowers/Generic.jl index b9f48389d557..2e825e7f835a 100644 --- a/src/Modules/ExteriorPowers/Generic.jl +++ b/src/Modules/ExteriorPowers/Generic.jl @@ -63,7 +63,7 @@ function wedge_multiplication_map(F::ModuleFP, G::ModuleFP, v::ModuleFPElem) success, orig_mod, p = _is_exterior_power(F) if !success Fwedge1, _ = exterior_power(F, 1) - id = hom(F, Fwedge1, gens(Fwedge1)) + id = hom(F, Fwedge1, gens(Fwedge1); check=false) tmp = wedge_multiplication_map(Fwedge1, G, v) return compose(id, tmp) end @@ -71,7 +71,7 @@ function wedge_multiplication_map(F::ModuleFP, G::ModuleFP, v::ModuleFPElem) success, orig_mod_2, q = _is_exterior_power(G) if !success Gwedge1, _ = exterior_power(G, 1) - id = hom(Gwedge1, G, gens(G)) + id = hom(Gwedge1, G, gens(G); check=false) tmp = wedge_multiplication_map(F, Gwedge1, v) return compose(tmp, id) end @@ -93,7 +93,7 @@ function wedge_multiplication_map(F::ModuleFP, G::ModuleFP, v::ModuleFPElem) # map the generators img_gens = [wedge(v, e, parent=G) for e in gens(F)] - return hom(F, G, img_gens) + return hom(F, G, img_gens; check=false) end # The wedge product of two or more elements. @@ -177,7 +177,7 @@ function induced_map_on_exterior_power(phi::FreeModuleHom{<:FreeMod, <:FreeMod, imgs = phi.(gens(F)) img_gens = [wedge(imgs[indices(ind)], parent=codomain) for ind in OrderedMultiIndexSet(p, m)] - return hom(domain, codomain, img_gens) + return hom(domain, codomain, img_gens; check=false) end # The induced map on exterior powers diff --git a/src/Modules/FreeModules-graded.jl b/src/Modules/FreeModules-graded.jl index 85445c728b86..5b9fa0347396 100644 --- a/src/Modules/FreeModules-graded.jl +++ b/src/Modules/FreeModules-graded.jl @@ -1100,7 +1100,7 @@ function hom(M::ModuleFP_dec, N::ModuleFP_dec) psi = kDelta[2]*pro[1] psi = hom(kDelta[1], H_s0_t0, [psi(g) for g = gens(kDelta[1])]) - H = quo(sub(D, kDelta[1]), image(rho)[1]) + H = quo_object(sub(D, kDelta[1]), image(rho)[1]) set_attribute!(H, :show => Hecke.show_hom, :hom => (M, N)) #x in ker delta: mH_s0_t0(pro[1](x)) should be a hom from M to N diff --git a/src/Modules/Iterators.jl b/src/Modules/Iterators.jl index 1044f45a3f10..be6ef24a0bcd 100644 --- a/src/Modules/Iterators.jl +++ b/src/Modules/Iterators.jl @@ -27,7 +27,7 @@ function Base.length(amm::AllModuleMonomials) d = degree(amm) result = 0 for i in 1:r - d_loc = d - Int(degree(F[i])[1]) + d_loc = d - Int(degree(F[i]; check=false)[1]) d_loc < 0 && continue result = result + length(monomials_of_degree(R, d_loc)) end @@ -40,9 +40,9 @@ function Base.iterate(amm::AllModuleMonomials, state::Nothing = nothing) d = degree(amm) R = base_ring(F) - i = findfirst(i -> d - Int(degree(F[i])[1]) >= 0, 1:ngens(F)) + i = findfirst(i -> d - Int(degree(F[i]; check=false)[1]) >= 0, 1:ngens(F)) i === nothing && return nothing - d_loc = d - Int(degree(F[i])[1]) + d_loc = d - Int(degree(F[i]; check=false)[1]) mon_it = monomials_of_degree(R, d_loc) res = iterate(mon_it, nothing) @@ -60,9 +60,9 @@ function Base.iterate(amm::AllModuleMonomials, state::Tuple{Int, AllMonomials, V i, mon_it, s = state res = iterate(mon_it, s) if res === nothing - i = findnext(i -> d - Int(degree(F[i])[1]) >= 0, 1:ngens(F), i + 1) + i = findnext(i -> d - Int(degree(F[i]; check=false)[1]) >= 0, 1:ngens(F), i + 1) i === nothing && return nothing - d_loc = d - Int(degree(F[i])[1]) + d_loc = d - Int(degree(F[i]; check=false)[1]) mon_it = monomials_of_degree(R, d_loc) res_loc = iterate(mon_it, nothing) @@ -106,7 +106,7 @@ function Base.length(amm::AllModuleExponents) d = degree(amm) result = 0 for i in 1:r - d_loc = d - Int(degree(F[i])[1]) + d_loc = d - Int(degree(F[i]; check=false)[1]) d_loc < 0 && continue result = result + length(MultiIndicesOfDegree(n, d_loc)) end @@ -120,9 +120,9 @@ function Base.iterate(amm::AllModuleExponents, state::Nothing = nothing) R = base_ring(F) n = ngens(R) - i = findfirst(i -> d - Int(degree(F[i])[1]) >= 0, 1:ngens(F)) + i = findfirst(i -> d - Int(degree(F[i]; check=false)[1]) >= 0, 1:ngens(F)) i === nothing && return nothing - d_loc = d - Int(degree(F[i])[1]) + d_loc = d - Int(degree(F[i]; check=false)[1]) exp_it = MultiIndicesOfDegree(n, d_loc) res = iterate(exp_it, nothing) @@ -141,9 +141,9 @@ function Base.iterate(amm::AllModuleExponents, state::Tuple{Int, MultiIndicesOfD i, exp_it, e = state res = iterate(exp_it, e) if res === nothing - i = findnext(i -> d - Int(degree(F[i])[1]) >= 0, 1:ngens(F), i + 1) + i = findnext(i -> d - Int(degree(F[i]; check=false)[1]) >= 0, 1:ngens(F), i + 1) i === nothing && return nothing - d_loc = d - Int(degree(F[i])[1]) + d_loc = d - Int(degree(F[i]; check=false)[1]) exp_it = MultiIndicesOfDegree(n, d_loc) res_loc = iterate(exp_it, nothing) diff --git a/src/Modules/ModuleTypes.jl b/src/Modules/ModuleTypes.jl index 92128f33a4a8..a2416d45c949 100644 --- a/src/Modules/ModuleTypes.jl +++ b/src/Modules/ModuleTypes.jl @@ -1,3 +1,5 @@ +import AbstractAlgebra.WeakKeyIdDict + @doc raw""" ModuleFP{T} @@ -74,8 +76,20 @@ option is set in suitable functions. S::Vector{Symbol} d::Union{Vector{FinGenAbGroupElem}, Nothing} - incoming_morphisms::Vector{<:ModuleFPHom} - outgoing_morphisms::Vector{<:ModuleFPHom} + # We register the incoming and outgoing natural morphisms. + # This must be done in a way that objects can be collected by the + # garbage collector. In particular, we can not store the actual + # map as the value for a specific key (domain or codomain depending + # on whether the map is incoming or outgoing), because then the + # value has a reference to the key and thus the pair will never be + # deleted. + # + # Instead, we store a sparse matrix which allows us to reconstruct + # the map and potentially a change of rings. This allows us to + # reconstruct the map on request (which should be of relatively + # low cost). + incoming::WeakKeyIdDict{<:ModuleFP, <:Tuple{<:SMat, <:Any}} + outgoing::WeakKeyIdDict{<:ModuleFP, <:Tuple{<:SMat, <:Any}} function FreeMod{T}(n::Int,R::Ring,S::Vector{Symbol}) where T <: RingElem r = new{elem_type(R)}() @@ -84,9 +98,8 @@ option is set in suitable functions. r.S = S r.d = nothing - r.incoming_morphisms = Vector{ModuleFPHom}() - r.outgoing_morphisms = Vector{ModuleFPHom}() - + r.incoming = WeakKeyIdDict{ModuleFP, Tuple{SMat, Any}}() + r.outgoing = WeakKeyIdDict{ModuleFP, Tuple{SMat, Any}}() return r end end @@ -232,8 +245,8 @@ option is set in suitable functions. groebner_basis::Dict{ModuleOrdering, ModuleGens{T}} - incoming_morphisms::Vector{<:ModuleFPHom} - outgoing_morphisms::Vector{<:ModuleFPHom} # TODO is it possible to make ModuleFPHom to SubQuoHom? + incoming::WeakKeyIdDict{<:ModuleFP, <:Tuple{<:SMat, <:Any}} + outgoing::WeakKeyIdDict{<:ModuleFP, <:Tuple{<:SMat, <:Any}} function SubquoModule{R}(F::FreeMod{R}) where {R} # this does not construct a valid subquotient @@ -241,8 +254,9 @@ option is set in suitable functions. r.F = F r.groebner_basis = Dict() - r.incoming_morphisms = Vector{ModuleFPHom}() - r.outgoing_morphisms = Vector{ModuleFPHom}() + + r.incoming = WeakKeyIdDict{ModuleFP, Tuple{SMat, Any}}() + r.outgoing = WeakKeyIdDict{ModuleFP, Tuple{SMat, Any}}() return r end @@ -343,6 +357,7 @@ mutable struct SubQuoHom{ ###@assert is_graded(D) == is_graded(C) @assert length(im) == ngens(D) @assert all(x-> parent(x) === C, im) + @check true # Will throw if checks are not supposed to be enabled r = new{T1, T2, Nothing}() r.header = MapHeader(D, C) @@ -350,7 +365,7 @@ mutable struct SubQuoHom{ r.header.preimage = x->preimage(r, x) r.im = Vector{elem_type(C)}(im) r.generators_map_to_generators = nothing - return set_grading(r) + return set_grading(r; check) end function SubQuoHom{T1,T2,RingMapType}(D::SubquoModule, C::SubquoModule, im::Vector; @@ -366,7 +381,7 @@ mutable struct SubQuoHom{ r.header.preimage = x->preimage(r, x) r.im = Vector{elem_type(C)}(im) r.generators_map_to_generators = nothing - return set_grading(r) + return set_grading(r; check) end function SubQuoHom{T1,T2,RingMapType}(D::SubquoModule, C::ModuleFP, im::Vector; @@ -382,7 +397,7 @@ mutable struct SubQuoHom{ r.header.preimage = x->preimage(r, x) r.im = Vector{elem_type(C)}(im) r.generators_map_to_generators = nothing - return set_grading(r) + return set_grading(r; check) end # Constructors for maps with change of base ring @@ -404,7 +419,7 @@ mutable struct SubQuoHom{ r.im = Vector{elem_type(C)}(im) r.ring_map = h r.generators_map_to_generators = nothing - return set_grading(r) + return set_grading(r; check) end function SubQuoHom{T1,T2,RingMapType}( @@ -425,7 +440,7 @@ mutable struct SubQuoHom{ r.im = Vector{elem_type(C)}(im) r.ring_map = h r.generators_map_to_generators = nothing - return set_grading(r) + return set_grading(r; check) end function SubQuoHom{T1,T2,RingMapType}( @@ -446,7 +461,7 @@ mutable struct SubQuoHom{ r.im = Vector{elem_type(C)}(im) r.ring_map = h r.generators_map_to_generators = nothing - return set_grading(r) + return set_grading(r; check) end end @@ -539,13 +554,15 @@ When computed, the corresponding matrix (via `matrix()`) and inverse isomorphism # generate homomorphism of free modules from F to G where the vector a contains the images of # the generators of F function FreeModuleHom( - F::AbstractFreeMod, G::S, a::Vector{ModuleElemType} + F::AbstractFreeMod, G::S, a::Vector{ModuleElemType}; + check::Bool=true ) where {S<:ModuleFP, ModuleElemType<:ModuleFPElem} ###@assert is_graded(F) == is_graded(G) @assert all(x->parent(x) === G, a) @assert length(a) == ngens(F) r = new{typeof(F), typeof(G), Nothing}() a=Vector{elem_type(G)}(a) + image_module = sub_object(G, a) function im_func(x::AbstractFreeModElem) # The lines below were an attempt to speed up mapping. # However, it turns out that checking the equality is more @@ -562,17 +579,55 @@ When computed, the corresponding matrix (via `matrix()`) and inverse isomorphism end function pr_func(x) @assert parent(x) === G - c = coordinates(repres(x), sub(G, a, :module)) + r.generators_map_to_generators === true && return FreeModElem(coordinates(simplify!(x)), F) + c = coordinates(repres(simplify!(x)), image_module) return FreeModElem(c, F) end r.header = MapHeader{typeof(F), typeof(G)}(F, G, im_func, pr_func) r.imgs_of_gens = Vector{elem_type(G)}(a) r.generators_map_to_generators = nothing - return set_grading(r) + return set_grading(r; check) end + # We need to introduce a separate constructor for decorated modules here + # because some of the generic functionality (sub_object) is not there yet. function FreeModuleHom( - F::AbstractFreeMod, G::T2, a::Vector{ModuleElemType}, h::RingMapType + F::FreeMod_dec, G::S, a::Vector{ModuleElemType}; + check::Bool=true + ) where {S<:ModuleFP, ModuleElemType<:ModuleFPElem} + ###@assert is_graded(F) == is_graded(G) + @assert all(x->parent(x) === G, a) + @assert length(a) == ngens(F) + r = new{typeof(F), typeof(G), Nothing}() + a=Vector{elem_type(G)}(a) + function im_func(x::AbstractFreeModElem) + # The lines below were an attempt to speed up mapping. + # However, it turns out that checking the equality is more + # expensive in average than the gain for actual mappings. + # Apparently, maps are likely to be used just once, or only + # few times. + # But the flag can (and probably should) be set by the constructors + # of maps whenever applicable. + #if r.generators_map_to_generators === nothing + # r.generators_map_to_generators = images_of_generators(r) == gens(codomain(r)) + #end + r.generators_map_to_generators === true && return codomain(r)(coordinates(x)) + return sum(b*a[i] for (i, b) in coordinates(x); init=zero(codomain(r))) + end + function pr_func(x) + @assert parent(x) === G + c = coordinates(repres(simplify!(x)), sub_object(G, a)) + return FreeModElem(c, F) + end + r.header = MapHeader{typeof(F), typeof(G)}(F, G, im_func, pr_func) + r.imgs_of_gens = Vector{elem_type(G)}(a) + r.generators_map_to_generators = nothing + return set_grading(r; check) + end + + function FreeModuleHom( + F::AbstractFreeMod, G::T2, a::Vector{ModuleElemType}, h::RingMapType; + check::Bool=true ) where {T2, ModuleElemType<:ModuleFPElem, RingMapType} ###@assert is_graded(F) == is_graded(G) @assert all(x->parent(x) === G, a) @@ -580,6 +635,7 @@ When computed, the corresponding matrix (via `matrix()`) and inverse isomorphism @assert h(one(base_ring(F))) == one(base_ring(G)) r = new{typeof(F), T2, RingMapType}() a=Vector{elem_type(G)}(a) + image_module = sub_object(G, a) function im_func(x::AbstractFreeModElem) iszero(x) && return zero(codomain(r)) # See the above comment @@ -591,7 +647,8 @@ When computed, the corresponding matrix (via `matrix()`) and inverse isomorphism end function pr_func(x) @assert parent(x) === G - c = coordinates(repres(x), sub(G, a, :module)) + #r.generators_map_to_generators === true && return FreeModElem(map_entries(x->preimage(h, x), coordinates(simplify!(x))), F) + c = coordinates(repres(x), image_module) cc = map_entries(x->preimage(h, x), c) return FreeModElem(cc, F) end @@ -599,14 +656,15 @@ When computed, the corresponding matrix (via `matrix()`) and inverse isomorphism r.ring_map = h r.imgs_of_gens = Vector{elem_type(G)}(a) r.generators_map_to_generators = nothing - return set_grading(r) + return set_grading(r; check) end end # Further constructors taking matrices as input function FreeModuleHom( - F::AbstractFreeMod{T}, G::S, mat::MatElem{T} + F::AbstractFreeMod{T}, G::S, mat::MatElem{T}; + check::Bool=true ) where {T<:RingElem,S<:AbstractFreeMod} @assert nrows(mat) == ngens(F) @assert ncols(mat) == ngens(G) @@ -616,33 +674,36 @@ function FreeModuleHom( end function FreeModuleHom( - F::AbstractFreeMod{T}, G::S, mat::MatElem{T} + F::AbstractFreeMod{T}, G::S, mat::MatElem{T}; + check::Bool=true ) where {T<:RingElem, S<:ModuleFP} @assert nrows(mat) == ngens(F) @assert ncols(mat) == ngens(G) - hom = FreeModuleHom(F, G, [SubquoModuleElem(sparse_row(mat[i:i,:]), G) for i=1:ngens(F)]) + hom = FreeModuleHom(F, G, [SubquoModuleElem(sparse_row(mat[i:i,:]), G) for i=1:ngens(F)]; check) hom.matrix = mat return hom end function FreeModuleHom( - F::AbstractFreeMod, G::S, mat::MatElem, h::RingMapType + F::AbstractFreeMod, G::S, mat::MatElem, h::RingMapType; + check::Bool=true ) where {S<:AbstractFreeMod, RingMapType} @assert nrows(mat) == ngens(F) @assert ncols(mat) == ngens(G) @assert base_ring(mat) === base_ring(G) - hom = FreeModuleHom(F, G, [FreeModElem(sparse_row(mat[i:i,:]), G) for i=1:ngens(F)], h) + hom = FreeModuleHom(F, G, [FreeModElem(sparse_row(mat[i:i,:]), G) for i=1:ngens(F)], h; check) hom.matrix = mat return hom end function FreeModuleHom( - F::AbstractFreeMod, G::S, mat::MatElem, h::RingMapType + F::AbstractFreeMod, G::S, mat::MatElem, h::RingMapType; + check::Bool=true ) where {S<:ModuleFP, RingMapType} @assert nrows(mat) == ngens(F) @assert ncols(mat) == ngens(G) @assert base_ring(mat) === base_ring(G) - hom = FreeModuleHom(F, G, [SubquoModuleElem(sparse_row(mat[i:i,:]), G) for i=1:ngens(F)], h) + hom = FreeModuleHom(F, G, [SubquoModuleElem(sparse_row(mat[i:i,:]), G) for i=1:ngens(F)], h; check) hom.matrix = mat return hom end diff --git a/src/Modules/ModulesGraded.jl b/src/Modules/ModulesGraded.jl index 65a2f575bcf2..f11731edbbd0 100644 --- a/src/Modules/ModulesGraded.jl +++ b/src/Modules/ModulesGraded.jl @@ -303,8 +303,8 @@ function forget_grading(F::FreeMod) @assert is_graded(F) "module must be graded" R = base_ring(F) result = FreeMod(R, ngens(F)) - phi = hom(F, result, gens(result)) - psi = hom(result, F, gens(F)) + phi = hom(F, result, gens(result); check=false) + psi = hom(result, F, gens(F); check=false) set_attribute!(phi, :inverse=>psi) set_attribute!(psi, :inverse=>phi) return result, phi @@ -339,16 +339,16 @@ function forget_grading(M::SubquoModule; new_sub = forget_grading(M.sub; ambient_forgetful_map) new_quo = forget_grading(M.quo; ambient_forgetful_map) result = SubquoModule(new_sub, new_quo) - phi = hom(M, result, gens(result)) - psi = hom(result, M, gens(M)) + phi = hom(M, result, gens(result); check=false) + psi = hom(result, M, gens(M); check=false) set_attribute!(phi, :inverse=>psi) set_attribute!(psi, :inverse=>phi) return result, phi elseif isdefined(M, :sub) new_sub = forget_grading(M.sub; ambient_forgetful_map) result = SubquoModule(new_sub) - phi = hom(M, result, gens(result)) - psi = hom(result, M, gens(M)) + phi = hom(M, result, gens(result); check=false) + psi = hom(result, M, gens(M); check=false) set_attribute!(phi, :inverse=>psi) set_attribute!(psi, :inverse=>phi) return result, phi @@ -356,8 +356,8 @@ function forget_grading(M::SubquoModule; new_quo = forget_grading(M.quo; ambient_forgetful_map) pre_result = SubquoModule(new_quo) result, _ = quo(FF, pre_result) - phi = hom(M, result, gens(result)) - psi = hom(result, M, gens(M)) + phi = hom(M, result, gens(result); check=false) + psi = hom(result, M, gens(M); check=false) set_attribute!(phi, :inverse=>psi) set_attribute!(psi, :inverse=>phi) return result, phi @@ -416,7 +416,7 @@ end function degrees(M::FreeMod) @assert is_graded(M) - return M.d + return M.d::Vector{FinGenAbGroupElem} end @doc raw""" @@ -534,14 +534,20 @@ true ``` """ function is_homogeneous(el::FreeModElem) - !is_graded(parent(el)) && error("The parent module is not graded.") + !isnothing(el.d) && return true + !is_graded(parent(el)) && error("the parent module is not graded") iszero(el) && return true el.d = isa(el.d, FinGenAbGroupElem) ? el.d : determine_degree_from_SR(coordinates(el), degrees(parent(el))) return isa(el.d, FinGenAbGroupElem) end +AnyGradedRingElem = Union{<:MPolyDecRingElem, <:MPolyQuoRingElem{<:MPolyDecRingElem}, + <:MPolyLocRingElem{<:Ring, <:RingElem, <:MPolyDecRing}, + <:MPolyQuoLocRingElem{<:Ring, <:RingElem, <:MPolyDecRing} + } + @doc raw""" - degree(f::FreeModElem) + degree(f::FreeModElem{T}; check::Bool=true) where {T<:AnyGradedRingElem} Given a homogeneous element `f` of a graded free module, return the degree of `f`. @@ -553,6 +559,8 @@ Given a homogeneous element `f` of a $\mathbb Z^m$-graded free module, return th Given a homogeneous element `f` of a $\mathbb Z$-graded free module, return the degree of `f`, converted to an integer number. +If `check` is set to `false`, then there is no check for homegeneity. This should be called +internally on provably sane input, as it speeds up computation significantly. # Examples ```jldoctest julia> R, (w, x, y, z) = graded_polynomial_ring(QQ, ["w", "x", "y", "z"]); @@ -573,26 +581,50 @@ julia> typeof(degree(Int, f)) Int64 ``` """ -function degree(f::FreeModElem) - !is_graded(parent(f)) && error("The parent module is not graded.") - A = grading_group(base_ring(parent(f))) - iszero(f) && return A[0] - f.d = isa(f.d, FinGenAbGroupElem) ? f.d : determine_degree_from_SR(coordinates(f), degrees(parent(f))) - isa(f.d, FinGenAbGroupElem) || error("The specified element is not homogeneous.") +function degree(f::FreeModElem{T}; check::Bool=true) where {T<:AnyGradedRingElem} + !isnothing(f.d) && return f.d::FinGenAbGroupElem + @check is_graded(parent(f)) "the parent module is not graded" + @check is_homogeneous(f) "the element is not homogeneous" + f.d = _degree_fast(f) return f.d::FinGenAbGroupElem end -function degree(::Type{Vector{Int}}, f::FreeModElem) +function _degree_of_parent_generator(f::FreeModElem, i::Int) + return f.parent.d[i]::FinGenAbGroupElem +end + +# TODO: This has the potential to be a "hot" function. +# Should we store the information in the parent of `f` directly? +# Or is it enough that things are cached in the generators +# of the `sub`? +function _degree_of_parent_generator(f::SubquoModuleElem, i::Int) + return _degree_fast(gen(parent(f), i))::FinGenAbGroupElem +end + +# Fast method only to be used on sane input; returns a `GrbAbFinGenElem`. +# This is exposed as an extra internal function so that `check=false` can be avoided. +function _degree_fast(f::FreeModElem) + iszero(f) && return zero(grading_group(base_ring(f))) + for (i, c) in coordinates(f) + !iszero(c) && return (_degree_fast(c) + _degree_of_parent_generator(f, i))::FinGenAbGroupElem + end + error("this line should never be reached") +end + + +function degree(::Type{Vector{Int}}, f::FreeModElem; check::Bool=true) @assert is_zm_graded(parent(f)) - d = degree(f) + d = degree(f; check) return Int[d[i] for i=1:ngens(parent(d))] end -function degree(::Type{Int}, f::FreeModElem) +function degree(::Type{Int}, f::FreeModElem; check::Bool=true) @assert is_z_graded(parent(f)) - return Int(degree(f)[1]) + return Int(degree(f; check)[1]) end +# Checks for homogeneity and computes the degree. +# If the input is not homogeneous, this returns nothing. function determine_degree_from_SR(coords::SRow, unit_vector_degrees::Vector{FinGenAbGroupElem}) element_degree = nothing for (position, coordval) in coords @@ -620,59 +652,70 @@ function graded_map(A::MatElem) return graded_map(Fcdm, A) end -function graded_map(F::FreeMod{T}, A::MatrixElem{T}) where {T <: RingElement} +function graded_map(F::FreeMod{T}, A::MatrixElem{T}; check::Bool=true) where {T <: RingElement} R = base_ring(F) G = grading_group(R) source_degrees = Vector{eltype(G)}() for i in 1:nrows(A) for j in 1:ncols(A) if !is_zero(A[i, j]) - push!(source_degrees, degree(A[i, j]) + degree(F[j])) + push!(source_degrees, degree(A[i, j]; check) + degree(F[j]; check)) break end end end Fcdm = graded_free_module(R, source_degrees) - phi = hom(Fcdm, F, A) + phi = hom(Fcdm, F, A; check) return phi end -function graded_map(F::FreeMod{T}, V::Vector{<:AbstractFreeModElem{T}}) where {T <: RingElement} +function graded_map(F::FreeMod{T}, V::Vector{<:AbstractFreeModElem{T}}; check::Bool=true) where {T <: RingElement} R = base_ring(F) G = grading_group(R) nrows = length(V) ncols = rank(F) + @check true # Trigger an error if checks are supposed to be disabled. source_degrees = Vector{eltype(G)}() - for i in 1:nrows - for j in 1:ncols - if !is_zero(coordinates(V[i])[j]) - push!(source_degrees, degree(coordinates(V[i])[j]) + degree(F[j])) + for (i, v) in enumerate(V) + if is_zero(v) + push!(source_degrees, zero(G)) + continue + end + for (j, c) in coordinates(v) + if !iszero(c) + push!(source_degrees, degree(coordinates(V[i])[j]; check) + degree(F[j]; check)) break end end end + @assert length(source_degrees) == nrows Fcdm = graded_free_module(R, source_degrees) - phi = hom(Fcdm, F, V) + @assert ngens(Fcdm) == length(V) "number of generators must be equal to the number of images" + phi = hom(Fcdm, F, V; check) return phi end -function graded_map(F::SubquoModule{T}, V::Vector{<:ModuleFPElem{T}}) where {T <: RingElement} +function graded_map(F::SubquoModule{T}, V::Vector{<:ModuleFPElem{T}}; check::Bool=true) where {T <: RingElement} R = base_ring(F) G = grading_group(R) nrows = length(V) source_degrees = Vector{eltype(G)}() - for i in 1:nrows - for (j, coord_val) in coordinates(V[i]) - if !is_zero(coord_val) - push!(source_degrees, degree(coord_val) + degree(F[j])) + for (i, v) in enumerate(V) + if is_zero(v) + push!(source_degrees, zero(G)) + continue + end + for (j, c) in coordinates(v) + if !iszero(c) + push!(source_degrees, degree(coordinates(V[i])[j]; check) + degree(F[j]; check)) break end end end Fcdm = graded_free_module(R, source_degrees) - phi = hom(Fcdm, F, V) + phi = hom(Fcdm, F, V; check) return phi end @@ -680,21 +723,21 @@ end # Graded Free Module homomorphisms functions ############################################################################### -function set_grading(f::FreeModuleHom{T1, T2}) where {T1 <: FreeMod, T2 <: Union{FreeMod, SubquoModule, Oscar.SubModuleOfFreeModule}} +function set_grading(f::FreeModuleHom{T1, T2}; check::Bool=true) where {T1 <: FreeMod, T2 <: Union{FreeMod, SubquoModule, Oscar.SubModuleOfFreeModule}} if !is_graded(domain(f)) || !is_graded(codomain(f)) return f end - f.d = degree(f) + f.d = degree(f; check) return f end -function set_grading(f::FreeModuleHom{T1, T2}) where {T1 <: FreeMod_dec, T2 <: FreeMod_dec} +function set_grading(f::FreeModuleHom{T1, T2}; check::Bool=true) where {T1 <: FreeMod_dec, T2 <: FreeMod_dec} return f end # for decorations: add SubquoModule_dec for codomain once it exists @doc raw""" - degree(a::FreeModuleHom) + degree(a::FreeModuleHom; check::Bool=true) If `a` is graded, return the degree of `a`. @@ -725,20 +768,31 @@ julia> degree(a) [1] ``` """ -function degree(f::FreeModuleHom) - if isdefined(f, :d) - return f.d - end - T1 = domain(f) - T2 = codomain(f) - if !is_graded(T1) || !is_graded(T2) - error("Both domain and codomain must be graded.") +function degree(f::FreeModuleHom; check::Bool=true) + # TODO: isdefined should not be necessary here. Can it be kicked? + isdefined(f, :d) && isnothing(f.d) && return nothing # This stands for the map being not homogeneous + isdefined(f, :d) && return f.d::FinGenAbGroupElem + + @check (is_graded(domain(f)) && is_graded(codomain(f))) "both domain and codomain must be graded" + @check is_graded(f) "map is not graded" + for i in 1:ngens(domain(f)) + if iszero(domain(f)[i]) || iszero(image_of_generator(f, i)) + continue + end + f.d = degree(image_of_generator(f, i); check) - degree(domain(f)[i]; check) + return f.d::FinGenAbGroupElem end + + # If we got here, the map is the zero map. Return degree zero in this case + return zero(grading_group(domain(f)))::FinGenAbGroupElem + + # Old code left for debugging + return degree(image_of_generator(f, 1)) domain_degrees = degrees(T1) df = nothing for i in 1:length(domain_degrees) image_vector = f(T1[i]) - if isempty(coordinates(image_vector)) + if isempty(coordinates(image_vector)) || is_zero(image_vector) continue end current_df = degree(image_vector) - domain_degrees[i] @@ -757,7 +811,7 @@ function degree(f::FreeModuleHom) end @doc raw""" - is_graded(a::FreeModuleHom) + is_graded(a::ModuleFPHom) Return `true` if `a` is graded, `false` otherwise. @@ -788,8 +842,33 @@ julia> is_graded(a) true ``` """ -function is_graded(f::FreeModuleHom) - return isdefined(f, :d) +function is_graded(f::ModuleFPHom) + isdefined(f, :d) && return true + (is_graded(domain(f)) && is_graded(codomain(f))) || return false + T1 = domain(f) + T2 = codomain(f) + domain_degrees = degrees_of_generators(T1) + df = nothing + for i in 1:length(domain_degrees) + image_vector = f(T1[i]) + if isempty(coordinates(image_vector)) || is_zero(image_vector) + continue + end + current_df = degree(image_vector) - domain_degrees[i] + if df === nothing + df = current_df + elseif df != current_df + return false + end + end + if df === nothing + R = base_ring(T1) + G = grading_group(R) + f.d = zero(G) + return true + end + f.d = df + return true end @doc raw""" @@ -880,8 +959,8 @@ function is_graded(M::SubModuleOfFreeModule) end -function degrees_of_generators(M::SubModuleOfFreeModule{T}) where T - return map(gen -> degree(gen), gens(M)) +function degrees_of_generators(M::SubModuleOfFreeModule{T}; check::Bool=true) where T + return map(gen -> degree(gen; check), gens(M)) end ############################################################################### @@ -946,7 +1025,7 @@ function grading_group(M::SubquoModule) end @doc raw""" - degrees_of_generators(M::SubquoModule) + degrees_of_generators(M::SubquoModule; check::Bool=true) Return the degrees of the generators of `M`. @@ -983,8 +1062,8 @@ julia> gens(M) z*e[2] ``` """ -function degrees_of_generators(M::SubquoModule{T}) where T - isempty(gens(M)) ? FinGenAbGroupElem[] : map(gen -> degree(repres(gen)), gens(M)) +function degrees_of_generators(M::SubquoModule{T}; check::Bool=true) where T + isempty(gens(M)) ? FinGenAbGroupElem[] : map(gen -> degree(repres(gen); check), gens(M)) end ############################################################################### @@ -1042,22 +1121,29 @@ x*e[1] + (y - z)*e[2] ``` """ function is_homogeneous(el::SubquoModuleElem) - if iszero(coordinates(el)) - return is_homogeneous(repres(el)) + el.is_reduced && return is_homogeneous(repres(el)) + return is_homogeneous(repres(simplify(el))) + + # The following call checks for homogeneity on the way and stores the degree thus determined. + degree = determine_degree_from_SR(coordinates(el), degrees_of_generators(parent(el))) + if degree === nothing + reduced_el = simplify(el) # TODO: What do we expect `simplify` to do here generically??? + degree_reduced = determine_degree_from_SR(coordinates(reduced_el), degrees_of_generators(parent(reduced_el))) + if degree_reduced === nothing + el.d = nothing + return false + else + el.d = degree_reduced + return true + end else - degree = determine_degree_from_SR(coordinates(el), degrees_of_generators(parent(el))) - if degree === nothing - reduced_el = simplify(el) - degree_reduced = determine_degree_from_SR(coordinates(reduced_el), degrees_of_generators(parent(reduced_el))) - return degree_reduced !== nothing - else - return true - end + el.d = degree + return true end end @doc raw""" - degree(m::SubquoModuleElem) + degree(m::SubquoModuleElem; check::Bool=true) Given a homogeneous element `m` of a graded subquotient, return the degree of `m`. @@ -1105,31 +1191,36 @@ julia> degree(m3) [2] ``` """ -function degree(el::SubquoModuleElem) - if !iszero(coordinates(el)) - result = determine_degree_from_SR(coordinates(el), degrees_of_generators(parent(el))) - if result === nothing - reduced_el = simplify(el) - result_reduced = determine_degree_from_SR(coordinates(reduced_el), degrees_of_generators(parent(reduced_el))) - @assert result_reduced !== nothing "The specified element is not homogeneous." - return result_reduced - else - return result - end - else - return degree(repres(el)) - end +function degree(el::SubquoModuleElem; check::Bool=true) + # In general we can not assume that we have a groebner basis reduction available + # as a backend to bring the element to normal form. + # In particular, this may entail that `coordinates` produces non-homogeneous + # vectors via differently implemented liftings. + # Thus, the only thing we can do is to assume that the representative is + # homogeneous. + return degree(repres(simplify!(el)); check) end -function degree(::Type{Vector{Int}}, el::SubquoModuleElem) +# When there is a Groebner basis backend, we can reduce to normal form. +function degree( + el::SubquoModuleElem{T}; + check::Bool=true + ) where {T <:Union{<:MPolyRingElem{<:FieldElem}}} + !el.is_reduced && return degree(simplify!(el); check) + return degree(repres(el); check) +end + +_degree_fast(el::SubquoModuleElem) = degree(el, check=false) + +function degree(::Type{Vector{Int}}, el::SubquoModuleElem; check::Bool=true) @assert is_zm_graded(parent(el)) - d = degree(el) + d = degree(el; check) return Int[d[i] for i=1:ngens(parent(d))] end -function degree(::Type{Int}, el::SubquoModuleElem) +function degree(::Type{Int}, el::SubquoModuleElem; check::Bool=true) @assert is_z_graded(parent(el)) - return Int(degree(el)[1]) + return Int(degree(el; check)[1]) end @@ -1137,16 +1228,16 @@ end # Graded subquotient homomorphisms functions ############################################################################### -function set_grading(f::SubQuoHom) +function set_grading(f::SubQuoHom; check::Bool=true) if !is_graded(domain(f)) || !is_graded(codomain(f)) return(f) end - f.d = degree(f) + f.d = degree(f; check) return f end @doc raw""" - degree(a::SubQuoHom) + degree(a::SubQuoHom; check::Bool=true) If `a` is graded, return the degree of `a`. @@ -1176,7 +1267,7 @@ julia> degree(a) [2] ``` """ -function degree(f::SubQuoHom) +function degree(f::SubQuoHom; check::Bool=true) if isdefined(f, :d) return f.d end @@ -1190,11 +1281,23 @@ function degree(f::SubQuoHom) G = grading_group(R) return G[0] end + @check is_graded(f) "homomorphism is not graded" + for (i, v) in enumerate(gens(T1)) + (is_zero(v) || is_zero(image_of_generator(f, i))) && continue + f.d = degree(image_of_generator(f, i); check) - degree(v; check) + return f.d::FinGenAbGroupElem + end + + # If we get here, we have the zero map + f.d = zero(grading_group(T1)) + return f.d::FinGenAbGroupElem + + # Old code left here for debugging domain_degrees = degrees_of_generators(T1) df = nothing for i in 1:length(domain_degrees) image_vector = f(T1[i]) - if isempty(coordinates(image_vector)) + if isempty(coordinates(image_vector)) || is_zero(image_vector) continue end current_df = degree(image_vector) - domain_degrees[i] @@ -1212,41 +1315,6 @@ function degree(f::SubQuoHom) return df end -@doc raw""" - is_graded(a::SubQuoHom) - -Return `true` if `a` is graded, `false` otherwise. - -# Examples -```jldoctest -julia> Rg, (x, y, z) = graded_polynomial_ring(QQ, ["x", "y", "z"]); - -julia> F = graded_free_module(Rg, 1); - -julia> A = Rg[x; y]; - -julia> B = Rg[x^2; y^3; z^4]; - -julia> M = SubquoModule(F, A, B); - -julia> N = M; - -julia> V = [y^2*N[1], x^2*N[2]]; - -julia> a = hom(M, N, V) -M -> M -x*e[1] -> x*y^2*e[1] -y*e[1] -> x^2*y*e[1] -Graded module homomorphism of degree [2] - -julia> is_graded(a) -true -``` -""" -function is_graded(f::SubQuoHom) - return isdefined(f, :d) -end - @doc raw""" grading_group(a::SubQuoHom) @@ -1776,7 +1844,7 @@ function _sheaf_cohomology_bgg(M::ModuleFP{T}, h::Int) where {T <: MPolyDecRingElem} sing_mod, weights = _weights_and_sing_mod(M) - reg = Int(cm_regularity(M)) + reg = Int(cm_regularity(M; check=false)) values = Singular.LibSheafcoh.sheafCohBGGregul_w(sing_mod, l, h, reg, @@ -2381,7 +2449,7 @@ end function forget_decoration(f::FreeModuleHom_dec) F = forget_decoration(domain(f)) G = forget_decoration(codomain(f)) - return hom(F, G, [forget_decoration(f(v)) for v in gens(domain(f))]) + return hom(F, G, [forget_decoration(f(v)) for v in gens(domain(f))]; check=false) end function matrix(a::FreeModuleHom_dec) @@ -2450,30 +2518,30 @@ julia> minimal_betti_table(A) total: 1 5 5 1 ``` """ -function minimal_betti_table(M::ModuleFP{T}) where {T<:MPolyDecRingElem} +function minimal_betti_table(M::ModuleFP{T}; check::Bool=true) where {T<:MPolyDecRingElem} error("Not implemented for the given type") end -function minimal_betti_table(M::SubquoModule{T}) where {T<:MPolyDecRingElem} - return minimal_betti_table(free_resolution(M)) +function minimal_betti_table(M::SubquoModule{T}; check::Bool=true) where {T<:MPolyDecRingElem} + return minimal_betti_table(free_resolution(M); check) end -function minimal_betti_table(F::FreeMod{T}) where {T<:MPolyDecRingElem} - return minimal_betti_table(free_resolution(M)) +function minimal_betti_table(F::FreeMod{T}; check::Bool=true) where {T<:MPolyDecRingElem} + return minimal_betti_table(free_resolution(M); check) end -function minimal_betti_table(A::MPolyQuoRing{T}) where {T<:MPolyDecRingElem} - return minimal_betti_table(free_resolution(A)) +function minimal_betti_table(A::MPolyQuoRing{T}; check::Bool=true) where {T<:MPolyDecRingElem} + return minimal_betti_table(free_resolution(A); check) end -function minimal_betti_table(I::MPolyIdeal{T}) where {T<:MPolyDecRingElem} - return minimal_betti_table(free_resolution(I)) +function minimal_betti_table(I::MPolyIdeal{T}; check::Bool=true) where {T<:MPolyDecRingElem} + return minimal_betti_table(free_resolution(I); check) end @doc raw""" - minimal_betti_table(F::FreeResolution{T}) where {T<:ModuleFP} + minimal_betti_table(F::FreeResolution{T}; check::Bool=true) where {T<:ModuleFP} Given a graded free resolution `F` over a standard $\mathbb Z$-graded multivariate polynomial ring with coefficients in a field, return the @@ -2517,7 +2585,7 @@ julia> minimal_betti_table(FA) total: 1 5 5 1 ``` """ -function minimal_betti_table(res::FreeResolution{T}) where {T<:ModuleFP} +function minimal_betti_table(res::FreeResolution{T}; check::Bool=true) where {T<:ModuleFP} @assert is_standard_graded(base_ring(res)) "resolution must be defined over a standard graded ring" @assert is_graded(res) "resolution must be graded" C = complex(res) @@ -2531,18 +2599,18 @@ function minimal_betti_table(res::FreeResolution{T}) where {T<:ModuleFP} phi = map(C, i) F = domain(phi) G = codomain(phi) - dom_degs = unique!([degree(g) for g in gens(F)]) - cod_degs = unique!([degree(g) for g in gens(G)]) + dom_degs = unique!([degree(g; check) for g in gens(F)]) + cod_degs = unique!([degree(g; check) for g in gens(G)]) for d in cod_degs d::FinGenAbGroupElem if d in dom_degs - _, _, sub_mat = _constant_sub_matrix(phi, d) + _, _, sub_mat = _constant_sub_matrix(phi, d; check) r = rank(sub_mat) c = ncols(sub_mat) - r - get(offsets, d, 0) !iszero(c) && (betti_hash_table[(i-1, d)] = c) offsets[d] = r else - c = length(_indices_of_generators_of_degree(G, d)) - get(offsets, d, 0) + c = length(_indices_of_generators_of_degree(G, d; check)) - get(offsets, d, 0) !iszero(c) && (betti_hash_table[(i-1, d)] = c) end end @@ -2554,29 +2622,32 @@ function hash_table(B::BettiTable) return B.B end +# TODO: Where is this called??? Adjust the use of `check` there! function generators_of_degree( C::FreeResolution{T}, i::Int, - d::FinGenAbGroupElem + d::FinGenAbGroupElem; + check::Bool=true ) where {T<:ModuleFP} F = C[i] return [g for g in gens(F) if degree(g) == d] end -function _indices_of_generators_of_degree(F::FreeMod{T}, d::FinGenAbGroupElem) where {T<:MPolyDecRingElem} - return Int[i for (i, g) in enumerate(gens(F)) if degree(g) == d] +function _indices_of_generators_of_degree(F::FreeMod{T}, d::FinGenAbGroupElem; check::Bool=true) where {T<:MPolyDecRingElem} + return Int[i for (i, g) in enumerate(gens(F)) if degree(g; check) == d] end function _constant_sub_matrix( phi::FreeModuleHom{T, T}, - d::FinGenAbGroupElem + d::FinGenAbGroupElem; + check::Bool=true ) where {RET<:MPolyDecRingElem{<:FieldElem}, T<:FreeMod{RET}} S = base_ring(domain(phi))::MPolyDecRing kk = coefficient_ring(S)::Field F = domain(phi) G = codomain(phi) - ind_dom = _indices_of_generators_of_degree(F, d) - ind_cod = _indices_of_generators_of_degree(G, d) + ind_dom = _indices_of_generators_of_degree(F, d; check) + ind_cod = _indices_of_generators_of_degree(G, d; check) m = length(ind_dom) n = length(ind_cod) result = zero_matrix(kk, m, n) @@ -2604,21 +2675,17 @@ end #############truncation############# @doc raw""" - truncate(M::ModuleFP, g::FinGenAbGroupElem, task::Symbol = :with_morphism) + truncate(I::ModuleFP, g::FinGenAbGroupElem, task::Symbol=:with_morphism) Given a finitely presented graded module `M` over a $\mathbb Z$-graded multivariate polynomial ring with positive weights, return the truncation of `M` at degree `g`. Put more precisely, return the truncation as an object of type `SubquoModule`. - Additionally, if `N` denotes this object, - - return the inclusion map `N` $\to$ `M` if `task = :with_morphism` (default), - return and cache the inclusion map `N` $\to$ `M` if `task = :cache_morphism`, - do none of the above if `task = :none`. - If `task = :only_morphism`, return only the inclusion map. - truncate(M::ModuleFP, d::Int, task::Symbol = :with_morphism) Given a module `M` as above, and given an integer `d`, convert `d` into an element `g` @@ -2658,11 +2725,11 @@ by submodule of F generated by 3 -> z^5*e[1] ``` """ -function truncate(I::ModuleFP, g::FinGenAbGroupElem, task::Symbol = :with_morphism) +function truncate(I::ModuleFP, g::FinGenAbGroupElem, task::Symbol=:with_morphism) return truncate(I, Int(g[1]), task) end -function truncate(I::ModuleFP, d::Int, task::Symbol = :with_morphism) +function truncate(I::ModuleFP, d::Int, task::Symbol=:with_morphism; check::Bool=true) @req I isa FreeMod || I isa SubquoModule "Not implemented for the given type" R = base_ring(I) @req coefficient_ring(R) isa AbstractAlgebra.Field "The coefficient ring must be a field" @@ -2671,20 +2738,20 @@ function truncate(I::ModuleFP, d::Int, task::Symbol = :with_morphism) W = [Int(W[i][1]) for i = 1:ngens(R)] @req minimum(W) > 0 "The weights must be positive" if is_zero(I) - return I + return _return_wrt_task((I, identity_map(I)), task) end - dmin = minimum(degree(Int, x) for x in gens(I)) + dmin = minimum(degree(Int, x; check) for x in gens(I)) if d <= dmin - return I + return _return_wrt_task((I, identity_map(I)), task) end - V = sort(gens(I), lt = (a, b) -> degree(Int, a) <= degree(Int, b)) + V = sort(gens(I), lt = (a, b) -> degree(Int, a; check) <= degree(Int, b; check)) RES = elem_type(I)[] s = dmin B = monomial_basis(R, d-s) for i = 1:length(V) - if degree(Int, V[i]) < d - if degree(Int, V[i]) > s - s = degree(Int, V[i]) + if degree(Int, V[i]; check) < d + if degree(Int, V[i]; check) > s + s = degree(Int, V[i]; check) B = monomial_basis(R, d-s) end append!(RES, [x*V[i] for x in B]) @@ -2692,14 +2759,30 @@ function truncate(I::ModuleFP, d::Int, task::Symbol = :with_morphism) push!(RES, V[i]) end end - return sub(I, RES, task) + return _return_wrt_task(sub(I, RES), task) +end + +function _return_wrt_task(result, task) + if task == :with_morphism + return result + elseif task == :cache_morphism + register_morphism!(result[2]) + return result[2] + elseif task == :only_morphism + return result[2] + elseif task == :none + return result[1] + else + error("task not recognized") + end end + ##################regularity####################### @doc raw""" - cm_regularity(M::ModuleFP) + cm_regularity(M::ModuleFP; check::Bool=true) Given a finitely presented graded module `M` over a standard $\mathbb Z$-graded multivariate polynomial ring with coefficients in a field, return the @@ -2759,22 +2842,21 @@ julia> minimal_betti_table(A) total: 1 3 2 ``` """ -function cm_regularity(M::ModuleFP) +function cm_regularity(M::ModuleFP; check::Bool=true) error("Not implemented for the given type") end -function cm_regularity(M::FreeMod) +function cm_regularity(M::FreeMod{T}; check::Bool=true) where {T<:MPolyRingElem{<:FieldElem}} R = base_ring(M) - @req coefficient_ring(R) isa AbstractAlgebra.Field "The coefficient ring must be a field" - @req is_standard_graded(R) "The base ring is not standard ZZ-graded" + @check is_standard_graded(R) "The base ring is not standard ZZ-graded" return 0 end -function cm_regularity(M::SubquoModule) +function cm_regularity(M::SubquoModule{T}; check::Bool=true) where {T<:MPolyRingElem{<:FieldElem}} R = base_ring(M) - @req coefficient_ring(R) isa AbstractAlgebra.Field "The coefficient ring must be a field" - @req is_standard_graded(R) "The base ring is not standard ZZ-graded" - B = minimal_betti_table(M) + @check coefficient_ring(R) isa AbstractAlgebra.Field "The coefficient ring must be a field" + @check is_standard_graded(R) "The base ring is not standard ZZ-graded" + B = minimal_betti_table(M; check) S = as_dictionary(B) V = [x[2][1] - x[1] for x in keys(S)] return maximum(V) @@ -2832,7 +2914,7 @@ function quotient_ring_as_module(I::MPolyIdeal) R = base_ring(I) F = is_graded(R) ? graded_free_module(R, 1) : free_module(R, 1) e1 = F[1] - return quo(F, [x * e1 for x = gens(I)], :module) + return quo_object(F, [x * e1 for x = gens(I)]) end #####ideals as modules##### @@ -2876,7 +2958,7 @@ function ideal_as_module(I::MPolyIdeal) R = base_ring(I) F = is_graded(R) ? graded_free_module(R, 1) : free_module(R, 1) e1 = F[1] - return sub(F, [x * e1 for x = gens(I)], :module) + return sub_object(F, [x * e1 for x = gens(I)]) end @@ -2937,8 +3019,8 @@ function twist(M::SubquoModule{T}, g::FinGenAbGroupElem) where {T<:Union{MPolyDe FN = twist(F, g) GN = free_module(R, ngens(M)) HN = free_module(R, length(relations(M))) - a = hom(GN, F, ambient_representatives_generators(M)) - b = hom(HN, F, relations(M)) + a = hom(GN, F, ambient_representatives_generators(M); check=false) + b = hom(HN, F, relations(M); check=false) A = matrix(a) B = matrix(b) N = subquotient(FN, A, B) @@ -2975,7 +3057,7 @@ function change_base_ring( S = codomain(f) r = ngens(F) FS = grade(FreeMod(S, F.S), degree.(gens(F))) - map = hom(F, FS, gens(FS), f) + map = hom(F, FS, gens(FS), f; check=false) return FS, map end @@ -2988,7 +3070,7 @@ function change_base_ring(f::RingFlattening{DomType, CodType}, M::SubquoModule) g = ambient_representatives_generators(M) rels = relations(M) MS = SubquoModule(FS, mapF.(g), mapF.(rels)) - map = SubQuoHom(M, MS, gens(MS), f) + map = SubQuoHom(M, MS, gens(MS), f; check=false) return MS, map end @@ -2997,11 +3079,11 @@ function _regularity_bound(M::SubquoModule) S = base_ring(M) G = grading_group(S) @assert is_free(G) && isone(rank(G)) "base ring must be ZZ-graded" - @assert all(x->degree(x)[1] >= 0, gens(S)) "base ring variables must be non-negatively graded" + @assert all(x->degree(Int, x; check=false) >= 0, gens(S)) "base ring variables must be non-negatively graded" res = free_resolution(M) - result = maximum((x->degree(x)[1]).(gens(res[0]))) + result = maximum((x->degree(Int, x; check=false)).(gens(res[0]))) for i in 0:first(chain_range(res)) - result = maximum(push!((x->degree(x)[1]).(gens(res[i])), result)) + result = maximum(push!((x->degree(Int, x; check=false)).(gens(res[i])), result)) end return result end diff --git a/src/Modules/UngradedModules/DirectSum.jl b/src/Modules/UngradedModules/DirectSum.jl index 589218cd38d2..38fd4e27b209 100644 --- a/src/Modules/UngradedModules/DirectSum.jl +++ b/src/Modules/UngradedModules/DirectSum.jl @@ -50,11 +50,11 @@ function direct_product(F::FreeMod{T}...; task::Symbol = :prod) where {T} i = 0 for f = F if task in [:sum, :both] - push!(emb, hom(f, G, Vector{elem_type(G)}([gen(G, j+i) for j=1:ngens(f)]))) + push!(emb, hom(f, G, Vector{elem_type(G)}([gen(G, j+i) for j=1:ngens(f)]); check=false)) injection_dictionary[length(emb)] = emb[length(emb)] end if task in [:prod, :both] - push!(pro, hom(G, f, vcat(elem_type(f)[zero(f) for j=1:i], gens(f), elem_type(f)[zero(f) for j=i+ngens(f)+1:ngens(G)]))) + push!(pro, hom(G, f, vcat(elem_type(f)[zero(f) for j=1:i], gens(f), elem_type(f)[zero(f) for j=i+ngens(f)+1:ngens(G)]); check=false)) projection_dictionary[length(pro)] = pro[length(pro)] end i += ngens(f) @@ -83,11 +83,11 @@ Additionally, return """ function direct_product(M::ModuleFP{T}...; task::Symbol = :prod) where T F, pro, mF = direct_product([ambient_free_module(x) for x = M]..., task = :both) - s, emb_sF = sub(F, vcat([elem_type(F)[mF[i](y) for y = ambient_representatives_generators(M[i])] for i=1:length(M)]...), :both) + s, emb_sF = sub(F, vcat([elem_type(F)[mF[i](y) for y = ambient_representatives_generators(M[i])] for i=1:length(M)]...)) q::Vector{elem_type(F)} = vcat([elem_type(F)[mF[i](y) for y = rels(M[i])] for i=1:length(M)]...) pro_quo = nothing if length(q) != 0 - s, pro_quo = quo(s, q, :both) + s, pro_quo = quo(s, q) end set_attribute!(s, :show => Hecke.show_direct_product, :direct_product => M) projection_dictionary = IdDict{Int,ModuleFPHom}() @@ -99,12 +99,12 @@ function direct_product(M::ModuleFP{T}...; task::Symbol = :prod) where T if task == :prod || task != :sum if pro_quo === nothing for i=1:length(pro) - pro[i] = hom(s, M[i], Vector{elem_type(M[i])}([M[i](pro[i](emb_sF(gen))) for gen in gens(s)])) # TODO distinction between pro on the left and pro on the right side! + pro[i] = hom(s, M[i], Vector{elem_type(M[i])}([M[i](pro[i](emb_sF(gen))) for gen in gens(s)]); check=false) # TODO distinction between pro on the left and pro on the right side! projection_dictionary[i] = pro[i] end else for i=1:length(pro) - pro[i] = hom(s, M[i], Vector{elem_type(M[i])}([M[i](pro[i](emb_sF(preimage(pro_quo,gen)))) for gen in gens(s)])) + pro[i] = hom(s, M[i], Vector{elem_type(M[i])}([M[i](pro[i](emb_sF(preimage(pro_quo,gen)))) for gen in gens(s)]); check=false) projection_dictionary[i] = pro[i] end end @@ -115,12 +115,12 @@ function direct_product(M::ModuleFP{T}...; task::Symbol = :prod) where T if task == :sum || task != :prod if pro_quo === nothing for i=1:length(mF) - mF[i] = hom(M[i], s, Vector{elem_type(s)}([preimage(emb_sF, mF[i](repres(g))) for g in gens(M[i])])) + mF[i] = hom(M[i], s, Vector{elem_type(s)}([preimage(emb_sF, mF[i](repres(g))) for g in gens(M[i])]); check=false) injection_dictionary[i] = mF[i] end else for i=1:length(mF) - mF[i] = hom(M[i], s, Vector{elem_type(s)}([pro_quo(preimage(emb_sF, mF[i](repres(g)))) for g in gens(M[i])])) + mF[i] = hom(M[i], s, Vector{elem_type(s)}([pro_quo(preimage(emb_sF, mF[i](repres(g)))) for g in gens(M[i])]); check=false) injection_dictionary[i] = mF[i] end end @@ -189,7 +189,7 @@ function canonical_injection(G::ModuleFP, i::Int) end @req 0 < i <= length(H) "index out of bound" j = sum(ngens(H[l]) for l in 1:i-1; init=0) - emb = hom(H[i], G, Vector{elem_type(G)}([G[l+j] for l in 1:ngens(H[i])])) + emb = hom(H[i], G, Vector{elem_type(G)}([G[l+j] for l in 1:ngens(H[i])]); check=false) injection_dictionary[i] = emb return emb end @@ -220,7 +220,7 @@ function canonical_projection(G::ModuleFP, i::Int) end @req 0 < i <= length(H) "index out of bound" j = sum(ngens(H[l]) for l in 1:i-1; init=0) - pro = hom(G, H[i], Vector{elem_type(H[i])}(vcat([zero(H[i]) for l in 1:j], gens(H[i]), [zero(H[i]) for l in 1+j+ngens(H[i]):ngens(G)]))) + pro = hom(G, H[i], Vector{elem_type(H[i])}(vcat([zero(H[i]) for l in 1:j], gens(H[i]), [zero(H[i]) for l in 1+j+ngens(H[i]):ngens(G)])); check=false) projection_dictionary[i] = pro return pro end diff --git a/src/Modules/UngradedModules/FreeModElem.jl b/src/Modules/UngradedModules/FreeModElem.jl index 5287d051a966..ea29e58f9ba1 100644 --- a/src/Modules/UngradedModules/FreeModElem.jl +++ b/src/Modules/UngradedModules/FreeModElem.jl @@ -289,3 +289,5 @@ Return `true` if `f` is zero, `false` otherwise. """ is_zero(f::AbstractFreeModElem) = iszero(coordinates(f)) +simplify!(a::FreeModElem) = a +simplify(a::FreeModElem) = a diff --git a/src/Modules/UngradedModules/FreeModuleHom.jl b/src/Modules/UngradedModules/FreeModuleHom.jl index 7357df575102..18d9021b581b 100644 --- a/src/Modules/UngradedModules/FreeModuleHom.jl +++ b/src/Modules/UngradedModules/FreeModuleHom.jl @@ -200,12 +200,12 @@ true ``` """ function hom(F::FreeMod, M::ModuleFP{T}, V::Vector{<:ModuleFPElem{T}}; check::Bool=true) where T - base_ring(F) === base_ring(M) || return FreeModuleHom(F, M, V, base_ring(M)) - return FreeModuleHom(F, M, V) + base_ring(F) === base_ring(M) || return FreeModuleHom(F, M, V, base_ring(M); check) + return FreeModuleHom(F, M, V; check) end function hom(F::FreeMod, M::ModuleFP{T}, A::MatElem{T}; check::Bool=true) where T - base_ring(F) === base_ring(M) || return FreeModuleHom(F, M, A, base_ring(M)) - return FreeModuleHom(F, M, A) + base_ring(F) === base_ring(M) || return FreeModuleHom(F, M, A, base_ring(M); check) + return FreeModuleHom(F, M, A; check) end @doc raw""" @@ -231,8 +231,8 @@ scalars in `base_ring(F)` to their images under `h`. If this degree is the zero element of the (common) grading group, we refer to the homomorphism under consideration as a *homogeneous module homomorphism*. """ -hom(F::FreeMod, M::ModuleFP{T}, V::Vector{<:ModuleFPElem{T}}, h::RingMapType; check::Bool=true) where {T, RingMapType} = FreeModuleHom(F, M, V, h) -hom(F::FreeMod, M::ModuleFP{T}, A::MatElem{T}, h::RingMapType; check::Bool=true) where {T, RingMapType} = FreeModuleHom(F, M, A, h) +hom(F::FreeMod, M::ModuleFP{T}, V::Vector{<:ModuleFPElem{T}}, h::RingMapType; check::Bool=true) where {T, RingMapType} = FreeModuleHom(F, M, V, h; check) +hom(F::FreeMod, M::ModuleFP{T}, A::MatElem{T}, h::RingMapType; check::Bool=true) where {T, RingMapType} = FreeModuleHom(F, M, A, h; check) @doc raw""" identity_map(M::ModuleFP) @@ -313,6 +313,7 @@ function Base.show(io::IO, fmh::FreeModuleHom{T1, T2, RingMapType}) where {T1 <: end end + @doc raw""" hom(F::FreeMod, G::FreeMod) @@ -400,6 +401,7 @@ function hom(F::FreeMod, G::FreeMod) return GH, to_hom_map end + @doc raw""" kernel(a::FreeModuleHom) @@ -458,36 +460,78 @@ Homogeneous module homomorphism) ``` """ -function kernel(h::FreeModuleHom) #ONLY for free modules... - G = domain(h) +function kernel(h::FreeModuleHom{<:FreeMod, <:FreeMod}) #ONLY for free modules... + error("not implemented for modules over rings of type $(typeof(base_ring(domain(h))))") +end + +# The following function is part of the requirement of atomic functions to be implemented +# in order to have the modules run over a specific type of ring. The documentation of this is +# pending and so far only orally communicated by Janko Boehm. +# +# The concrete method below uses Singular as a backend to achieve its task. In order +# to have only input which Singular can actually digest, we restrict the signature +# to those cases. The method used to be triggered eventually also for rings which +# did not have a groebner basis backend in Singular, but Singular did not complain. +# This lead to false results without notification. By restricting the signature, +# the user gets the above error message instead. +function kernel( + h::FreeModuleHom{<:FreeMod{T}, <:FreeMod{T}, Nothing} + ) where {S<: Union{ZZRingElem, <:FieldElem}, T <: MPolyRingElem{S}} + is_zero(h) && return sub(domain(h), gens(domain(h))) + is_graded(h) && return _graded_kernel(h) + return _simple_kernel(h) +end + +function _simple_kernel(h::FreeModuleHom{<:FreeMod, <:FreeMod}) + F = domain(h) + G = codomain(h) + g = images_of_generators(h) + b = ModuleGens(g, G, default_ordering(G)) + M = syzygy_module(b) + v = elem_type(F)[sum(c*F[i] for (i, c) in coordinates(repres(v)); init=zero(F)) for v in gens(M)] + I, inc = sub(F, v) + return sub(F, v) +end + +function _graded_kernel(h::FreeModuleHom{<:FreeMod, <:FreeMod}) + I, inc = _simple_kernel(h) + @assert is_graded(I) + @assert is_homogeneous(inc) + return I, inc +end + +function kernel(h::FreeModuleHom{<:FreeMod, <:SubquoModule}) + is_zero(h) && return sub(domain(h), gens(domain(h))) + F = domain(h) + M = codomain(h) + G = ambient_free_module(M) + # We have to take the representatives of the reduced elements! + # Otherwise we might get wrong degrees. + g = [repres(simplify(v)) for v in images_of_generators(h)] + g = vcat(g, relations(M)) R = base_ring(G) - if ngens(G) == 0 - s = sub(G, gens(G), :module) - help = hom(s, G, gens(G), check=false) - help.generators_map_to_generators = true - return s, help - end - g = map(h, basis(G)) - if isa(codomain(h), SubquoModule) - g = [repres(x) for x = g] - if isdefined(codomain(h), :quo) - append!(g, collect(codomain(h).quo.gens)) - end - end - #TODO allow sub-quo here as well - ambient_free_module_codomain = ambient_free_module(codomain(h)) - b = ModuleGens(g, ambient_free_module_codomain, default_ordering(ambient_free_module_codomain)) - k = syzygy_module(b) - if isa(codomain(h), SubquoModule) - s = collect(k.sub.gens) - k = sub(G, [FreeModElem(x.coords[R,1:dim(G)], G) for x = s], :module) - else - #the syzygie_module creates a new free module to work in - k = sub(G, [FreeModElem(x.coords, G) for x = collect(k.sub.gens)], :module) - end - @assert k.F === G - c = collect(k.sub.gens) - return k, hom(k, parent(c[1]), c, check=false) + H = FreeMod(R, length(g)) + phi = hom(H, G, g) + K, inc = kernel(phi) + r = ngens(F) + v = elem_type(F)[sum(c*F[i] for (i, c) in coordinates(v) if i <= r; init=zero(F)) for v in images_of_generators(inc)] + return sub(F, v) +end + +function is_welldefined(H::SubQuoHom{<:SubquoModule}) + M = domain(H) + pres = presentation(M) + # is a short exact sequence with maps + # M <--eps-- F0 <--g-- F1 + # and H : M -> N + eps = map(pres, 0) + g = map(pres, 1) + F0 = pres[0] + N = codomain(H) + # the induced map phi : F0 --> N + phi = hom(F0, N, elem_type(N)[H(eps(v)) for v in gens(F0)]; check=false) + # now phi ∘ g : F1 --> N has to be zero. + return iszero(compose(g, phi)) end @doc raw""" @@ -560,7 +604,7 @@ Homogeneous module homomorphism) """ function image(h::FreeModuleHom) si = filter(!iszero, images_of_generators(h)) - s = sub(codomain(h), si, :module) + s = sub_object(codomain(h), si) phi = hom(s, codomain(h), si, check=false) return s, phi end diff --git a/src/Modules/UngradedModules/FreeResolutions.jl b/src/Modules/UngradedModules/FreeResolutions.jl index 17f0a2530951..088a9c9bb7e4 100644 --- a/src/Modules/UngradedModules/FreeResolutions.jl +++ b/src/Modules/UngradedModules/FreeResolutions.jl @@ -212,7 +212,7 @@ function _extend_free_resolution(cc::Hecke.ComplexOfMorphisms, idx::Int) SM = SubModuleOfFreeModule(codom, res[j]) #generator_matrix(SM) #map = graded_map(codom, SM.matrix) # going via matrices does a lot of unnecessary allocation and copying! - map = graded_map(codom, gens(SM)) + map = graded_map(codom, gens(SM); check=false) dom = domain(map) AbstractAlgebra.set_name!(dom, "$br_name^$rk") else @@ -221,7 +221,7 @@ function _extend_free_resolution(cc::Hecke.ComplexOfMorphisms, idx::Int) SM = SubModuleOfFreeModule(codom, res[j]) AbstractAlgebra.set_name!(dom, "$br_name^$rk") #generator_matrix(SM) - map = hom(dom, codom, gens(SM)) + map = hom(dom, codom, gens(SM); check=false) end pushfirst!(cc, map) j += 1 @@ -229,8 +229,8 @@ function _extend_free_resolution(cc::Hecke.ComplexOfMorphisms, idx::Int) # Finalize maps. if slen < len Z = FreeMod(br, 0) - AbstractAlgebra.set_name!(Z, "0") - pushfirst!(cc, hom(Z, domain(cc.maps[1]), Vector{elem_type(domain(cc.maps[1]))}())) + set_attribute!(Z, :name => "0") + pushfirst!(cc, hom(Z, domain(cc.maps[1]), Vector{elem_type(domain(cc.maps[1]))}(); check=false)) cc.complete = true end set_attribute!(cc, :show => free_show) @@ -371,7 +371,7 @@ function free_resolution(M::SubquoModule{<:MPolyRingElem}; SM = SubModuleOfFreeModule(codom, res[j]) #generator_matrix(SM) #ff = graded_map(codom, SM.matrix) - ff = graded_map(codom, gens(SM)) + ff = graded_map(codom, gens(SM); check=false) dom = domain(ff) AbstractAlgebra.set_name!(dom, "$br_name^$rk") insert!(maps, 1, ff) @@ -382,8 +382,8 @@ function free_resolution(M::SubquoModule{<:MPolyRingElem}; dom = free_module(br, rk) SM = SubModuleOfFreeModule(codom, res[j]) #generator_matrix(SM) - AbstractAlgebra.set_name!(dom, "$br_name^$rk") - insert!(maps, 1, hom(dom, codom, gens(SM))) + set_attribute!(dom, :name => "$br_name^$rk") + insert!(maps, 1, hom(dom, codom, gens(SM); check=false)) j += 1 end end @@ -394,8 +394,8 @@ function free_resolution(M::SubquoModule{<:MPolyRingElem}; else Z = FreeMod(br, 0) end - AbstractAlgebra.set_name!(Z, "0") - insert!(maps, 1, hom(Z, domain(maps[1]), Vector{elem_type(domain(maps[1]))}())) + set_attribute!(Z, :name => "0") + insert!(maps, 1, hom(Z, domain(maps[1]), Vector{elem_type(domain(maps[1]))}(); check=false)) end cc = Hecke.ComplexOfMorphisms(Oscar.ModuleFP, maps, check = false, seed = -2) @@ -422,7 +422,7 @@ function free_resolution(M::SubquoModule{T}) where {T<:RingElem} if iszero(N) # Fill up with zero maps C.complete = true - phi = hom(N, N, elem_type(N)[]) + phi = hom(N, N, elem_type(N)[]; check=false) pushfirst!(C.maps, phi) continue end @@ -430,8 +430,8 @@ function free_resolution(M::SubquoModule{T}) where {T<:RingElem} K, inc = kernel(map(C, i)) nz = findall(x->!iszero(x), gens(K)) F = FreeMod(R, length(nz)) - iszero(length(nz)) && AbstractAlgebra.set_name!(F, "0") - phi = hom(F, C[i], iszero(length(nz)) ? elem_type(C[i])[] : inc.(gens(K)[nz])) + iszero(length(nz)) && set_attribute!(F, :name => "0") + phi = hom(F, C[i], iszero(length(nz)) ? elem_type(C[i])[] : inc.(gens(K)[nz]); check=false) pushfirst!(C.maps, phi) end return first(C.maps) @@ -458,11 +458,11 @@ function free_resolution_via_kernels(M::SubquoModule, limit::Int = -1) nz = findall(x->!iszero(x), gens(k)) if length(nz) == 0 if is_graded(domain(mp[1])) - h = graded_map(domain(mp[1]), Vector{elem_type(domain(mp[1]))}()) + h = graded_map(domain(mp[1]), Vector{elem_type(domain(mp[1]))}(); check=false) else Z = FreeMod(base_ring(M), 0) - AbstractAlgebra.set_name!(Z, "0") - h = hom(Z, domain(mp[1]), Vector{elem_type(domain(mp[1]))}()) + set_attribute!(Z, :name => "0") + h = hom(Z, domain(mp[1]), Vector{elem_type(domain(mp[1]))}(); check=false) end insert!(mp, 1, h) break @@ -470,10 +470,10 @@ function free_resolution_via_kernels(M::SubquoModule, limit::Int = -1) break end if is_graded(codomain(mk)) - g = graded_map(codomain(mk), collect(k.sub.gens)[nz]) + g = graded_map(codomain(mk), collect(k.sub.gens)[nz]; check=false) else F = FreeMod(base_ring(M), length(nz)) - g = hom(F, codomain(mk), collect(k.sub.gens)[nz]) + g = hom(F, codomain(mk), collect(k.sub.gens)[nz]; check=false) end insert!(mp, 1, g) end diff --git a/src/Modules/UngradedModules/Hom_and_ext.jl b/src/Modules/UngradedModules/Hom_and_ext.jl index 8bd774eff373..7a8d6354baf8 100644 --- a/src/Modules/UngradedModules/Hom_and_ext.jl +++ b/src/Modules/UngradedModules/Hom_and_ext.jl @@ -8,12 +8,14 @@ function iszero(f::ModuleFPHom) end @doc raw""" - hom(M::ModuleFP, N::ModuleFP) + hom(M::ModuleFP, N::ModuleFP; algorithm::Symbol=:maps) Return the module `Hom(M,N)` as an object of type `SubquoModule`. Additionally, if `H` is that object, return the map which sends an element of `H` to the corresponding homomorphism `M` $\to$ `N`. +The keyword `algorithm` can be set to `:maps` for the default algorithm or to `:matrices` for an alternative based on matrices. + # Examples ```jldoctest julia> R, (x, y) = polynomial_ring(QQ, ["x", "y"]); @@ -22,7 +24,7 @@ julia> F = FreeMod(R, 2); julia> V = [x*F[1], y^2*F[2]]; -julia> M = quo(F, V)[1] +julia> M = quo_object(F, V) Subquotient of Submodule with 2 generators 1 -> e[1] 2 -> e[2] @@ -46,7 +48,7 @@ julia> relations(H) y^2*(e[2] -> e[2]) ``` """ -function hom(M::ModuleFP, N::ModuleFP, algorithm::Symbol=:maps) +function hom(M::ModuleFP, N::ModuleFP; algorithm::Symbol=:maps) #source: Janko's CA script: https://www.mathematik.uni-kl.de/~boehm/lehre/17_CA/ca.pdf if algorithm == :matrices && M isa SubquoModule && N isa SubquoModule if is_graded(M) && is_graded(N) @@ -61,6 +63,12 @@ function hom(M::ModuleFP, N::ModuleFP, algorithm::Symbol=:maps) f1 = map(p1, 1) g0 = map(p2, 0) g1 = map(p2, 1) + if is_graded(M) && is_graded(N) + @assert is_graded(f0) + @assert is_graded(f1) + @assert is_graded(g0) + @assert is_graded(g1) + end #step 2 H_s0_t0, mH_s0_t0 = hom(domain(f0), domain(g0)) @@ -69,23 +77,23 @@ function hom(M::ModuleFP, N::ModuleFP, algorithm::Symbol=:maps) H_s1_t0, mH_s1_t0 = hom(domain(f1), domain(g0)) - delta = hom(D, H_s1_t0, Vector{elem_type(H_s1_t0)}([preimage(mH_s1_t0, f1*mH_s0_t0(pro[1](g))-mH_s1_t1(pro[2](g))*g1) for g = gens(D)])) + delta = hom(D, H_s1_t0, elem_type(H_s1_t0)[preimage(mH_s1_t0, f1*mH_s0_t0(pro[1](g))-mH_s1_t1(pro[2](g))*g1) for g = gens(D)]) H_s0_t1, mH_s0_t1 = hom(domain(f0), domain(g1)) - rho_prime = hom(H_s0_t1, H_s0_t0, Vector{elem_type(H_s0_t0)}([preimage(mH_s0_t0, mH_s0_t1(C)*g1) for C in gens(H_s0_t1)])) + rho_prime = hom(H_s0_t1, H_s0_t0, elem_type(H_s0_t0)[preimage(mH_s0_t0, mH_s0_t1(C)*g1) for C in gens(H_s0_t1)]) kDelta = kernel(delta) projected_kernel::Vector{elem_type(H_s0_t0)} = filter(v -> !is_zero(v), FreeModElem[pro[1](repres(AB)) for AB in gens(kDelta[1])]) - H = quo(sub(H_s0_t0, projected_kernel, :module), image(rho_prime)[1], :module) + H = quo_object(sub_object(H_s0_t0, projected_kernel), image(rho_prime)[1]) H_simplified, s_inj, s_proj = simplify_light(H) function im(x::SubquoModuleElem) #@assert parent(x) === H @assert parent(x) === H_simplified - return hom(M, N, Vector{elem_type(N)}([g0(mH_s0_t0(repres(s_inj(x)))(preimage(f0, g))) for g = gens(M)])) + return hom(M, N, elem_type(N)[g0(mH_s0_t0(repres(s_inj(x)))(preimage(f0, g))) for g = gens(M)]) end function pre(f::ModuleFPHom) @@ -93,7 +101,7 @@ function hom(M::ModuleFP, N::ModuleFP, algorithm::Symbol=:maps) @assert codomain(f) === N Rs0 = domain(f0) Rt0 = domain(g0) - g = hom(Rs0, Rt0, Vector{elem_type(Rt0)}([preimage(g0, f(f0(g))) for g = gens(Rs0)])) + g = hom(Rs0, Rt0, elem_type(Rt0)[preimage(g0, f(f0(g))) for g = gens(Rs0)]) return s_proj(SubquoModuleElem(repres(preimage(mH_s0_t0, g)), H)) end @@ -102,6 +110,256 @@ function hom(M::ModuleFP, N::ModuleFP, algorithm::Symbol=:maps) return H_simplified, to_hom_map end +#= +### New and hopefully more maintainable code +# Disabled for the moment because of the book chapter. We want to keep code output stable. +# Eventually we will gradually merge this in. +function hom(F::FreeMod, G::ModuleFP) + R = base_ring(F) + R === base_ring(G) || error("base rings must be the same") + + # We construct Hom(F, G) as Hom(F, R¹) ⊗ G. + # Then we can use coordinate independent methods to construct + # induced homomorphisms. + Fdual, interp = dual(F) + H, mult_map = tensor_product(Fdual, G; task=:with_map) + + function _elem_to_hom1(v::ModuleFPElem) + result = hom(F, G, elem_type(G)[zero(G) for i in 1:ngens(F)]; check=false) + for (i, c) in coordinates(v) + # decompose the i-th generator as ψ : F → R¹ and g ∈ G + (u, g) = preimage(mult_map, H[i]) + psi = element_to_homomorphism(u) + # construct the homomorphism by applying it manually + # to the generators; psi(w)[1] is the value considered + # as an element of the ring R ≅ R¹. + result = result + hom(F, G, elem_type(G)[c*psi(w)[1] * g for w in gens(F)]; check=false) + end + return result + end + + function _hom_to_elem1(phi::ModuleFPHom) + @assert domain(phi) === F + @assert codomain(phi) === G + return sum(mult_map((Fdual[i], phi(v))) for (i, v) in enumerate(gens(F)); init=zero(H)) + end + + to_hom_map1 = MapFromFunc(H, Hecke.MapParent(F, G, "homomorphisms"), _elem_to_hom1, _hom_to_elem1) + set_attribute!(H, :show => Hecke.show_hom, :hom => (F, G), :module_to_hom_map => to_hom_map1) + return H, to_hom_map1 +end + +function hom(M::SubquoModule, N::ModuleFP) + R = base_ring(M) + R === base_ring(N) || error("base rings must coincide") + pres = presentation(M) + # pres : F1 --phi--> F0 --eps--> M --> 0 + # Construct the induced hom-sequence + # hom(pres, N) : hom(F1, N) <--phi^T-- hom(F0, N) <--eps^T-- hom(M, N) <-- 0 + F0 = pres[0]::FreeMod + F1 = pres[1]::FreeMod + phi = map(pres, 1) + @assert codomain(phi) === F0 + @assert domain(phi) === F1 + eps = map(pres, 0) + + phi_transp = hom(phi, N) # The induced map in the first argument + hom_F0_N = domain(phi_transp) + @assert get_attribute(hom_F0_N, :hom) === (F0, N) + hom_F1_N = codomain(phi_transp) + @assert get_attribute(hom_F1_N, :hom) === (F1, N) + + K, inc = kernel(phi_transp) + + # The output will look horribly difficult in general. Simplification is indicated. + # H, iso = prune_with_map(K) # Still buggy + # H, iso_inv, iso = Oscar._alt_simplify(K) # Takes too long in some cases + H, iso, iso_inv = simplify_light(K) + + + function _elem_to_hom2(v::ModuleFPElem) + w = inc(iso(v)) + @assert parent(w) === hom_F0_N + psi = element_to_homomorphism(w) + img_gens = elem_type(N)[psi(preimage(eps, g)) for g in gens(M)] + return hom(M, N, img_gens; check=false) + end + + function _hom_to_elem2(phi::ModuleFPHom) + # phi : M --> N + @assert domain(phi) === M + @assert codomain(phi) === N + # The following is using that we have a 1:1-correspondence of the generators + # of M with those of F0 due to the implementation of `presentation`. + phi_lift = hom(F0, N, images_of_generators(phi); check=false)::FreeModuleHom{<:FreeMod} + w = homomorphism_to_element(hom_F0_N, phi_lift) + return preimage(iso, preimage(inc, w)) + end + + to_hom_map2 = MapFromFunc(H, Hecke.MapParent(M, N, "homomorphisms"), _elem_to_hom2, _hom_to_elem2) + set_attribute!(H, :show => Hecke.show_hom, :hom => (M, N), :module_to_hom_map => to_hom_map2) + return H, to_hom_map2 +end + +# The induced hom on the first argument +function hom( + phi::FreeModuleHom{<:FreeMod, <:FreeMod}, N::ModuleFP; + domain::ModuleFP=hom(Oscar.codomain(phi), N)[1], + codomain::ModuleFP=hom(Oscar.domain(phi), N)[1] + ) + R = base_ring(N) + R === base_ring(domain) === base_ring(codomain) || error("base rings must coincide") + + img_gens = elem_type(codomain)[] + for (i, g) in enumerate(gens(domain)) + # The map codomain(phi) --> N + psi = element_to_homomorphism(g) + comp = compose(phi, psi) + push!(img_gens, homomorphism_to_element(codomain, comp)) + end + return hom(domain, codomain, img_gens; check=false) +end + +@doc raw""" + hom(F::FreeMod, G::FreeMod) + +Return a free module $S$ such that $\text{Hom}(F,G) \cong S$ along with a function +that converts elements from $S$ into morphisms $F \to G$. + +# Examples +```jldoctest +julia> R, _ = polynomial_ring(QQ, ["x", "y", "z"]); + +julia> F1 = free_module(R, 3) +Free module of rank 3 over Multivariate polynomial ring in 3 variables over QQ + +julia> F2 = free_module(R, 2) +Free module of rank 2 over Multivariate polynomial ring in 3 variables over QQ + +julia> V, f = hom(F1, F2) +(hom of (F1, F2), Map: V -> set of all homomorphisms from F1 to F2) + +julia> f(V[1]) +Map with following data +Domain: +======= +Free module of rank 3 over Multivariate polynomial ring in 3 variables over QQ +Codomain: +========= +Free module of rank 2 over Multivariate polynomial ring in 3 variables over QQ + +``` + +```jldoctest +julia> Rg, (x, y, z) = graded_polynomial_ring(QQ, ["x", "y", "z"]); + +julia> F1 = graded_free_module(Rg, [1,2,2]) +Graded free module Rg^1([-1]) + Rg^2([-2]) of rank 3 over Rg + +julia> F2 = graded_free_module(Rg, [3,5]) +Graded free module Rg^1([-3]) + Rg^1([-5]) of rank 2 over Rg + +julia> V, f = hom(F1, F2) +(hom of (F1, F2), Map: V -> set of all homomorphisms from F1 to F2) + +julia> f(V[1]) +F1 -> F2 +e[1] -> e[1] +e[2] -> 0 +e[3] -> 0 +Graded module homomorphism of degree [2] + +``` +""" +function hom(F::FreeMod, G::FreeMod) + if is_graded(F) && is_graded(G) + return _hom_graded(F, G) + else + return _hom_simple(F, G) + end +end + +function _hom_simple(F::FreeMod, G::FreeMod) + R = base_ring(F) + R === base_ring(G) || error("base rings must be the same") + m = ngens(F) + n = ngens(G) + + mn = m*n + H = FreeMod(R, mn) + # Custom printing of hom-module generators + if rank(G) == 1 + H.S = [Symbol("($i)*") for i = F.S] + else + H.S = [Symbol("($i "*(is_unicode_allowed() ? "→" : "->")*" $j)") for i = F.S for j = G.S] + end + + # We think of elements of H as matrices A ∈ Rᵐˣⁿ stored + # in concatenated lines: + # v = (a₁₁, a₁₂, …, a₁ₙ, a₂₁, …) + + function _elem_to_hom3(v::FreeModElem) + img_gens = [sum(c*G[j] for (j, c) in coordinates(v)[(i-1)*n+1:i*n]; init=zero(G)) for i in 1:m] + return hom(F, G, img_gens; check=false) + end + + function _hom_to_elem3(phi::FreeModuleHom) + @assert domain(phi) === F + @assert codomain(phi) === G + v = zero(H) + for (i, g) in enumerate(images_of_generators(phi)) + v = v + sum(c*H[(i-1)*n + j] for (j, c) in coordinates(g); init=zero(H)) + end + return v + end + + to_hom_map3 = MapFromFunc(H, Hecke.MapParent(F, G, "homomorphisms"), _elem_to_hom3, _hom_to_elem3) + set_attribute!(H, :show => Hecke.show_hom, :hom => (F, G), :module_to_hom_map => to_hom_map3) + return H, to_hom_map3 +end + +function _hom_graded(F::FreeMod, G::FreeMod) + R = base_ring(F) + GG = grading_group(R) + R === base_ring(G) || error("base rings must be the same") + m = ngens(F) + n = ngens(G) + + mn = m*n + H = graded_free_module(R, [_degree_fast(G[j]) - _degree_fast(F[i]) for i in 1:m for j in 1:n]) + # Custom printing of hom-module generators + if rank(G) == 1 && iszero(_degree_fast(G[1])) + H.S = [Symbol("($i)*") for i = F.S] + else + H.S = [Symbol("($i "*(is_unicode_allowed() ? "→" : "->")*" $j)") for i = F.S for j = G.S] + end + + # We think of elements of H as matrices A ∈ Rᵐˣⁿ stored + # in concatenated lines: + # v = (a₁₁, a₁₂, …, a₁ₙ, a₂₁, …) + + function _elem_to_hom4(v::FreeModElem) + img_gens = [sum(c*G[j] for (j, c) in coordinates(v)[(i-1)*n+1:i*n]; init=zero(G)) for i in 1:m] + return hom(F, G, img_gens; check=false) + end + + function _hom_to_elem4(phi::FreeModuleHom) + @assert domain(phi) === F + @assert codomain(phi) === G + v = zero(H) + for (i, g) in enumerate(images_of_generators(phi)) + v = v + sum(c*H[(i-1)*n + j] for (j, c) in coordinates(g); init=zero(H)) + end + return v + end + + to_hom_map4 = MapFromFunc(H, Hecke.MapParent(F, G, "homomorphisms"), _elem_to_hom4, _hom_to_elem4) + set_attribute!(H, :show => Hecke.show_hom, :hom => (F, G), :module_to_hom_map => to_hom_map4) + return H, to_hom_map4 +end +=# + + @doc raw""" element_to_homomorphism(f::ModuleFPElem) @@ -115,7 +373,7 @@ julia> F = FreeMod(R, 2); julia> V = [x*F[1], y^2*F[2]]; -julia> M = quo(F, V)[1] +julia> M = quo_object(F, V) Subquotient of Submodule with 2 generators 1 -> e[1] 2 -> e[2] @@ -181,7 +439,7 @@ julia> F = FreeMod(R, 2); julia> V = [x*F[1], y^2*F[2]]; -julia> M = quo(F, V)[1] +julia> M = quo_object(F, V) Subquotient of Submodule with 2 generators 1 -> e[1] 2 -> e[2] @@ -221,7 +479,7 @@ julia> m = homomorphism_to_element(H, a) function homomorphism_to_element(H::ModuleFP, a::ModuleFPHom) to_hom_map = get_attribute(H, :module_to_hom_map) to_hom_map === nothing && error("module must be a hom module") - map_to_hom = to_hom_map.g + map_to_hom = pseudo_inv(to_hom_map) return map_to_hom(a) end @@ -232,7 +490,7 @@ Return the multiplication by `a` as an endomorphism on `M`. """ function multiplication_morphism(a::RingElem, M::ModuleFP) @assert base_ring(M) === parent(a) - return hom(M, M, [a*v for v in gens(M)]) + return hom(M, M, [a*v for v in gens(M)]; check=false) end @doc raw""" @@ -260,7 +518,7 @@ function multiplication_induced_morphism(F::FreeMod, H::ModuleFP) M_N === nothing && error("module must be a hom module") M,N = M_N @assert M === N - return hom(F, H, [homomorphism_to_element(H, multiplication_morphism(F[1], M))]) + return hom(F, H, [homomorphism_to_element(H, multiplication_morphism(F[1], M))]; check=false) end diff --git a/src/Modules/UngradedModules/HomologicalAlgebra.jl b/src/Modules/UngradedModules/HomologicalAlgebra.jl index 401d7dd11734..81aebe3e72df 100644 --- a/src/Modules/UngradedModules/HomologicalAlgebra.jl +++ b/src/Modules/UngradedModules/HomologicalAlgebra.jl @@ -214,8 +214,9 @@ by Submodule with 4 generators 4 -> x*y*e[1] \otimes e[1] julia> T1 = tor(Q, M, 1) -Subquotient of Submodule with 1 generator -1 -> -x*e[1] \otimes e[1] +Subquotient of Submodule with 2 generators +1 -> x*e[1] \otimes e[1] +2 -> x*y*e[1] \otimes e[1] by Submodule with 3 generators 1 -> x^2*e[1] \otimes e[1] 2 -> y^3*e[1] \otimes e[1] @@ -524,9 +525,9 @@ function homology(C::Hecke.ComplexOfMorphisms{<:ModuleFP}, i::Int) return cokernel(f) elseif i in chain_range if Hecke.is_chain_complex(C) - return quo(kernel(map(C,i))[1], image(map(C,i+1))[1], :module) + return quo_object(kernel(map(C,i))[1], image(map(C,i+1))[1]) else - return quo(kernel(map(C,i))[1], image(map(C,i-1))[1], :module) + return quo_object(kernel(map(C,i))[1], image(map(C,i-1))[1]) end else return FreeMod(base_ring(obj(C,first(chain_range))),0) @@ -549,7 +550,7 @@ julia> F = FreeMod(R, 1); julia> V = [x*F[1], y*F[1]]; -julia> M = quo(F, V)[1] +julia> M = quo_object(F, V) Subquotient of Submodule with 1 generator 1 -> e[1] by Submodule with 2 generators @@ -560,26 +561,25 @@ julia> ext(M, M, 0) Subquotient of Submodule with 1 generator 1 -> (e[1] -> e[1]) by Submodule with 2 generators -1 -> x*(e[1] -> e[1]) -2 -> y*(e[1] -> e[1]) +1 -> y*(e[1] -> e[1]) +2 -> x*(e[1] -> e[1]) julia> ext(M, M, 1) Subquotient of Submodule with 2 generators -1 -> (e[2] -> e[1]) -2 -> (e[1] -> e[1]) +1 -> (e[1] -> e[1]) +2 -> (e[2] -> e[1]) by Submodule with 4 generators -1 -> x*(e[1] -> e[1]) -2 -> y*(e[1] -> e[1]) -3 -> x*(e[2] -> e[1]) -4 -> y*(e[2] -> e[1]) +1 -> y*(e[1] -> e[1]) +2 -> x*(e[1] -> e[1]) +3 -> y*(e[2] -> e[1]) +4 -> x*(e[2] -> e[1]) julia> ext(M, M, 2) Subquotient of Submodule with 1 generator 1 -> (e[1] -> e[1]) -by Submodule with 3 generators -1 -> x*(e[1] -> e[1]) -2 -> y*(e[1] -> e[1]) -3 -> -x*(e[1] -> e[1]) +by Submodule with 2 generators +1 -> y*(e[1] -> e[1]) +2 -> x*(e[1] -> e[1]) julia> ext(M, M, 3) Submodule with 0 generators diff --git a/src/Modules/UngradedModules/Methods.jl b/src/Modules/UngradedModules/Methods.jl index d0250dc6e6eb..a27fcd35d187 100644 --- a/src/Modules/UngradedModules/Methods.jl +++ b/src/Modules/UngradedModules/Methods.jl @@ -65,7 +65,7 @@ is not equal to 1 an error is thrown. """ function ideal_to_module(I::MPolyIdeal{T}, F::FreeMod{T}) where T @assert rank(F) == 1 - return sub(F, [x*gen(F,1) for x in gens(I)], :module) + return sub_object(F, [x*gen(F,1) for x in gens(I)]) end @doc raw""" @@ -93,27 +93,23 @@ function find_sequence_of_morphisms(N::SubquoModule, M::SubquoModule) if M===N return [identity_map(M)] end - parent_hom = IdDict{SubquoModule,ModuleFPHom}() + parent_hom = IdDict{SubquoModule, ModuleFPHom}() modules = [M] found_N = false for A in modules - for H in A.incoming_morphisms - B = domain(H) - if B!==A # on trees "B!==A" is enough! - if findfirst(x->x===B,modules) === nothing #if !(B in modules) doesn't work since it uses == instead of === - parent_hom[B] = H - push!(modules,B) - end - end - if B===N - found_N = true - break - end - end - if found_N + if N in keys(A.incoming) + parent_hom[N] = _recreate_morphism(N, A, A.incoming[N]) + found_N = true break end + + for (I, f) in A.incoming + I === A && continue + parent_hom[I] = _recreate_morphism(I, A, f) + push!(modules, I) + end end + if !found_N throw(DomainError("There is no path of canonical homomorphisms between the modules!")) end @@ -127,6 +123,15 @@ function find_sequence_of_morphisms(N::SubquoModule, M::SubquoModule) return morphisms end +function _recreate_morphism(dom::ModuleFP, cod::ModuleFP, t::Tuple{<:SMat, <:Any}) + A, bc = t + if bc === nothing + return hom(dom, cod, [sum(a*cod[i] for (i, a) in v; init=zero(cod)) for v in A], check=false) + else + return hom(dom, cod, [sum(a*cod[i] for (i, a) in v; init=zero(cod)) for v in A], bc, check=false) + end +end + @doc raw""" transport(M::SubquoModule, v::SubquoModuleElem) @@ -164,19 +169,18 @@ function find_morphisms(N::SubquoModule, M::SubquoModule) all_paths = [] - function helper_dfs!(U::SubquoModule, D::SubquoModule, visited::Vector{<:ModuleFPHom}, path::Vector) + function helper_dfs!(U::SubquoModule, D::SubquoModule, visited::Vector{<:ModuleFP}, path::Vector) if U === D push!(all_paths, path) return end - for neighbor_morphism in U.outgoing_morphisms - if findfirst(x->x===neighbor_morphism, visited) === nothing #if !(neighbor_morphism in visited) doesn't work since it uses == instead of === - helper_dfs!(codomain(neighbor_morphism), D, vcat(visited, [neighbor_morphism]), union(path, [neighbor_morphism])) - end + for (cod, neighbor_morphism) in U.outgoing + any(x->x===cod, visited) && continue + helper_dfs!(cod, D, push!(visited, cod), union(path, [_recreate_morphism(U, cod, neighbor_morphism)])) end end - helper_dfs!(N, M, Vector{ModuleFPHom}(), []) + helper_dfs!(N, M, Vector{ModuleFP}(), []) morphisms = Vector{ModuleFPHom}() for path in all_paths @@ -200,10 +204,30 @@ end Cache the morphism `f` in the corresponding caches of the domain and codomain of `f`. """ function register_morphism!(f::ModuleFPHom) - push!(domain(f).outgoing_morphisms, f) - push!(codomain(f).incoming_morphisms, f) + dom = domain(f) + cod = codomain(f) + dom.outgoing[cod] = sparse_matrix(f), ring_map(f) + cod.incoming[dom] = sparse_matrix(f), ring_map(f) + f +end + +# Some missing methods for the above to work +function sparse_matrix(f::ModuleFPHom) + dom = domain(f) + R = base_ring(codomain(f)) + result = sparse_matrix(R, 0, ngens(codomain(f))) + for v in gens(dom) + push!(result, coordinates(f(v))) + end + return result end +ring_map(f::FreeModuleHom{<:AbstractFreeMod, <:ModuleFP, Nothing}) = nothing +ring_map(f::FreeModuleHom) = f.ring_map + +ring_map(f::SubQuoHom{<:AbstractFreeMod, <:ModuleFP, Nothing}) = nothing +ring_map(f::SubQuoHom) = f.ring_map + ############################# #TODO move to Hecke # re-evaluate and use or not @@ -357,7 +381,7 @@ function hom_matrices(M::SubquoModule{T},N::SubquoModule{T},simplify_task=true) to_homomorphism = function(elem::SubquoModuleElem{T}) elem2 = i(elem) A = convert_to_matrix(elem2) - return SubQuoHom(M,N,A) + return SubQuoHom(M,N,A; check=false) end to_subquotient_elem = function(H::ModuleFPHom) m = length(matrix(H)) @@ -379,7 +403,7 @@ function hom_matrices(M::SubquoModule{T},N::SubquoModule{T},simplify_task=true) end to_homomorphism = function(elem::SubquoModuleElem{T}) A = convert_to_matrix(elem) - return SubQuoHom(M,N,A) + return SubQuoHom(M,N,A; check=false) end to_hom_map = MapFromFunc(SQ, Hecke.MapParent(M, N, "homomorphisms"), to_homomorphism, to_subquotient_elem) @@ -413,7 +437,7 @@ function change_base_ring(S::Ring, M::SubquoModule) g = ambient_representatives_generators(M) rels = relations(M) MS = SubquoModule(FS, mapF.(g), mapF.(rels)) - map = SubQuoHom(M, MS, gens(MS), MapFromFunc(R, S, x->S(x))) + map = SubQuoHom(M, MS, gens(MS), MapFromFunc(R, S, x->S(x)); check=false) return MS, map end @@ -426,13 +450,13 @@ function change_base_ring(f::Map{DomType, CodType}, M::SubquoModule) where {DomT g = ambient_representatives_generators(M) rels = relations(M) MS = SubquoModule(FS, mapF.(g), mapF.(rels)) - map = SubQuoHom(M, MS, gens(MS), f) + map = SubQuoHom(M, MS, gens(MS), f; check=false) return MS, map end ### Duals of modules @doc raw""" - dual(M::ModuleFP; cod::FreeMod=FreeMod(base_ring(M), 1)) + dual(M::ModuleFP; codomain::Union{FreeMod, Nothing}=nothing) Return a pair ``(M*, i)`` consisting of the dual of ``M`` and its interpretation map ``i``, turning an element ``φ`` of ``M*`` into @@ -441,11 +465,11 @@ a homomorphism ``M → R``. The optional argument allows to specify a free module of rank ``1`` for the codomain of the dualizing functor. """ -function dual(M::ModuleFP; cod::Union{FreeMod, Nothing}=nothing) +function dual(M::ModuleFP; codomain::Union{FreeMod, Nothing}=nothing) R = base_ring(M) - cod = cod === nothing ? (is_graded(M) ? graded_free_module(R, 1) : FreeMod(R, 1)) : cod - base_ring(cod) === R && rank(cod) == 1 || error("codomain must be free of rank one over the base ring of the first argument") - return hom(M, cod) + codomain = codomain === nothing ? (is_graded(M) ? graded_free_module(R, 1) : FreeMod(R, 1)) : codomain + base_ring(codomain) === R && rank(codomain) == 1 || error("codomain must be free of rank one over the base ring of the first argument") + return hom(M, codomain) end @doc raw""" @@ -455,49 +479,49 @@ For a finite ``R``-module ``M`` return a pair ``(M**, ϕ)`` consisting of its double dual ``M** = Hom(Hom(M, R), R)`` together with the canonical map ``ϕ : M → M**, v ↦ (φ ↦ φ(v)) ∈ Hom(M*, R)``. """ -function double_dual(M::FreeMod{T}; cod::Union{FreeMod, Nothing}=nothing) where T +function double_dual(M::FreeMod{T}; codomain::Union{FreeMod, Nothing}=nothing, check::Bool=true) where T R = base_ring(M) - cod = cod === nothing ? (is_graded(M) ? graded_free_module(R, 1) : FreeMod(R, 1)) : cod - M_dual, _ = dual(M, cod=cod) - M_double_dual, _ = dual(M_dual, cod=cod) + codomain = codomain === nothing ? (is_graded(M) ? graded_free_module(R, 1) : FreeMod(R, 1)) : codomain + M_dual, _ = dual(M, codomain=codomain) + M_double_dual, _ = dual(M_dual, codomain=codomain) if length(gens(M_dual)) == 0 psi_gens = [zero(M_double_dual) for _ in gens(M)] else psi_gens = [ homomorphism_to_element( M_double_dual, - FreeModuleHom(M_dual, cod, [element_to_homomorphism(phi)(x) for phi in gens(M_dual)]) + FreeModuleHom(M_dual, codomain, [element_to_homomorphism(phi)(x) for phi in gens(M_dual)]; check) ) for x in gens(M) ] end - psi = FreeModuleHom(M, M_double_dual, psi_gens) + psi = FreeModuleHom(M, M_double_dual, psi_gens; check) return M_double_dual, psi end -function double_dual(M::SubquoModule{T}; cod::Union{FreeMod, Nothing}=nothing) where T +function double_dual(M::SubquoModule{T}; codomain::Union{FreeMod, Nothing}=nothing, check::Bool=true) where T R = base_ring(M) - cod = cod === nothing ? (is_graded(M) ? graded_free_module(R, 1) : FreeMod(R, 1)) : cod - M_dual, _ = dual(M, cod=cod) - M_double_dual, _ = dual(M_dual, cod=cod) + codomain = codomain === nothing ? (is_graded(M) ? graded_free_module(R, 1) : FreeMod(R, 1)) : codomain + M_dual, _ = dual(M, codomain=codomain) + M_double_dual, _ = dual(M_dual, codomain=codomain) if length(gens(M_dual)) == 0 psi_gens = [zero(M_double_dual) for _ in gens(M)] else psi_gens = [ homomorphism_to_element( M_double_dual, - SubQuoHom(M_dual, cod, [element_to_homomorphism(phi)(x) for phi in gens(M_dual)]) + SubQuoHom(M_dual, codomain, [element_to_homomorphism(phi)(x) for phi in gens(M_dual)]; check) ) for x in gens(M) ] end - psi = SubQuoHom(M, M_double_dual, psi_gens) + psi = SubQuoHom(M, M_double_dual, psi_gens; check) return M_double_dual, psi end @doc raw""" - dual(f::ModuleFPHom; cod::FreeMod) + dual(f::ModuleFPHom; codomain::FreeMod) Given a morphism of modules ``f : M → N``, return the morphism ``fᵀ : N* → M*, φ ↦ (v ↦ φ(f(v)))`` induced on the duals. @@ -506,13 +530,13 @@ The optional argument allows to specify a free module of rank one over the base ring of ``f`` for building the duals of ``M`` and ``N``. """ function dual(f::ModuleFPHom{<:ModuleFP, <:ModuleFP, Nothing}; # Third parameter assures same base ring - cod::FreeMod=FreeMod(base_ring(domain(f)), 1), - domain_dual::ModuleFP=dual(domain(f), cod=cod)[1], - codomain_dual::ModuleFP=dual(codomain(f), cod=cod)[1] + codomain::FreeMod=FreeMod(base_ring(domain(f)), 1), + domain_dual::ModuleFP=dual(Oscar.domain(f), codomain=codomain)[1], + codomain_dual::ModuleFP=dual(Oscar.codomain(f), codomain=codomain)[1] ) - M = domain(f) - N = codomain(f) - R = base_ring(domain(f)) + M = Oscar.domain(f) + N = Oscar.codomain(f) + R = base_ring(Oscar.domain(f)) R === base_ring(N) || error("modules must be defined over the same rings") M_dual = domain_dual @@ -520,7 +544,7 @@ function dual(f::ModuleFPHom{<:ModuleFP, <:ModuleFP, Nothing}; # Third parameter return hom(N_dual, M_dual, [homomorphism_to_element(M_dual, - hom(M, cod, + hom(M, codomain, [element_to_homomorphism(phi)(f(v)) for v in gens(M)] ) ) @@ -613,7 +637,7 @@ function vector_space_dimension(M::SubquoModule{T} M_shift,_,_ = shifted_module(Mq) o = negdegrevlex(base_ring(M_shift))*lex(ambient_free_module(M_shift)) LM = leading_module(M_shift,o) - return vector_space_dimension(quo(ambient_free_module(LM),gens(LM))[1]) + return vector_space_dimension(quo_object(ambient_free_module(LM),gens(LM))) end function vector_space_dimension(M::SubquoModule{T},d::Int64 @@ -625,7 +649,7 @@ function vector_space_dimension(M::SubquoModule{T},d::Int64 M_shift,_,_ = shifted_module(Mq) o = negdegrevlex(base_ring(M_shift))*lex(ambient_free_module(M_shift)) LM = leading_module(M_shift,o) - return vector_space_dimension(quo(ambient_free_module(LM),gens(LM))[1],d) + return vector_space_dimension(quo_object(ambient_free_module(LM),gens(LM)),d) end function vector_space_dimension(M::SubquoModule{T} @@ -730,7 +754,7 @@ function vector_space_basis(M::SubquoModule{T} end LM = leading_module(M_shift,o) - return vector_space_basis(quo(ambient_free_module(LM),gens(LM))[1]) + return vector_space_basis(quo_object(ambient_free_module(LM),gens(LM))) end function vector_space_basis(M::SubquoModule{T},d::Int64 @@ -747,7 +771,7 @@ function vector_space_basis(M::SubquoModule{T},d::Int64 end LM = leading_module(M_shift,o) - return vector_space_basis(quo(ambient_free_module(LM),gens(LM))[1],d) + return vector_space_basis(quo_object(ambient_free_module(LM),gens(LM)),d) end function vector_space_basis(M::SubquoModule{T} diff --git a/src/Modules/UngradedModules/Presentation.jl b/src/Modules/UngradedModules/Presentation.jl index daf6ae982ef3..9f6af19307e0 100644 --- a/src/Modules/UngradedModules/Presentation.jl +++ b/src/Modules/UngradedModules/Presentation.jl @@ -6,11 +6,18 @@ Return a free presentation of `M`. """ function presentation(SQ::SubquoModule) + if is_graded(SQ) + return _presentation_graded(SQ) + else + return _presentation_simple(SQ) + end + + # Old code left for debugging #A+B/B is generated by A and B #the relations are A meet B? written wrt to A R = base_ring(SQ) if is_graded(SQ) - h_F_SQ = graded_map(SQ, gens(SQ)) + h_F_SQ = graded_map(SQ, gens(SQ); check=false) F = domain(h_F_SQ) else F = FreeMod(R, ngens(SQ.sub)) @@ -28,7 +35,7 @@ function presentation(SQ::SubquoModule) end else if is_graded(SQ) - s, _ = kernel(graded_map(ambient_free_module(SQ), gens(SQ.sum))) + s, _ = kernel(graded_map(ambient_free_module(SQ), filter(!iszero, gens(SQ.sum)); check=false)) else s, _ = kernel(hom(FreeMod(R,ngens(SQ.sum)), ambient_free_module(SQ), gens(SQ.sum))) end @@ -39,12 +46,10 @@ function presentation(SQ::SubquoModule) for x = c b = sparse_row(R) - e = zero(SQ.F) for (i,v) = x.coords if i>ngens(SQ) break end - e += v*repres(gen(SQ, i)) push!(b.pos, i) push!(b.values, v) end @@ -54,14 +59,21 @@ function presentation(SQ::SubquoModule) push!(q, FreeModElem(b, F)) end end + for i in 1:length(q) + if !is_homogeneous(q[i]) + for m in terms(q[i]) + end + end + end #want R^a -> R^b -> SQ -> 0 #from Hans: # as a complex R^b has index 0 # R^a 1 # so 0 has index -2, hence seed has to be -2 #TODO sort decoration and fix maps, same decoration should be bundled (to match pretty printing) + q = elem_type(F)[g for g in q if !is_zero(g)] if is_graded(SQ) - h_G_F = graded_map(F, q) + h_G_F = graded_map(F, q; check=false) G = domain(h_G_F) else G = FreeMod(R, length(q)) @@ -84,6 +96,94 @@ function presentation(SQ::SubquoModule) return M end +function _presentation_graded(SQ::SubquoModule) + R = base_ring(SQ) + + # Prepare to set some names + br_name = AbstractAlgebra.find_name(R) + if br_name === nothing + br_name = "br" + end + + # Create the free module for the presentation + # + # We have to take representatives of the simplified + # generators, because otherwise the degrees are not correctly + # inferred. + # + # At the same time, we can not just throw away zero + # generators, because other code relies on the 1:1-correspondence + # of the generators in a presentation. + F0_to_SQ = graded_map(SQ, gens(SQ); check=false) + F0_to_SQ.generators_map_to_generators = true + F0 = domain(F0_to_SQ) + set_attribute!(F0, :name => "$br_name^$(ngens(SQ.sub))") + + K, inc_K = kernel(F0_to_SQ) + F1_to_F0 = graded_map(F0, images_of_generators(inc_K)) + F1 = domain(F1_to_F0) + #F1 = graded_free_module(R, [degree(x; check=false) for x in images_of_generators(inc_K)]) + #F1_to_F0 = hom(F1, F0, images_of_generators(inc_K), check=false) + set_attribute!(F1, :name => "$br_name^$(ngens(F1))") + + # When there is no kernel, clean things up + if is_zero(F1) + F1 = graded_free_module(R, elem_type(grading_group(R))[]) + F1_to_F0 = hom(F1, F0, elem_type(F0)[]; check=false) + end + + # prepare the end of the presentation + Z = graded_free_module(R, elem_type(grading_group(R))[]) + set_attribute!(Z, :name => "0") + SQ_to_Z = hom(SQ, Z, elem_type(Z)[zero(Z) for i in 1:ngens(SQ)]; check=false) + + # compile the presentation complex + M = Hecke.ComplexOfMorphisms(ModuleFP, ModuleFPHom[F1_to_F0, F0_to_SQ, SQ_to_Z], check=false, seed = -2) + @assert M[0] === F0::FreeMod + @assert M[1] === F1::FreeMod + set_attribute!(M, :show => Hecke.pres_show) + return M +end + +function _presentation_simple(SQ::SubquoModule) + R = base_ring(SQ) + + # Prepare to set some names + br_name = AbstractAlgebra.find_name(R) + if br_name === nothing + br_name = "br" + end + + # Create the free module for the presentation + F0 = FreeMod(R, length(gens(SQ))) + F0_to_SQ = hom(F0, SQ, gens(SQ); check=false) + F0_to_SQ.generators_map_to_generators = true + set_attribute!(F0, :name => "$br_name^$(ngens(SQ.sub))") + + K, inc_K = kernel(F0_to_SQ) + @assert codomain(inc_K) === F0 + @assert all(x->parent(x) === F0, images_of_generators(inc_K)) + F1 = FreeMod(R, ngens(K)) + F1_to_F0 = hom(F1, F0, images_of_generators(inc_K), check=false) + set_attribute!(F1, :name => "$br_name^$(ngens(F1))") + + # When there is no kernel, clean things up + if is_zero(F1) + F1 = FreeMod(R, 0) + F1_to_F0 = hom(F1, F0, elem_type(F0)[]; check=false) + end + + # prepare the end of the presentation + Z = FreeMod(R, 0) + set_attribute!(Z, :name => "0") + SQ_to_Z = hom(SQ, Z, elem_type(Z)[zero(Z) for i in 1:ngens(SQ)]; check=false) + + # compile the presentation complex + M = Hecke.ComplexOfMorphisms(ModuleFP, ModuleFPHom[F1_to_F0, F0_to_SQ, SQ_to_Z], check=false, seed = -2) + set_attribute!(M, :show => Hecke.pres_show) + return M +end + @doc raw""" presentation(F::FreeMod) @@ -294,7 +394,7 @@ function present_as_cokernel(SQ::SubquoModule, task::Symbol = :none) R_b = obj(chainComplex, 0) f = map(chainComplex, 1) g = map(chainComplex, 0) - presentation_module = quo(R_b, image(f)[1], :module) + presentation_module = quo_object(R_b, image(f)[1]) if task == :none return presentation_module diff --git a/src/Modules/UngradedModules/SubQuoHom.jl b/src/Modules/UngradedModules/SubQuoHom.jl index 32c6cec52cc7..96ed1a31225c 100644 --- a/src/Modules/UngradedModules/SubQuoHom.jl +++ b/src/Modules/UngradedModules/SubQuoHom.jl @@ -8,8 +8,8 @@ Return the morphism $D \to C$ for a subquotient $D$ where `D[i]` is mapped to `im[i]`. In particular, `length(im) == ngens(D)` must hold. """ -SubQuoHom(D::SubquoModule, C::ModuleFP{T}, im::Vector{<:ModuleFPElem{T}}; check::Bool=true) where {T} = SubQuoHom{typeof(D), typeof(C), Nothing}(D, C, im) -SubQuoHom(D::SubquoModule, C::ModuleFP{T}, im::Vector{<:ModuleFPElem{T}}, h::RingMapType; check::Bool=true) where {T, RingMapType} = SubQuoHom{typeof(D), typeof(C), RingMapType}(D, C, im, h) +SubQuoHom(D::SubquoModule, C::ModuleFP{T}, im::Vector{<:ModuleFPElem{T}}; check::Bool=true) where {T} = SubQuoHom{typeof(D), typeof(C), Nothing}(D, C, im; check) +SubQuoHom(D::SubquoModule, C::ModuleFP{T}, im::Vector{<:ModuleFPElem{T}}, h::RingMapType; check::Bool=true) where {T, RingMapType} = SubQuoHom{typeof(D), typeof(C), RingMapType}(D, C, im, h; check) @doc raw""" SubQuoHom(D::SubquoModule, C::ModuleFP{T}, mat::MatElem{T}) @@ -21,10 +21,10 @@ function SubQuoHom(D::SubquoModule, C::ModuleFP{T}, mat::MatElem{T}; check::Bool @assert nrows(mat) == ngens(D) @assert ncols(mat) == ngens(C) if C isa FreeMod - hom = SubQuoHom(D, C, [FreeModElem(sparse_row(mat[i:i,:]), C) for i=1:ngens(D)]) + hom = SubQuoHom(D, C, [FreeModElem(sparse_row(mat[i:i,:]), C) for i=1:ngens(D)]; check) return hom else - hom = SubQuoHom(D, C, [SubquoModuleElem(sparse_row(mat[i:i,:]), C) for i=1:ngens(D)]) + hom = SubQuoHom(D, C, [SubquoModuleElem(sparse_row(mat[i:i,:]), C) for i=1:ngens(D)]; check) return hom end end @@ -33,10 +33,10 @@ function SubQuoHom(D::SubquoModule, C::ModuleFP{T}, mat::MatElem{T}, h::RingMapT @assert nrows(mat) == ngens(D) @assert ncols(mat) == ngens(C) if C isa FreeMod - hom = SubQuoHom(D, C, [FreeModElem(sparse_row(mat[i,:]), C) for i=1:ngens(D)], h) + hom = SubQuoHom(D, C, [FreeModElem(sparse_row(mat[i:i,:]), C) for i=1:ngens(D)], h; check) return hom else - hom = SubQuoHom(D, C, [SubquoModuleElem(sparse_row(mat[i,:]), C) for i=1:ngens(D)], h) + hom = SubQuoHom(D, C, [SubquoModuleElem(sparse_row(mat[i:i,:]), C) for i=1:ngens(D)], h; check) return hom end end @@ -307,15 +307,29 @@ Return `true` if `a` is well-defined, and `false` otherwise. hom(M::SubquoModule, N::ModuleFP{T}, V::Vector{<:ModuleFPElem{T}}, h::RingMapType; check::Bool=true) where {T, RingMapType} = SubQuoHom(M, N, V, h; check) hom(M::SubquoModule, N::ModuleFP{T}, A::MatElem{T}, h::RingMapType; check::Bool=true) where {T, RingMapType} = SubQuoHom(M, N, A, h; check) -function is_welldefined(H::ModuleFPHom) - if H isa Union{FreeModuleHom,FreeModuleHom_dec} - return true - end +function is_welldefined(H::Union{FreeModuleHom,FreeModuleHom_dec}) + return true +end + +function is_welldefined(H::SubQuoHom) M = domain(H) + pres = presentation(M) + # is a short exact sequence with maps + # M <--eps-- F0 <--g-- F1 + # and H : M -> N + eps = map(pres, 0) + g = map(pres, 1) + F0 = pres[0] + N = codomain(H) + # the induced map phi : F0 --> N + phi = hom(F0, N, elem_type(N)[H(eps(v)) for v in gens(F0)]; check=false) + # now phi ∘ g : F1 --> N has to be zero. + return iszero(compose(g, phi)) + C = present_as_cokernel(M).quo n = ngens(C) m = rank(C.F) - ImH = map(x -> H(x), gens(M)) + ImH = images_of_generators(H) for i=1:n if !iszero(sum([C[i][j]*ImH[j] for j=1:m]; init=zero(codomain(H)))) return false @@ -540,8 +554,8 @@ Return the image of `a` as an object of type `SubquoModule`. Additionally, if `I` denotes this object, return the inclusion map `I` $\to$ `codomain(a)`. """ -function image(h::SubQuoHom) - s = sub(codomain(h), images_of_generators(h), :module) +@attr Tuple{<:SubquoModule, <:ModuleFPHom} function image(h::SubQuoHom) + s = sub_object(codomain(h), images_of_generators(h)) inc = hom(s, codomain(h), images_of_generators(h), check=false) return s, inc end @@ -724,7 +738,7 @@ function kernel(h::SubQuoHom) @assert codomain(inc_K) === F v = gens(D) imgs = Vector{elem_type(D)}(filter(!iszero, [sum(a*v[i] for (i, a) in coordinates(g); init=zero(D)) for g in images_of_generators(inc_K)])) - k = sub(D, imgs, :module) + k = sub_object(D, imgs) return k, hom(k, D, imgs, check=false) end @@ -866,22 +880,19 @@ Graded module homomorphism of degree [2] julia> kernel(a) (Graded subquotient of submodule of F generated by -1 -> -y*e[1] -2 -> (x^2 - y^2)*e[1] -3 -> -x*y*e[1] +1 -> y*e[1] +2 -> -x*y*e[1] by submodule of F generated by 1 -> x^2*e[1] 2 -> y^3*e[1] 3 -> z^4*e[1], Graded subquotient of submodule of F generated by -1 -> -y*e[1] -2 -> (x^2 - y^2)*e[1] -3 -> -x*y*e[1] +1 -> y*e[1] +2 -> -x*y*e[1] by submodule of F generated by 1 -> x^2*e[1] 2 -> y^3*e[1] 3 -> z^4*e[1] -> M --y*e[1] -> -y*e[1] -(x^2 - y^2)*e[1] -> (x^2 - y^2)*e[1] +y*e[1] -> y*e[1] -x*y*e[1] -> -x*y*e[1] Homogeneous module homomorphism) @@ -983,16 +994,16 @@ of the domain of `H`. The relations of `M` must be the relations of the domain of `H`. """ function restrict_domain(H::SubQuoHom, M::SubquoModule) - for i in M.outgoing_morphisms - if codomain(i) === domain(H) - return i*H + for (cod, t) in M.outgoing + if cod === domain(H) + return _recreate_morphism(M, cod, t)*H end end # else there is no cached map if ngens(M) > 0 @assert M.quo == domain(H).quo end - i = sub(domain(H), map(m -> SubquoModuleElem(repres(m), domain(H)), gens(M)), :cache_morphism)[2] + _, i = sub(domain(H), map(m -> SubquoModuleElem(repres(m), domain(H)), gens(M)), cache_morphism=true) return i*H end @@ -1082,7 +1093,7 @@ function preimage(H::SubQuoHom,elems::Vector{SubquoModuleElem{T}}, task::Symbol cod_coker,i_cod_coker_inv = present_as_cokernel(codomain(H), :with_morphism) i_cod_coker = inv(i_cod_coker_inv) # this is cheap elems_in_coker = map(x->i_cod_coker(x),elems) - cokernel_modulo_elmes,projection = quo(cod_coker,elems_in_coker,:with_morphism) + cokernel_modulo_elmes,projection = quo(cod_coker,elems_in_coker) preimage, emb = kernel(H*i_cod_coker*projection) if task != :none diff --git a/src/Modules/UngradedModules/SubquoModule.jl b/src/Modules/UngradedModules/SubquoModule.jl index 8a4552694ab9..23befe8994db 100644 --- a/src/Modules/UngradedModules/SubquoModule.jl +++ b/src/Modules/UngradedModules/SubquoModule.jl @@ -558,7 +558,7 @@ by submodule of G generated by ``` """ function cokernel(f::ModuleFPHom{T1, T2}) where {T1, T2} - return quo(codomain(f), image(f)[1], :module)::SubquoModule{elem_type(base_ring_type(T2))} + return quo_object(codomain(f), image(f)[1])::SubquoModule{elem_type(base_ring_type(T2))} end @doc raw""" @@ -1324,8 +1324,8 @@ function sum(M::SubquoModule{T},N::SubquoModule{T}) where T end end - iM = SubQuoHom(M,SQ,[SQ[i] for i=1:ngens(M)]) - iN = SubQuoHom(N,SQ,[SQ[i] for i=ngens(M)+1:ngens(SQ)]) + iM = SubQuoHom(M,SQ,[SQ[i] for i=1:ngens(M)]; check=false) + iN = SubQuoHom(N,SQ,[SQ[i] for i=ngens(M)+1:ngens(SQ)]; check=false) register_morphism!(iM) register_morphism!(iN) @@ -1597,7 +1597,7 @@ function intersect(M::SubquoModule{T}, N::SubquoModule{T}) where T F1 = FreeMod(R, ngens(M.sub) + ngens(N.sub) + ngens(M_quo)) F2 = ambient_free_module(M) - phi = FreeModuleHom(F1,F2,vcat(gens(M.sub),gens(N.sub),gens(M_quo))) + phi = FreeModuleHom(F1,F2,vcat(gens(M.sub),gens(N.sub),gens(M_quo)); check=false) K,i = kernel(phi) intersection_gens_array_with_zeros = [sum([repres(k)[i]*M.sub[i] for i=1:ngens(M.sub)]; init=zero(ambient_free_module(M))) for k in gens(K)] @@ -1607,8 +1607,8 @@ function intersect(M::SubquoModule{T}, N::SubquoModule{T}) where T SQ = SubquoModule(intersection_gens,M_quo) m = ngens(M) - M_hom = SubQuoHom(SQ,M,[sum([repres(k)[i]*M[i] for i=1:m]; init=zero(M)) for k in gens(K)][iszero_array]) - N_hom = SubQuoHom(SQ,N,[sum([repres(k)[i]*N[i-m] for i=m+1:m+ngens(N)]; init=zero(N)) for k in gens(K)][iszero_array]) + M_hom = SubQuoHom(SQ,M,[sum([repres(k)[i]*M[i] for i=1:m]; init=zero(M)) for k in gens(K)][iszero_array]; check=false) + N_hom = SubQuoHom(SQ,N,[sum([repres(k)[i]*N[i-m] for i=m+1:m+ngens(N)]; init=zero(N)) for k in gens(K)][iszero_array]; check=false) register_morphism!(M_hom) register_morphism!(N_hom) diff --git a/src/Modules/UngradedModules/SubquoModuleElem.jl b/src/Modules/UngradedModules/SubquoModuleElem.jl index 3cc557ddca95..b81aa401a465 100644 --- a/src/Modules/UngradedModules/SubquoModuleElem.jl +++ b/src/Modules/UngradedModules/SubquoModuleElem.jl @@ -73,6 +73,7 @@ Sparse row with positions [1, 2] and values QQMPolyRingElem[z, 1] """ function coordinates(m::SubquoModuleElem) if !isdefined(m, :coeffs) + @assert isdefined(m, :repres) "neither coeffs nor repres is defined on a SubquoModuleElem" m.coeffs = coordinates(repres(m), parent(m)) end return m.coeffs @@ -87,16 +88,28 @@ Return a free module element that is a representative of `v`. """ function repres(v::SubquoModuleElem) if !isdefined(v, :repres) + @assert isdefined(v, :coeffs) "neither coeffs nor repres is defined on a SubquoModuleElem" M = parent(v) - v.repres = sum(a*M.sub[i] for (i, a) in coordinates(v); init=zero(M.sub)) + v.repres = sum(a*M.sub[i] for (i, a) in v.coeffs; init=zero(M.sub)) end return v.repres end ####################################################### -function simplify(el::SubquoModuleElem{<:MPolyRingElem{<:FieldElem}}) +# simplify modifies the representative v of el as follows: +# +# - if el is zero, v is zero +# - if el is homogeneous, but the current representative is not +# then a homogeneous representative is returned. +# - it sets the field is_reduced to true. +function simplify(el::SubquoModuleElem{<:MPolyRingElem{T}}) where {T<:Union{<:FieldElem, <:ZZRingElem}} el.is_reduced && return el + if is_zero(el) # We have to do this check because otherwise the coordinates of the representative are not reset. + result = zero(parent(el)) + result.is_reduced = true # Todo: Should be done in zero(...) + return result + end if !isdefined(parent(el), :quo) || is_zero(parent(el).quo) el.is_reduced = true return el @@ -107,8 +120,13 @@ function simplify(el::SubquoModuleElem{<:MPolyRingElem{<:FieldElem}}) return result end -function simplify!(el::SubquoModuleElem{<:MPolyRingElem{<:FieldElem}}) +function simplify!(el::SubquoModuleElem{<:MPolyRingElem{T}}) where {T<:Union{<:FieldElem, <:ZZRingElem}} el.is_reduced && return el + if is_zero(el) # We have to do this check because otherwise the coordinates of the representative are not reset. + result = zero(parent(el)) + result.is_reduced = true # Todo: Should be done in zero(...) + return result + end if !isdefined(parent(el), :quo) || is_zero(parent(el).quo) el.is_reduced = true return el @@ -119,6 +137,31 @@ function simplify!(el::SubquoModuleElem{<:MPolyRingElem{<:FieldElem}}) return el end +# The default only checks whether an element is zero. +function simplify(el::SubquoModuleElem) + el.is_reduced && return el + if is_zero(el) + result = zero(parent(el)) + result.is_reduced = true # Todo: Should be done in zero(...) + return result + end + el.is_reduced = true + return el +end + +function simplify!(el::SubquoModuleElem) + el.is_reduced && return el + if is_zero(el) + el.coeffs = sparse_row(base_ring(parent(el))) + el.repres = zero(ambient_free_module(parent(el))) + el.is_reduced = true + return el + end + el.is_reduced = true + return el +end + + ####################################################### @doc raw""" ambient_representative(m::SubquoModuleElem) @@ -405,103 +448,121 @@ function Base.deepcopy_internal(a::SubquoModuleElem, dict::IdDict) end @doc raw""" - sub(F::FreeMod{T}, V::Vector{<:FreeModElem{T}}, task::Symbol = :with_morphism) where T - -Given a vector `V` of (homogeneous) elements of `F`, return the (graded) submodule of `F` generated by these elements. - -Put more precisely, return the submodule as an object of type `SubquoModule`. + sub(F::FreeMod{T}, V::Vector{<:FreeModElem{T}}; cache_morphism::Bool=false) where {T} -Additionally, if `N` denotes this object, +Given a vector `V` of (homogeneous) elements of `F`, return a pair `(I, inc)` +consisting of the (graded) submodule `I` of `F` generated by these elements +and its inclusion map `inc : I ↪ F`. -- return the inclusion map `N` $\to$ `F` if `task = :with_morphism` (default), -- return and cache the inclusion map `N` $\to$ `F` if `task = :cache_morphism`, -- do none of the above if `task = :none`. +When `cache_morphism` is set to true, then `inc` will be cached and available +for `transport` and friends. -If `task = :only_morphism`, return only the inclusion map. +If only the submodule itself is desired, use `sub_object` instead. """ -function sub(F::FreeMod{T}, V::Vector{<:FreeModElem{T}}, task::Symbol = :with_morphism) where T +function sub(F::FreeMod{T}, V::Vector{<:FreeModElem{T}}; cache_morphism::Bool=false) where {T} s = SubquoModule(F, V) emb = hom(s, F, V; check=false) set_attribute!(s, :canonical_inclusion => emb) - return return_sub_wrt_task(s, emb, task) + cache_morphism && register_morphism!(emb) + return s, emb end -@doc raw""" - sub(F::FreeMod{T}, A::MatElem{T}, task::Symbol = :with_morphism) where {T} - -Given a (homogeneous) matrix `A`, return the (graded) submodule of `F` generated by the rows of `A`. +function sub_object(F::FreeMod{T}, V::Vector{<:FreeModElem{T}}) where {T} + return SubquoModule(F, V) +end -Put more precisely, return this submodule as an object of type `SubquoModule`. +@doc raw""" + sub(F::FreeMod{T}, A::MatElem{T}; cache_morphism::Bool=false) where {T} -Additionally, if `N` denotes this submodule, +Given a (homogeneous) matrix `A` interpret the rows of `A` as elements +of the free module `F` and return a pair `(I, inc)` +consisting of the (graded) submodule `I` of `F` generated by these row vectors, +together with its inclusion map `inc : I ↪ F`. -- return the inclusion map `N` $\to$ `F` if `task = :with_morphism` (default), -- return and cache the inclusion map `N` $\to$ `F` if `task = :cache_morphism`, -- do none of the above if `task = :none`. +When `cache_morphism` is set to true, then `inc` will be cached and available +for `transport` and friends. -If `task = :only_morphism`, return only the inclusion map. +If only the submodule itself is desired, use `sub_object` instead. """ -function sub(F::FreeMod{T}, A::MatElem{T}, task::Symbol = :with_morphism) where {T} +function sub(F::FreeMod{T}, A::MatElem{T}; cache_morphism::Bool=false) where {T} M = SubquoModule(SubModuleOfFreeModule(F, A)) #M = SubquoModule(F, A, zero_matrix(base_ring(F), 1, rank(F))) emb = hom(M, F, ambient_representatives_generators(M); check=false) emb.matrix = A - set_attribute!(M, :canonical_inclusion => emb) - return return_sub_wrt_task(M, emb, task) + set_attribute!(M, :canonical_inclusion => emb) # TODO: Can this be removed? + cache_morphism && register_morphism!(emb) + return M, emb +end + +function sub_object(F::FreeMod{T}, A::MatElem{T}) where {T} + return SubquoModule(SubModuleOfFreeModule(F, A)) end @doc raw""" - sub(F::FreeMod{T}, O::Vector{<:SubquoModuleElem{T}}, task::Symbol = :with_morphism) where T + sub(F::FreeMod{T}, O::Vector{<:SubquoModuleElem{T}}; cache_morphism::Bool=false) where T + +Suppose the `ambient_free_module` of the `parent` `M` of the elements `v_i` +in `O` is `F` and `M` is a submodule (i.e. no relations are present). +Then this returns a pair `(I, inc)` consisting of the submodule `I` +generated by the elements in `O` in `F`, together with its inclusion +morphism `inc : I ↪ F`. -Return `S` as a submodule of `F`, where `S` is generated by `O`. -The embedding module of the parent of the elements of `O` must be `F`. -If `task` is set to `:none` or to `:module` return only `S`. -If `task` is set to `:with_morphism` (default option) or to `:both` return also the canonical injection morphism -$S \to F$. -If `task` is set to `:cache_morphism` the morphism is also cached. -If `task` is set to `:only_morphism` return only the morphism. +When `cache_morphism` is set to true, then `inc` will be cached and available +for `transport` and friends. + +If only the submodule itself is desired, use `sub_object` instead. """ -function sub(F::FreeMod{T}, O::Vector{<:SubquoModuleElem{T}}, task::Symbol = :with_morphism) where T +function sub(F::FreeMod{T}, O::Vector{<:SubquoModuleElem{T}}; cache_morphism::Bool=false) where T s = SubquoModule(F, [repres(x) for x = O]) - return sub(F, s, task) + return sub(F, s; cache_morphism) +end + +function sub_object(F::FreeMod{T}, O::Vector{<:SubquoModuleElem{T}}) where T + return SubquoModule(F, [repres(x) for x = O]) end @doc raw""" - sub(F::FreeMod{T}, s::SubquoModule{T}, task::Symbol = :with_morphism) where T + sub(F::FreeMod{T}, M::SubquoModule{T}; cache_morphism::Bool=false) where T -Return `s` as a submodule of `F`, that is the embedding free module of `s` must -be `F` and `s` has no relations. -If `task` is set to `:none` or to `:module` return only `s`. -If `task` is set to `:with_morphism` (default option) or to `:both` return also the canonical injection morphism -$s \to F$. -If `task` is set to `:cache_morphism` the morphism is also cached. -If `task` is set to `:only_morphism` return only the morphism. +Return `M` as a submodule of `F`, together with its inclusion morphism +`inc : M ↪ F`. + +When `cache_morphism` is set to true, then `inc` will be cached and available +for `transport` and friends. + +The `ambient_free_module` of `M` needs to be `F` and `M` has to have no +relations. + +If only the submodule itself is desired, use `sub_object` instead. """ -function sub(F::FreeMod{T}, s::SubquoModule{T}, task::Symbol = :with_morphism) where T +function sub(F::FreeMod{T}, s::SubquoModule{T}; cache_morphism::Bool=false) where T @assert !isdefined(s, :quo) @assert s.F === F emb = hom(s, F, elem_type(F)[repres(x) for x in gens(s)]; check=false) #emb = hom(s, F, [FreeModElem(x.repres.coords, F) for x in gens(s)]) set_attribute!(s, :canonical_inclusion => emb) - return return_sub_wrt_task(s, emb, task) + cache_morphism && register_morphism!(emb) + return s, emb end -@doc raw""" - sub(M::SubquoModule{T}, V::Vector{<:SubquoModuleElem{T}}, task::Symbol = :with_morphism) where T - -Given a vector `V` of (homogeneous) elements of `M`, return the (graded) submodule of `M` generated by these elements. +function sub_object(F::FreeMod{T}, s::SubquoModule{T}) where T + @assert !isdefined(s, :quo) + @assert s.F === F + return s +end -Put more precisely, return this submodule as an object of type `SubquoModule`. +@doc raw""" + sub(M::SubquoModule{T}, V::Vector{<:SubquoModuleElem{T}}; cache_morphism::Bool=false) where T -Additionally, if `N` denotes this object, +Given a vector `V` of (homogeneous) elements of `M`, return the (graded) submodule `I` of `M` generated by these elements +together with its inclusion map `inc : I ↪ M. -- return the inclusion map `N` $\to$ `M` if `task = :with_morphism` (default), -- return and cache the inclusion map `N` $\to$ `M` if `task = :cache_morphism`, -- do none of the above if `task = :none`. +When `cache_morphism` is set to true, then `inc` will be cached and available +for `transport` and friends. -If `task = :only_morphism`, return only the inclusion map. +If only the submodule itself is desired, use `sub_object` instead. """ -function sub(M::SubquoModule{T}, V::Vector{<:SubquoModuleElem{T}}, task::Symbol = :with_morphism) where T +function sub(M::SubquoModule{T}, V::Vector{<:SubquoModuleElem{T}}; cache_morphism::Bool=false) where T @assert all(x -> x.parent === M, V) t = SubquoModule(M.F, FreeModElem[repres(x) for x in V]) if isdefined(M, :quo) @@ -509,24 +570,31 @@ function sub(M::SubquoModule{T}, V::Vector{<:SubquoModuleElem{T}}, task::Symbol t.sum = sum(t.sub, t.quo) end emb = hom(t, M, V; check=false) - set_attribute!(t, :canonical_inclusion => emb) - return return_sub_wrt_task(t, emb, task) + set_attribute!(t, :canonical_inclusion => emb) # TODO: Can this be removed? + cache_morphism && register_morphism!(emb) + return t, emb end -@doc raw""" - sub(M::ModuleFP{T}, V::Vector{<:ModuleFPElem{T}}, task::Symbol = :with_morphism) where T - -Given a vector `V` of (homogeneous) elements of `M`, return the (graded) submodule of `M` generated by these elements. +function sub_object(M::SubquoModule{T}, V::Vector{<:SubquoModuleElem{T}}) where T + @assert all(x -> x.parent === M, V) + t = SubquoModule(M.F, FreeModElem[repres(x) for x in V]) + if isdefined(M, :quo) + t.quo = M.quo + t.sum = sum(t.sub, t.quo) + end + return t +end -Put more precisely, return this submodule as an object of type `SubquoModule`. +@doc raw""" + sub(M::ModuleFP{T}, V::Vector{<:ModuleFPElem{T}}; cache_morphism::Bool=false) where T -Additionally, if `N` denotes this object, +Given a vector `V` of (homogeneous) elements of `M`, return the (graded) submodule `I` of `M` generated by these elements +together with its inclusion map `inc : I ↪ M. -- return the inclusion map `N` $\to$ `M` if `task = :with_morphism` (default), -- return and cache the inclusion map `N` $\to$ `M` if `task = :cache_morphism`, -- do none of the above if `task = :none`. +When `cache_morphism` is set to true, then `inc` will be cached and available +for `transport` and friends. -If `task = :only_morphism`, return only the inclusion map. +If only the submodule itself is desired, use `sub_object` instead. # Examples ```jldoctest @@ -559,10 +627,11 @@ Codomain: Free module of rank 1 over Multivariate polynomial ring in 3 variables over QQ ``` """ -function sub(M::ModuleFP{T}, V::Vector{<:ModuleFPElem{T}}, task::Symbol = :with_morphism) where T +function sub(M::ModuleFP{T}, V::Vector{<:ModuleFPElem{T}}; cache_morphism::Bool=false) where T error("sub is not implemented for the given types.") end +#= @doc raw""" return_sub_wrt_task(M::SubquoModule, emb::SubQuoHom, task::Symbol) @@ -576,82 +645,102 @@ function return_sub_wrt_task(M::SubquoModule, emb::SubQuoHom, task::Symbol) (task == :cache_morphism || task == :both || task == :with_morphism) && return M, emb error("No valid option for task.") end +=# @doc raw""" - quo(F::FreeMod{T}, V::Vector{<:FreeModElem{T}}, task::Symbol = :with_morphism) where T - -Given a vector `V` of (homogeneous) elements of `F`, return the quotient of `F` by the (graded) submodule of `F` which is generated by these elements. - -Put more precisely, return this quotient as an object of type `SubquoModule`. + quo(F::FreeMod{T}, V::Vector{<:FreeModElem{T}}; cache_morphism::Bool=false) where T -Additionally, if `N` denotes this object, +Given a vector `V` of (homogeneous) elements of `F`, return a pair `(M, pr)` consisting +of the quotient `M = F/⟨V⟩` and the projection map `pr : F → M`. -- return the projection map `F` $\to$ `N` if `task = :with_morphism` (default), -- return and cache the projection map `F` $\to$ `N` if `task = :cache_morphism`, -- do none of the above if `task = :none` or `task = :module`. +If one is only interested in the actual object `M`, but not the map, use `quo_object` instead. -If `task = :only_morphism`, return only the projection map. +If `cache_morphism` is set to `true`, the projection is cached and available to `transport` and friends. """ -function quo(F::FreeMod{T}, V::Vector{<:FreeModElem{T}}, task::Symbol = :with_morphism) where T +function quo(F::FreeMod{T}, V::Vector{<:FreeModElem{T}}; cache_morphism::Bool=false) where T S = SubquoModule(F, basis(F)) Q = SubquoModule(S, V) + phi = hom(F, Q, gens(Q), check=false) + cache_morphism && register_morphism!(phi) + return Q, phi +end - return return_quo_wrt_task(F, Q, task) +function quo_object(F::FreeMod{T}, V::Vector{<:FreeModElem{T}}) where T + S = SubquoModule(F, basis(F)) + Q = SubquoModule(S, V) + return Q end @doc raw""" - quo(F::FreeMod{T}, A::MatElem{T}, task::Symbol = :with_morphism) where {T} - -Given a (homogeneous) matrix `A`, return the quotient of `F` by the graded submodule of `F` which is generated by -the rows of `A`. + quo(F::FreeMod{T}, A::MatElem{T}; cache_morphism::Bool=false) where {T} -Put more precisely, return this quotient as an object of type `SubquoModule`. +Given a matrix `A`, interpret the row vectors `v_i` of `A` as elements of `F` +and return a pair `(M, pr)` consisting of the quotient `M = F/I` of `F` by the +submodule `I ⊂ F` generated by the rows of `A`, together with the projection +map `pr : F → M`. -Additionally, if `N` denotes this object, +If one is only interested in the actual object `M`, but not the map, use `quo_object` instead. -- return the projection map `F` $\to$ `N` if `task = :with_morphism` (default), -- return and cache the projection map `F` $\to$ `N` if `task = :cache_morphism`, -- do none of the above if `task = :none` or `task = :module`. - -If `task = :only_morphism`, return only the projection map. +If `cache_morphism` is set to `true`, the projection is cached and available to `transport` and friends. """ -function quo(F::FreeMod{T}, A::MatElem{T}, task::Symbol = :with_morphism) where {T} +function quo(F::FreeMod{T}, A::MatElem{T}; cache_morphism::Bool=false) where {T} E = identity_matrix(base_ring(F), rank(F)) Q = SubquoModule(F, E, A) - return return_quo_wrt_task(F, Q, task) + phi = hom(F, Q, gens(Q), check=false) + cache_morphism && register_morphism!(phi) + return Q, phi +end + +function quo_object(F::FreeMod{T}, A::MatElem{T}) where {T} + E = identity_matrix(base_ring(F), rank(F)) + Q = SubquoModule(F, E, A) + return Q end @doc raw""" - quo(F::FreeMod{T}, O::Vector{<:SubquoModuleElem{T}}, task::Symbol = :with_morphism) where T + quo(F::FreeMod{T}, O::Vector{<:SubquoModuleElem{T}}; cache_morphism::Bool=false) where T +Given a vector `O` of (homogeneous) elements of some submodule `I` of `F`, +return a pair `(M, pr)` consisting of the quotient `M = F/⟨V⟩` and +the projection map `pr : F → M`. + +If one is only interested in the actual object `M`, but not the map, use `quo_object` instead. Compute $F / T$, where $T$ is generated by $O$. -The embedding free module of the parent of the elements of `O` must be `F`. -If `task` is set to `:with_morphism` (default option) or to `:both` return also the -canonical projection morphism $F \to F/T$. -If `task` is set to `:cache_morphism` the morphism is also cached. -If `task` is set to `:only_morphism` return only the morphism. -If `task` is set to `:none` or `:module` return only the module. -""" -function quo(F::FreeMod{T}, O::Vector{<:SubquoModuleElem{T}}, task::Symbol = :with_morphism) where T + +Note that the submodule `I` must have `F` as its `ambient_free_module`. + +If `cache_morphism` is set to `true`, the projection is cached and available to `transport` and friends. +""" +function quo(F::FreeMod{T}, O::Vector{<:SubquoModuleElem{T}}; cache_morphism::Bool=false) where T S = SubquoModule(F, basis(F)) Q = SubquoModule(S, [repres(x) for x = O]) - return return_quo_wrt_task(F, Q, task) + phi = hom(F, Q, gens(Q), check=false) + cache_morphism && register_morphism!(phi) + return Q, phi +end + +function quo_object(F::FreeMod{T}, O::Vector{<:SubquoModuleElem{T}}) where T + S = SubquoModule(F, basis(F)) + Q = SubquoModule(S, [repres(x) for x = O]) + return Q end @doc raw""" - quo(F::SubquoModule{T}, O::Vector{<:FreeModElem{T}}, task::Symbol = :with_morphism) where T + quo(S::SubquoModule{T}, O::Vector{<:FreeModElem{T}}; cache_morphism::Bool=false) where T -Compute $F / T$, where $T$ is generated by $O$. -The elements of `O` must be elements of the embedding free module of `S`. -If `task` is set to `:with_morphism` (default) or to `:both` return also the -canonical projection morphism $F \to F/T$. -If `task` is set to `:cache_morphism` the morphism is also cached. -If `task` is set to `:only_morphism` return only the morphism. -If `task` is set to `:none` or `:module` return only the module. -""" -function quo(F::SubquoModule{T}, O::Vector{<:FreeModElem{T}}, task::Symbol = :with_morphism) where T +Given a vector `V` of (homogeneous) elements of `S`, return a pair `(M, pr)` consisting +of the quotient `M = S/⟨V⟩` and the projection map `pr : S → M`. + +If one is only interested in the actual object `M`, but not the map, use `quo_object` instead. + +Note that the elements of `O` must belong to the `ambient_free_module` of `S` and represent +elements of `S`. + +If `cache_morphism` is set to `true`, the projection is cached and available to `transport` and friends. +""" +function quo(F::SubquoModule{T}, O::Vector{<:FreeModElem{T}}; cache_morphism::Bool=false) where T if length(O) > 0 @assert parent(O[1]) === F.F end @@ -660,45 +749,56 @@ function quo(F::SubquoModule{T}, O::Vector{<:FreeModElem{T}}, task::Symbol = :wi singular_assure(F.quo.gens) s = Singular.Module(base_ring(F.quo.gens.SF), [F.quo.gens.SF(x) for x = [O; oscar_generators(F.quo.gens)]]...) Q = SubquoModule(F.F, singular_generators(F.sub.gens), s) - return return_quo_wrt_task(F, Q, task) + phi = hom(F, Q, gens(Q), check=false) + cache_morphism && register_morphism!(phi) + return Q, phi end Q = SubquoModule(F, O) - return return_quo_wrt_task(F, Q, task) + phi = hom(F, Q, gens(Q), check=false) + cache_morphism && register_morphism!(phi) + return Q, phi end -@doc raw""" - quo(M::SubquoModule{T}, V::Vector{<:SubquoModuleElem{T}}, task::Symbol = :with_morphism) where T - -Given a vector `V` of (homogeneous) elements of `M`, return the quotient of `M` by the (graded) submodule of `M` which is generated by these elements. +function quo_object(F::SubquoModule{T}, O::Vector{<:FreeModElem{T}}) where T + if length(O) > 0 + @assert parent(O[1]) === F.F + end + if isdefined(F, :quo) + oscar_assure(F.quo.gens) + singular_assure(F.quo.gens) + s = Singular.Module(base_ring(F.quo.gens.SF), [F.quo.gens.SF(x) for x = [O; oscar_generators(F.quo.gens)]]...) + return SubquoModule(F.F, singular_generators(F.sub.gens), s) + end + return SubquoModule(F, O) +end -Put more precisely, return the quotient as an object of type `SubquoModule`. +@doc raw""" + quo(S::SubquoModule{T}, V::Vector{<:SubquoModuleElem{T}}; cache_morphism::Bool=false) where T -Additionally, if `N` denotes this object, +Given a vector `V` of (homogeneous) elements of `S`, return a pair `(M, pr)` consisting +of the quotient `M = S/⟨V⟩` and the projection map `pr : S → M`. -- return the projection map `M` $\to$ `N` if `task = :with_morphism` (default), -- return and cache the projection map `M` $\to$ `N` if `task = :cache_morphism`, -- do none of the above if `task = :none` or `task = :module`. +If one is only interested in the actual object `M`, but not the map, use `quo_object` instead. -If `task = :only_morphism`, return only the projection map. +If `cache_morphism` is set to `true`, the projection is cached and available to `transport` and friends. """ -function quo(M::SubquoModule{T}, V::Vector{<:SubquoModuleElem{T}}, task::Symbol = :with_morphism) where T - return quo(M, [repres(x) for x = V], task) +function quo(M::SubquoModule{T}, V::Vector{<:SubquoModuleElem{T}}; cache_morphism::Bool=false) where T + return quo(M, [repres(x) for x = V]; cache_morphism) end -@doc raw""" - quo(M::ModuleFP{T}, V::Vector{<:ModuleFPElem{T}}, task::Symbol = :with_morphism) where T - -Given a vector `V` of (homogeneous) elements of `M`, return the quotient of `M` by the (graded) submodule of `M` which is generated by these elements. +function quo_object(M::SubquoModule{T}, V::Vector{<:SubquoModuleElem{T}}) where T + return quo_object(M, [repres(x) for x = V]) +end -Put more precisely, return the quotient as an object of type `SubquoModule`. +@doc raw""" + quo(M::ModuleFP{T}, V::Vector{<:ModuleFPElem{T}}; cache_morphism::Bool=false) where T -Additionally, if `N` denotes this object, +Given a vector `V` of (homogeneous) elements of `M`, return a pair `(N, pr)` consisting +of the quotient `N = M/⟨V⟩` and the projection map `pr : M → N`. -- return the projection map `M` $\to$ `N` if `task = :with_morphism` (default), -- return and cache the projection map `M` $\to$ `N` if `task = :cache_morphism`, -- do none of the above if `task = :none` or `task = :module`. +If one is only interested in the actual object `M`, but not the map, use `quo_object` instead. -If `task = :only_morphism`, return only the projection map. +If `cache_morphism` is set to `true`, the projection is cached and available to `transport` and friends. # Examples ```jldoctest @@ -733,25 +833,22 @@ by Submodule with 3 generators 3 -> z^4*e[1] ``` """ -function quo(M::ModuleFP{T}, V::Vector{<:ModuleFPElem{T}}, task::Symbol = :with_morphism) where T +function quo(M::ModuleFP{T}, V::Vector{<:ModuleFPElem{T}}; cache_morphism::Bool=false) where T error("quo is not implemented for the given types.") end @doc raw""" - quo(M::SubquoModule{T}, U::SubquoModule{T}, task::Symbol = :with_morphism) where T + quo(M::SubquoModule{T}, U::SubquoModule{T}) where T -Return the quotient $M / U$. +Return a pair `(N, pr)` consisting of the quotient $N = M / U$ together with the projection +map `pr : M → N`. -Put more precisely, if `N` denotes this quotient, return `N` as an object of type `SubquoModule`. Additionally, +If one is only interested in the actual object `N`, but not the map, use `quo_object` instead. -- return the projection map `M` $\to$ `N` if `task = :with_morphism` (default), -- return and cache the projection map `M` $\to$ `N` if `task = :cache_morphism`, -- do none of the above if `task = :none` or `task = :module`. - -If `task = :only_morphism`, return only the projection map. +If `cache_morphism` is set to `true`, the projection is cached and available to `transport` and friends. """ -function quo(M::SubquoModule{T}, U::SubquoModule{T}, task::Symbol = :with_morphism) where T +function quo(M::SubquoModule{T}, U::SubquoModule{T}; cache_morphism::Bool=false) where T if isdefined(M, :quo) && isdefined(U, :quo) F = ambient_free_module(M) @assert F === ambient_free_module(U) @@ -762,51 +859,63 @@ function quo(M::SubquoModule{T}, U::SubquoModule{T}, task::Symbol = :with_morphi @assert !isdefined(M, :quo) && !isdefined(U, :quo) end Q = SubquoModule(M, gens(U.sub)) - return return_quo_wrt_task(M, Q, task) + pr = hom(M, Q, gens(Q), check=false) + cache_morphism && register_morphism!(pr) + return Q, pr end -function quo(M::SubquoModule{T}, U::SubquoModule{T}, task::Symbol = :with_morphism) where {T<:MPolyRingElem} +function quo_object(M::SubquoModule{T}, U::SubquoModule{T}) where T + if isdefined(M, :quo) && isdefined(U, :quo) + F = ambient_free_module(M) + @assert F === ambient_free_module(U) + # We can not assume that the SubModuleOfFreeModule layer is implemented in general, + # so we deflect to the Subquo-layer instead. + @assert SubquoModule(F, relations(M)) == SubquoModule(F, relations(U)) + else + @assert !isdefined(M, :quo) && !isdefined(U, :quo) + end + return SubquoModule(M, gens(U.sub)) +end + +function quo(M::SubquoModule{T}, U::SubquoModule{T}; cache_morphism::Bool=false) where {T<:MPolyRingElem} if isdefined(M, :quo) && isdefined(U, :quo) @assert M.quo == U.quo else @assert !isdefined(M, :quo) && !isdefined(U, :quo) end Q = SubquoModule(M, oscar_generators(U.sub.gens)) - return return_quo_wrt_task(M, Q, task) + pr = hom(M, Q, gens(Q), check=false) + cache_morphism && register_morphism!(pr) + return Q, pr +end + +function quo_object(M::SubquoModule{T}, U::SubquoModule{T}) where {T<:MPolyRingElem} + if isdefined(M, :quo) && isdefined(U, :quo) + @assert M.quo == U.quo + else + @assert !isdefined(M, :quo) && !isdefined(U, :quo) + end + return SubquoModule(M, oscar_generators(U.sub.gens)) end @doc raw""" - quo(F::FreeMod{R}, T::SubquoModule{R}, task::Symbol = :with_morphism) where R + quo(F::FreeMod{R}, T::SubquoModule{R}; cache_morphism::Bool=false) where R + +Return a pair `(N, pr)` consisting of the quotient $N = F / T$ together with the projection +map `pr : F → N`. -Compute $F / T$. -If `task` is set to `:with_morphism` (default option) or to `:both` return also the -canonical projection morphism $F \to F/T$. -If `task` is set to `:cache_morphism` the morphism is also cached. -If `task` is set to `:only_morphism` return only the morphism. -If `task` is set to `:none` or `:module` return only the module. +If one is only interested in the actual object `N`, but not the map, use `quo_object` instead. + +If `cache_morphism` is set to `true`, the projection is cached and available to `transport` and friends. """ -function quo(F::FreeMod{R}, T::SubquoModule{R}, task::Symbol = :with_morphism) where R +function quo(F::FreeMod{R}, T::SubquoModule{R}; cache_morphism::Bool=false) where R @assert !isdefined(T, :quo) - return quo(F, gens(T), task) + return quo(F, gens(T); cache_morphism) end -@doc raw""" - return_quo_wrt_task(M::ModuleFP, Q::ModuleFP, task) - -This helper function returns the module `Q = M / N` for some `N` -along with the canonical projection morphism $M \to Q$ according to the -given `task`. -""" -function return_quo_wrt_task(M::ModuleFP, Q::ModuleFP, task) - if task == :none || task == :module - return Q - else - pro = hom(M, Q, gens(Q); check=false) - pro.generators_map_to_generators = true # Makes evaluation of the inclusion easier - task == :cache_morphism && register_morphism!(pro) - task == :only_morphism && return pro - return Q, pro - end +function quo_object(F::FreeMod{R}, T::SubquoModule{R}) where R + @assert !isdefined(T, :quo) + return quo_object(F, gens(T)) end @doc raw""" @@ -995,7 +1104,7 @@ function is_zero(m::SubquoModuleElem) return (ambient_representative(m) in parent(m).quo) end -function iszero(m::SubquoModuleElem{<:MPolyRingElem}) +function is_zero(m::SubquoModuleElem{<:MPolyRingElem{T}}) where {T<:Union{ZZRingElem, <:FieldElem}} C = parent(m) if !isdefined(C, :quo) return iszero(repres(m)) diff --git a/src/Modules/UngradedModules/Tensor.jl b/src/Modules/UngradedModules/Tensor.jl index 6aaf3781fa9a..99249fe8c9d6 100644 --- a/src/Modules/UngradedModules/Tensor.jl +++ b/src/Modules/UngradedModules/Tensor.jl @@ -126,12 +126,12 @@ function tensor_product(G::ModuleFP...; task::Symbol = :none) corresponding_tuples = map(index_tuple -> Tuple(map(index -> G[index][index_tuple[index]],1:length(index_tuple))), corresponding_tuples_as_indices) generating_tensors::Vector{elem_type(F)} = map(mF, map(tuple -> map(x -> parent(x) isa FreeMod ? x : repres(x), tuple), corresponding_tuples)) - s, emb = sub(F, generating_tensors, :with_morphism) + s, emb = sub(F, generating_tensors) #s, emb = sub(F, vec([mF(x) for x = Base.Iterators.ProductIterator(Tuple(gens(x, ambient_free_module(x)) for x = G))]), :with_morphism) q::Vector{elem_type(F)} = vcat([vec([mF(x) for x = Base.Iterators.ProductIterator(Tuple(i == j ? rels(G[i]) : gens(ambient_free_module(G[i])) for i=1:length(G)))]) for j=1:length(G)]...) local projection_map if length(q) != 0 - s, projection_map = quo(s, q, :with_morphism) + s, projection_map = quo(s, q) end tuples_pure_tensors_dict = IdDict(zip(corresponding_tuples_as_indices, gens(s))) @@ -163,7 +163,7 @@ function tensor_product(G::ModuleFP...; task::Symbol = :none) return s end - return s, MapFromFunc(Hecke.TupleParent(Tuple([zero(g) for g = G])), s, pure) + return s, MapFromFunc(Hecke.TupleParent(Tuple([zero(g) for g = G])), s, pure, decompose_generator) end diff --git a/src/Modules/UngradedModules/flattenings.jl b/src/Modules/UngradedModules/flattenings.jl new file mode 100644 index 000000000000..4d6fe3a78ad4 --- /dev/null +++ b/src/Modules/UngradedModules/flattenings.jl @@ -0,0 +1,17 @@ +######################################################################## +# Rerouting of the module functionality via flattenings +######################################################################## +function submodule_membership(::HasRingFlattening, a::FreeModElem, M::SubModuleOfFreeModule) + F = ambient_free_module(M) + Fb, iso_F = flatten(F) + Mb, iso_M = flatten(M) + return iso_F(a) in Mb +end + +function _kernel(::HasRingFlattening, phi::FreeModuleHom{ModuleType, ModuleType}) where {ModuleType <: FreeMod} + phi_b, iso_dom, iso_cod = flatten(phi) + Kb, inc_Kb = kernel(phi_b) + K, inc_K = sub(domain(phi), inverse(iso_dom).(gens(Kb))) + #TODO: Cache the flattenings of K and inc_K. + return K, inc_K +end diff --git a/src/Modules/flattenings.jl b/src/Modules/flattenings.jl index 5a3fa8bfc969..a7db9778cb17 100644 --- a/src/Modules/flattenings.jl +++ b/src/Modules/flattenings.jl @@ -1,14 +1,19 @@ -### Flattenings of (graded) modules +### Flattenings of (graded) modules over polynomial rings and quotients of polynomial rings function flatten(F::ModuleFP) return flatten(base_ring(F))(F) end -function (flat_map::RingFlattening)(F::ModuleFP{T}) where {T <: MPolyRingElem{<:Union{MPolyRingElem, MPolyQuoRingElem, - MPolyQuoLocRingElem, MPolyLocRingElem}}} +FlattableRingElemType = Union{<:MPolyRingElem{<:Union{MPolyRingElem, MPolyQuoRingElem, + MPolyQuoLocRingElem, MPolyLocRingElem}}, + <:MPolyQuoRingElem{<:MPolyRingElem{<:Union{MPolyRingElem, MPolyQuoRingElem, + MPolyQuoLocRingElem, MPolyLocRingElem}}} + } + +function (flat_map::RingFlattening)(F::FreeMod{T}) where {T <: FlattableRingElemType} if !haskey(flat_counterparts(flat_map), F) - F_flat, iso = change_base_ring(flat_map, F) - iso_inv = hom(F_flat, F, gens(F), inverse(flat_map)) + F_flat, iso = _change_base_ring_and_preserve_gradings(flat_map, F) + iso_inv = hom(F_flat, F, gens(F), inverse(flat_map); check=false) set_attribute!(iso, :inverse, iso_inv) set_attribute!(iso_inv, :inverse, iso) flat_counterparts(flat_map)[F] = (F_flat, iso, iso_inv) @@ -18,10 +23,28 @@ function (flat_map::RingFlattening)(F::ModuleFP{T}) where {T <: MPolyRingElem{<: return F_flat, iso, iso_inv end +function (flat_map::RingFlattening)(M::SubquoModule{T}) where {T <: FlattableRingElemType} + if !haskey(flat_counterparts(flat_map), M) + F = ambient_free_module(M) + F_flat, iso_F, iso_inv_F = flat_map(F) + M_flat = SubquoModule(F_flat, + iso_F.(ambient_representatives_generators(M)), + iso_F.(relations(M)) + ) + iso = hom(M, M_flat, gens(M_flat), flat_map; check=false) + iso_inv = hom(M_flat, M, gens(M), inverse(flat_map); check=false) + set_attribute!(iso, :inverse, iso_inv) + set_attribute!(iso_inv, :inverse, iso) + flat_counterparts(flat_map)[M] = (M_flat, iso, iso_inv) + end + + M_flat, iso, iso_inv = flat_counterparts(flat_map)[M]::Tuple{<:ModuleFP, <:ModuleFPHom, <:ModuleFPHom} + return M_flat, iso, iso_inv +end + function flatten( a::FreeModElem{T} - ) where {T <: MPolyRingElem{<:Union{MPolyRingElem, MPolyQuoRingElem, - MPolyQuoLocRingElem, MPolyLocRingElem}}} + ) where {T <: FlattableRingElemType} F = parent(a) R = base_ring(F) flat_map = flatten(R) @@ -38,29 +61,29 @@ function (flat::RingFlattening)(a::FreeModElem) return flat_counterparts(flat)[a]::FreeModElem end - +### TODO: The following two functions should not be necessary if the module code +# was successfully referring everything to the SubModuleOfFreeModule-layer. +# Once these layers are finally documented, this should be cleaned up function Base.in( a::FreeModElem{T}, M::SubquoModule{T} - ) where {T <: MPolyRingElem{<:Union{MPolyRingElem, MPolyQuoRingElem, - MPolyQuoLocRingElem, MPolyLocRingElem}}} + ) where {T <: FlattableRingElemType} flat = flatten(base_ring(parent(a))) return flat(a) in flat(M)[1] end function coordinates( a::FreeModElem{T}, M::SubquoModule{T} - ) where {T <: MPolyRingElem{<:Union{MPolyRingElem, MPolyQuoRingElem, - MPolyQuoLocRingElem, MPolyLocRingElem}}} + ) where {T <: FlattableRingElemType} flat = flatten(base_ring(parent(a))) c = coordinates(flat(a), flat(M)[1]) + is_zero(c) && return sparse_row(base_ring(a)) return map_entries(inverse(flat), c) end function free_resolution( M::SubquoModule{T} - ) where {T <: MPolyRingElem{<:Union{MPolyRingElem, MPolyQuoRingElem, - MPolyQuoLocRingElem, MPolyLocRingElem}}} + ) where {T <: FlattableRingElemType} flat = flatten(base_ring(M)) M_flat, iso_M, iso_M_inv = flat(M) comp = free_resolution(M_flat) # assuming that this is potentially cached @@ -75,8 +98,8 @@ function free_resolution( @assert F_flat === domain(map(comp, i)) @assert domain(last(isos)) === codomain(map(comp, i)) F, iso_F_inv = _change_base_ring_and_preserve_gradings(inverse(flat), F_flat) - iso_F = hom(F, F_flat, gens(F_flat), flat) - push!(res_maps, hom(F, last(res_obj), last(isos).(map(comp, i).(iso_F.(gens(F)))))) + iso_F = hom(F, F_flat, gens(F_flat), flat; check=false) + push!(res_maps, hom(F, last(res_obj), last(isos).(map(comp, i).(iso_F.(gens(F)))); check=false)) push!(res_obj, F) push!(isos, iso_F_inv) end @@ -88,23 +111,40 @@ function free_resolution( return flat_counterparts(flat)[comp]::FreeResolution end +function (phi::RingFlattening)(f::ModuleFPHom) + if !haskey(flat_counterparts(phi), f) + dom = domain(f) + dom_b, iso_dom, iso_inv_dom = phi(dom) + cod = codomain(f) + cod_b, iso_cod, iso_inv_cod = phi(cod) + fb = hom(dom_b, cod_b, iso_cod.(f.(gens(dom))); check=false) + flat_counterparts(phi)[f] = fb + end + return flat_counterparts(phi)[f]::ModuleFPHom +end + # TODO: We need this special routine, because we can not write a generic # base change method for morphisms of graded rings. See pr #2677 function _change_base_ring_and_preserve_gradings(phi::Any, F::FreeMod) R = base_ring(F) S = parent(phi(zero(R))) - FS = (is_graded(F) ? graded_free_module(S, degree.(gens(F))) : FreeMod(S, ngens(F))) + FS = (is_graded(F) ? graded_free_module(S, [degree(g; check=false) for g in gens(F)]) : FreeMod(S, ngens(F))) FS.S = F.S - return FS, hom(F, FS, gens(FS), phi) + return FS, hom(F, FS, gens(FS), phi; check=false) end -function _change_base_ring_and_preserve_gradings(phi::Any, M::SubquoModule) - R = base_ring(M) - S = parent(phi(zero(R))) - F = ambient_free_module(M) - FF, iso_F = _change_base_ring_and_preserve_gradings(phi, F) - MM = SubquoModule(FF, iso_F.(ambient_representatives_generators(M)), iso_F.(relations(M))) - return MM, hom(M, MM, gens(MM), phi) +function _change_base_ring_and_preserve_gradings( + phi::Any, M::SubquoModule; + ambient_base_change::FreeModuleHom=begin + F = ambient_free_module(M) + FF, iso_F = _change_base_ring_and_preserve_gradings(phi, F) + iso_F + end + ) + FF = codomain(ambient_base_change) + MM = SubquoModule(FF, ambient_base_change.(ambient_representatives_generators(M)), + ambient_base_change.(relations(M))) + return MM, hom(M, MM, gens(MM), phi; check=false) end function _change_base_ring_and_preserve_gradings( @@ -114,7 +154,79 @@ function _change_base_ring_and_preserve_gradings( ) D = codomain(domain_change) C = codomain(codomain_change) - result = hom(D, C, codomain_change.(f.(gens(domain(f))))) + result = hom(D, C, codomain_change.(f.(gens(domain(f)))); check=false) return result end +# SubModuleOfFreeModule needs its own treatment as they differ from the user facing +# modules in that they don't have their own elements and they dont have their own +# homomorphisms. +function (flat_map::RingFlattening)( + I::SubModuleOfFreeModule{T} + ) where {T <: FlattableRingElemType} + if !haskey(flat_counterparts(flat_map), I) + F = ambient_free_module(I) + R = base_ring(I) + flat_map = flatten(R) + Fb, iso_F = flat_map(F) + I_flat = _change_base_ring_and_preserve_gradings(flat_map, I; ambient_base_change=iso_F) + flat_counterparts(flat_map)[I] = I_flat + end + + I_flat = flat_counterparts(flat_map)[I]::SubModuleOfFreeModule + return I_flat +end + +function _change_base_ring_and_preserve_gradings( + phi::Any, M::SubModuleOfFreeModule; + ambient_base_change::FreeModuleHom=begin + F = ambient_free_module(M) + FF, iso_F = _change_base_ring_and_preserve_gradings(phi, F) + iso_F + end + ) + FF = codomain(ambient_base_change) + MM = SubModuleOfFreeModule(FF, ambient_base_change.(gens(M))) + # These modules dont have their own homomorphisms. + # Hence the return signature differs. + return MM +end + +### The magic three functions for the SubModuleOfFreeModule layer for flattenings. +function Base.in( + a::FreeModElem{T}, M::SubModuleOfFreeModule{T} + ) where {T <: FlattableRingElemType} + flat = flatten(base_ring(parent(a))) + return flat(a) in flat(M) +end + +function coordinates( + a::FreeModElem{T}, M::SubModuleOfFreeModule{T} + ) where {T <: FlattableRingElemType} + flat = flatten(base_ring(parent(a))) + c = coordinates(flat(a), flat(M)) + is_zero(c) && return sparse_row(base_ring(a)) + return map_entries(inverse(flat), c) +end + +function kernel( + phi::FreeModuleHom{ + <:FreeMod{<:FlattableRingElemType}, + <:FreeMod{<:FlattableRingElemType}, + Nothing + } + ) + R = base_ring(domain(phi)) + flat_map = flatten(R) + dom_flat, iso_dom, iso_dom_inv = flat_map(domain(phi)) + cod_flat, iso_cod, iso_cod_inv = flat_map(codomain(phi)) + phi_b = flat_map(phi) + Kb, inc_Kb = kernel(phi_b) + K, inc_K = sub(domain(phi), iso_dom_inv.(ambient_representatives_generators(Kb))) + iso_K = hom(K, Kb, gens(Kb), flat_map; check=false) + iso_inv_K = hom(Kb, K, gens(K), inverse(flat_map); check=false) + flat_counterparts(flat_map)[K] = Kb, iso_K, iso_inv_K + flat_counterparts(flat_map)[inc_K] = inc_Kb + return K, inc_K +end + diff --git a/src/Modules/hilbert.jl b/src/Modules/hilbert.jl index ded9486e2609..f5c60a0b301f 100644 --- a/src/Modules/hilbert.jl +++ b/src/Modules/hilbert.jl @@ -18,7 +18,7 @@ function HSNum_module(SubM::SubquoModule{T}, HSRing::Ring, backend::Symbol=:Abbo P = base_ring(C.quo); # short-cut for module R^0 (to avoid problems with empty sum below) if iszero(r) - return multi_hilbert_series(quo(P,ideal(P,[1]))[1]; parent=HSRing, backend=backend)[1][1] + return multi_hilbert_series(quo(P,ideal(P, one(P)))[1]; parent=HSRing, backend=backend)[1][1] end GensLM = gens(LM); L = [[] for _ in 1:r]; # L[k] will be list of monomial gens for k-th coord @@ -119,7 +119,7 @@ end function multi_hilbert_series(F::FreeMod{T}; parent::Union{Nothing,Ring} = nothing, backend::Symbol = :Abbott) where T <: MPolyRingElem @req is_positively_graded(base_ring(F)) "ring must be positively graded" - return multi_hilbert_series(sub(F,gens(F))[1]; parent=parent, backend=backend) + return multi_hilbert_series(sub_object(F,gens(F)); parent=parent, backend=backend) end @@ -174,5 +174,5 @@ function hilbert_series(F::FreeMod{T}; parent::Union{Nothing,Ring} = nothing, ba if parent === nothing parent, _ = laurent_polynomial_ring(ZZ, :t) end - return hilbert_series(sub(F,gens(F))[1]; parent=parent, backend=backend) + return hilbert_series(sub_object(F,gens(F)); parent=parent, backend=backend) end diff --git a/src/Modules/homological-algebra.jl b/src/Modules/homological-algebra.jl index a920971ee39c..0f72cde55219 100644 --- a/src/Modules/homological-algebra.jl +++ b/src/Modules/homological-algebra.jl @@ -30,7 +30,7 @@ julia> U = matrix([x^3-y^2 o; o x^3-y^2; -x^2 y; -y x]) [ -x^2 y] [ -y x] -julia> M = quo(F,U)[1] +julia> M = quo_object(F,U) Subquotient of Submodule with 2 generators 1 -> e[1] 2 -> e[2] @@ -105,7 +105,7 @@ julia> U = matrix([x^3-y^2 o; o x^3-y^2; -x^2 y; -y x]) [ -x^2 y] [ -y x] -julia> M = quo(F,U)[1] +julia> M = quo_object(F,U) Subquotient of Submodule with 2 generators 1 -> e[1] 2 -> e[2] @@ -162,7 +162,7 @@ julia> U = matrix([x^3-y^2 o; o x^3-y^2; -x^2 y; -y x]) [ -x^2 y] [ -y x] -julia> M = quo(F,U)[1] +julia> M = quo_object(F,U) Subquotient of Submodule with 2 generators 1 -> e[1] 2 -> e[2] diff --git a/src/Modules/local_rings.jl b/src/Modules/local_rings.jl index bcb6856e6d99..65758327da2b 100644 --- a/src/Modules/local_rings.jl +++ b/src/Modules/local_rings.jl @@ -12,7 +12,7 @@ end R = base_ring(M) P = prime_ideal(inverted_set(R)) F = FreeMod(R, 1) - N, _ = quo(F, (R(P)*F)[1]) + N = quo_object(F, (R(P)*F)[1]) k = 0 MM = M p = identity_map(M) diff --git a/src/Modules/mpoly-localizations.jl b/src/Modules/mpoly-localizations.jl index 1ae10fdb66c0..f785c031ef70 100644 --- a/src/Modules/mpoly-localizations.jl +++ b/src/Modules/mpoly-localizations.jl @@ -170,7 +170,7 @@ the shift map ``Φ : R → R`` which is moving the point of ``𝔪`` to the orig Fb, F_shift, F_backshift = shifted_module(ambient_free_module(M)) Mp_sub = F_shift.(ambient_representatives_generators(Mp)) Mp_rel = F_shift.(relations(Mp)) - result = quo(sub(Fb, Mp_sub)[1], Mp_rel)[1] + result = quo_object(sub_object(Fb, Mp_sub), Mp_rel) a = hom(Mp, result, gens(result), shift) b = hom(result, Mp, gens(Mp), backshift) return result, a, b diff --git a/src/Modules/mpolyquo.jl b/src/Modules/mpolyquo.jl index 903a1705b01a..b38e939155e0 100644 --- a/src/Modules/mpolyquo.jl +++ b/src/Modules/mpolyquo.jl @@ -44,6 +44,7 @@ end # Methods which should not be necessary, but the stuff doesn't work, # # unless we implement them. # ######################################################################## +#= @attr function kernel( f::FreeModuleHom{DomainType, CodomainType} ) where { @@ -63,6 +64,7 @@ end KK, inc2 = sub(domain(f), tr.(gens(K))) return KK, inc2 end +=# function coordinates( v::FreeModElem{T}, diff --git a/src/Rings/MPolyQuo.jl b/src/Rings/MPolyQuo.jl index 926e475b024e..239d7985472e 100644 --- a/src/Rings/MPolyQuo.jl +++ b/src/Rings/MPolyQuo.jl @@ -1331,20 +1331,25 @@ julia> typeof(degree(Int, f)) Int64 ``` """ -function degree(a::MPolyQuoRingElem{<:MPolyDecRingElem}) +function degree(a::MPolyQuoRingElem{<:MPolyDecRingElem}; check::Bool=true) simplify(a) @req !iszero(a) "Element must be non-zero" - return degree(a.f) + return degree(a.f; check) end -function degree(::Type{Int}, a::MPolyQuoRingElem{<:MPolyDecRingElem}) +function _degree_fast(a::MPolyQuoRingElem{<:MPolyDecRingElem}) + simplify(a) + @req !iszero(a) "Element must be non-zero" + return _degree_fast(a.f) +end +function degree(::Type{Int}, a::MPolyQuoRingElem{<:MPolyDecRingElem}; check::Bool=true) @assert is_z_graded(base_ring(parent(a))) - return Int(degree(a)[1]) + return Int(degree(a; check)[1]) end -function degree(::Type{Vector{Int}}, a::MPolyQuoRingElem{<:MPolyDecRingElem}) +function degree(::Type{Vector{Int}}, a::MPolyQuoRingElem{<:MPolyDecRingElem}; check::Bool=true) @assert is_zm_graded((base_ring(parent(a)))) - d = degree(a) + d = degree(a; check) return Int[d[i] for i=1:ngens(parent(d))] end diff --git a/src/Rings/ReesAlgebra.jl b/src/Rings/ReesAlgebra.jl index ebada7abda6c..855abf45bdd7 100644 --- a/src/Rings/ReesAlgebra.jl +++ b/src/Rings/ReesAlgebra.jl @@ -105,11 +105,11 @@ end function _versal_morphism_to_free_module(M::SubquoModule) R = base_ring(M) R1 = FreeMod(R, 1) - M_double_dual, psi = double_dual(M, cod=R1) + M_double_dual, psi = double_dual(M, codomain=R1) M_dual = domain(element_to_homomorphism(zero(M_double_dual))) pres_M_dual = presentation(M_dual)::ComplexOfMorphisms g = map(pres_M_dual, 0) # The projection of a free module onto M_dual - g_dual = dual(g, cod=R1, codomain_dual=M_double_dual) + g_dual = dual(g, codomain=R1, codomain_dual=M_double_dual) return compose(psi, g_dual) end diff --git a/src/Rings/mpoly-graded.jl b/src/Rings/mpoly-graded.jl index 7eae9699e350..de98e5464319 100644 --- a/src/Rings/mpoly-graded.jl +++ b/src/Rings/mpoly-graded.jl @@ -346,7 +346,7 @@ false return true end end - try + try homogeneous_component(R, zero(G)) catch e if e isa ArgumentError && e.msg == "Polyhedron not bounded" @@ -894,7 +894,9 @@ julia> typeof(degree(Int, f)) Int64 ``` """ -function degree(a::MPolyDecRingElem) +function degree(a::MPolyDecRingElem; check::Bool=true) + !check && !is_filtered(parent(a)) && return _degree_fast(a) + # TODO: Also provide a fast track for the filtered case. @req !iszero(a) "Element must be non-zero" W = parent(a) w = W.D[0] @@ -917,14 +919,24 @@ function degree(a::MPolyDecRingElem) return w end -function degree(::Type{Int}, a::MPolyDecRingElem) +function _degree_fast(a::MPolyDecRingElem) + f = forget_grading(a) + w = parent(a).d + z = zero(grading_group(parent(a))) + is_zero(f) && return z + for (c, e) in zip(coefficients(f), exponents(f)) + !iszero(c) && return sum(b*w[i] for (i, b) in enumerate(e); init=z) + end +end + +function degree(::Type{Int}, a::MPolyDecRingElem; check::Bool=true) @assert is_z_graded(parent(a)) - return Int(degree(a)[1]) + return Int(degree(a; check)[1]) end -function degree(::Type{Vector{Int}}, a::MPolyDecRingElem) +function degree(::Type{Vector{Int}}, a::MPolyDecRingElem); check::Bool=true @assert is_zm_graded(parent(a)) - d = degree(a) + d = degree(a; check) return Int[d[i] for i=1:ngens(parent(d))] end @@ -1229,7 +1241,7 @@ function monomial_basis(W::MPolyDecRing, d::FinGenAbGroupElem) #Ax = b, Cx >= 0 C = identity_matrix(FlintZZ, ngens(W)) A = reduce(vcat, [x.coeff for x = W.d]) - k = solve_mixed(transpose(A), transpose(d.coeff), C) + k = solve_mixed(transpose(A), transpose(d.coeff), C) for ee = 1:nrows(k) e = k[ee, :] a = MPolyBuildCtx(forget_decoration(W)) @@ -1252,7 +1264,7 @@ function monomial_basis(R::MPolyDecRing, g::IntegerUnion) end @doc raw""" - homogeneous_component(R::MPolyDecRing, g::FinGenAbGroupElem) + homogeneous_component(R::MPolyDecRing, g::FinGenAbGroupElem) Given a polynomial ring `R` over a field which is graded by a free group of type `FinGenAbGroup`, and given an element `g` of that group, @@ -1392,7 +1404,7 @@ end ########################################### # needs re-thought -function (W::MPolyDecRing)(m::Generic.FreeModuleElem) +function (W::MPolyDecRing)(m::Generic.FreeModuleElem) h = has_relshp(parent(m), W) if h !== nothing return h(m) @@ -1439,11 +1451,11 @@ mutable struct HilbertData W = R.d W = [Int(W[i][1]) for i = 1:ngens(R)] - + @req minimum(W) > 0 "The weights must be positive" @req coefficient_ring(R) isa AbstractAlgebra.Field "The coefficient ring must be a field" @req all(is_homogeneous, gens(I)) "The generators of the ideal must be homogeneous" - + G = groebner_assure(I) h = Singular.hilbert_series(G.S, W) return new(h, W, I) @@ -1470,13 +1482,13 @@ end function hilbert_polynomial(H::HilbertData) @req all(isone, H.weights) "All weights must be 1" - + q, dn = hilbert_series_reduced(H) a = QQFieldElem[] nf = QQFieldElem(1) d = degree(dn)-1 for i=1:d+1 - push!(a, q(1)//nf) + push!(a, q(1)//nf) nf *= i q = derivative(q) end @@ -1494,7 +1506,7 @@ end function Oscar.degree(H::HilbertData) @req all(isone, H.weights) "All weights must be 1" - + P = hilbert_polynomial(H) if iszero(P) q, _ = hilbert_series_reduced(H) diff --git a/src/Rings/mpoly-localizations.jl b/src/Rings/mpoly-localizations.jl index 0f53b1b8a5a3..60ec70c6e97e 100644 --- a/src/Rings/mpoly-localizations.jl +++ b/src/Rings/mpoly-localizations.jl @@ -3213,8 +3213,20 @@ function grading_group(L::MPolyLocRing{<:Ring, <:RingElem, <:MPolyDecRing}) return grading_group(base_ring(L)) end -function degree(a::MPolyLocRingElem{<:Ring, <:RingElem, <:MPolyDecRing}) - return degree(numerator(a)) - degree(denominator(a)) +function degree(a::MPolyLocRingElem{<:Ring, <:RingElem, <:MPolyDecRing}; check::Bool=true) + return degree(numerator(a); check) - degree(denominator(a); check) +end + +function degree(::Type{Int}, a::MPolyLocRingElem{<:Ring, <:RingElem, <:MPolyDecRing}; check::Bool=true) + return degree(Int, numerator(a); check) - degree(Int, denominator(a); check) +end + +function degree(::Type{Vector{Int}}, a::MPolyLocRingElem{<:Ring, <:RingElem, <:MPolyDecRing}; check::Bool=true) + return degree(Vector{Int}, numerator(a); check) - degree(Vector{Int}, denominator(a); check) +end + +function _degree_fast(a::MPolyLocRingElem{<:Ring, <:RingElem, <:MPolyDecRing}) + return _degree_fast(numerator(a)) - _degree_fast(denominator(a)) end function is_homogeneous(a::MPolyLocRingElem{<:Ring, <:RingElem, <:MPolyDecRing}) diff --git a/src/Rings/mpolyquo-localizations.jl b/src/Rings/mpolyquo-localizations.jl index e5b88af17666..bae23f57a234 100644 --- a/src/Rings/mpolyquo-localizations.jl +++ b/src/Rings/mpolyquo-localizations.jl @@ -2296,8 +2296,20 @@ function grading_group(L::MPolyQuoLocRing{<:Ring, <:RingElem, <:MPolyDecRing}) return grading_group(base_ring(L)) end -function degree(a::MPolyQuoLocRingElem{<:Ring, <:RingElem, <:MPolyDecRing}) - return degree(numerator(a)) - degree(denominator(a)) +function degree(a::MPolyQuoLocRingElem{<:Ring, <:RingElem, <:MPolyDecRing}; check::Bool=true) + return degree(numerator(a); check) - degree(denominator(a); check) +end + +function degree(::Type{Int}, a::MPolyQuoLocRingElem{<:Ring, <:RingElem, <:MPolyDecRing}; check::Bool=true) + return degree(Int, numerator(a); check) - degree(Int, denominator(a); check) +end + +function degree(::Type{Vector{Int}}, a::MPolyQuoLocRingElem{<:Ring, <:RingElem, <:MPolyDecRing}; check::Bool=true) + return degree(Vector{Int}, numerator(a); check) - degree(Vector{Int}, denominator(a); check) +end + +function _degree_fast(a::MPolyQuoLocRingElem{<:Ring, <:RingElem, <:MPolyDecRing}) + return _degree_fast(numerator(a)) - _degree_fast(denominator(a)) end function is_homogeneous(a::MPolyQuoLocRingElem{<:Ring, <:RingElem, <:MPolyDecRing}) diff --git a/src/exports.jl b/src/exports.jl index 74c4da894801..d326c628d8e4 100644 --- a/src/exports.jl +++ b/src/exports.jl @@ -1217,6 +1217,7 @@ export pyramid export quadratic_form export quaternion_group export quo +export quo_object export quotient export quotient_ring_as_module export radical @@ -1395,6 +1396,7 @@ export structure_sheaf export sub export subalgebra_membership export subalgebra_membership_homogeneous +export sub_object export subgroup_classes export subquo_type export subquotient diff --git a/test/Modules/ModulesGraded.jl b/test/Modules/ModulesGraded.jl index 4613b223b53e..4ddb4a75f3b1 100644 --- a/test/Modules/ModulesGraded.jl +++ b/test/Modules/ModulesGraded.jl @@ -166,7 +166,10 @@ end B = Rg[x^2; y^3; z^4] M = SubquoModule(F, A, B) N = M; - V = [y^2*N[1], x^2*N[2]] + # Problem with the previous test: V[2] is zero and + # the homomorphism is hence not graded. + # V = [y^2*N[1], x^2*N[2]] + V = [y^2*N[1], x*y*N[2]] a = hom(M, N, V); @test is_graded(a) @test degree(a) == 2*Z[1] @@ -179,10 +182,11 @@ end B = Rg[x^2; y^3; z^4] M = SubquoModule(F, A, B) N = M; - V = [y^2*N[1], x^2*N[2]] + #V = [y^2*N[1], x^2*N[2]] + V = [y^2*N[1], x*y*N[2]] a = hom(M, N, V); K, incl = kernel(a); - @test ngens(K) == 3 + @test ngens(K) == 2 @test domain(incl) == K end @@ -252,10 +256,12 @@ end B = Rg[x^2; y^3; z^4] M = SubquoModule(F, A, B) N = M - V = [y^2*N[1], x^2*N[2]] + # V = [y^2*N[1], x^2*N[2]] + V = [y^2*N[1], x*y*N[2]] a = hom(M, N, V) @test is_welldefined(a) - W = Rg[y^2 0; 0 x^2] + #W = Rg[y^2 0; 0 x^2] + W = Rg[y^2 0; 0 x*y] b = hom(M, N, W) @test a == b @test nrows(matrix(a)) == 2 @@ -383,7 +389,7 @@ end @test degrees_of_generators(H) == [Z[0], Z[0]] @test degrees_of_generators(H.quo) == [Z[1], 2*Z[1], Z[1], 2*Z[1]] @test is_homogeneous(f(H[1])) - a = element_to_homomorphism(x*H[1]+y*H[2]) + a = element_to_homomorphism(x*H[1] + y*H[2]) @test matrix(a) == Rg[x 0; 0 y] W = [x*M[1], y*M[2]]; a = hom(M, M, W); @@ -398,17 +404,17 @@ end Z = grading_group(Rg) F1 = graded_free_module(Rg, 1) F2 = graded_free_module(Rg, 2) - F2v, ev = dual(F2, cod=F1) + F2v, ev = dual(F2, codomain=F1) @test ev(F2v[1])(F2[1]) == F1[1] FF, psi = double_dual(F2) @test degrees_of_generators(FF) == [Z[0], Z[0]] @test is_injective(psi) M, inc = sub(F2, [x*F2[1], y*F2[1]]) F1 = graded_free_module(Rg, 1) - Mv, ev = dual(M, cod=F1) + Mv, ev = dual(M, codomain=F1) @test degrees_of_generators(Mv) == [Z[0]] @test ev(Mv[1])(M[1]) == x*F1[1] - Mvv, psi = double_dual(M, cod=F1) + Mvv, psi = double_dual(M, codomain=F1) @test matrix(psi) == Rg[x; y] F = graded_free_module(Rg, 2); V = [x*F[1], y^2*F[2]]; @@ -444,9 +450,7 @@ end B2 = Rg[y^3;] F1 = graded_free_module(Rg, 1) M2 = SubquoModule(F1, A2,B2) - SQ = hom(M1,M2)[1] - v = gens(SQ)[1] - @test v == homomorphism_to_element(SQ, element_to_homomorphism(v)) + SQ = hom(M1,M2)[1] # This is the zero module end @testset "Multiplication morphism" begin @@ -875,14 +879,14 @@ end M1_to_N2 = iszero(H12) ? SubQuoHom(M1,N2,zero_matrix(R,3,2)) : element_to_homomorphism(H12[1]) M2_to_N1 = iszero(H21) ? SubQuoHom(M2,N1,zero_matrix(R,2,3)) : element_to_homomorphism(x^3*H21[1]) M2_to_N2 = SubQuoHom(M2, N2, [0*N2[1],0*N2[1],0*N2[1]]) - @assert degree(M1_to_N1) == Z[0] - @assert degree(M1_to_N2) == 6*Z[1] - @assert degree(M2_to_N1) == 6*Z[1] - @assert degree(M2_to_N2) == Z[0] - @assert is_welldefined(M1_to_N1) - @assert is_welldefined(M1_to_N2) - @assert is_welldefined(M2_to_N1) - @assert is_welldefined(M2_to_N2) + @test degree(M1_to_N1) == Z[0] + @test degree(M1_to_N2) == 6*Z[1] + @test degree(M2_to_N1) == 6*Z[1] + @test degree(M2_to_N2) == Z[0] + @test is_welldefined(M1_to_N1) + @test is_welldefined(M1_to_N2) + @test is_welldefined(M2_to_N1) + @test is_welldefined(M2_to_N2) phi = hom_product(prod_M,prod_N,[M1_to_N1 M1_to_N2; M2_to_N1 M2_to_N2]) @test degree(phi) == 6*Z[1] diff --git a/test/Modules/UngradedModules.jl b/test/Modules/UngradedModules.jl index 89d3be5929b6..22d20853d51b 100644 --- a/test/Modules/UngradedModules.jl +++ b/test/Modules/UngradedModules.jl @@ -21,13 +21,14 @@ function randpoly(R::Oscar.Ring,coeffs=0:9,max_exp=4,max_terms=8) end @testset "Modules: Constructors" begin + Oscar.set_seed!(235) R, (x,y,z) = polynomial_ring(QQ, ["x", "y", "z"]) F = FreeMod(R,3) v = [x, x^2*y+z^3, R(-1)] @test v == Vector(F(v)) - M = sub(F, [F(v), F([z, R(1), R(0)])], :none) - N = quo(M, [SubquoModuleElem([x+y^2, y^3*z^2+1], M)], :none) + M = sub_object(F, [F(v), F([z, R(1), R(0)])]) + N = quo_object(M, [SubquoModuleElem([x+y^2, y^3*z^2+1], M)]) AN, ai = ambient_module(N, :with_morphism) @test AN.quo === N.quo for i=1:ngens(N) @@ -57,6 +58,7 @@ end end @testset "Modules: Simplify elements of subquotients" begin + Oscar.set_seed!(235) R, (x,y,z) = polynomial_ring(QQ, ["x", "y", "z"]) F1 = free_module(R, 3) F2 = free_module(R, 1) @@ -71,6 +73,7 @@ end end @testset "Intersection of modules" begin + Oscar.set_seed!(235) R, (x, y, z) = polynomial_ring(QQ, ["x", "y", "z"]) A1 = R[x y; @@ -126,6 +129,7 @@ end end @testset "Presentation" begin + Oscar.set_seed!(235) # over Integers R, (x,y,z) = polynomial_ring(ZZ, ["x", "y", "z"]) @@ -269,6 +273,7 @@ end end @testset "Prune With Map" begin + Oscar.set_seed!(235) # ungraded R, (x, y) = polynomial_ring(QQ, ["x", "y"]) M = SubquoModule(identity_matrix(R, 3), R[1 x x]) @@ -292,6 +297,7 @@ end end @testset "Ext, Tor" begin + Oscar.set_seed!(235) # These tests are only meant to check that the ext and tor function don't throw any error # These tests don't check the correctness of ext and tor @@ -321,7 +327,8 @@ end E1 = ext(Q, M, 1) E2 = ext(Q, M, 2) @test is_canonically_isomorphic(present_as_cokernel(E0), M_coker) - @test is_canonically_isomorphic(E1, M_coker) + # test was dependend on internal design which has changed + #@test is_canonically_isomorphic(E1, M_coker) @test iszero(E2) E0 = ext(M, Q, 0) E1 = ext(M, Q, 1) @@ -336,6 +343,7 @@ end end @testset "Gröbner bases" begin + Oscar.set_seed!(235) R, (x,y) = polynomial_ring(QQ, ["x", "y"]) F = FreeMod(R, 1) @@ -390,6 +398,7 @@ end @testset "Test kernel" begin + Oscar.set_seed!(235) # over Integers R, (x,y,z) = polynomial_ring(ZZ, ["x", "y", "z"]) @@ -434,6 +443,7 @@ end end @testset "iszero(SubquoModule)" begin + Oscar.set_seed!(235) R, (x,y) = polynomial_ring(QQ, ["x", "y"]) A = R[x^2+2*x*y y^2*x-2*x^2*y;-y x*y] B = R[x^2 y^2*x;-y x*y] @@ -447,6 +457,7 @@ end end @testset "simplify subquotient" begin + Oscar.set_seed!(235) R, (x,y) = polynomial_ring(QQ, ["x", "y"]) A1 = R[x*y R(0)] B1 = R[R(0) R(1)] @@ -522,12 +533,13 @@ end end @testset "quotient modules" begin + Oscar.set_seed!(235) R, (x,y) = polynomial_ring(QQ, ["x", "y"]) F3 = FreeMod(R,3) M1 = SubquoModule(F3,R[x^2*y^3-x*y y^3 x^2*y; 2*x^2 3*y^2*x 4],R[x^4*y^5 x*y y^4]) N1 = SubquoModule(F3,R[x^4*y^5-4*x^2 x*y-6*y^2*x y^4-8],R[x^4*y^5 x*y y^4]) - Q1,p1 = quo(M1,N1,:cache_morphism) + Q1,p1 = quo(M1,N1, cache_morphism=true) @test Q1 == SubquoModule(F3,R[x^2*y^3-x*y y^3 x^2*y],R[x^4*y^5 x*y y^4; x^4*y^5-4*x^2 -6*x*y^2+x*y y^4-8]) @test p1 == find_morphism(M1, Q1) @@ -539,7 +551,7 @@ end F2 = FreeMod(R,2) M2 = SubquoModule(F2,R[x*y^2+x*y x^3+2*y; x^4 y^3; x^2*y^2+y^2 x*y],R[x^3-y^2 y^4-x-y]) elems = [SubquoModuleElem(sparse_row(R[x*y -x*y^2 x*y]), M2), SubquoModuleElem(sparse_row(R[x R(0) R(-1)]), M2)] - Q2,p2 = quo(M2,elems,:cache_morphism) + Q2,p2 = quo(M2,elems, cache_morphism=true) @test Q2 == SubquoModule(F2,R[x*y^2+x*y x^3+2*y; x^4 y^3; x^2*y^2+y^2 x*y], R[x^3-y^2 y^4-x-y; x^2*y^3+x^2*y^2+x^3*y^3+x*y^3-x^5*y^2 x^4*y+2*x*y^2-x*y^5+x^2*y^2; x^2*y-y^2 x^4+x*y]) @@ -551,9 +563,9 @@ end M3 = SubquoModule(F3,R[x^2*y+13*x*y+2x-1 x^4 2*x*y; y^4 3*x -1],R[y^2 x^3 y^2]) #N3 = SubquoModule(F3,R[x^2*y+13*x*y+2x-1-x*y^2 0 x^4-x*y^2; y^4-x*y^2 3*x-x^4 -1-x*y^2],R[2*y^2 2*x^3 2*y^2]) N3 = SubquoModule(F3,R[x^2*y+13*x*y+2x-1-x*y^2 0 2*x*y-x*y^2; y^4-x*y^2 3*x-x^4 -1-x*y^2],R[2*y^2 2*x^3 2*y^2]) - Q3,p3 = quo(M3,N3,:cache_morphism) + Q3,p3 = quo(M3,N3, cache_morphism=true) - @test iszero(quo(M3,M3, :none)) + @test iszero(quo_object(M3,M3)) @test iszero(Q3) for k=1:5 elem = SubquoModuleElem(sparse_row(matrix([randpoly(R) for _=1:1,i=1:1])), M3) @@ -563,11 +575,12 @@ end end @testset "submodules" begin + Oscar.set_seed!(235) R, (x,y) = polynomial_ring(QQ, ["x", "y"]) F2 = FreeMod(R,2) M1 = SubquoModule(F2,R[x^2*y+x*y x*y^2-x; x+x*y^2 y^3],R[x^2 y^3-x]) - S1,i1 = sub(M1, [M1(sparse_row(R[1 1])),M1(sparse_row(R[y -x]))], :cache_morphism) + S1,i1 = sub(M1, [M1(sparse_row(R[1 1])),M1(sparse_row(R[y -x]))], cache_morphism=true) @test S1 == SubquoModule(F2,R[x*y^2+x^3-x^2 x*y^3-x*y-x^2; x^2*y+x*y^2+x*y-x^2+x x*y^2],R[x^2 y^3-x]) @test i1 == find_morphism(S1, M1) @@ -577,7 +590,7 @@ end end M2 = SubquoModule(F2,R[x*y^2+x*y x^3+2*y; x^4 y^3; x^2*y^2+y^2 x*y],R[x^3-y^2 y^4-x-y]) - S2,i2 = sub(M2,[M2(sparse_row(R[x*y -x*y^2 x*y])),M2(sparse_row(R[x 0 -1]))], :cache_morphism) + S2,i2 = sub(M2,[M2(sparse_row(R[x*y -x*y^2 x*y])),M2(sparse_row(R[x 0 -1]))], cache_morphism=true) @test S2 == SubquoModule(F2,R[x^2*y^3+x^2*y^2+x^3*y^3+x*y^3-x^5*y^2 x^4*y+2*x*y^2-x*y^5+x^2*y^2; x^2*y-y^2 x^4+x*y],R[x^3-y^2 y^4-x-y]) @test i2 == find_morphisms(S2, M2)[1] @@ -588,7 +601,7 @@ end M3 = SubquoModule(F2,R[x*y^2 x^3+2*y; x^4 y^3; x*y+y^2 x*y],R[x^3-y^2 y^4-x-y]) elems = [M3(sparse_row(R[0 6 0])),M3(sparse_row(R[9 0 -x])),M3(sparse_row(R[0 0 -42]))] - S3,i3 = sub(M3,elems,:cache_morphism) + S3,i3 = sub(M3,elems; cache_morphism=true) @test S3 == M3 for k=1:5 @@ -598,6 +611,7 @@ end end @testset "Hom module" begin + Oscar.set_seed!(235) R, (x0,x1,x2,x3,x4,x5) = polynomial_ring(QQ, ["x0", "x1", "x2", "x3", "x4", "x5"]) f1= transpose(R[-x2*x3 -x4*x5 0; x0*x1 0 -x4*x5; 0 x0*x1 -x2*x3]) g1 = transpose(R[x0*x1 x2*x3 x4*x5]) @@ -649,7 +663,7 @@ end A2 = R[x;] B2 = R[y^3;] M2 = SubquoModule(A2,B2) - SQ = hom(M1,M2,:matrices)[1] + SQ = hom(M1,M2, algorithm=:matrices)[1] for v in gens(SQ) @test v == homomorphism_to_element(SQ, element_to_homomorphism(v)) end @@ -680,7 +694,7 @@ end B2 = matrix([randpoly(R,0:15,2,1) for i=1:1,j=1:2]) N = SubquoModule(A1,B1) M = SubquoModule(A2,B2) - HomNM = k <= 5 ? hom(N,M)[1] : hom(N,M,:matrices)[1] + HomNM = k <= 5 ? hom(N,M)[1] : hom(N,M, algorithm=:matrices)[1] for l=1:10 v = sparse_row(matrix([randpoly(R,0:15,2,1) for _=1:1, j=1:AbstractAlgebra.ngens(HomNM)])) H = HomNM(v) @@ -691,6 +705,7 @@ end end @testset "tensoring morphisms" begin + Oscar.set_seed!(235) R, (x,y,z) = polynomial_ring(QQ, ["x", "y", "z"]) F2 = FreeMod(R,2) @@ -734,6 +749,7 @@ end end @testset "direct product" begin + Oscar.set_seed!(235) R, (x,y,z) = polynomial_ring(QQ, ["x", "y", "z"]) F2 = FreeMod(R,2) @@ -834,6 +850,7 @@ end end @testset "Coordinates (lift)" begin + Oscar.set_seed!(235) Z3, a = finite_field(3,1,"a") R, (x,y) = polynomial_ring(Z3, ["x", "y"]) coeffs = [Z3(i) for i=0:1] @@ -857,6 +874,7 @@ end end @testset "module homomorphisms" begin + Oscar.set_seed!(235) R, (x,y) = polynomial_ring(QQ, ["x", "y"]) F3 = FreeMod(R,3) @@ -886,7 +904,7 @@ end KerH,iKerH = kernel(H) ImH,iImH = image(H) - NmodKerH, pNmodKerH = quo(N,KerH, :cache_morphism) + NmodKerH, pNmodKerH = quo(N,KerH, cache_morphism=true) Hbar = SubQuoHom(NmodKerH,M,matrix(H)) Hbar = restrict_codomain(Hbar,ImH) # induced map N/KerH --> ImH @@ -914,7 +932,7 @@ end #2) H: N --> M = N/(submodule of N) canonical projection - M,H = quo(N,[N(sparse_row(R[1 x^2-1 x*y^2])),N(sparse_row(R[y^3 y*x^2 x^3]))],:cache_morphism) + M,H = quo(N,[N(sparse_row(R[1 x^2-1 x*y^2])),N(sparse_row(R[y^3 y*x^2 x^3]))], cache_morphism=true) @test is_welldefined(H) ## test addition/subtraction of morphisms @@ -930,7 +948,7 @@ end KerH,iKerH = kernel(H) ImH,iImH = image(H) - NmodKerH, pNmodKerH = quo(N,KerH, :cache_morphism) + NmodKerH, pNmodKerH = quo(N,KerH, cache_morphism=true) Hbar = SubQuoHom(NmodKerH,M,matrix(H)) # induced map N/KerH --> M Hbar = restrict_codomain(Hbar,ImH) # induced map N/KerH --> ImH @@ -961,7 +979,7 @@ end u1 = R[3*y 14*y^2 6*x*y^2 x^2*y 3*x^2*y^2] u2 = R[5*x*y^2 10*y^2 4*x*y 7*x^2*y^2 7*x^2] u3 = R[13*x^2*y 4*x*y 2*x 7*x^2 9*x^2] - N,iN = sub(NN,[NN(sparse_row(u1)), NN(sparse_row(u2)), NN(sparse_row(u3))], :cache_morphism) + N,iN = sub(NN,[NN(sparse_row(u1)), NN(sparse_row(u2)), NN(sparse_row(u3))], cache_morphism=true) H = restrict_domain(p1*iM,N) @test is_welldefined(H) @@ -970,7 +988,7 @@ end KerH,iKerH = kernel(H) ImH,iImH = image(H) - NmodKerH, pNmodKerH = quo(N,KerH, :cache_morphism) + NmodKerH, pNmodKerH = quo(N,KerH, cache_morphism=true) Hbar = SubQuoHom(NmodKerH,M,matrix(H)) # induced map N/KerH --> M Hbar = restrict_codomain(Hbar,ImH) # induced map N/KerH --> ImH @@ -994,7 +1012,7 @@ end N = SubquoModule(F2,A1,B1) M = SubquoModule(F2,A2,B2) HomNM = hom(N,M)[1] - u1 = R[x^2*y^2 4*x^2*y^2 0 5*x*y^2] + u1 = R[x^2*y^2 4*x^2*y^2] # 0 5*x*y^2] # original vector was longer but current output is too small. H = HomNM(sparse_row(u1)) H = element_to_homomorphism(H) @test is_welldefined(H) @@ -1003,7 +1021,7 @@ end KerH,iKerH = kernel(H) ImH,iImH = image(H) - NmodKerH, pNmodKerH = quo(N,KerH, :cache_morphism) + NmodKerH, pNmodKerH = quo(N,KerH, cache_morphism=true) Hbar = SubQuoHom(NmodKerH,M,matrix(H)) # induced map N/KerH --> M Hbar = restrict_codomain(Hbar,ImH) # induced map N/KerH --> ImH @@ -1046,6 +1064,7 @@ end @testset "preimage" begin + Oscar.set_seed!(235) R, (x,y) = polynomial_ring(QQ, ["x", "y"]) for _=1:10 @@ -1064,14 +1083,15 @@ end H = element_to_homomorphism(H) u = [SubquoModuleElem(sparse_row(matrix([randpoly(R) for _=1:1, _=1:ngens(N)])), N) for _=1:3] - image_of_u = sub(M,map(x -> H(x),u), :none) - preimage_test_module = image_of_u + sub(M,[M[1]], :none) + image_of_u = sub_object(M,map(x -> H(x),u)) + preimage_test_module = image_of_u + sub_object(M,[M[1]]) _,emb = preimage(H,preimage_test_module,:with_morphism) - @test issubset(sub(N,u, :none), image(emb)[1]) + @test issubset(sub_object(N,u), image(emb)[1]) end end @testset "change of base rings" begin + Oscar.set_seed!(235) R, (x,y) = QQ["x", "y"] U = Oscar.MPolyPowersOfElement(x) S = Oscar.MPolyLocRing(R, U) @@ -1095,10 +1115,11 @@ end end @testset "duals" begin + Oscar.set_seed!(235) R, (x,y,z) = QQ["x", "y", "z"] F1 = FreeMod(R, 1) F2 = FreeMod(R, 2) - F2v, ev = Oscar.dual(F2, cod=F1) + F2v, ev = Oscar.dual(F2, codomain=F1) @test ev(F2v[1])(F2[1]) == F1[1] # the first generator FF, psi = Oscar.double_dual(F2) @@ -1107,10 +1128,10 @@ end M, inc = sub(F2, [x*F2[1], y*F2[1]]) F1 = FreeMod(R, 1) - Mv, ev = dual(M, cod=F1) + Mv, ev = dual(M, codomain=F1) @test ev(Mv[1])(M[1]) == x*F1[1] - Mvv, psi = Oscar.double_dual(M, cod=F1) + Mvv, psi = Oscar.double_dual(M, codomain=F1) @test matrix(psi) == R[x; y] ### Quotient rings @@ -1120,7 +1141,7 @@ end F1 = FreeMod(Q, 1) F2 = FreeMod(Q, 2) - F2v, ev = Oscar.dual(F2, cod=F1) + F2v, ev = Oscar.dual(F2, codomain=F1) @test ev(F2v[1])(F2[1]) == F1[1] # the first generator FF, psi = Oscar.double_dual(F2) @@ -1128,13 +1149,14 @@ end @test is_surjective(psi) M, pr = quo(F2, [sum(A[i, j]*F2[j] for j in 1:ngens(F2)) for i in 1:nrows(A)]) - Mv, ev = Oscar.dual(M, cod=F1) - Mvv, psi = Oscar.double_dual(M, cod=F1) + Mv, ev = Oscar.dual(M, codomain=F1) + Mvv, psi = Oscar.double_dual(M, codomain=F1) @test is_injective(psi) @test is_surjective(psi) # works correctly! end @testset "free resolution in case of no relations" begin + Oscar.set_seed!(235) R, (x,y,z) = polynomial_ring(QQ, ["x", "y", "z"]) Z = abelian_group(0) F = free_module(R, 3) @@ -1144,10 +1166,11 @@ end Mk = kernel(a) Mk1 = Mk[1] fr = free_resolution(Mk1) - @test rank(domain(map(fr.C,1))) == 0 + @test is_zero(map(fr.C,1)) end @testset "length of free resolution" begin + Oscar.set_seed!(235) S, (x0, x1, x2, x3, x4) = graded_polynomial_ring(GF(3), ["x0", "x1", "x2", "x3", "x4"]); m = ideal(S, [x1^2+(-x1+x2+x3-x4)*x0, x1*x2+(x1-x3+x4)*x0, x1*x3+(-x1+x4+x0)*x0, @@ -1161,6 +1184,7 @@ end end @testset "vector_space_dimension and vector_space_basis" begin + Oscar.set_seed!(235) R,(x,y,z,w) = QQ["x","y","z","w"] U=complement_of_point_ideal(R,[0,0,0,0]) RL, loc_map = localization(R,U) @@ -1173,7 +1197,60 @@ end @test length(vector_space_basis(Mloc,0)) == 1 end +@testset "canonical maps and garbage collection" begin + Oscar.set_seed!(235) + R, (x, y) = QQ[:x, :y] + + F = FreeMod(R, 1) + + # we need to wrap the creation of I in a scope of its own so + # that gc works within the test suite. + function dummy(F::FreeMod) + I, inc = sub(F, [x*F[1]], cache_morphism=true) + + @test haskey(F.incoming, I) + @test Oscar._recreate_morphism(I, F, F.incoming[I]) == inc + + @test haskey(I.outgoing, F) + @test Oscar._recreate_morphism(I, F, I.outgoing[F]) == inc + + I = 5 + inc = "a" + end + dummy(F) + + GC.gc() + GC.gc() + + @test length(keys(F.incoming)) == 0 + # The other way around it will not work, because I has a reference to its ambient_free_module f. + + function dummy2(F::FreeMod) + I, inc_I = sub(F, [x*F[1]], cache_morphism=true) + J, inc_J = sub(I, [x^2*I[1]], cache_morphism=true) + + @test haskey(J.outgoing, I) + @test haskey(I.incoming, J) + @test Oscar._recreate_morphism(J, I, J.outgoing[I]) == inc_J + @test Oscar._recreate_morphism(J, I, I.incoming[J]) == inc_J + + I = 5 + inc_I = 6 + end + dummy2(F) + + GC.gc() + GC.gc() + + # The inclusion map J -> I is still stored in the attributes of J as :canonical_inclusion. + # However, even removing that and calling gc() again does not remove the entry in J.outgoing. + # So there is still a memory leak somewhere! + @test_broken length(keys(J.outgoing)) == 0 +end + + @testset "issue 3107" begin + Oscar.set_seed!(235) X = veronese(); I = defining_ideal(X); Pn = base_ring(I) @@ -1181,4 +1258,3 @@ end F = graded_free_module(Pn, 1) dualFIC = hom(FI.C, F) end - diff --git a/test/Modules/flattenings.jl b/test/Modules/flattenings.jl new file mode 100644 index 000000000000..1901d379e9ca --- /dev/null +++ b/test/Modules/flattenings.jl @@ -0,0 +1,42 @@ +@testset "flattenings of modules I" begin + kk = GF(40009); + B, (t,) = polynomial_ring(kk, [:t]); + IP5 = projective_space(B, [:u, :v, :w, :x, :y, :z]); + S = homogeneous_coordinate_ring(IP5); + (u, v, w, x, y, z) = gens(S); + f = x*y - t^2*v^2 - w^2; + g = z*w - t*u*v; + I = ideal(S, [f, g]); + X, inc_X = sub(IP5, I); + Om1X = Oscar.relative_cotangent_module(X); + SX = homogeneous_coordinate_ring(X); + F1X = graded_free_module(SX,[0]); + TX,_ = hom(Om1X,F1X); + TXamb,_ = pushforward(inc_X,TX); + W1X,_ = hom(TX,F1X) + M, a, b = Oscar._alt_simplify(W1X) + @test is_isomorphism(a) + @test is_isomorphism(b) + @test compose(a, b) == identity_map(domain(a)) + @test compose(b, a) == identity_map(domain(b)) +end + +@testset "flattenings of modules II" begin + # The same as above, but over a quotient ring as coefficient ring + kk = GF(40009); + B, (t,) = polynomial_ring(kk, [:t]); + B, _ = quo(B, ideal(B, [t^3])) + IP5 = projective_space(B, [:u, :v, :w, :x, :y, :z]); + S = homogeneous_coordinate_ring(IP5); + (u, v, w, x, y, z) = gens(S); + f = x*y - t^2*v^2 - w^2; + g = z*w - t*u*v; + I = ideal(S, [f, g]); + X, inc_X = sub(IP5, I); + Om1X = Oscar.relative_cotangent_module(X); + M, a, b = Oscar._alt_simplify(Om1X) + @test is_isomorphism(a) + @test is_isomorphism(b) + @test compose(a, b) == identity_map(domain(a)) + @test compose(b, a) == identity_map(domain(b)) +end From cf09d1720dc4046c8ab2ae5c3822af246b960e96 Mon Sep 17 00:00:00 2001 From: Johannes Schmitt Date: Wed, 21 Feb 2024 21:47:39 +0100 Subject: [PATCH 23/29] Bump dependencies (#3374) * `ordering` -> `internal_ordering` for polynomial rings * Adjust to unexported symbols from Hecke * `find_name` now lives in `PrettyPrinting` (cherry picked from commit d32efdd549e0ecc41f6276ab72b28a73f9cb181a) --- Project.toml | 10 ++++----- docs/src/CommutativeAlgebra/rings.md | 8 +++---- examples/ZeroDec.jl | 2 +- experimental/GModule/GaloisCohomology.jl | 22 +++++++++---------- experimental/GaloisGrp/src/Subfields.jl | 8 +++---- .../QuadFormAndIsom/src/embeddings.jl | 4 ++-- .../src/hermitian_miranda_morrison.jl | 18 +++++++-------- experimental/Schemes/elliptic_surface.jl | 4 ++-- src/AlgebraicGeometry/Surfaces/K3Auto.jl | 8 +++---- src/Groups/matrices/iso_nf_fq.jl | 2 +- src/InvariantTheory/types.jl | 11 +++++----- .../UngradedModules/FreeResolutions.jl | 10 ++++----- src/Modules/UngradedModules/Presentation.jl | 16 +++++++------- src/NumberTheory/GaloisGrp/RelGalois.jl | 8 +++---- src/NumberTheory/NmbThy.jl | 6 ++--- src/Rings/NumberField.jl | 6 ++--- src/Rings/PBWAlgebra.jl | 2 +- src/Rings/groebner.jl | 4 ++-- src/Rings/mpoly-graded.jl | 2 +- src/Rings/mpoly-ideals.jl | 1 - src/Rings/mpoly.jl | 8 +++---- src/exports.jl | 1 + src/imports.jl | 2 +- .../InvariantTheory/fundamental_invariants.jl | 4 ++-- test/InvariantTheory/invariant_rings.jl | 4 ++-- test/InvariantTheory/secondary_invariants.jl | 4 ++-- test/Rings/NumberField.jl | 2 +- test/Rings/groebner.jl | 2 +- test/Rings/mpoly.jl | 8 ++++--- test/Rings/orderings.jl | 5 +++-- 30 files changed, 97 insertions(+), 95 deletions(-) diff --git a/Project.toml b/Project.toml index cc876615086e..9693d69ac0e4 100644 --- a/Project.toml +++ b/Project.toml @@ -26,23 +26,23 @@ UUIDs = "cf7118a7-6976-5b1a-9a39-7adc72f591a4" cohomCalg_jll = "5558cf25-a90e-53b0-b813-cadaa3ae7ade" [compat] -AbstractAlgebra = "0.39.0" -AlgebraicSolving = "0.4.10" +AbstractAlgebra = "0.40.0" +AlgebraicSolving = "0.4.11" Distributed = "1.6" DocStringExtensions = "0.8, 0.9" GAP = "0.10.2" -Hecke = "0.28.0" +Hecke = "0.29.0" JSON = "^0.20, ^0.21" JSON3 = "1.13.2" LazyArtifacts = "1.6" -Nemo = "0.42.1" +Nemo = "0.43.0" Pkg = "1.6" Polymake = "0.11.13" Preferences = "1" Random = "1.6" RandomExtensions = "0.4.3" Serialization = "1.6" -Singular = "0.22.0" +Singular = "0.22.3" TOPCOM_jll = "0.17.8" UUIDs = "1.6" cohomCalg_jll = "0.32.0" diff --git a/docs/src/CommutativeAlgebra/rings.md b/docs/src/CommutativeAlgebra/rings.md index 8878bb8e0b9b..60c6d5f35e73 100644 --- a/docs/src/CommutativeAlgebra/rings.md +++ b/docs/src/CommutativeAlgebra/rings.md @@ -25,15 +25,13 @@ of the coefficient ring of the polynomial ring. The basic constructor below allows one to build multivariate polynomial rings: ```@julia -polynomial_ring(C::Ring, V::Vector{String}; ordering=:lex, cached::Bool = true) +polynomial_ring(C::Ring, V::Vector{String}; cached::Bool = true) ``` Its return value is a tuple, say `R, vars`, consisting of a polynomial ring `R` with coefficient ring `C` and a vector `vars` of generators (variables) which print according to the strings in the vector `V` . -The input `ordering=:lex` refers to the lexicograpical monomial ordering which specifies the default way of storing and displaying polynomials in OSCAR (terms are sorted in descending -order). The other possible choices are `:deglex` and `:degrevlex`. Gröbner bases, however, can be computed with respect to any monomial ordering. See the section on Gröbner bases. !!! note - Caching is used to ensure that a given ring constructed from given parameters is unique in the system. For example, there is only one ring of multivariate polynomials over $\mathbb{Z}$ with variables printing as x, y, z, and with `ordering=:lex`. + Caching is used to ensure that a given ring constructed from given parameters is unique in the system. For example, there is only one ring of multivariate polynomials over $\mathbb{Z}$ with variables printing as x, y, z. ###### Examples @@ -264,7 +262,7 @@ grade(R::MPolyRing, W::Vector{<:Vector{<:IntegerUnion}}) grade(R::MPolyRing, W::Vector{<:IntegerUnion}) ``` ```@docs -graded_polynomial_ring(C::Ring, V::Vector{String}, W; ordering=:lex) +graded_polynomial_ring(C::Ring, V::Vector{String}, W) ``` ## Tests on Graded Rings diff --git a/examples/ZeroDec.jl b/examples/ZeroDec.jl index bd4afd851801..2df78ad172af 100644 --- a/examples/ZeroDec.jl +++ b/examples/ZeroDec.jl @@ -27,7 +27,7 @@ before returning the primary decomposition. #OUTPUT: Primary decomposition of I with associated primes in a list function zerodecomp(I::Singular.sideal, outputReduced::Bool = false, usefglm::Bool = false) - if ordering(I.base_ring) != :lex + if Singular.ordering(I.base_ring) != :lex Icopy = changeOrderOfBasering(I, :lex); else Icopy = Singular.deepcopy(I) diff --git a/experimental/GModule/GaloisCohomology.jl b/experimental/GModule/GaloisCohomology.jl index c610f5c32505..7a8e8e928798 100644 --- a/experimental/GModule/GaloisCohomology.jl +++ b/experimental/GModule/GaloisCohomology.jl @@ -88,8 +88,8 @@ end The natural `ZZ[H]` module where `H`, a subgroup of the automorphism group acts on the ray class group. """ -function Oscar.gmodule(H::PermGroup, mR::MapRayClassGrp, mG = automorphism_group(PermGroup, nf(order(codomain((mR)))))[2]) - k = nf(order(codomain(mR))) +function Oscar.gmodule(H::PermGroup, mR::MapRayClassGrp, mG = automorphism_group(PermGroup, Hecke.nf(order(codomain((mR)))))[2]) + k = Hecke.nf(order(codomain(mR))) G = domain(mG) ac = Hecke.induce_action(mR, [image(mG, G(g)) for g = gens(H)]) @@ -145,14 +145,14 @@ function Oscar.gmodule(H::PermGroup, mu::Map{FinGenAbGroup, FacElemMon{AbsSimple return _gmodule(base_ring(codomain(mu)), H, mu, mG) end -function Oscar.gmodule(H::PermGroup, mu::Map{FinGenAbGroup, AbsSimpleNumFieldOrder}, mG = automorphism_group(PermGroup, nf(codomain(mu)))[2]) +function Oscar.gmodule(H::PermGroup, mu::Map{FinGenAbGroup, AbsSimpleNumFieldOrder}, mG = automorphism_group(PermGroup, Hecke.nf(codomain(mu)))[2]) #TODO: preimage for sunits can fail (inf. loop) if # (experimentally) the ideals in S are not coprime or include 1 # or if the s-unit is not in the image (eg. action and not closed set S) u = domain(mu) U = [mu(g) for g = gens(u)] zk = codomain(mu) - k = nf(zk) + k = Hecke.nf(zk) G = domain(mG) ac = [hom(u, u, [preimage(mu, zk(mG(G(g))(k(x)))) for x = U]) for g = gens(H)] return gmodule(H, ac) @@ -1045,7 +1045,7 @@ function Oscar.galois_group(A::ClassField, ::QQField; idel_parent::Union{IdelPar mR = A.rayclassgroupmap mQ = A.quotientmap zk = order(m0) - @req order(automorphism_group(nf(zk))[1]) == degree(zk) "base field must be normal" + @req order(automorphism_group(Hecke.nf(zk))[1]) == degree(zk) "base field must be normal" if gcd(degree(A), degree(base_field(A))) == 1 s, ms = split_extension(gmodule(A)) return permutation_group(s), ms @@ -1060,7 +1060,7 @@ function Oscar.galois_group(A::ClassField, ::QQField; idel_parent::Union{IdelPar @assert Oscar.GrpCoh.istwo_cocycle(a) gA = gmodule(A, idel_parent.mG) qA = cohomology_group(gA, 2) - n = degree(nf(zk)) + n = degree(Hecke.nf(zk)) aa = map_entries(a, parent = gA) do x x = parent(x)(Hecke.mod_sym(x.coeff, gcd(n, degree(A)))) J = ideal(idel_parent, x, coprime = m0) @@ -1125,15 +1125,15 @@ For a 2-cochain with with values in the multiplicative group of a number field, compute the local invariant of the algebra at the completion at the prime ideal or embeddings given. """ -function local_index(CC::GrpCoh.CoChain{2, PermGroupElem, GrpCoh.MultGrpElem{AbsSimpleNumFieldElem}}, P::AbsSimpleNumFieldOrderIdeal, mG::Map = automorphism_group(PermGroup, nf(order(P)))[2]; B = nothing, index_only::Bool = false) +function local_index(CC::GrpCoh.CoChain{2, PermGroupElem, GrpCoh.MultGrpElem{AbsSimpleNumFieldElem}}, P::AbsSimpleNumFieldOrderIdeal, mG::Map = automorphism_group(PermGroup, Hecke.nf(order(P)))[2]; B = nothing, index_only::Bool = false) return local_index([CC], P, mG, B = B, index_only = index_only)[1] end -function local_index(C::GrpCoh.CoChain{2, PermGroupElem, GrpCoh.MultGrpElem{AbsSimpleNumFieldElem}}, emb::Hecke.NumFieldEmb, mG::Map = automorphism_group(PermGroup, nf(order(P)))[2]; index_only::Bool = false) +function local_index(C::GrpCoh.CoChain{2, PermGroupElem, GrpCoh.MultGrpElem{AbsSimpleNumFieldElem}}, emb::Hecke.NumFieldEmb, mG::Map = automorphism_group(PermGroup, Hecke.nf(order(P)))[2]; index_only::Bool = false) return local_index([C], emb, mG)[1] end -function local_index(CC::Vector{GrpCoh.CoChain{2, PermGroupElem, GrpCoh.MultGrpElem{AbsSimpleNumFieldElem}}}, emb::Hecke.NumFieldEmb, mG::Map = automorphism_group(PermGroup, nf(order(P)))[2]; index_only::Bool = false) +function local_index(CC::Vector{GrpCoh.CoChain{2, PermGroupElem, GrpCoh.MultGrpElem{AbsSimpleNumFieldElem}}}, emb::Hecke.NumFieldEmb, mG::Map = automorphism_group(PermGroup, Hecke.nf(order(P)))[2]; index_only::Bool = false) if is_real(emb) return [Hecke.QmodnZ()(0) for x = CC] end @@ -1198,8 +1198,8 @@ function induce_hom(ml::Hecke.CompletionMap, mL::Hecke.CompletionMap, mkK::NumFi return hom(l, L, hom(bl, bL, rt), im_data) end -function local_index(CC::Vector{GrpCoh.CoChain{2, PermGroupElem, GrpCoh.MultGrpElem{AbsSimpleNumFieldElem}}}, P::AbsSimpleNumFieldOrderIdeal, mG::Map = automorphism_group(PermGroup, nf(order(P)))[2]; B::Any = nothing, index_only::Bool = false) - k = nf(order(P)) +function local_index(CC::Vector{GrpCoh.CoChain{2, PermGroupElem, GrpCoh.MultGrpElem{AbsSimpleNumFieldElem}}}, P::AbsSimpleNumFieldOrderIdeal, mG::Map = automorphism_group(PermGroup, Hecke.nf(order(P)))[2]; B::Any = nothing, index_only::Bool = false) + k = Hecke.nf(order(P)) if B !== nothing && haskey(B.lp, P) data = B.lp[P] diff --git a/experimental/GaloisGrp/src/Subfields.jl b/experimental/GaloisGrp/src/Subfields.jl index 7250538a3565..50674544e219 100644 --- a/experimental/GaloisGrp/src/Subfields.jl +++ b/experimental/GaloisGrp/src/Subfields.jl @@ -314,8 +314,8 @@ function _subfields(K::AbsSimpleNumField; pStart = 2*degree(K)+1, prime = 0) @show pr = clog(B, p) @show pr *= div(n,2) @show pr += 2*clog(2*n, p) - H = factor_mod_pk_init(f, p) - @show factor_mod_pk(H, 1) + H = Hecke.factor_mod_pk_init(f, p) + @show Hecke.factor_mod_pk(H, 1) b = basis(K) b .*= inv(derivative(f)(gen(K))) @@ -324,7 +324,7 @@ function _subfields(K::AbsSimpleNumField; pStart = 2*degree(K)+1, prime = 0) bz = [Zx(bd[i]*bt[i]) for i=1:length(bd)] @assert parent(f) == parent(bz[1]) - lf = factor_mod_pk(Array, H, 1) + lf = Hecke.factor_mod_pk(Array, H, 1) #the roots in G are of course roots of the lf[i] #roots that belong to the same factor would give rise #to the same principal subfield. So we can save on LLL calls. @@ -334,7 +334,7 @@ function _subfields(K::AbsSimpleNumField; pStart = 2*degree(K)+1, prime = 0) rt_to_lf = [findall(x->iszero(f[1](x)), r) for f = lf] done = zeros(Int, length(lf)) while true - lf = factor_mod_pk(Array, H, pr) + lf = Hecke.factor_mod_pk(Array, H, pr) ppr = ZZRingElem(p)^pr @assert parent(lf[1][1]) == parent(f) @assert all(x->is_monic(x[1]), lf) diff --git a/experimental/QuadFormAndIsom/src/embeddings.jl b/experimental/QuadFormAndIsom/src/embeddings.jl index dd10d558fdff..98bd143fde62 100644 --- a/experimental/QuadFormAndIsom/src/embeddings.jl +++ b/experimental/QuadFormAndIsom/src/embeddings.jl @@ -170,7 +170,7 @@ function _overlattice(gamma::TorQuadModuleMap, z = zero_matrix(QQ, 0, degree(A)) glue = reduce(vcat, QQMatrix[matrix(QQ, 1, degree(A), g) for g in _glue]; init=z) glue = vcat(basis_matrix(A+B), glue) - Fakeglue = FakeFmpqMat(glue) + Fakeglue = Hecke.FakeFmpqMat(glue) _FakeB = hnf(Fakeglue) _B = QQ(1, denominator(Fakeglue))*change_base_ring(QQ, numerator(_FakeB)) C = lattice(ambient_space(A), _B[end-rank(A)-rank(B)+1:end, :]) @@ -182,7 +182,7 @@ function _overlattice(gamma::TorQuadModuleMap, z = zero_matrix(QQ, 0, degree(cover(D))) glue = reduce(vcat, QQMatrix[matrix(QQ, 1, degree(cover(D)), g) for g in _glue]; init=z) glue = vcat(block_diagonal_matrix(basis_matrix.(ZZLat[A, B])), glue) - Fakeglue = FakeFmpqMat(glue) + Fakeglue = Hecke.FakeFmpqMat(glue) _FakeB = hnf(Fakeglue) _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, :]) diff --git a/experimental/QuadFormAndIsom/src/hermitian_miranda_morrison.jl b/experimental/QuadFormAndIsom/src/hermitian_miranda_morrison.jl index 6a51c1c18f40..081022e284d7 100644 --- a/experimental/QuadFormAndIsom/src/hermitian_miranda_morrison.jl +++ b/experimental/QuadFormAndIsom/src/hermitian_miranda_morrison.jl @@ -12,7 +12,7 @@ function _get_quotient_split(P::Hecke.RelNumFieldOrderIdeal, i::Int) OE = order(P) - E = nf(OE) + E = Hecke.nf(OE) Eabs, EabstoE = absolute_simple_field(E) Pabs = EabstoE\P @@ -57,7 +57,7 @@ end function _get_quotient_inert(P::Hecke.RelNumFieldOrderIdeal, i::Int) OE = order(P) OK = base_ring(OE) - E = nf(OE) + E = Hecke.nf(OE) K = base_field(E) p = minimum(P) @@ -109,7 +109,7 @@ end function _get_quotient_ramified(P::Hecke.RelNumFieldOrderIdeal, i::Int) OE = order(P) - E = nf(OE) + E = Hecke.nf(OE) p = minimum(P) e = valuation(different(OE), P) @@ -182,7 +182,7 @@ function _get_quotient(O::Hecke.RelNumFieldOrder, p::Hecke.AbsSimpleNumFieldOrde @hassert :ZZLatWithIsom 1 is_prime(p) @hassert :ZZLatWithIsom 1 is_maximal(order(p)) @hassert :ZZLatWithIsom 1 order(p) === base_ring(O) - E = nf(O) + E = Hecke.nf(O) F = prime_decomposition(O, p) P = F[1][1] if i == 0 @@ -489,7 +489,7 @@ end function _is_special(L::HermLat, p::AbsSimpleNumFieldOrderIdeal) OE = base_ring(L) - E = nf(OE) + E = Hecke.nf(OE) lp = prime_decomposition(OE, p) if lp[1][2] != 2 || !iseven(rank(L)) return false @@ -588,14 +588,14 @@ end # the minimum P-valuation among all the non-zero entries of M function _scale_valuation(M::T, P::Hecke.RelNumFieldOrderIdeal) where T <: MatrixElem{Hecke.RelSimpleNumFieldElem{AbsSimpleNumFieldElem}} - @hassert :ZZLatWithIsom 1 nf(order(P)) === base_ring(M) + @hassert :ZZLatWithIsom 1 Hecke.nf(order(P)) === base_ring(M) iszero(M) && return inf return minimum(valuation(v, P) for v in collect(M) if !iszero(v)) end # the minimum P-valuation among all the non-zero diagonal entries of M function _norm_valuation(M::T, P::Hecke.RelNumFieldOrderIdeal) where T <: MatrixElem{Hecke.RelSimpleNumFieldElem{AbsSimpleNumFieldElem}} - @hassert :ZZLatWithIsom 1 nf(order(P)) === base_ring(M) + @hassert :ZZLatWithIsom 1 Hecke.nf(order(P)) === base_ring(M) iszero(diagonal(M)) && return inf r = minimum(valuation(v, P) for v in diagonal(M) if !iszero(v)) return r @@ -671,7 +671,7 @@ end # function _approximate_isometry(H::HermLat, H2::HermLat, g::AutomorphismGroupElem{TorQuadModule}, P::Hecke.RelNumFieldOrderIdeal, e::Int, a::Int, k::Int, res::AbstractSpaceRes) E = base_field(H) - @hassert :ZZLatWithIsom 1 nf(order(P)) === E + @hassert :ZZLatWithIsom 1 Hecke.nf(order(P)) === E ok, b = is_modular(H, minimum(P)) if ok && b == -a return identity_matrix(E, 1) @@ -743,7 +743,7 @@ end # that part is taken from the Sage implementation of Simon Brandhorst function _find_rho(P::Hecke.RelNumFieldOrderIdeal, e::Int) OE = order(P) - E = nf(OE) + E = Hecke.nf(OE) lp = prime_decomposition(OE, minimum(P)) dya = is_dyadic(P) if !dya diff --git a/experimental/Schemes/elliptic_surface.jl b/experimental/Schemes/elliptic_surface.jl index 57ff77e54e91..a4aa8147302e 100644 --- a/experimental/Schemes/elliptic_surface.jl +++ b/experimental/Schemes/elliptic_surface.jl @@ -338,7 +338,7 @@ function weierstrass_model(X::EllipticSurface) @assert has_decomposition_info(default_covering(P)) # Create the singular Weierstrass model S of the elliptic K3 surface X - a = a_invars(E) + a = a_invariants(E) U = affine_charts(P)[1] # the standard Weierstrass chart (x, y, t) = gens(OO(U)) @assert all(denominator(i)==1 for i in a) @@ -1639,7 +1639,7 @@ function _elliptic_parameter_conversion(X::EllipticSurface, u::VarietyFunctionFi f_loc = first(gens(modulus(OO(U)))) @assert f == R_to_kkt_frac_XY(f_loc) && _is_in_weierstrass_form(f) "local equation is not in Weierstrass form" - a = a_invars(E) + a = a_invariants(E) u_loc = u[U]::AbstractAlgebra.Generic.FracFieldElem # the representative on the Weierstrass chart diff --git a/src/AlgebraicGeometry/Surfaces/K3Auto.jl b/src/AlgebraicGeometry/Surfaces/K3Auto.jl index ce64ad6677b8..084a97972961 100644 --- a/src/AlgebraicGeometry/Surfaces/K3Auto.jl +++ b/src/AlgebraicGeometry/Surfaces/K3Auto.jl @@ -561,7 +561,7 @@ end function short_vectors_affine(gram::MatrixElem, v::MatrixElem, alpha::QQFieldElem, d) # find a solution = alpha with x in L if it exists w = gram*transpose(v) - tmp = FakeFmpqMat(w) + tmp = Hecke.FakeFmpqMat(w) wn = numerator(tmp) wd = denominator(tmp) b, x = can_solve_with_solution(transpose(wn), matrix(ZZ, 1, 1, [alpha*wd]); side = :right) @@ -1074,7 +1074,7 @@ function _alg58_close_vector(data::BorcherdsCtx, w::ZZMatrix) # to avoid repeated calculation of the same stuff e.g. K and Q # find a solution = alpha with x in L if it exists ww = transpose(wS) - tmp = FakeFmpqMat(ww) + tmp = Hecke.FakeFmpqMat(ww) wn = numerator(tmp) wd = denominator(tmp) K = kernel(wn; side = :left) @@ -1156,7 +1156,7 @@ function _walls_of_chamber(data::BorcherdsCtx, weyl_vector, algorithm::Symbol=:s d = rank(data.S) walls = Vector{ZZMatrix}(undef,d) for i in 1:d - vs = numerator(FakeFmpqMat(walls1[i])) + vs = numerator(Hecke.FakeFmpqMat(walls1[i])) g = gcd(_vec(vs)) if g != 1 vs = divexact(vs, g) @@ -1174,7 +1174,7 @@ function _walls_of_chamber(data::BorcherdsCtx, weyl_vector, algorithm::Symbol=:s for i in 1:d v = matrix(QQ, 1, degree(data.SS), r[i]) # rescale v to be primitive in S - vs = numerator(FakeFmpqMat(v)) + vs = numerator(Hecke.FakeFmpqMat(v)) g = gcd(_vec(vs)) if g!=1 vs = divexact(vs, g) diff --git a/src/Groups/matrices/iso_nf_fq.jl b/src/Groups/matrices/iso_nf_fq.jl index d839f268c980..2e7457e741cd 100644 --- a/src/Groups/matrices/iso_nf_fq.jl +++ b/src/Groups/matrices/iso_nf_fq.jl @@ -54,7 +54,7 @@ end # Small helper function to make the reduction call uniform function _reduce(M::MatrixElem{AbsSimpleNumFieldElem}, OtoFq) - e = extend(OtoFq, nf(domain(OtoFq))) + e = extend(OtoFq, Hecke.nf(domain(OtoFq))) return map_entries(e, M) end diff --git a/src/InvariantTheory/types.jl b/src/InvariantTheory/types.jl index 299a63eff4a7..c300cff9853f 100644 --- a/src/InvariantTheory/types.jl +++ b/src/InvariantTheory/types.jl @@ -53,8 +53,9 @@ mutable struct InvRing{FldT, GrpT, PolyRingElemT, PolyRingT, ActionT} field::FldT poly_ring::PolyRingT - # The underlying polynomial ring needs to be created with ordering = :degrevlex - # for the application of divrem in the secondary and fundamental invariants. + # The underlying polynomial ring needs to be created with + # internal_ordering = :degrevlex for the application of divrem in the secondary + # and fundamental invariants. # If the user gave us a polynomial ring (which is stored in poly_ring), this # might not be the case. poly_ring_internal::PolyRingT @@ -78,7 +79,7 @@ mutable struct InvRing{FldT, GrpT, PolyRingElemT, PolyRingT, ActionT} n = degree(G) # We want to use divrem w.r.t. degrevlex for the computation of secondary # invariants and fundamental invariants - R, = graded_polynomial_ring(K, "x" => 1:n, cached = false, ordering = :degrevlex) + R, = graded_polynomial_ring(K, "x" => 1:n, cached = false, internal_ordering = :degrevlex) return InvRing(K, G, action, R) end @@ -103,8 +104,8 @@ mutable struct InvRing{FldT, GrpT, PolyRingElemT, PolyRingT, ActionT} # We want to use divrem w.r.t. degrevlex for the computation of secondary # invariants and fundamental invariants - if ordering(poly_ring) != :degrevlex - z.poly_ring_internal, _ = graded_polynomial_ring(K, ngens(poly_ring), cached = false, ordering = :degrevlex) + if internal_ordering(poly_ring) != :degrevlex + z.poly_ring_internal, _ = graded_polynomial_ring(K, ngens(poly_ring), cached = false, internal_ordering = :degrevlex) end return z diff --git a/src/Modules/UngradedModules/FreeResolutions.jl b/src/Modules/UngradedModules/FreeResolutions.jl index 088a9c9bb7e4..de1e53c24f87 100644 --- a/src/Modules/UngradedModules/FreeResolutions.jl +++ b/src/Modules/UngradedModules/FreeResolutions.jl @@ -229,7 +229,7 @@ function _extend_free_resolution(cc::Hecke.ComplexOfMorphisms, idx::Int) # Finalize maps. if slen < len Z = FreeMod(br, 0) - set_attribute!(Z, :name => "0") + AbstractAlgebra.set_name!(Z, "0") pushfirst!(cc, hom(Z, domain(cc.maps[1]), Vector{elem_type(domain(cc.maps[1]))}(); check=false)) cc.complete = true end @@ -382,7 +382,7 @@ function free_resolution(M::SubquoModule{<:MPolyRingElem}; dom = free_module(br, rk) SM = SubModuleOfFreeModule(codom, res[j]) #generator_matrix(SM) - set_attribute!(dom, :name => "$br_name^$rk") + AbstractAlgebra.set_name!(dom, "$br_name^$rk") insert!(maps, 1, hom(dom, codom, gens(SM); check=false)) j += 1 end @@ -394,7 +394,7 @@ function free_resolution(M::SubquoModule{<:MPolyRingElem}; else Z = FreeMod(br, 0) end - set_attribute!(Z, :name => "0") + AbstractAlgebra.set_name!(Z, "0") insert!(maps, 1, hom(Z, domain(maps[1]), Vector{elem_type(domain(maps[1]))}(); check=false)) end @@ -430,7 +430,7 @@ function free_resolution(M::SubquoModule{T}) where {T<:RingElem} K, inc = kernel(map(C, i)) nz = findall(x->!iszero(x), gens(K)) F = FreeMod(R, length(nz)) - iszero(length(nz)) && set_attribute!(F, :name => "0") + iszero(length(nz)) && AbstractAlgebra.set_name!(F, "0") phi = hom(F, C[i], iszero(length(nz)) ? elem_type(C[i])[] : inc.(gens(K)[nz]); check=false) pushfirst!(C.maps, phi) end @@ -461,7 +461,7 @@ function free_resolution_via_kernels(M::SubquoModule, limit::Int = -1) h = graded_map(domain(mp[1]), Vector{elem_type(domain(mp[1]))}(); check=false) else Z = FreeMod(base_ring(M), 0) - set_attribute!(Z, :name => "0") + AbstractAlgebra.set_name!(Z, "0") h = hom(Z, domain(mp[1]), Vector{elem_type(domain(mp[1]))}(); check=false) end insert!(mp, 1, h) diff --git a/src/Modules/UngradedModules/Presentation.jl b/src/Modules/UngradedModules/Presentation.jl index 9f6af19307e0..b538351f8245 100644 --- a/src/Modules/UngradedModules/Presentation.jl +++ b/src/Modules/UngradedModules/Presentation.jl @@ -100,7 +100,7 @@ function _presentation_graded(SQ::SubquoModule) R = base_ring(SQ) # Prepare to set some names - br_name = AbstractAlgebra.find_name(R) + br_name = AbstractAlgebra.get_name(R) if br_name === nothing br_name = "br" end @@ -117,14 +117,14 @@ function _presentation_graded(SQ::SubquoModule) F0_to_SQ = graded_map(SQ, gens(SQ); check=false) F0_to_SQ.generators_map_to_generators = true F0 = domain(F0_to_SQ) - set_attribute!(F0, :name => "$br_name^$(ngens(SQ.sub))") + AbstractAlgebra.set_name!(F0, "$br_name^$(ngens(SQ.sub))") K, inc_K = kernel(F0_to_SQ) F1_to_F0 = graded_map(F0, images_of_generators(inc_K)) F1 = domain(F1_to_F0) #F1 = graded_free_module(R, [degree(x; check=false) for x in images_of_generators(inc_K)]) #F1_to_F0 = hom(F1, F0, images_of_generators(inc_K), check=false) - set_attribute!(F1, :name => "$br_name^$(ngens(F1))") + AbstractAlgebra.set_name!(F1, "$br_name^$(ngens(F1))") # When there is no kernel, clean things up if is_zero(F1) @@ -134,7 +134,7 @@ function _presentation_graded(SQ::SubquoModule) # prepare the end of the presentation Z = graded_free_module(R, elem_type(grading_group(R))[]) - set_attribute!(Z, :name => "0") + AbstractAlgebra.set_name!(Z, "0") SQ_to_Z = hom(SQ, Z, elem_type(Z)[zero(Z) for i in 1:ngens(SQ)]; check=false) # compile the presentation complex @@ -149,7 +149,7 @@ function _presentation_simple(SQ::SubquoModule) R = base_ring(SQ) # Prepare to set some names - br_name = AbstractAlgebra.find_name(R) + br_name = AbstractAlgebra.get_name(R) if br_name === nothing br_name = "br" end @@ -158,14 +158,14 @@ function _presentation_simple(SQ::SubquoModule) F0 = FreeMod(R, length(gens(SQ))) F0_to_SQ = hom(F0, SQ, gens(SQ); check=false) F0_to_SQ.generators_map_to_generators = true - set_attribute!(F0, :name => "$br_name^$(ngens(SQ.sub))") + AbstractAlgebra.set_name!(F0, "$br_name^$(ngens(SQ.sub))") K, inc_K = kernel(F0_to_SQ) @assert codomain(inc_K) === F0 @assert all(x->parent(x) === F0, images_of_generators(inc_K)) F1 = FreeMod(R, ngens(K)) F1_to_F0 = hom(F1, F0, images_of_generators(inc_K), check=false) - set_attribute!(F1, :name => "$br_name^$(ngens(F1))") + AbstractAlgebra.set_name!(F1, "$br_name^$(ngens(F1))") # When there is no kernel, clean things up if is_zero(F1) @@ -175,7 +175,7 @@ function _presentation_simple(SQ::SubquoModule) # prepare the end of the presentation Z = FreeMod(R, 0) - set_attribute!(Z, :name => "0") + AbstractAlgebra.set_name!(Z, "0") SQ_to_Z = hom(SQ, Z, elem_type(Z)[zero(Z) for i in 1:ngens(SQ)]; check=false) # compile the presentation complex diff --git a/src/NumberTheory/GaloisGrp/RelGalois.jl b/src/NumberTheory/GaloisGrp/RelGalois.jl index a7da59bb1744..440916886fbb 100644 --- a/src/NumberTheory/GaloisGrp/RelGalois.jl +++ b/src/NumberTheory/GaloisGrp/RelGalois.jl @@ -16,7 +16,7 @@ end function GaloisCtx(f::PolyRingElem{AbsSimpleNumFieldElem}, P::AbsSimpleNumFieldOrderIdeal) k = base_ring(f) - @assert k == nf(order(P)) + @assert k == Hecke.nf(order(P)) zk = order(P) C, mC = Hecke.completion_easy(k, P) setprecision!(C, 10) @@ -174,7 +174,7 @@ function isinteger(C::GaloisCtx{Hecke.vanHoeijCtx}, y::BoundRingElem{ZZRingElem} P = C.C.P zk = order(P) if any(i->!iszero(coeff(x, i)), 1:length(x)-1) - return false, zero(nf(zk)) + return false, zero(Hecke.nf(zk)) end mkc = C.data[1] c = codomain(mkc) @@ -183,7 +183,7 @@ function isinteger(C::GaloisCtx{Hecke.vanHoeijCtx}, y::BoundRingElem{ZZRingElem} P = C.C.P zk = order(P) x *= map_coeff(C, C.data[5]) #the den - a = nf(zk)(Hecke.reco(zk(preimage(mkc, c(coeff(x, 0)))), C.C.Ml, C.C.pMr)) + a = Hecke.nf(zk)(Hecke.reco(zk(preimage(mkc, c(coeff(x, 0)))), C.C.Ml, C.C.pMr)) a = a*inv(C.data[5]) if ceil(ZZRingElem, length(a)) <= value(y)^2 return true, a @@ -210,7 +210,7 @@ function bound_to_precision(C::GaloisCtx{Hecke.vanHoeijCtx}, y::BoundRingElem{ZZ #step 2: copy the precision estimate from NumField/NfAbs/PolyFactor.jl P = C.C.P zk = order(P) - k = nf(zk) + k = Hecke.nf(zk) N = ceil(Int, degree(k)/2/log(norm(P))*(log(c1*c2) + 2*log(v))) return N end diff --git a/src/NumberTheory/NmbThy.jl b/src/NumberTheory/NmbThy.jl index 50a04d723f84..ea2f8a3f30ab 100644 --- a/src/NumberTheory/NmbThy.jl +++ b/src/NumberTheory/NmbThy.jl @@ -44,10 +44,10 @@ norm_equation(R::AbsNumFieldOrder, k::Base.Integer; abs::Bool = false) = norm_eq function norm_equation_fac_elem(R::Hecke.RelNumFieldOrder{AbsSimpleNumFieldElem,Hecke.AbsSimpleNumFieldOrderFractionalIdeal}, a::AbsNumFieldOrderElem{AbsSimpleNumField,AbsSimpleNumFieldElem}) @assert Hecke.is_maximal(R) - Ka, mKa, mkK = absolute_field(nf(R)) + Ka, mKa, mkK = absolute_field(Hecke.nf(R)) Ra = maximal_order(Ka) class_group(Ra) - k = nf(parent(a)) + k = Hecke.nf(parent(a)) class_group(parent(a)) lp = factor(Ra(mkK(k(a)))*Ra) @@ -253,5 +253,5 @@ julia> disc_log(gen(F), a) """ function disc_log(b::T, x::T) where {T <: FinFieldElem} @assert parent(b) === parent(x) - return disc_log_bs_gs(b, x, order(parent(b))) + return Hecke.disc_log_bs_gs(b, x, order(parent(b))) end diff --git a/src/Rings/NumberField.jl b/src/Rings/NumberField.jl index 66c98ceb6afd..1e57dedb3dff 100644 --- a/src/Rings/NumberField.jl +++ b/src/Rings/NumberField.jl @@ -522,7 +522,7 @@ for t in [Base.Integer, Base.Rational{<:Base.Integer}, ZZRingElem, QQFieldElem] end function (K::NfNSGen{T, S})(x::AbsNumFieldOrderElem{NfNSGen{T, S}, <:Any}) where {T, S} - @req nf(parent(x)) === K "Parent of element must be an order of the number field" + @req Hecke.nf(parent(x)) === K "Parent of element must be an order of the number field" return elem_in_nf(x) end @@ -619,13 +619,13 @@ function elem_to_mat_row!(M::ZZMatrix, i::Int, d::ZZRingElem, a::NfNSGenElem{QQF end function basis_matrix(v::Vector{NfNSGenElem{QQFieldElem, QQMPolyRingElem}}, - ::Type{FakeFmpqMat}) + ::Type{Hecke.FakeFmpqMat}) d = degree(parent(v[1])) z = zero_matrix(FlintQQ, length(v), d) for i in 1:length(v) elem_to_mat_row!(z, i, v[i]) end - return FakeFmpqMat(z) + return Hecke.FakeFmpqMat(z) end ################################################################################ diff --git a/src/Rings/PBWAlgebra.jl b/src/Rings/PBWAlgebra.jl index 01336c8bd689..d7f9d7afd4a4 100644 --- a/src/Rings/PBWAlgebra.jl +++ b/src/Rings/PBWAlgebra.jl @@ -529,7 +529,7 @@ function _opposite(a::PBWAlgRing{T, S}) where {T, S} n = length(revs) bsring = Singular.PluralRing{S}(ptr, a.sring.base_ring, revs) bspolyring, _ = Singular.polynomial_ring(a.sring.base_ring, - revs, ordering = ordering(bsring)) + revs, ordering = Singular.ordering(bsring)) bsrel = Singular.zero_matrix(bspolyring, n, n) for i in 1:n-1, j in i+1:n bsrel[i,j] = _unsafe_coerce(bspolyring, a.relations[n+1-j,n+1-i], true) diff --git a/src/Rings/groebner.jl b/src/Rings/groebner.jl index 8e197377a66c..27f78a457047 100644 --- a/src/Rings/groebner.jl +++ b/src/Rings/groebner.jl @@ -318,13 +318,13 @@ See [Fau99](@cite) for more information. # Examples ```jldoctest -julia> R,(x,y,z) = polynomial_ring(GF(101), ["x","y","z"], ordering=:degrevlex) +julia> R,(x,y,z) = polynomial_ring(GF(101), ["x","y","z"]) (Multivariate polynomial ring in 3 variables over GF(101), FqMPolyRingElem[x, y, z]) julia> I = ideal(R, [x+2*y+2*z-1, x^2+2*y^2+2*z^2-x, 2*x*y+2*y*z-y]) Ideal generated by x + 2*y + 2*z + 100 - x^2 + 2*y^2 + 2*z^2 + 100*x + x^2 + 100*x + 2*y^2 + 2*z^2 2*x*y + 2*y*z + 100*y julia> groebner_basis_f4(I) diff --git a/src/Rings/mpoly-graded.jl b/src/Rings/mpoly-graded.jl index de98e5464319..782383a31a51 100644 --- a/src/Rings/mpoly-graded.jl +++ b/src/Rings/mpoly-graded.jl @@ -2163,7 +2163,7 @@ Return the ideal in the underlying ungraded ring. """ forget_grading(I::MPolyIdeal{<:MPolyDecRingElem}) = forget_decoration(I) -Generic.ordering(S::MPolyDecRing) = ordering(S.R) +Generic.internal_ordering(S::MPolyDecRing) = internal_ordering(S.R) #############truncation############# diff --git a/src/Rings/mpoly-ideals.jl b/src/Rings/mpoly-ideals.jl index 2e9b7d7a9281..16924fec7bc5 100644 --- a/src/Rings/mpoly-ideals.jl +++ b/src/Rings/mpoly-ideals.jl @@ -1959,7 +1959,6 @@ julia> grassmann_pluecker_ideal(R, 2, 4) Ideal generated by x[1, 1]*x[2, 3] + 6*x[2, 1]*x[1, 3] + x[1, 2]*x[2, 2] ``` - """ function grassmann_pluecker_ideal(ring::MPolyRing, subspace_dimension::Int, diff --git a/src/Rings/mpoly.jl b/src/Rings/mpoly.jl index 7e0b185185cb..c4864147b7e0 100644 --- a/src/Rings/mpoly.jl +++ b/src/Rings/mpoly.jl @@ -158,7 +158,7 @@ mutable struct IdealGens{S} r.isGB = S.isGB r.isReduced = isReduced if T <: Union{MPolyRing, MPolyRingLoc} - r.ord = monomial_ordering(Ox, ordering(base_ring(S))) + r.ord = monomial_ordering(Ox, Singular.ordering(base_ring(S))) end r.keep_ordering = true return r @@ -311,7 +311,7 @@ function singular_generators(B::IdealGens, monorder::MonomialOrdering=default_or singular_assure(B) # in case of quotient rings, monomial ordering is ignored so far in singular_poly_ring isa(B.gens.Ox, MPolyQuoRing) && return B.gens.S - isdefined(B, :ord) && B.ord == monorder && monomial_ordering(B.Ox, ordering(base_ring(B.S))) == B.ord && return B.gens.S + isdefined(B, :ord) && B.ord == monorder && monomial_ordering(B.Ox, Singular.ordering(base_ring(B.S))) == B.ord && return B.gens.S SR = singular_poly_ring(B.Ox, monorder) f = Singular.AlgebraHomomorphism(B.Sx, SR, gens(SR)) return Singular.map_ideal(f, B.gens.S) @@ -544,7 +544,7 @@ function singular_poly_ring(Rx::MPolyRing{T}; keep_ordering::Bool = false) where if keep_ordering return Singular.polynomial_ring(singular_coeff_ring(base_ring(Rx)), _variables_for_singular(symbols(Rx)), - ordering = ordering(Rx), + ordering = internal_ordering(Rx), cached = false)[1] else return Singular.polynomial_ring(singular_coeff_ring(base_ring(Rx)), @@ -613,7 +613,7 @@ Fields: function MPolyIdeal(Ox::T, s::Singular.sideal) where {T <: MPolyRing} r = MPolyIdeal(IdealGens(Ox, s)) #=if s.isGB - ord = monomial_ordering(Ox, ordering(base_ring(s))) + ord = monomial_ordering(Ox, Singular.ordering(base_ring(s))) r.ord = ord r.isGB = true r.gb[ord] = r.gens diff --git a/src/exports.jl b/src/exports.jl index d326c628d8e4..df002cd2f7f0 100644 --- a/src/exports.jl +++ b/src/exports.jl @@ -1117,6 +1117,7 @@ export orbit_polytope export orbit_representatives_and_stabilizers export orbits export order, has_order, set_order +export ordering export order_field_of_definition export orders_centralizers export orders_class_representatives diff --git a/src/imports.jl b/src/imports.jl index b17da7fc48b9..f2df7ed9bc66 100644 --- a/src/imports.jl +++ b/src/imports.jl @@ -101,7 +101,7 @@ import AbstractAlgebra: NCRingElem, number_of_generators, number_of_variables, - ordering, + internal_ordering, parent_type, polynomial_ring, PolyRing, diff --git a/test/InvariantTheory/fundamental_invariants.jl b/test/InvariantTheory/fundamental_invariants.jl index 58a6ac09dd1e..609c8ea57a53 100644 --- a/test/InvariantTheory/fundamental_invariants.jl +++ b/test/InvariantTheory/fundamental_invariants.jl @@ -1,8 +1,8 @@ @testset "Fundamental invariants (for matrix groups)" begin # Char 0 K, a = cyclotomic_field(3, "a") - # Force use of internal polynomial_ring with ordering = :lex - R, _ = graded_polynomial_ring(K, 3, ordering = :lex) + # Force use of internal polynomial_ring with internal_ordering = :lex + R, _ = graded_polynomial_ring(K, 3, internal_ordering = :lex) M1 = matrix(K, 3, 3, [ 0, 1, 0, 0, 0, 1, 1, 0, 0 ]) M2 = matrix(K, 3, 3, [ 1, 0, 0, 0, a, 0, 0, 0, -a - 1 ]) RG0 = invariant_ring(R, matrix_group(M1, M2)) diff --git a/test/InvariantTheory/invariant_rings.jl b/test/InvariantTheory/invariant_rings.jl index d1f135b371f8..b6999af78eed 100644 --- a/test/InvariantTheory/invariant_rings.jl +++ b/test/InvariantTheory/invariant_rings.jl @@ -9,7 +9,7 @@ invariant_ring(K, [ M1, M2 ]) invariant_ring(matrix_group([ M1, M2 ])) - R, _ = graded_polynomial_ring(K, 3, "x", ones(Int, 3), ordering = :degrevlex) + R, _ = graded_polynomial_ring(K, 3, "x", ones(Int, 3), internal_ordering = :degrevlex) @test polynomial_ring(invariant_ring(R, [ M1, M2 ])) === R @test polynomial_ring(invariant_ring(R, M1, M2)) === R @test polynomial_ring(invariant_ring(R, matrix_group(M1, M2))) === R @@ -118,7 +118,7 @@ end F3 = GF(3) RGM = invariant_ring(F3, G) # char. p, modular - R, _ = graded_polynomial_ring(K, 3, "x", ones(Int, 3), ordering = :degrevlex) + R, _ = graded_polynomial_ring(K, 3, "x", ones(Int, 3), internal_ordering = :degrevlex) @test polynomial_ring(invariant_ring(R, G)) === R @test coefficient_ring(RGQ) == QQ diff --git a/test/InvariantTheory/secondary_invariants.jl b/test/InvariantTheory/secondary_invariants.jl index 105a07fe4d36..d60f8b141dd8 100644 --- a/test/InvariantTheory/secondary_invariants.jl +++ b/test/InvariantTheory/secondary_invariants.jl @@ -1,7 +1,7 @@ @testset "Secondary invariants (for matrix groups)" begin K, a = cyclotomic_field(3, "a") - # Force use of internal polynomial_ring with ordering = :lex - R, _ = graded_polynomial_ring(K, 3, ordering = :lex) + # Force use of internal polynomial_ring with internal_ordering = :lex + R, _ = graded_polynomial_ring(K, 3, internal_ordering = :lex) M1 = matrix(K, 3, 3, [ 0, 1, 0, 1, 0, 0, 0, 0, 1 ]) M2 = matrix(K, 3, 3, [ 1, 0, 0, 0, a, 0, 0, 0, -a - 1 ]) RG0 = invariant_ring(R, matrix_group(M1, M2)) diff --git a/test/Rings/NumberField.jl b/test/Rings/NumberField.jl index 5f4a3edb9ea3..5e7c20b65c50 100644 --- a/test/Rings/NumberField.jl +++ b/test/Rings/NumberField.jl @@ -206,7 +206,7 @@ if Bk == FlintQQ for i in 1:10 BB = [rand(K, -2:2) for j in 1:rand(1:10)] - M = @inferred basis_matrix(BB, FakeFmpqMat) + M = @inferred basis_matrix(BB, Hecke.FakeFmpqMat) @test nrows(M) == length(BB) @test ncols(M) == degree(K) for n in 1:nrows(M) diff --git a/test/Rings/groebner.jl b/test/Rings/groebner.jl index 5005d865b830..a06d2e390259 100644 --- a/test/Rings/groebner.jl +++ b/test/Rings/groebner.jl @@ -147,7 +147,7 @@ end end @testset "f4" begin - R, (x1,x2,x3,x4) = polynomial_ring(GF(next_prime(2^28)), ["x1", "x2", "x3", "x4"], ordering=:degrevlex) + R, (x1,x2,x3,x4) = polynomial_ring(GF(next_prime(2^28)), ["x1", "x2", "x3", "x4"]) I = ideal(R,[x1+2*x2+2*x3+2*x4-1, x1^2+2*x2^2+2*x3^2+2*x4^2-x1, 2*x1*x2+2*x2*x3+2*x3*x4-x2, diff --git a/test/Rings/mpoly.jl b/test/Rings/mpoly.jl index 01eceacb8aee..7d46fd7ce031 100644 --- a/test/Rings/mpoly.jl +++ b/test/Rings/mpoly.jl @@ -232,14 +232,16 @@ end # are native to singular while FpFieldElem now has a proper wrapper for Zn in [residue_ring(ZZ, 11)[1], residue_ring(ZZ, ZZRingElem(10)^50+151)[1], GF(11), GF(ZZRingElem(10)^50+151)] - R, (x, y) = polynomial_ring(Zn, ["x", "y"], ordering = :degrevlex) + # Setting the internal_ordering is necessary for divrem to use the correct ordering + R, (x, y) = polynomial_ring(Zn, ["x", "y"], internal_ordering = :degrevlex) l = [x*y+x^3+1, x*y^2+x^2+1] g = gens(groebner_basis(ideal(R, l); ordering = degrevlex(gens(R)))) @test iszero(divrem(l[1] + l[2], g)[2]) end F, a = finite_field(11, 2, "a") - R, (x, y, z) = polynomial_ring(F, ["x", "y", "z"], ordering = :degrevlex) + # Setting the internal_ordering is necessary for divrem to use the correct ordering + R, (x, y, z) = polynomial_ring(F, ["x", "y", "z"], internal_ordering = :degrevlex) l = [3*x^5 + a*x*y^2 + a^2*z^2, z^3*x^2 + 7*y^3 + z] gb = gens(groebner_basis(ideal(R, l); ordering = degrevlex(gens(R)))) @test iszero(divrem(l[1] + l[2], gb)[2]) @@ -298,7 +300,7 @@ end end @testset "Grassmann Plücker Relations" begin - R, x = polynomial_ring(residue_ring(ZZ, 7)[1], "x" => (1:2, 1:3), ordering=:degrevlex) + R, x = polynomial_ring(residue_ring(ZZ, 7)[1], "x" => (1:2, 1:3)) test_ideal = ideal([x[1, 2]*x[2, 2] + 6*x[2, 1]*x[1, 3] + x[1, 1]*x[2, 3]]) @test grassmann_pluecker_ideal(R, 2, 4) == test_ideal end diff --git a/test/Rings/orderings.jl b/test/Rings/orderings.jl index a0f7c397db45..522d2373e6b5 100644 --- a/test/Rings/orderings.jl +++ b/test/Rings/orderings.jl @@ -168,7 +168,8 @@ end (leading_coefficient(f), leading_exponent(f)) Fp = GF(7) - R, (x, y, z) = polynomial_ring(Fp, 3, ordering = :deglex) + # Explicitly using an ordering different from the internal_ordering + R, (x, y, z) = polynomial_ring(Fp, 3, internal_ordering = :deglex) f = x*y + 5*z^3 @test collect(monomials(f; ordering = lex(R))) == [ x*y, z^3 ] @test leading_monomial(f; ordering = lex(R)) == x*y @@ -322,7 +323,7 @@ end negdeglex([x,y,s])*negdegrevlex([t,u]), negwdeglex([x,y,s],[1,2,3])*negwdegrevlex([t,u],[1,2])) @test O == monomial_ordering(R, singular(O)) - @test O == monomial_ordering(R, ordering(singular_poly_ring(R, O))) + @test O == monomial_ordering(R, Singular.ordering(singular_poly_ring(R, O))) end @test_throws ErrorException monomial_ordering(R, Singular.ordering_lp(4)) From 12a3e05f9f65b27528563905733740a31e289a5c Mon Sep 17 00:00:00 2001 From: JohnAAbbott <124266874+JohnAAbbott@users.noreply.github.com> Date: Thu, 22 Feb 2024 18:06:49 +0100 Subject: [PATCH 24/29] Corrected defn of deg(ideal); correction from W Decker (#3412) * Corrected defn of deg(ideal); correction from W Decker * Removed spaces at end of lines (to force GitHub to try again) (cherry picked from commit 290734f72c7d0231669cd848cb5aa7fb3a7826bf) --- src/Rings/mpoly-graded.jl | 23 ++++++++++++----------- 1 file changed, 12 insertions(+), 11 deletions(-) diff --git a/src/Rings/mpoly-graded.jl b/src/Rings/mpoly-graded.jl index 782383a31a51..a779894feaec 100644 --- a/src/Rings/mpoly-graded.jl +++ b/src/Rings/mpoly-graded.jl @@ -346,7 +346,7 @@ false return true end end - try + try homogeneous_component(R, zero(G)) catch e if e isa ArgumentError && e.msg == "Polyhedron not bounded" @@ -1241,7 +1241,7 @@ function monomial_basis(W::MPolyDecRing, d::FinGenAbGroupElem) #Ax = b, Cx >= 0 C = identity_matrix(FlintZZ, ngens(W)) A = reduce(vcat, [x.coeff for x = W.d]) - k = solve_mixed(transpose(A), transpose(d.coeff), C) + k = solve_mixed(transpose(A), transpose(d.coeff), C) for ee = 1:nrows(k) e = k[ee, :] a = MPolyBuildCtx(forget_decoration(W)) @@ -1264,7 +1264,7 @@ function monomial_basis(R::MPolyDecRing, g::IntegerUnion) end @doc raw""" - homogeneous_component(R::MPolyDecRing, g::FinGenAbGroupElem) + homogeneous_component(R::MPolyDecRing, g::FinGenAbGroupElem) Given a polynomial ring `R` over a field which is graded by a free group of type `FinGenAbGroup`, and given an element `g` of that group, @@ -1404,7 +1404,7 @@ end ########################################### # needs re-thought -function (W::MPolyDecRing)(m::Generic.FreeModuleElem) +function (W::MPolyDecRing)(m::Generic.FreeModuleElem) h = has_relshp(parent(m), W) if h !== nothing return h(m) @@ -1451,11 +1451,11 @@ mutable struct HilbertData W = R.d W = [Int(W[i][1]) for i = 1:ngens(R)] - + @req minimum(W) > 0 "The weights must be positive" @req coefficient_ring(R) isa AbstractAlgebra.Field "The coefficient ring must be a field" @req all(is_homogeneous, gens(I)) "The generators of the ideal must be homogeneous" - + G = groebner_assure(I) h = Singular.hilbert_series(G.S, W) return new(h, W, I) @@ -1482,13 +1482,13 @@ end function hilbert_polynomial(H::HilbertData) @req all(isone, H.weights) "All weights must be 1" - + q, dn = hilbert_series_reduced(H) a = QQFieldElem[] nf = QQFieldElem(1) d = degree(dn)-1 for i=1:d+1 - push!(a, q(1)//nf) + push!(a, q(1)//nf) nf *= i q = derivative(q) end @@ -1506,7 +1506,7 @@ end function Oscar.degree(H::HilbertData) @req all(isone, H.weights) "All weights must be 1" - + P = hilbert_polynomial(H) if iszero(P) q, _ = hilbert_series_reduced(H) @@ -2383,11 +2383,12 @@ julia> degree(I) 6 ``` """ -@attr Int function degree(I::MPolyIdeal) +@attr ZZRingElem function degree(I::MPolyIdeal) P = base_ring(I) if !is_standard_graded(P) H = homogenizer(P, "_h") I = H(I) end - return Int(degree(HilbertData(I))) + A, _ = quo(base_ring(I), I) + return degree(A) end From 82ec9dadc87a1d3f1a19d64f165f177182982564 Mon Sep 17 00:00:00 2001 From: antonydellavecchia Date: Fri, 23 Feb 2024 00:07:21 +0100 Subject: [PATCH 25/29] Serialize Polyhedral Objects over Oscar fields (#3386) * some progress on serializing dicts * saving * serialization: add helpers to deconstruct polymake bigobject to dict currently with a few warnings that might be removed later * updates * starting on load * fix type string for saving * adds work around for vector{Int} * use new qualified bigobject name * serialize dicts * still need to work out loading * can load polyhedral object over different fields * some updates * add helpers for conversion from oscar graphs back to polymake * tiny improvement * fix inner types, store coeff only once * polymake: improve matrix conversion helpers, allow float in some places * adds serialzation for sets * adds test for dicts * adds test for sets * replace johnson matrices with Johnson solids * replace johnson matrices with solids * pretty print the rest of the Johnson Solids * pretty print * padding, + file extension and not pretty printed * fixes polyhedral test * update file version tag * file version tag + add extension for surface files * fix surface loading * fix typo * adds fix for polyhedron of floats and adds test * fix typo * better padding implementation * adds catch for unsupported loading types * remove Nothing type for coeff inputs, and fixed vector collect * adds tests for serializing polyhdral objects over oscar fields * fixes to MILP * MILP: add missing specialization for QQ to avoid saving other fields for now * polymake: change warnings to debug when saving unsupported polymake properties * polyhedral: add missing field for loading milp * fix for polyhedron with floats * serialization: fix load distinction between different fields, fix loading float polytopes * Update test/Serialization/PolyhedralGeometry.jl * Apply suggestions from code review Co-authored-by: Lars Kastner --------- Co-authored-by: Benjamin Lorenz Co-authored-by: Benjamin Lorenz Co-authored-by: Lars Kastner (cherry picked from commit 52c123663ba4215c47f6d1901bb5fc59f0ac03ae) --- Project.toml | 2 +- data/JohnsonMatrices/j10.mat | 1 - data/JohnsonMatrices/j13.mat | 1 - data/JohnsonMatrices/j16.mat | 1 - data/JohnsonMatrices/j17.mat | 1 - data/JohnsonMatrices/j18.mat | 1 - data/JohnsonMatrices/j20.mat | 1 - data/JohnsonMatrices/j21.mat | 1 - data/JohnsonMatrices/j22.mat | 1 - data/JohnsonMatrices/j23.mat | 1 - data/JohnsonMatrices/j24.mat | 1 - data/JohnsonMatrices/j25.mat | 1 - data/JohnsonMatrices/j30.mat | 1 - data/JohnsonMatrices/j32.mat | 1 - data/JohnsonMatrices/j33.mat | 1 - data/JohnsonMatrices/j34.mat | 1 - data/JohnsonMatrices/j35.mat | 1 - data/JohnsonMatrices/j36.mat | 1 - data/JohnsonMatrices/j38.mat | 1 - data/JohnsonMatrices/j39.mat | 1 - 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data/Surfaces/bielliptic_d10_pi6 | 1 - data/Surfaces/bielliptic_d10_pi6.mrdi | 1 + data/Surfaces/bielliptic_d15_pi21 | 1 - data/Surfaces/bielliptic_d15_pi21.mrdi | 1 + data/Surfaces/bordiga | 1 - data/Surfaces/bordiga.mrdi | 1 + data/Surfaces/castelnuovo | 1 - data/Surfaces/castelnuovo.mrdi | 1 + data/Surfaces/cubic_scroll | 1 - data/Surfaces/cubic_scroll.mrdi | 1 + data/Surfaces/elliptic_d10_pi10 | 1 - data/Surfaces/elliptic_d10_pi10.mrdi | 1 + data/Surfaces/elliptic_d10_pi9 | 1 - data/Surfaces/elliptic_d10_pi9.mrdi | 1 + data/Surfaces/elliptic_d11_pi12 | 1 - data/Surfaces/elliptic_d11_pi12.mrdi | 1 + data/Surfaces/elliptic_d12_pi13 | 1 - data/Surfaces/elliptic_d12_pi13.mrdi | 1 + data/Surfaces/elliptic_d12_pi14_ss_0 | 1 - data/Surfaces/elliptic_d12_pi14_ss_0.mrdi | 1 + data/Surfaces/elliptic_d12_pi14_ss_inf | 1 - data/Surfaces/elliptic_d12_pi14_ss_inf.mrdi | 1 + data/Surfaces/elliptic_d7_pi6 | 1 - data/Surfaces/elliptic_d7_pi6.mrdi | 1 + data/Surfaces/elliptic_d8_pi7 | 1 - 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data/Surfaces/rational_d8_pi5.mrdi delete mode 100644 data/Surfaces/rational_d8_pi6 create mode 100644 data/Surfaces/rational_d8_pi6.mrdi delete mode 100644 data/Surfaces/rational_d9_pi6 create mode 100644 data/Surfaces/rational_d9_pi6.mrdi delete mode 100644 data/Surfaces/rational_d9_pi7 create mode 100644 data/Surfaces/rational_d9_pi7.mrdi delete mode 100644 data/Surfaces/veronese create mode 100644 data/Surfaces/veronese.mrdi diff --git a/Project.toml b/Project.toml index 9693d69ac0e4..fd6c71950f60 100644 --- a/Project.toml +++ b/Project.toml @@ -37,7 +37,7 @@ JSON3 = "1.13.2" LazyArtifacts = "1.6" Nemo = "0.43.0" Pkg = "1.6" -Polymake = "0.11.13" +Polymake = "0.11.14" Preferences = "1" Random = "1.6" RandomExtensions = "0.4.3" diff --git a/data/JohnsonMatrices/j10.mat b/data/JohnsonMatrices/j10.mat deleted file mode 100644 index 51584e6e0747..000000000000 --- a/data/JohnsonMatrices/j10.mat +++ /dev/null @@ -1 +0,0 @@ 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\ No newline at end of file diff --git a/src/AlgebraicGeometry/Surfaces/SurfacesP4.jl b/src/AlgebraicGeometry/Surfaces/SurfacesP4.jl index 6eaff26ae551..59b269779f78 100644 --- a/src/AlgebraicGeometry/Surfaces/SurfacesP4.jl +++ b/src/AlgebraicGeometry/Surfaces/SurfacesP4.jl @@ -48,7 +48,7 @@ export rational_d11_pi11_ss_inf export veronese function surface(n::String) - n = joinpath(oscardir, "data", "Surfaces", n) + n = joinpath(oscardir, "data", "Surfaces", "$n" * ".mrdi") I = load(n) S = base_ring(I) R = grade(S)[1] diff --git a/src/PolyhedralGeometry/Polyhedron/standard_constructions.jl b/src/PolyhedralGeometry/Polyhedron/standard_constructions.jl index 4c221c75bc5d..aca35c61ff0c 100644 --- a/src/PolyhedralGeometry/Polyhedron/standard_constructions.jl +++ b/src/PolyhedralGeometry/Polyhedron/standard_constructions.jl @@ -318,9 +318,9 @@ function johnson_solid(index::Int) if haskey(_johnson_names, index) # code used for generation of loaded files can be found at: # https://github.com/dmg-lab/JohnsonSrc - vertices = load(joinpath(oscardir, "data", "JohnsonMatrices", string("j", index, ".mat"))) - parent_field = base_ring(vertices) - return convex_hull(parent_field, vertices; non_redundant = true) + str_index = lpad(index, 2, '0') + filename = "j$str_index" * ".mrdi" + return load(joinpath(oscardir, "data", "JohnsonSolids", filename)) end pmp = Polymake.polytope.johnson_solid(index) return polyhedron(pmp) diff --git a/src/PolyhedralGeometry/helpers.jl b/src/PolyhedralGeometry/helpers.jl index 21f481749b8d..061e45191959 100644 --- a/src/PolyhedralGeometry/helpers.jl +++ b/src/PolyhedralGeometry/helpers.jl @@ -122,29 +122,17 @@ matrix_for_polymake(x::Union{Oscar.ZZMatrix, Oscar.QQMatrix, AbstractMatrix}) = number_of_rows(x::SubArray{T, 2, U, V, W}) where {T, U, V, W} = size(x, 1) -function Polymake.Matrix{Polymake.Rational}(x::Union{Oscar.QQMatrix,AbstractMatrix{Oscar.QQFieldElem}}) - res = Polymake.Matrix{Polymake.Rational}(size(x)...) - for i in eachindex(x) - res[i] = x[i] - end - return res -end - -function Polymake.Matrix{Polymake.OscarNumber}(x::Union{MatElem, AbstractMatrix{<:FieldElem}}) - res = Polymake.Matrix{Polymake.OscarNumber}(size(x)...) - for i in eachindex(x) - res[i] = x[i] - end - return res -end - _isempty_halfspace(x::Pair{<:Union{Oscar.MatElem, AbstractMatrix}, Any}) = isempty(x[1]) _isempty_halfspace(x) = isempty(x) +function Polymake.Matrix{T}(x::Union{MatElem,AbstractMatrix{<:FieldElem}}) where T<:Union{Float64, Polymake.Rational, Polymake.Integer, Polymake.OscarNumber} + res = Polymake.Matrix{T}(size(x)...) + return res .= x +end -Base.convert(::Type{Polymake.QuadraticExtension{Polymake.Rational}}, x::QQFieldElem) = Polymake.QuadraticExtension(convert(Polymake.Rational, x)) +Base.convert(::Type{Polymake.Matrix{T}}, x::MatElem) where T = Polymake.Matrix{T}(x) -Base.convert(T::Type{<:Polymake.Matrix}, x::Union{ZZMatrix,QQMatrix}) = Base.convert(T, Matrix(x)) +Base.convert(::Type{Polymake.QuadraticExtension{Polymake.Rational}}, x::QQFieldElem) = Polymake.QuadraticExtension(convert(Polymake.Rational, x)) Base.convert(::Type{<:Polymake.Integer}, x::ZZRingElem) = GC.@preserve x return Polymake.new_integer_from_fmpz(x) @@ -182,8 +170,6 @@ Base.convert(::Type{Polymake.OscarNumber}, x::FieldElem) = Polymake.OscarNumber( (::Type{T})(x::Polymake.OscarNumber) where T<:FieldElem = convert(T, Polymake.unwrap(x)) -Base.convert(::Type{Polymake.Matrix{Polymake.OscarNumber}}, x::MatElem{<:FieldElem}) = Polymake.Matrix{Polymake.OscarNumber}(x) - (R::QQField)(x::Polymake.Rational) = convert(QQFieldElem, x) (Z::ZZRing)(x::Polymake.Rational) = convert(ZZRingElem, x) @@ -202,12 +188,16 @@ end (F::Field)(x::Polymake.Rational) = F(QQ(x)) (F::Field)(x::Polymake.OscarNumber) = F(Polymake.unwrap(x)) -Polymake.convert_to_pm_type(::Type{Oscar.ZZMatrix}) = Polymake.Matrix{Polymake.Integer} -Polymake.convert_to_pm_type(::Type{Oscar.QQMatrix}) = Polymake.Matrix{Polymake.Rational} -Polymake.convert_to_pm_type(::Type{Oscar.ZZRingElem}) = Polymake.Integer -Polymake.convert_to_pm_type(::Type{Oscar.QQFieldElem}) = Polymake.Rational +Polymake.convert_to_pm_type(::Type{ZZMatrix}) = Polymake.Matrix{Polymake.Integer} +Polymake.convert_to_pm_type(::Type{QQMatrix}) = Polymake.Matrix{Polymake.Rational} +Polymake.convert_to_pm_type(::Type{ZZRingElem}) = Polymake.Integer +Polymake.convert_to_pm_type(::Type{QQFieldElem}) = Polymake.Rational Polymake.convert_to_pm_type(::Type{T}) where T<:FieldElem = Polymake.OscarNumber Polymake.convert_to_pm_type(::Type{<:Oscar.MatElem}) = Polymake.Matrix{Polymake.OscarNumber} +Polymake.convert_to_pm_type(::Type{<:Graph{T}}) where T<:Union{Directed,Undirected} = Polymake.Graph{T} +Polymake.convert_to_pm_type(::Type{<:MatElem{Float64}}) = Polymake.Matrix{Float64} + +Base.convert(::Type{<:Polymake.Graph{T}}, g::Graph{T}) where T<:Union{Directed,Undirected} = Oscar.pm_object(g) function remove_zero_rows(A::AbstractMatrix) A[findall(x->!iszero(x),collect(eachrow(A))),:] diff --git a/src/PolyhedralGeometry/mixed_integer_linear_program.jl b/src/PolyhedralGeometry/mixed_integer_linear_program.jl index b7715d2e9652..a4d0fcaa2287 100644 --- a/src/PolyhedralGeometry/mixed_integer_linear_program.jl +++ b/src/PolyhedralGeometry/mixed_integer_linear_program.jl @@ -2,15 +2,16 @@ struct MixedIntegerLinearProgram{T} <: PolyhedralObject{T} feasible_region::Polyhedron{T} polymake_milp::Polymake.BigObject convention::Symbol + parent_field::Field MixedIntegerLinearProgram{T}( - fr::Polyhedron{T}, milp::Polymake.BigObject, c::Symbol - ) where {T<:scalar_types} = new{T}(fr, milp, c) + fr::Polyhedron{T}, milp::Polymake.BigObject, c::Symbol, parent_field::Field + ) where {T<:scalar_types} = new{T}(fr, milp, c, parent_field) end # no default = `QQFieldElem` here; scalar type can be derived from the feasible region mixed_integer_linear_program(p::Polyhedron{T}, x...) where {T<:scalar_types} = - MixedIntegerLinearProgram{T}(p, x...) + MixedIntegerLinearProgram{T}(p, x..., coefficient_field(p)) @doc raw""" mixed_integer_linear_program(P, c; integer_variables = [], k = 0, convention = :max) @@ -45,10 +46,10 @@ function mixed_integer_linear_program( Polymake.attach(milp, "convention", "min") end Polymake.add(pm_object(P), "MILP", milp) - MixedIntegerLinearProgram{T}(P, milp, convention) + MixedIntegerLinearProgram{T}(P, milp, convention, coefficient_field(P)) end -mixed_integer_linear_program( +function mixed_integer_linear_program( ::Type{T}, A::Union{Oscar.MatElem,AbstractMatrix}, b, @@ -56,9 +57,13 @@ mixed_integer_linear_program( integer_variables=Vector{Int64}([]), k=0, convention=:max, -) where {T<:scalar_types} = mixed_integer_linear_program( - polyhedron(T, A, b), c; integer_variables=integer_variables, k=k, convention=convention -) + ) where {T<:scalar_types} + P = polyhedron(T, A, b) + return mixed_integer_linear_program( + P, c, coefficient_field(P); + integer_variables=integer_variables, k=k, convention=convention + ) +end pm_object(milp::MixedIntegerLinearProgram) = milp.polymake_milp diff --git a/src/Serialization/Fields.jl b/src/Serialization/Fields.jl index 9fa63fcf5600..6df50bdc2bcb 100644 --- a/src/Serialization/Fields.jl +++ b/src/Serialization/Fields.jl @@ -52,6 +52,10 @@ function load_object(s:: DeserializerState, ::Type{Field}) return load_typed_object(s) end +################################################################################ +# floats +@register_serialization_type AbstractAlgebra.Floats{Float64} "Floats" + ################################################################################ # field of rationals (singleton type) @register_serialization_type QQField diff --git a/src/Serialization/PolyhedralGeometry.jl b/src/Serialization/PolyhedralGeometry.jl index 1d9132593f49..c16c4dc399b2 100644 --- a/src/Serialization/PolyhedralGeometry.jl +++ b/src/Serialization/PolyhedralGeometry.jl @@ -39,27 +39,51 @@ function save_type_params(s::SerializerState, obj::T) where T <: PolyhedralObjec end end -function save_object(s::SerializerState, obj::PolyhedralObject) +function save_object(s::SerializerState, obj::PolyhedralObject{S}) where S <: Union{QQFieldElem, Float64} save_object(s, pm_object(obj)) end +function save_object(s::SerializerState, obj::PolyhedralObject{<:FieldElem}) + if typeof(obj) <: Union{MixedIntegerLinearProgram, LinearProgram} + T = typeof(obj) + error("Unsupported type $T for serialization") + end + save_data_dict(s) do + save_typed_object(s, _polyhedral_object_as_dict(obj)) + end +end + function load_type_params(s::DeserializerState, ::Type{<:PolyhedralObject}) return load_typed_object(s) end -function load_object(s::DeserializerState, T::Type{<:PolyhedralObject}, field::Field) - return load_from_polymake(T{elem_type(field)}, Dict{Symbol, Any}(s.obj)) +function load_object(s::DeserializerState, T::Type{<:PolyhedralObject}, + field::U) where {U <: Union{QQField, AbstractAlgebra.Floats}} + return load_from_polymake(T{elem_type(field)}, Dict{Symbol, Any}(s.obj)) end function load_object(s::DeserializerState, T::Type{<:PolyhedralObject{S}}, - field::Field) where S <: FieldElem + field::U) where {S <: Union{QQFieldElem, Float64}, U <: Union{QQField, AbstractAlgebra.Floats}} return load_from_polymake(T, Dict{Symbol, Any}(s.obj)) end +function load_object(s::DeserializerState, T::Type{<:PolyhedralObject}, field::Field) + polymake_dict = load_typed_object(s) + bigobject = _dict_to_bigobject(polymake_dict) + return T{elem_type(field)}(bigobject, field) +end + +function load_object(s::DeserializerState, T::Type{<:PolyhedralObject{S}}, + field::Field) where S <: FieldElem + polymake_dict = load_typed_object(s) + bigobject = _dict_to_bigobject(polymake_dict) + return T(bigobject, field) +end + ############################################################################## @register_serialization_type LinearProgram uses_params -function save_object(s::SerializerState, lp::LinearProgram) +function save_object(s::SerializerState, lp::LinearProgram{QQFieldElem}) lpcoeffs = lp.polymake_lp.LINEAR_OBJECTIVE serialized = Polymake.call_function(Symbol("Core::Serializer"), :serialize, lpcoeffs) jsonstr = Polymake.call_function(:common, :encode_json, serialized) @@ -70,7 +94,7 @@ function save_object(s::SerializerState, lp::LinearProgram) end end -function load_object(s::DeserializerState, ::Type{<:LinearProgram}, field::Field) +function load_object(s::DeserializerState, ::Type{<:LinearProgram}, field::QQField) coeff_type = elem_type(field) fr = load_object(s, Polyhedron, field, :feasible_region) conv = load_object(s, String, :convention) @@ -92,7 +116,7 @@ end ############################################################################## @register_serialization_type MixedIntegerLinearProgram uses_params -function save_object(s::SerializerState, milp::MixedIntegerLinearProgram) +function save_object(s::SerializerState, milp::MixedIntegerLinearProgram{QQFieldElem}) milp_coeffs = milp.polymake_milp.LINEAR_OBJECTIVE int_vars = milp.polymake_milp.INTEGER_VARIABLES coeffs_serialized = Polymake.call_function( @@ -109,7 +133,7 @@ function save_object(s::SerializerState, milp::MixedIntegerLinearProgram) end end -function load_object(s::DeserializerState, ::Type{<: MixedIntegerLinearProgram}, field::Field) +function load_object(s::DeserializerState, ::Type{<: MixedIntegerLinearProgram}, field::QQField) fr = load_object(s, Polyhedron, field, :feasible_region) conv = load_object(s, String, :convention) milp_coeffs = load_node(s, :milp_coeffs) do coeffs @@ -137,7 +161,7 @@ function load_object(s::DeserializerState, ::Type{<: MixedIntegerLinearProgram}, end lp = Polymake._lookup_multi(pm_object(fr), "MILP", index-1) T = elem_type(field) - return MixedIntegerLinearProgram{T}(fr, lp, Symbol(conv)) + return MixedIntegerLinearProgram{T}(fr, lp, Symbol(conv), field) end # use generic serialization for the other types: diff --git a/src/Serialization/containers.jl b/src/Serialization/containers.jl index 6f656c6f11d9..705623614bed 100644 --- a/src/Serialization/containers.jl +++ b/src/Serialization/containers.jl @@ -9,8 +9,8 @@ function save_type_params(s::SerializerState, obj::S) where {T, S <:MatVecType{T save_data_dict(s) do save_object(s, encode_type(S), :name) if serialize_with_params(T) && !isempty(obj) - if hasmethod(parent, (T,)) - parents = map(parent, obj) + if !(T <: MatVecType) && hasmethod(parent, (T,)) + parents = parent.(obj) parents_all_equal = all(map(x -> isequal(first(parents), x), parents)) @req parents_all_equal "Not all parents of Vector or Matrix entries are the same, consider using a Tuple" end @@ -84,7 +84,8 @@ function load_object(s::DeserializerState, ::Type{<: Vector}, params::Tuple) return T[] else loaded_v = [] - for i in 1:length(v) + len = length(v) + for i in 1:len load_node(s, i) do _ push!(loaded_v, load_object(s, T, params[2])) end @@ -114,7 +115,7 @@ function save_type_params(s::SerializerState, tup::T) where T <: Tuple save_data_dict(s) do save_object(s, encode_type(Tuple), :name) n = fieldcount(T) - save_data_array(s, :params) do + save_data_array(s, :params) do for i in 1:n U = fieldtype(T, i) if serialize_with_params(U) @@ -141,7 +142,7 @@ function load_type_params(s::DeserializerState, ::Type{Tuple}) end function save_object(s::SerializerState, obj::Tuple) - save_data_array(s) do + save_data_array(s) do for entry in obj if serialize_with_id(typeof(entry)) ref = save_as_ref(s, entry) @@ -176,7 +177,7 @@ function save_type_params(s::SerializerState, obj::T) where T <: NamedTuple save_data_dict(s) do save_object(s, encode_type(NamedTuple), :name) save_data_dict(s, :params) do - save_data_array(s, :tuple_params) do + save_data_array(s, :tuple_params) do for (i, value) in enumerate(values(obj)) U = fieldtype(T, i) if serialize_with_params(U) @@ -221,7 +222,7 @@ end ################################################################################ # Saving and loading matrices @register_serialization_type Matrix uses_params - + function save_object(s::SerializerState, mat::Matrix) m, n = size(mat) save_data_array(s) do @@ -236,8 +237,9 @@ function load_object(s::DeserializerState, ::Type{<:Matrix}, params::Type) if isempty(entries) return zero_matrix(parent_type(params)(), 0, 0) end + len = length(entries) m = reduce(vcat, [ - permutedims(load_object(s, Vector, params, i)) for i in 1:length(entries) + permutedims(load_object(s, Vector, params, i)) for i in 1:len ]) return Matrix{params}(m) end @@ -245,9 +247,169 @@ end function load_object(s::DeserializerState, ::Type{<:Matrix}, params::Tuple) load_node(s) do entries + if isempty(entries) + return params[1][] + end + + len = length(entries) m = reduce(vcat, [ - permutedims(load_object(s, Vector, params, i)) for i in 1:length(entries) + permutedims(load_object(s, Vector, params, i)) for i in 1:len ]) return Matrix{params[1]}(m) end end + +################################################################################ +# Saving and loading dicts +@register_serialization_type Dict uses_params + +function save_type_params(s::SerializerState, obj::Dict{S, T}) where {S <: Union{Symbol, String, Int}, T} + save_data_dict(s) do + save_object(s, encode_type(Dict), :name) + save_data_dict(s, :params) do + save_object(s, encode_type(S), :key_type) + for (k, v) in obj + U = typeof(v) + if serialize_with_params(U) + save_type_params(s, v, Symbol(k)) + else + save_object(s, encode_type(U), Symbol(k)) + end + end + end + end +end + +function load_type_params(s::DeserializerState, ::Type{<:Dict}) + params_dict = Dict{Symbol, Any}() + for (k, _) in s.obj + load_node(s, k) do _ + value_type = decode_type(s) + + if serialize_with_params(value_type) + params_dict[k] = Dict{Symbol, Any}( + type_key => value_type, + :params => load_params_node(s) + ) + else + params_dict[k] = value_type + end + end + end + return params_dict +end + +function save_object(s::SerializerState, obj::Dict{S, T}) where {S <: Union{Symbol, String, Int}, T} + save_data_dict(s) do + for (k, v) in obj + save_object(s, v, Symbol(k)) + end + end +end + +function load_object(s::DeserializerState, ::Type{<:Dict}, params::Dict{Symbol, Any}) + key_type = params[:key_type] + + dict = Dict{key_type, Any}() + for (k, _) in s.obj + if k == :key_type + continue + end + + if key_type == Int + key = parse(Int, string(k)) + else + key = key_type(k) + end + + if params[k] isa Type + dict[key] = load_object(s, params[k], k) + else + dict[key] = load_object(s, params[k][type_key], params[k][:params], k) + end + end + + return dict +end + +################################################################################ +# Saving and loading sets +@register_serialization_type Set uses_params + +function save_type_params(s::SerializerState, obj::Set{T}) where T + save_data_dict(s) do + save_object(s, encode_type(Set), :name) + if serialize_with_params(T) && !isempty(obj) + save_type_params(s, first(obj), :params) + else + save_object(s, encode_type(T), :params) + end + end +end + +function load_type_params(s::DeserializerState, ::Type{<:Set}) + T = decode_type(s) + if serialize_with_params(T) && haskey(s, :params) + params = load_params_node(s) + return (T, params) + end + return T +end + +function save_object(s::SerializerState, x::Set) + save_data_array(s) do + for elem in x + if serialize_with_id(typeof(elem)) + ref = save_as_ref(s, elem) + save_object(s, ref) + else + save_object(s, elem) + end + end + end +end + +function load_object(s::DeserializerState, ::Type{<: Set}, params::Any) + load_node(s) do v + if serialize_with_id(params) + loaded_v = params[load_ref(s, x) for x in v] + else + loaded_v = params[] + for (i, entry) in enumerate(v) + push!(loaded_v, load_object(s, params, i)) + end + end + return Set(loaded_v) + end +end + +# handles nested +function load_object(s::DeserializerState, ::Type{<: Set}, params::Tuple) + T = params[1] + load_node(s) do v + if isempty(v) + return Set{T}() + else + loaded_v = Set{T}() + len = length(v) + for i in 1:len + load_node(s, i) do _ + push!(loaded_v, load_object(s, T, params[2])) + end + end + return Set{typeof(first(loaded_v))}(loaded_v) + end + end +end + +function load_object(s::DeserializerState, ::Type{<: Set}, params::Ring) + T = elem_type(params) + loaded_entries = load_array_node(s) do _ + if serialize_with_params(T) + return load_object(s, T, params) + else + return load_object(s, T) + end + end + return Set{T}(loaded_entries) +end diff --git a/src/Serialization/main.jl b/src/Serialization/main.jl index 6abfe7d2dd25..0b262856b958 100644 --- a/src/Serialization/main.jl +++ b/src/Serialization/main.jl @@ -42,7 +42,7 @@ function version_number(v_number::String) return VersionNumber(v_number) end -# needed for older versions +# needed for older versions function version_number(dict::Dict) return VersionNumber(dict[:major], dict[:minor], dict[:patch]) end @@ -97,7 +97,7 @@ function decode_type(s::DeserializerState) error("unsupported type '$unsupported_type' for decoding") end end - + if type_key in keys(s.obj) return load_node(s, type_key) do _ decode_type(s) @@ -175,7 +175,7 @@ function save_typed_object(s::SerializerState, x::T, key::Symbol) where T ref = save_as_ref(s, x) save_object(s, ref) else - save_data_dict(s) do + save_data_dict(s) do save_typed_object(s, x) end end @@ -202,7 +202,11 @@ function load_typed_object(s::DeserializerState; override_params::Any = nothing) if Base.issingletontype(T) && return T() elseif serialize_with_params(T) if !isnothing(override_params) - params = override_params + if override_params isa Dict + error("Unsupported override type") + else + params = override_params + end else # depending on the type, :params is either an object to be loaded or a # dict with keys and object values to be loaded @@ -284,8 +288,10 @@ import Distributed.AbstractSerializer # add these here so that the proper errors are thrown # when the type hasn't been registered serialize_with_id(::Type) = false +serialize_with_id(obj::Any) = false serialize_with_params(::Type) = false + function register_serialization_type(ex::Any, str::String, uses_id::Bool, uses_params::Bool) return esc( quote @@ -304,12 +310,13 @@ function register_serialization_type(ex::Any, str::String, uses_id::Bool, uses_p # Types like ZZ, QQ, and ZZ/nZZ do not require ids since there is no syntactic # ambiguities in their encodings. - serialize_with_id(obj::T) where T <: $ex = $uses_id + serialize_with_id(obj::T) where T <: $ex = $uses_id serialize_with_id(T::Type{<:$ex}) = $uses_id serialize_with_params(T::Type{<:$ex}) = $uses_params # only extend serialize on non std julia types - if !($ex <: Union{Number, String, Bool, Symbol, Vector, Tuple, Matrix, NamedTuple}) + non_oscar_types = Union{Number, String, Bool, Symbol, Vector, Tuple, Matrix, NamedTuple, Dict, Set} + if !($ex <: non_oscar_types) function serialize(s::AbstractSerializer, obj::T) where T <: $ex serialize_type(s, T) save(s.io, obj; serializer_type=IPCSerializer) @@ -426,9 +433,9 @@ function save(io::IO, obj::T; metadata::Union{MetaData, Nothing}=nothing, global_serializer_state.id_to_obj[ref] = obj end save_object(s, string(ref), :id) - + end - + # this should be handled by serializers in a later commit / PR if !isempty(s.refs) && serializer_type == JSONSerializer save_data_dict(s, refs_key) do @@ -441,7 +448,7 @@ function save(io::IO, obj::T; metadata::Union{MetaData, Nothing}=nothing, end end end - + if !isnothing(metadata) save_json(s, json(metadata), :meta) end @@ -483,7 +490,7 @@ See [`save`](@ref). ```jldoctest julia> save("/tmp/fourtitwo.json", 42); - + julia> load("/tmp/fourtitwo.json") 42 @@ -611,4 +618,3 @@ function load(filename::String; params::Any = nothing, type::Any = nothing) return load(file; params=params, type=type) end end - diff --git a/src/Serialization/polymake.jl b/src/Serialization/polymake.jl index 59246167da25..4b876581d5e3 100644 --- a/src/Serialization/polymake.jl +++ b/src/Serialization/polymake.jl @@ -35,9 +35,14 @@ const polymake2OscarTypes = Dict{String, Type}([ function load_from_polymake(::Type{T}, jsondict::Dict{Symbol, Any}) where { T<:Union{Cone{<:scalar_types}, Polyhedron{<:scalar_types}, PolyhedralFan{<:scalar_types}, PolyhedralComplex{<:scalar_types}, SubdivisionOfPoints{<:scalar_types}, SimplicialComplex}} - inner_object = Polymake.call_function(:common, :deserialize_json_string, json(jsondict)) - return T(inner_object) + if T <: PolyhedralObject{QQFieldElem} + return T(inner_object) + elseif T <: PolyhedralObject{Float64} + return T(inner_object, AbstractAlgebra.Floats{Float64}()) + else + error("Unsupported object type $T for loading polymake object") + end end @@ -64,3 +69,85 @@ function load_from_polymake(jsondict::Dict{Symbol, Any}) end end +_pmdata_for_oscar(bo::Polymake.BigObject, coeff::Field) = _bigobject_to_dict(bo, coeff) + +_pmdata_for_oscar(::Nothing, coeff::Field) = nothing +_pmdata_for_oscar(v::Union{Bool,Int64,Float64,String}, coeff::Field) = v +if Polymake.CxxWrap.CxxLong != Int64 + _pmdata_for_oscar(i::Polymake.CxxWrap.CxxLong, coeff::Field) = Int64(i) +end + +_pmdata_for_oscar(im::IncidenceMatrix, coeff::Field) = im + +_pmdata_for_oscar(g::Polymake.Graph{T}, coeff::Field) where T = Graph{T}(g) + +_pmdata_for_oscar(m::Polymake.Matrix, coeff::Field) = matrix(coeff, m) +_pmdata_for_oscar(m::Polymake.Matrix{<:Polymake.Integer}, coeff::Field) = matrix(ZZ, m) +_pmdata_for_oscar(m::Polymake.Matrix{<:Polymake.Rational}, coeff::Field) = matrix(QQ, m) + +_pmdata_for_oscar(m::Polymake.SparseMatrix, coeff::Field) = _pmdata_for_oscar(Polymake.common.dense(m), coeff) + +_pmdata_for_oscar(v::Polymake.Vector, coeff::Field) = collect(elem_type(coeff), map(coeff, v)) +_pmdata_for_oscar(v::Polymake.Vector{<:Polymake.Integer}, coeff::Field) = collect(ZZRingElem, map(ZZ, v)) +_pmdata_for_oscar(v::Polymake.Vector{<:Polymake.Rational}, coeff::Field) = collect(QQFieldElem, map(QQ, v)) + +_pmdata_for_oscar(v::Polymake.SparseVector, coeff::Field) = _pmdata_for_oscar(Polymake.common.dense(v), coeff) + +_pmdata_for_oscar(s::Polymake.Integer, coeff::Field) = ZZ(s) +_pmdata_for_oscar(s::Polymake.Rational, coeff::Field) = QQ(s) +_pmdata_for_oscar(s::Polymake.OscarNumber, coeff::Field) = coeff(s) + +_pmdata_for_oscar(s::Polymake.CxxWrap.StdString, coeff::Field) = String(s) + +_pmdata_for_oscar(a::Polymake.Array, coeff::Field) = [_pmdata_for_oscar(e, coeff) for e in a] +_pmdata_for_oscar(s::Polymake.Set, coeff::Field) = Set(_pmdata_for_oscar(e, coeff) for e in s) + + +function _bigobject_to_dict(bo::Polymake.BigObject, coeff::Field) + data = Dict{String,Any}() + for pname in Polymake.list_properties(bo) + p = Polymake.give(bo, pname) + if p isa Polymake.PropertyValue + @debug "missing c++ mapping: skipping $pname of type $(Polymake.typeinfo_string(p, true))" + else + try + obj = _pmdata_for_oscar(p, coeff) + data[pname] = obj + catch e + if e isa MethodError + @debug "failed to convert $pname of type $(typeof(p)) to Oscar, skipping" + else + rethrow(e) + end + end + end + end + data +end + +function _polyhedral_object_as_dict(x::Oscar.PolyhedralObjectUnion) + bo = Oscar.pm_object(x) + data = _bigobject_to_dict(bo, coefficient_field(x)) + data["_type"] = Polymake.bigobject_qualifiedname(bo) + data["_coeff"] = coefficient_field(x) + return data +end + +function _load_bigobject_from_dict!(obj::Polymake.BigObject, dict::Dict, parent_key::String="") + for (k, v) in dict + key_str = parent_key == "" ? k : parent_key * "." * k + first(k) == '_' && continue + + if v isa Dict + _load_bigobject_from_dict!(obj, v, key_str) + else + Polymake.take(obj, key_str, convert(Polymake.PolymakeType, v)) + end + end +end + +function _dict_to_bigobject(dict::Dict{String, Any}) + obj = Polymake.BigObject(Polymake.BigObjectType(dict["_type"])) + _load_bigobject_from_dict!(obj, dict) + return obj +end diff --git a/src/Serialization/serializers.jl b/src/Serialization/serializers.jl index 62e6d446d90e..0a2df3d52c14 100644 --- a/src/Serialization/serializers.jl +++ b/src/Serialization/serializers.jl @@ -231,7 +231,7 @@ function deserializer_open(io::IO, T::Type{IPCSerializer}) # Using a JSON3.Object from JSON3 version 1.13.2 causes # @everywhere using Oscar # to hang. So we use a Dict here for now. - + obj = JSON.parse(io, dicttype=Dict{Symbol, Any}) return T(DeserializerState(obj, nothing, nothing)) end diff --git a/test/PolyhedralGeometry/polyhedron.jl b/test/PolyhedralGeometry/polyhedron.jl index 18e41a83a6be..c2f3000ec46f 100644 --- a/test/PolyhedralGeometry/polyhedron.jl +++ b/test/PolyhedralGeometry/polyhedron.jl @@ -585,11 +585,9 @@ end @testset "Johnson solids" begin for i in keys(Oscar._johnson_names) - j = johnson_solid(i) @test j isa Polyhedron{<:EmbeddedNumFieldElem} @test Polymake.polytope.isomorphic(Oscar.pm_object(j), Polymake.polytope.johnson_solid(i)) - end end diff --git a/test/Serialization/PolyhedralGeometry.jl b/test/Serialization/PolyhedralGeometry.jl index f7782ba246f5..2b80ea0de0e6 100644 --- a/test/Serialization/PolyhedralGeometry.jl +++ b/test/Serialization/PolyhedralGeometry.jl @@ -1,69 +1,96 @@ using Oscar: _integer_variables @testset "PolyhedralGeometry" begin - + Qx, x = QQ[:x] + F, a = embedded_number_field(x^2 - 2, -1.0) + mktempdir() do path @testset "Graph" begin G = complete_graph(4) test_save_load_roundtrip(path, G) do loaded - @test loaded isa Graph{Undirected} - @test Base.propertynames(G) == Base.propertynames(loaded) @test n_vertices(G) == n_vertices(loaded) @test n_edges(G) == n_edges(loaded) end end @testset "Cone" begin - C = positive_hull([1 0; 0 1]) - test_save_load_roundtrip(path, C) do loaded - @test loaded isa Cone - @test Base.propertynames(C) == Base.propertynames(loaded) - @test n_rays(C) == n_rays(loaded) - @test dim(C) == dim(loaded) - @test C == loaded - end + C = positive_hull([1 0; 0 1]) + test_save_load_roundtrip(path, C) do loaded + @test n_rays(C) == n_rays(loaded) + @test dim(C) == dim(loaded) + @test C == loaded + end + + CF = positive_hull(F, [F(1) F(0); F(0) F(1)]) + test_save_load_roundtrip(path, CF) do loaded + @test n_rays(CF) == n_rays(loaded) + @test dim(CF) == dim(loaded) + @test CF == loaded + end end @testset "Polyhedron" begin - square = cube(2) - test_save_load_roundtrip(path, square) do loaded - @test loaded isa Polyhedron - @test Base.propertynames(square) == Base.propertynames(loaded) - @test n_vertices(square) == n_vertices(loaded) - @test dim(square) == dim(loaded) - @test square == loaded - end + square = cube(2) + test_save_load_roundtrip(path, square) do loaded + @test n_vertices(square) == n_vertices(loaded) + @test dim(square) == dim(loaded) + @test square == loaded + end + + d_hedron = dodecahedron() + facets(d_hedron) + vertices(d_hedron) + + dict_ps = Dict{String, Any}( + "unprecise" => polyhedron( + Polymake.common.convert_to{Float64}(Oscar.pm_object(d_hedron)) + ), + "precise" => d_hedron + ) + + test_save_load_roundtrip(path, dict_ps) do loaded + @test dict_ps["precise"] == loaded["precise"] + end end @testset "PolyhedralComplex" begin - IM = IncidenceMatrix([[1,2,3],[1,3,4]]) - vr = [0 0; 1 0; 1 1; 0 1] - PC = polyhedral_complex(IM, vr) - test_save_load_roundtrip(path, PC) do loaded - @test loaded isa PolyhedralComplex - @test Base.propertynames(PC) == Base.propertynames(loaded) - @test n_rays(PC) == n_rays(loaded) - @test number_of_maximal_polyhedra(PC) == number_of_maximal_polyhedra(loaded) - @test dim(PC) == dim(loaded) - end + IM = IncidenceMatrix([[1,2,3],[1,3,4]]) + vr = [0 0; 1 0; 1 1; 0 1] + PC = polyhedral_complex(IM, vr) + test_save_load_roundtrip(path, PC) do loaded + @test n_rays(PC) == n_rays(loaded) + @test number_of_maximal_polyhedra(PC) == number_of_maximal_polyhedra(loaded) + @test dim(PC) == dim(loaded) + end + + vr_F = F.([0 0; 1 0; 1 1; 0 1]) + PC_F = polyhedral_complex(IM, vr_F) + test_save_load_roundtrip(path, PC_F) do loaded + @test n_rays(PC_F) == n_rays(loaded) + @test number_of_maximal_polyhedra(PC_F) == number_of_maximal_polyhedra(loaded) + @test dim(PC_F) == dim(loaded) + end end @testset "PolyhedralFan" begin - nfsquare = normal_fan(cube(2)) - test_save_load_roundtrip(path, nfsquare) do loaded - @test loaded isa PolyhedralFan - @test Base.propertynames(nfsquare) == Base.propertynames(loaded) - @test n_rays(nfsquare) == n_rays(loaded) - @test number_of_maximal_cones(nfsquare) == number_of_maximal_cones(loaded) - @test dim(nfsquare) == dim(loaded) - end + nfsquare = normal_fan(cube(2)) + test_save_load_roundtrip(path, nfsquare) do loaded + @test n_rays(nfsquare) == n_rays(loaded) + @test number_of_maximal_cones(nfsquare) == number_of_maximal_cones(loaded) + @test dim(nfsquare) == dim(loaded) + end + + nfdodecahedron = normal_fan(dodecahedron()) + test_save_load_roundtrip(path, nfdodecahedron) do loaded + @test n_rays(nfdodecahedron) == n_rays(loaded) + @test number_of_maximal_cones(nfdodecahedron) == number_of_maximal_cones(loaded) + @test dim(nfdodecahedron) == dim(loaded) + end end @testset "LinearProgram" begin P = cube(3) LP = linear_program(P,[3,-2,4];k=2,convention = :min) test_save_load_roundtrip(path, LP) do loaded - @test loaded isa LinearProgram - @test Base.propertynames(LP) == Base.propertynames(loaded) @test objective_function(LP) == objective_function(loaded) @test feasible_region(LP) == feasible_region(loaded) end @@ -79,8 +106,6 @@ using Oscar: _integer_variables integer_variables=[1, 2] ) test_save_load_roundtrip(path, MILP) do loaded - @test loaded isa MixedIntegerLinearProgram - @test Base.propertynames(MILP) == Base.propertynames(loaded) @test objective_function(MILP) == objective_function(loaded) @test feasible_region(MILP) == feasible_region(loaded) @test Oscar._integer_variables(MILP) == Oscar._integer_variables(loaded) @@ -88,27 +113,28 @@ using Oscar: _integer_variables end @testset "SubdivisionOfPoints" begin - moaepts = [4 0 0; 0 4 0; 0 0 4; 2 1 1; 1 2 1; 1 1 2] - moaeimnonreg0 = IncidenceMatrix([[4,5,6],[1,4,2],[2,4,5],[2,3,5],[3,5,6],[1,3,6],[1,4,6]]) - MOAE = subdivision_of_points(moaepts, moaeimnonreg0) - test_save_load_roundtrip(path, MOAE) do loaded - @test loaded isa SubdivisionOfPoints - @test Base.propertynames(MOAE) == Base.propertynames(loaded) - @test number_of_maximal_cells(MOAE) == number_of_maximal_cells(loaded) - @test number_of_points(MOAE) == number_of_points(loaded) - end - end + moaepts = [4 0 0; 0 4 0; 0 0 4; 2 1 1; 1 2 1; 1 1 2] + moaeimnonreg0 = IncidenceMatrix([[4,5,6],[1,4,2],[2,4,5],[2,3,5],[3,5,6],[1,3,6],[1,4,6]]) + MOAE = subdivision_of_points(moaepts, moaeimnonreg0) + test_save_load_roundtrip(path, MOAE) do loaded + @test number_of_maximal_cells(MOAE) == number_of_maximal_cells(loaded) + @test number_of_points(MOAE) == number_of_points(loaded) + end + MOAEF = subdivision_of_points(F, F.(moaepts), moaeimnonreg0) + test_save_load_roundtrip(path, MOAEF) do loaded + @test number_of_maximal_cells(MOAEF) == number_of_maximal_cells(loaded) + @test number_of_points(MOAEF) == number_of_points(loaded) + end + end @testset "SimplicialComplex" begin cpp = complex_projective_plane() test_save_load_roundtrip(path, cpp) do loaded - @test loaded isa SimplicialComplex @test Base.propertynames(cpp) == Base.propertynames(loaded) @test euler_characteristic(cpp) == euler_characteristic(loaded) @test n_vertices(cpp) == n_vertices(loaded) end end end - end diff --git a/test/Serialization/containers.jl b/test/Serialization/containers.jl index 9907031c8ccd..37bdd31b8eff 100644 --- a/test/Serialization/containers.jl +++ b/test/Serialization/containers.jl @@ -105,7 +105,7 @@ @test original == loaded end end - + @testset "(de)serialization NamedTuple{$(S), $(T)}" for (S, T) in ( (UInt, UInt128), (UInt16, UInt32), (UInt64, UInt8), @@ -119,6 +119,37 @@ end end + @testset "(de)serialization Dict{$S, Any}" for (S, keys) in + ( + (String, ["a", "b"]), (Int, [1, 2]), (Symbol, [:a, :b]) + ) + Qx, x = QQ[:x] + p = x^2 + 1 + original = Dict(keys[1] => cube(:2), keys[2] => p) + test_save_load_roundtrip(path, original) do loaded + @test original == loaded + end + end + + @testset "Testing (de)serialization of Set" begin + original = Set([Set([1, 2])]) + test_save_load_roundtrip(path, original) do loaded + @test original == loaded + end + + Qx, x = QQ[:x] + p = x^2 + 1 + q = x + original = Set([p, q]) + test_save_load_roundtrip(path, original) do loaded + @test original == loaded + end + + test_save_load_roundtrip(path, original; params=Qx) do loaded + @test original == loaded + end + end + @testset "Test for backwards compatibility" begin loaded_container = load(joinpath(@__DIR__, "old-containers.json")) @test loaded_container == (r = QQFieldElem(1, 2), m = QQFieldElem[1//2 1; 0 1], t = (1, 2, 3)) From ffd5ad3855db434c8020ec0419ffacfc7b5ba52e Mon Sep 17 00:00:00 2001 From: Stevell Muller <78619134+StevellM@users.noreply.github.com> Date: Thu, 22 Feb 2024 14:11:15 +0100 Subject: [PATCH 26/29] `QuadFormAndIsom`: fixes and a new feature (#3394) (cherry picked from commit 376b3f013e4efb054fda6f65252a02cb9bbc1045) --- experimental/QuadFormAndIsom/README.md | 13 +- .../QuadFormAndIsom/docs/src/enumeration.md | 23 +- .../QuadFormAndIsom/docs/src/introduction.md | 13 +- .../QuadFormAndIsom/docs/src/latwithisom.md | 7 +- .../QuadFormAndIsom/docs/src/primembed.md | 26 +- .../QuadFormAndIsom/src/embeddings.jl | 176 ++++++++---- .../QuadFormAndIsom/src/enumeration.jl | 251 ++++++++++-------- .../src/hermitian_miranda_morrison.jl | 219 ++++++++------- .../src/lattices_with_isometry.jl | 85 ++---- .../src/spaces_with_isometry.jl | 4 +- experimental/QuadFormAndIsom/test/runtests.jl | 13 +- 11 files changed, 480 insertions(+), 350 deletions(-) diff --git a/experimental/QuadFormAndIsom/README.md b/experimental/QuadFormAndIsom/README.md index f8c0db4399e6..d5b293719d42 100644 --- a/experimental/QuadFormAndIsom/README.md +++ b/experimental/QuadFormAndIsom/README.md @@ -25,7 +25,7 @@ of finite order with at most two prime divisors. The methods we resort to for this purpose are developed in the paper [BH23](@cite). We also provide some algorithms computing isomorphism classes of primitive -embeddings of even lattices following Nikulin's theory. More precisely, the +embeddings of integral lattices following Nikulin's theory. More precisely, the function `primitive_embeddings` offers, under certain conditions, the possibility to compute representatives of primitive embeddings and classify them in different ways. Note nonetheless that these functions are not efficient @@ -33,12 +33,13 @@ in the case were the discriminant groups have a large number of subgroups. ## Status -This project has been slightly tested on simple and known examples. It is -currently being tested on a larger scale to test its reliability. Moreover, -there are still computational bottlenecks due to non-optimized algorithms. +Currently, the project features the following: -Among the possible improvements and extensions: -* Implement extra methods for lattices with isometries of infinite order; +- enumeration of conjugacy classes of isometries of finite order for even lattices (in the case of at most 2 prime divisors); +- enumeration of conjugacy classes of isometries with irreducible and reciprocal minimal polynomial for integral lattices (with maximal equation order); +- primitive embeddings/extensions for integral lattices; +- equivariant primitive extensions for integral lattices; +- miscellaneous operations on integral/rational quadratic form endowed with an isometry. ## Current applications of this project diff --git a/experimental/QuadFormAndIsom/docs/src/enumeration.md b/experimental/QuadFormAndIsom/docs/src/enumeration.md index 06fa5245e73a..8f7bff774581 100644 --- a/experimental/QuadFormAndIsom/docs/src/enumeration.md +++ b/experimental/QuadFormAndIsom/docs/src/enumeration.md @@ -4,7 +4,7 @@ CurrentModule = Oscar # Enumeration of isometries -One of the main features of this project is the enumeration of lattices with +One of the main features of this project is the enumeration of even lattices with isometry of finite order with at most two prime divisors. This is the content of [BH23](@cite) which has been implemented. We guide the user here to the global aspects of the available theory, and we refer to the paper [BH23](@cite) for further @@ -48,7 +48,25 @@ isometries of integral integer lattices. For more details such as the proof of the algorithms and the theory behind them, we refer to the reference paper [BH23](@cite). -### Global function +### The hermitian case + +For an irreducible reciprocal polynomial $\chi$ and a genus symbol $G$ +of integral integer lattices, if the equation order $\mathbb{Z}[\chi]$ is maximal, +one can compute representatives of isomorphism classes of lattices with isometry +$(L, f)$ such that $L\in G$ and $\chi(f) = 0$. + +```@docs +representatives_of_hermitian_type(::Union{ZZLat, ZZGenus}, ::Union{ZZPolyRingElem, QQPolyRingElem}, ::Bool) +``` + +In the case of finite order isometries, when $\chi$ is cyclotomic, one can use +as a shortcut the following function instead: + +```@docs +representatives_of_hermitian_type(::Union{ZZGenus, ZZLat}, ::Int, ::Bool) +``` + +### Orders with two prime divisors As we will see later, the algorithms from [BH23](@cite) are specialized on the requirement for the input and regular users might not be able to choose between @@ -88,3 +106,4 @@ embeddings and their equivariant version. We use this basis to introduce the method [`admissible_equivariant_primitive_extensions`](@ref) (Algorithm 2 in [BH23](@cite)) which is the major tool making the previous enumeration possible and fast, from an algorithmic point of view. + diff --git a/experimental/QuadFormAndIsom/docs/src/introduction.md b/experimental/QuadFormAndIsom/docs/src/introduction.md index 812fd913f97e..fc96d4cc147b 100644 --- a/experimental/QuadFormAndIsom/docs/src/introduction.md +++ b/experimental/QuadFormAndIsom/docs/src/introduction.md @@ -25,7 +25,7 @@ of finite order with at most two prime divisors. The methods we resort to for this purpose are developed in the paper [BH23](@cite). We also provide some algorithms computing isomorphism classes of primitive -embeddings of even lattices following Nikulin's theory. More precisely, the +embeddings of integral lattices following Nikulin's theory. More precisely, the function [`primitive_embeddings`](@ref) offers, under certain conditions, the possibility to compute representatives of primitive embeddings and classify them in different ways. Note nonetheless that these functions are not efficient @@ -33,12 +33,13 @@ in the case were the discriminant groups have a large number of subgroups. ## Status -This project has been slightly tested on simple and known examples. It is -currently being tested on a larger scale to test its reliability. Moreover, -there are still computational bottlenecks due to non-optimized algorithms. +Currently, the project features the following: -Among the possible improvements and extensions: -* Implement extra methods for lattices with isometries of infinite order; +- enumeration of conjugacy classes of isometries of finite order for even lattices (in the case of at most 2 prime divisors); +- enumeration of conjugacy classes of isometries with irreducible and reciprocal minimal polynomial for integral lattices (with maximal equation order); +- primitive embeddings/extensions for integral lattices; +- equivariant primitive extensions for integral lattices; +- miscellaneous operations on integral/rational quadratic form endowed with an isometry. ## Current applications of this project diff --git a/experimental/QuadFormAndIsom/docs/src/latwithisom.md b/experimental/QuadFormAndIsom/docs/src/latwithisom.md index 502158794e11..7fb9347224c8 100644 --- a/experimental/QuadFormAndIsom/docs/src/latwithisom.md +++ b/experimental/QuadFormAndIsom/docs/src/latwithisom.md @@ -15,7 +15,7 @@ ZZLatWithIsom ``` It is seen as a quadruple $(Vf, L, f, n)$ where $Vf = (V, f_a)$ consists of -the ambient rational quadratic space $V$ of $L$ and an isometry $f_a$ of $V$ +the ambient rational quadratic space $V$ of $L$, and an isometry $f_a$ of $V$ preserving $L$ and inducing $f$ on $L$. The integer $n$ is the order of $f$, which is a divisor of the order of the isometry $f_a\in O(V)$. @@ -115,8 +115,7 @@ rescale(::ZZLatWithIsom, ::RationalUnion) ## Type for finite order isometries Given a lattice with isometry $Lf := (L, f)$ where $f$ is of finite order $n$, -one can compute the *type* of $Lf$, which can be seen as an equivalent of the -*genus* used to classified single lattices. +one can compute the *type* of $Lf$. ```@docs type(::ZZLatWithIsom) @@ -183,6 +182,8 @@ project and it can be indirectly used through the general following method: image_centralizer_in_Oq(::ZZLatWithIsom) ``` +Note: hermitian Miranda-Morrison is only available for even lattices. + For an implementation of the regular Miranda-Morrison theory, we refer to the function `image_in_Oq` which actually computes the image of $\pi$ in both the definite and the indefinite case. diff --git a/experimental/QuadFormAndIsom/docs/src/primembed.md b/experimental/QuadFormAndIsom/docs/src/primembed.md index e14c4a00755d..3bf01561bdde 100644 --- a/experimental/QuadFormAndIsom/docs/src/primembed.md +++ b/experimental/QuadFormAndIsom/docs/src/primembed.md @@ -25,11 +25,13 @@ given invariants (see Theorem 1.12.2 in [Nik79](@cite)). More generally, the author also provides methods to compute primitive embeddings of any even lattice into an even lattice of a given genus (see Proposition 1.15.1 in [Nik79](@cite)). In the latter proposition, it is explained how to classify such embeddings as -isomorphic embeddings or as isomorphic sublattices. +isomorphic embeddings or as isomorphic sublattices. Moreover, with enough care, +one can generalize the previous results for embeddings in odd lattices. -Such a method can be algorithmically implemented, however it tends to be slow -and inefficient in general for large rank or determinant. But, in the case -where the discriminant groups are (elementary) $p$-groups, the method can be +A general method to compute primitive embeddings between integral lattices +can be algorithmically implemented, however it tends to be slow and inefficient +in general for large rank or determinant. But, in the case where the +discriminant groups are (elementary) $p$-groups, the method can be made more efficient. We provide 4 kinds of output: @@ -48,16 +50,15 @@ first input: ```@docs primitive_embeddings(::ZZGenus, ::ZZLat) -primitive_embeddings(::TorQuadModule, ::Tuple{Int, Int}, -::ZZLat) +primitive_embeddings(::TorQuadModule, ::Tuple{Int, Int}, ::ZZLat) ``` In order to compute such primitive embeddings of a lattice $M$ into a lattice $L$, we follow the proof of Proposition 1.15.1 of [Nik79](@cite). -Note: for the implementation of the algorithm, we construct an even lattice -$T := M(-1)\oplus U$ where $U$ is a hyperbolic plane - $T$ is unique in its -genus and $O(T)\to O(D_T)$ is surjective. We then classify all primitive +Note: for the implementation of the algorithm, we construct a lattice $T$ which +is unique in its genus, such that $D_T$ and $D_M(-1)$ are isometric and +$O(T)\to O(D_T)$ is surjective. We then classify all primitive extensions of $M\oplus T$ modulo $O(D_T)$ (and modulo $O(M)$ for a classification of primitive sublattices). To classify such primitive extensions, we use Proposition 1.5.1 of [Nik79](@cite): @@ -91,13 +92,12 @@ equivariant_primitive_extensions(::Union{ZZLatWithIsom, ZZLat}, ::Union{ZZLatWit ## Admissible equivariant primitive extensions The following function is a major tool provided by [BH23](@cite). Given -a triple of integer lattices with isometry $((A, a), (B, b), (C, c))$ and two prime -numbers $p$ and $q$ (possibly equal), if $(A, B, C)$ is $p$-admissible, this -function returns representatives of isomorphism classes of equivariant primitive +a triple of even integer lattices with isometry $((A, a), (B, b), (C, c))$ +and two prime numbers $p$ and $q$ (possibly equal), if $(A, B, C)$ is $p$-admissible, +this function returns representatives of isomorphism classes of equivariant primitive extensions $(A, a)\oplus (B, b)\to (D, d)$ such that the type of $(D, d^q)$ is equal to the type of $(C, c)$ (see [`type(::ZZLatWithIsom)`](@ref)). ```@docs admissible_equivariant_primitive_extensions(::ZZLatWithIsom, ::ZZLatWithIsom, ::ZZLatWithIsom, ::IntegerUnion, ::IntegerUnion) ``` - diff --git a/experimental/QuadFormAndIsom/src/embeddings.jl b/experimental/QuadFormAndIsom/src/embeddings.jl index 98bd143fde62..2f6b81d8d3d8 100644 --- a/experimental/QuadFormAndIsom/src/embeddings.jl +++ b/experimental/QuadFormAndIsom/src/embeddings.jl @@ -390,8 +390,8 @@ function _fitting_isometries(OqfN::AutomorphismGroup{TorQuadModule}, push!(orb_and_rep, (p, orbit(m, p))) end end + reporb = QQMatrix[solve(basis_matrix(N), basis_matrix(N)*matrix(a[1]); side=:left) for a in orb_and_rep] end - reporb = QQMatrix[solve(basis_matrix(N), basis_matrix(N)*matrix(a[1]); side = :left) for a in orb_and_rep] return reporb end @@ -646,8 +646,9 @@ function _primitive_extensions_generic( if elM || elN || (ok && ek == 1) # We look for a glue kernel which is an elementary p-group - _, VMinqM = _get_V(id_hom(qM), minimal_polynomial(identity_matrix(QQ, 1)), max(pM, pN, pk)) - subsM = _subgroups_orbit_representatives_and_stabilizers_elementary(VMinqM, GM, k, fqM) + _p = max(pM, pN, pk) + _, VMinqM = _get_V(id_hom(qM), minimal_polynomial(identity_matrix(QQ, 1)), _p) + subsM = _subgroups_orbit_representatives_and_stabilizers_elementary(VMinqM, GM, k, _p, fqM) elseif prM || prN || ok # We look for a glue kernel which is a p-group _, VMinqM = primary_part(qM, max(pM, pN, pk)) @@ -847,45 +848,30 @@ end function _subgroups_orbit_representatives_and_stabilizers_elementary(Vinq::TorQuadModuleMap, G::AutomorphismGroup{TorQuadModule}, ord::IntegerUnion, + _p::IntegerUnion, f::Union{TorQuadModuleMap, AutomorphismGroupElem{TorQuadModule}} = id_hom(codomain(Vinq)), l::IntegerUnion = -1) res = Tuple{TorQuadModuleMap, AutomorphismGroup{TorQuadModule}}[] + p = ZZ(_p) + V = domain(Vinq) - # If V is trivial, then we ignore f and l, we just need to ensure that the - # order wanted is also 1 - if order(V) == 1 - ord != 1 && (return res) - push!(res, (Vinq, G)) + if ord > order(V) return res end q = codomain(Vinq) - p = elementary_divisors(V)[1] pq, pqtoq = primary_part(q, p) l = l < 0 ? valuation(order(pq), p) : l g = valuation(ord, p) - # some other trivial cases: if ord is 1, then l should be null (-1 by default) - # Otherwise, if ord == order(V), since V is preserved by f and contained the - # good subgroup of q, we just return V - if ord == 1 - l < valuation(order(pq), p) && (return res) - _, triv = sub(codomain(Vinq), TorQuadModuleElem[]) - push!(res, (triv, G)) - return res - elseif ord == order(V) - push!(res, (Vinq, G)) - return res - end - # In theory, V should contain H0 := p^l*pq where pq is the p-primary part of q all(a -> has_preimage_with_preimage(Vinq, (p^l)*pqtoq(a))[1], gens(pq)) || return res H0, H0inq = sub(q, elem_type(q)[q(lift((p^l)*a)) for a in gens(pq)]) @hassert :ZZLatWithIsom 1 is_invariant(f, H0inq) - # H0 should be contained in the group we want. So either H0 is the only one + # H0 should be contained in the groups we want. So either H0 is the only one # and we return it, or if order(H0) > ord, there are no subgroups as wanted if order(H0) >= ord order(H0) > ord && return res @@ -893,6 +879,15 @@ function _subgroups_orbit_representatives_and_stabilizers_elementary(Vinq::TorQu return res end + # Now the groups we look for should strictly contain H0. + # If ord == order(V), then there is only V satisfying the given + # conditions, and V is stabilized by the all G + if ord == order(V) + push!(res, (Vinq, G)) + return res + end + + # Now the groups we look for are strictly contained between H0 and V H0inV = hom(H0, V, elem_type(V)[V(lift(a)) for a in gens(H0)]) @hassert :ZZLatWithIsom 1 is_injective(H0inV) @@ -908,7 +903,6 @@ function _subgroups_orbit_representatives_and_stabilizers_elementary(Vinq::TorQu # We descend G to V for computing stabilizers later on GV, GtoGV = restrict_automorphism_group(G, Vinq; check = false) - satV, j = kernel(GtoGV) # Automorphisms in G preserved V and H0, since the construction of H0 is # natural. Therefore, the action of G descends to the quotient and we look for @@ -916,10 +910,11 @@ function _subgroups_orbit_representatives_and_stabilizers_elementary(Vinq::TorQu # generators and putting them with H0 will give us invariant subgroups as # wanted) act_GV = dense_matrix_type(elem_type(base_ring(Qp)))[change_base_ring(base_ring(Qp), matrix(gg)) for gg in gens(GV)] - act_GV = dense_matrix_type(elem_type(base_ring(Qp)))[solve(VptoQp.matrix, g*VptoQp.matrix) for g in act_GV] + act_GV = dense_matrix_type(elem_type(base_ring(Qp)))[solve(VptoQp.matrix, g*VptoQp.matrix; side=:right) for g in act_GV] MGp = matrix_group(base_ring(Qp), dim(Qp), act_GV) GVtoMGp = hom(GV, MGp, MGp.(act_GV); check = false) GtoMGp = compose(GtoGV, GVtoMGp) + satV, _ = kernel(GtoMGp) g-ngens(snf(abelian_group(H0))[1]) >= dim(Qp) && return res @@ -983,7 +978,7 @@ function _classes_isomorphic_subgroups(q::TorQuadModule, if ok if e == 1 _, Vinq = _get_V(id_hom(q), minimal_polynomial(identity_matrix(QQ, 1)), p) - sors = _subgroups_orbit_representatives_and_stabilizers_elementary(Vinq, O, ordH, f) + sors = _subgroups_orbit_representatives_and_stabilizers_elementary(Vinq, O, ordH, p, f) else _, Vinq = primary_part(q, p) sors = _subgroups_orbit_representatives_and_stabilizers(Vinq, O, ordH, f) @@ -1028,7 +1023,7 @@ function _classes_isomorphic_subgroups(q::TorQuadModule, fqp = restrict_endomorphism(f, qpinq; check = false) if ordHp == p || (!isnothing(H) && is_elementary(T, p)) _, j = _get_V(id_hom(qp), minimal_polynomial(identity_matrix(QQ, 1)), p) - sors = _subgroups_orbit_representatives_and_stabilizers_elementary(j, Oqp, ordHp, fqp) + sors = _subgroups_orbit_representatives_and_stabilizers_elementary(j, Oqp, ordHp, p, fqp) else sors = _subgroups_orbit_representatives_and_stabilizers(id_hom(qp), Oqp, ordHp, fqp) end @@ -1306,13 +1301,8 @@ function primitive_embeddings(G::ZZGenus, M::ZZLat; classification::Symbol = :su # In the non-even case, we need to consider several cases, i.e double odd, # even-odd or odd-even. # - # If M is even, then the complement can be even with discriminant form being - # qM(-1), or odd with discriminant form being bM(-1) - # - # If M is odd, it is more tricky: either the complement is odd with form bM(-1) - # or it is even with bM(-1) too. But in the latter case, their might be two - # possibilities for the quadratic form: we might need to add 1 to each - # diagonal entries of the gram matrix of the bilinear form bM before rescaling + # The complement can be even with discriminant form being + # qM(-1), or odd with discriminant form being bM(-1). # # Then for each possible form, we check which one defines a genus with the # given signature pair and then we do our extension routine. @@ -1355,9 +1345,6 @@ function primitive_embeddings(G::ZZGenus, M::ZZLat; classification::Symbol = :su return (length(results) > 0), results end - if cs != :none && cs != :first - cs = :subsub - end # Now we go on the harder case, which relies on the previous one # We follow the proof of Nikulin: we create `T` unique in its genus and with # surjective O(T) -> O(qT), and such that qT and q are anti-isometric @@ -1373,8 +1360,8 @@ function primitive_embeddings(G::ZZGenus, M::ZZLat; classification::Symbol = :su end # The algorithm goes on with finding primitive extensions of M+T and then - # embeddings such in a big unimodular lattice (which we take unique in its - # genus) + # embedding such extensions in a big unimodular lattice (which we take + # unique in its genus) _, Vs = primitive_extensions(M, T; even, classification = cs) # GL is our big unimodular genus where we embed each of the V in Vs @@ -1387,9 +1374,60 @@ function primitive_embeddings(G::ZZGenus, M::ZZLat; classification::Symbol = :su end # M2 is M seen in V, and T2 is T seen in V for (V, M2, T2) in Vs - okV, resV = primitive_embeddings(GL, V; classification) - !okV && continue - classification == :none && return okV, results + resV = Tuple{ZZLat, ZZLat, ZZLat}[] + if rank(V) == rank(GL) + genus(V) != genus(GL) && continue + push!(resV, (V, V, orthogonal_submodule(V, V))) + continue + end + + # We need to classify the primitive embeddings of V in GL up to the actions + # of O(T) and O(M) (for sublattices; otherwise only up to O(T)) + # + # For this, we need the representation of the subgroup of isometries of V + # which preserves the primitive extension M\oplus T \subseteq V. This + # corresponds to the diagonal in \bar{O(T)}\times GM where GM is trivial + # for embedding classification, \bar{O(M)} otherwise. + # + # We use `_glue_stabilizers` which has been designed especially to compute + # such diagonal subgroup. + GV, _ = _glue_stabilizers(V, M2, T2) + qV = domain(GV) + qK = rescale(qV, -1) # Bilinear form of a complement of V in GL + + GKs = ZZGenus[] + posK = signature_tuple(GL)[1] - signature_tuple(V)[1] + negK = signature_tuple(GL)[3] - signature_tuple(V)[3] + if even + _G = try genus(qK, (posK, negK)) + catch + nothing + end + !isnothing(_G) && push!(GKs, _G) + else + _Ge = try genus(qK, (posK, negK); parity=2) + catch + nothing + end + !isnothing(_Ge) && push!(GKs, _Ge) + _Go = try genus(qK, (posK, negK); parity=1) + catch + nothing + end + !isnothing(_Go) && push!(GKs, _Go) + end + is_empty(GKs) && continue + unique!(GKs) + orths = reduce(vcat, Vector{ZZLat}[representatives(_GK) for _GK in GKs]) + for K in orths + GK, _ = image_in_Oq(K) + ok, pe = _primitive_extensions_generic(V, K, GV, GK, (:plain, :plain); even, exist_only=(classification == :none), first=(classification == :first), q=discriminant_group(GL)) + !ok && continue + classification == :none && true, results + !isempty(pe) && append!(resV, Tuple{ZZLat, ZZLat, ZZLat}[lattice.(t) for t in pe]) + end + isempty(resV) && continue + for (S, V2, W2) in resV # This is T seen in S T3 = lattice_in_same_ambient_space(S, hcat(basis_matrix(T2), zero_matrix(QQ, rank(T2), degree(W2)-degree(T2)))) @@ -1405,7 +1443,7 @@ function primitive_embeddings(G::ZZGenus, M::ZZLat; classification::Symbol = :su N = orthogonal_submodule(L, M3) # 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. + # necessary information about the embedding. 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)) @@ -1714,10 +1752,10 @@ function admissible_equivariant_primitive_extensions(A::ZZLatWithIsom, # This is done by computing orbits and stabilizers of VA/lpqA (resp VB/lpqB) # seen as a F_p-vector space under the action of GA (resp. GB). Then we check which ones # are fA-stable (resp. fB-stable) - subsA = _subgroups_orbit_representatives_and_stabilizers_elementary(VAinqA, GA, p^g, fqA, ZZ(l)) + subsA = _subgroups_orbit_representatives_and_stabilizers_elementary(VAinqA, GA, p^g, p, fqA, ZZ(l)) is_empty(subsA) && return results - subsB = _subgroups_orbit_representatives_and_stabilizers_elementary(VBinqB, GB, p^g, fqB, ZZ(l)) + subsB = _subgroups_orbit_representatives_and_stabilizers_elementary(VBinqB, GB, p^g, p, fqB, ZZ(l)) is_empty(subsB) && return results # now, for each pair of anti-isometric potential kernels, we need to massage the gluing @@ -1787,7 +1825,7 @@ function admissible_equivariant_primitive_extensions(A::ZZLatWithIsom, stabSB, _ = intersect(center, imB) iso = isomorphism(PermGroup, center) - reps = double_cosets(codomain(iso), iso(stabSB)[1], iso(stabSAphi)[1]) + reps = double_cosets(codomain(iso), iso(stabSAphi)[1], iso(stabSB)[1]) # We iterate over all double cosets. Each representative, define a new # classe of admissible gluing and so, for each such representative we compute the @@ -2000,3 +2038,49 @@ function _glue_stabilizers(phi::TorQuadModuleMap, unique!(stab) return disc, stab end + +function _glue_stabilizers(L::ZZLatWithIsom, M::ZZLatWithIsom, N::ZZLatWithIsom; subM::Bool = true, subN::Bool = true) + qM, fqM = discriminant_group(M) + GM = subM ? image_centralizer_in_Oq(M)[1] : Oscar._orthogonal_group(qM, ZZMatrix[matrix(id_hom(qM))]; check=false) + + qN, fqN = discriminant_group(N) + GN = subN ? image_centralizer_in_Oq(N)[1] : Oscar._orthogonal_group(qN, ZZMatrix[matrix(id_hom(qN))]; check=false) + + phi, HMinqM, HNinqN = glue_map(lattice(L), lattice(M), lattice(N); check=false) + HM = domain(HMinqM) + OHM = orthogonal_group(HM) + + HN = domain(HNinqN) + OHN = orthogonal_group(HN) + + _, qMinD, qNinD, _, OqMinOD, OqNinOD = _sum_with_embeddings_orthogonal_groups(qM, qN) + HMinD = compose(HMinqM, qMinD) + HNinD = compose(HNinqN, qNinD) + + stabM, _ = stabilizer(GM, HMinqM) + stabN, _ = stabilizer(GN, HNinqN) + + actM = hom(stabM, OHM, elem_type(OHM)[OHM(restrict_automorphism(x, HMinqM; check=false)) for x in gens(stabM)]) + actN = hom(stabN, OHN, elem_type(OHN)[OHN(restrict_automorphism(x, HNinqN; check=false)) for x in gens(stabN)]) + + _, _, graph = _overlattice(phi, HMinD, HNinD, isometry(M), isometry(N); same_ambient=true) + disc, _stab = _glue_stabilizers(phi, actM, actN, OqMinOD, OqNinOD, graph) + qL, fqL = discriminant_group(L) + OqL = orthogonal_group(qL) + + psi = hom(qL, disc, TorQuadModuleElem[disc(lift(x)) for x in gens(qL)]) + @hassert :ZZLatWithIsom 1 is_isometry(psi) + @hassert :ZZLatWithIsom 1 qL == disc + + ipsi = inv(psi) + stab = sub(OqL, elem_type(OqL)[OqL(compose(psi, compose(g, ipsi)); check=false) for g in _stab]) + @hassert :ZZLatWithIsom 1 fqL in stab[1] + return stab +end + +function _glue_stabilizers(L::ZZLat, M::ZZLat, N::ZZLat; subM::Bool = true, subN::Bool = true) + Lf = integer_lattice_with_isometry(L) + Mg = integer_lattice_with_isometry(M) + Nh = integer_lattice_with_isometry(N) + return _glue_stabilizers(Lf, Mg, Nh; subM, subN) +end diff --git a/experimental/QuadFormAndIsom/src/enumeration.jl b/experimental/QuadFormAndIsom/src/enumeration.jl index d459133cfde7..46cb33dd80eb 100644 --- a/experimental/QuadFormAndIsom/src/enumeration.jl +++ b/experimental/QuadFormAndIsom/src/enumeration.jl @@ -366,63 +366,64 @@ function _ideals_of_norm(E::Field, d::ZZRingElem) end end for I in Hecke.cartesian_product_iterator(primes) - I = prod(I) - if absolute_norm(I) == d - push!(ids, fractional_ideal(OE, I)) + if prod(absolute_norm.(I)) != d + continue end + I = prod(I) + @hassert :ZZLatWithIsom 1 absolute_norm(I) == d + push!(ids, fractional_ideal(OE, I)) end return ids end -# given a cyclotomic field (as cm extension) E/K, return all +# Given a degree 2 extension of number fields E/K, return all # the possible signatures dictionaries of any hermitian lattice over -# E/K of rank rk, whose trace lattice has signature (s1, s2). -# if `fix_root`, we do not consider permutations of a set of signatures since -# any permutation correspond to a change of a choice of a primitive root of -# unity. +# E/K of rank rk, and whose trace lattice has negative signature s2. +# In the cyclotomic case, if `fix_root = true`, we do not consider +# permutations of a set of signatures since any permutation correspond +# to a change of a choice of a primitive root of unity. -function _possible_signatures(s1::IntegerUnion, s2::IntegerUnion, E::Field, rk::IntegerUnion, fix_root::Bool = false) - @hassert :ZZLatWithIsom 1 E isa Hecke.RelSimpleNumField - ok, q = Hecke.is_cyclotomic_type(E) - @hassert :ZZLatWithIsom 1 ok - @hassert :ZZLatWithIsom 1 iseven(s2) - @hassert :ZZLatWithIsom 1 divides(2*(s1+s2), euler_phi(q))[1] - l = divexact(s2, 2) +function _possible_signatures(s2::IntegerUnion, E::Field, rk::IntegerUnion, fix_root::Bool = false) + lb = iseven(s2) ? 0 : 1 K = base_field(E) - inf = real_places(K) + inf = Hecke.place_type(K)[p for p in real_places(K) if length(extend(p, E)) == 1] + r = length(real_places(K)) - length(inf) s = length(inf) - signs = Dict{typeof(inf[1]), Int}[] - parts = Vector{Int}[] + signs = Dict{Hecke.place_type(K), Int}[] if !fix_root perm = AllPerms(s) end - for v in AllParts(l) - if any(i -> i > rk, v) - continue - end - if length(v) > s - continue - end - while length(v) != s - push!(v, 0) - end - push!(parts, copy(v)) - if !fix_root - for vv in perm - v2 = v[vv.d] - v2 in parts ? continue : push!(parts, v2) + for l in lb:2:min(s2, rk*r) + parts = Vector{Int}[] + l = divexact(s2-l, 2) + for v in AllParts(l) + if any(i -> i > rk, v) + continue + end + if length(v) > s + continue + end + while length(v) != s + push!(v, 0) + end + push!(parts, copy(v)) + if !fix_root + for vv in perm + v2 = v[vv.d] + v2 in parts ? continue : push!(parts, v2) + end end end - end - for v in parts - push!(signs, Dict(a => b for (a,b) in zip(inf, v))) + for v in parts + push!(signs, Dict(a => b for (a,b) in zip(inf, v))) + end end return signs end @doc raw""" representatives_of_hermitian_type(Lf::ZZLatWithIsom, m::Int = 1) - -> Vector{ZZLatWithIsom} + -> Vector{ZZLatWithIsom} Given a lattice with isometry $(L, f)$ of finite hermitian type (i.e. the minimal polynomial of $f$ is irreducible cyclotomic) and a positive integer $m$, @@ -452,115 +453,146 @@ function representatives_of_hermitian_type(Lf::ZZLatWithIsom, m::Int = 1, fix_ro @req m >= 1 "m must be a positive integer" @req is_of_hermitian_type(Lf) "Lf must be of hermitian type" - rk = rank(Lf) - d = det(Lf) n = order_of_isometry(Lf) @req is_finite(n) "Isometry must be of finite order" - s1, _, s2 = signature_tuple(Lf) + reps = representatives_of_hermitian_type(genus(Lf), cyclotomic_polynomial(n*m), fix_root) + filter!(M -> is_of_same_type(M^m, Lf), reps) + return reps +end + +@doc raw""" + representatives_of_hermitian_type(G::ZZGenus, m::Int) + representatives_of_hermitian_type(L::ZZLat, m::Int) + -> Vector{ZZLatWithIsom} + +Given a non-empty genus of integer lattices $G$, return a list of +representatives of isomorphism classes of pairs $(M, g)$ consisting of a lattice +$M$ in $G$ and $g \in O(M)$ is an isometry of minimal polynomial $\Phi_m(X)$, +the $m-$th cyclotomic polynomial. + +If $m = 1,2$, this goes back to enumerate $G$ as a genus of integer lattices. + +One can also provide a representative $L$ of $G$ instead. +""" +representatives_of_hermitian_type(::Union{ZZGenus, ZZLat}, ::Int, ::Bool) + +representatives_of_hermitian_type(G::ZZGenus, m::Int, fix_root::Bool = false) = representatives_of_hermitian_type(G, cyclotomic_polynomial(m), fix_root) + +representatives_of_hermitian_type(L::ZZLat, m::Int, fix_root::Bool = false) = representatives_of_hermitian_type(genus(L), cyclotomic_polynomial(m), fix_root) + +@doc raw""" + representatives_of_hermitian_type(G::ZZGenus, chi::Union{ZZPolyRingElem, QQPolyRingElem}) + representatives_of_hermitian_type(L::ZZLat, chi::Union{ZZPolyRingElem, QQPolyRingElem}) + -> Vector{ZZLatWithIsom} + +Given a non-empty genus of integer lattices $G$ and a polynomial $chi$ irreducible +over $\mathbb Q$, such that the equation order of the associated number field is +maximal, return a list of representatives of isomorphism classes of pairs $(M, g)$ +consiting of a lattice $M$ in $G$ and $g \in O(M)$ is an isometry of minimal polynomial +$chi$. + +One can also provide a representative $L$ of $G$ instead. +""" +representatives_of_hermitian_type(::Union{ZZLat, ZZGenus}, ::Union{ZZPolyRingElem, QQPolyRingElem}, ::Bool) + +function representatives_of_hermitian_type(G::ZZGenus, chi::Union{ZZPolyRingElem, QQPolyRingElem}, fix_root::Bool = false) + @req is_irreducible(chi) "Polynomial must be irreducible" + @req is_integral(G) "For now G must be a genus symbol for integral lattices" + + rk = rank(G) + d = abs(det(G)) + s1, _, s2 = signature_tuple(G) reps = ZZLatWithIsom[] - nm = n*m + rank(G) == 0 && return ZZLatWithIsom[integer_lattice_with_isometry(integer_lattice(; gram=matrix(QQ, 0, 0, QQFieldElem[])))] - if nm < 3 + if degree(chi) == 1 + @hassert :ZZLatWithIsom 1 iszero(chi(1)*chi(-1)) @vprintln :ZZLatWithIsom 1 "Order smaller than 3" - f = (-1)^(nm+1)*identity_matrix(QQ, rk) - G = genus(Lf) + f = iszero(chi(1)) ? identity_matrix(QQ, rk) : -identity_matrix(QQ, rk) repre = representatives(G) @vprintln :ZZLatWithIsom 1 "$(length(repre)) representative(s)" while !is_empty(repre) LL = pop!(repre) - is_of_same_type(integer_lattice_with_isometry(LL, f^m; check = false), Lf) && push!(reps, integer_lattice_with_isometry(LL, f; check = false)) + push!(reps, integer_lattice_with_isometry(LL, f; ambient_representation=false, check=false)) end return reps end - !iseven(s2) && return reps + !iseven(degree(chi)) && return reps @vprintln :ZZLatWithIsom 1 "Order bigger than 3" - ok, rk = divides(rk, euler_phi(nm)) + ok, rk = divides(rk, degree(chi)) ok || return reps - E, b = cyclotomic_field_as_cm_extension(nm) + R = parent(chi) + list_cyc = Int[k for k in euler_phi_inv(degree(chi))] + j = findfirst(k -> chi == cyclotomic_polynomial(k, R), list_cyc) + if !isnothing(j) + E, b = cyclotomic_field_as_cm_extension(list_cyc[j]) + else + Etemp, btemp = number_field(chi; cached=false) + @req is_maximal(equation_order(Etemp)) "For infinite isometries, the equation order of the associated number field must be maximal" + K, a = number_field(minpoly(btemp + inv(btemp)), "a"; cached=false) + Kt, t = K["t"] + E, b = number_field(t^2-a*t+1, "b"; cached=false) + end + gene = Hecke.genus_herm_type(E)[] - Eabs, EabstoE = absolute_simple_field(E) - DE = EabstoE(different(maximal_order(Eabs))) + DEK = different(maximal_order(E)) + DK = different(base_ring(maximal_order(E))) + DE = DK*maximal_order(E)*DEK - @vprintln :ZZLatWithIsom 1 "We have the different" + @vprintln :ZZLatWithIsom 1 "We have the differents" ndE = d*inv(QQ(absolute_norm(DE)))^rk detE = _ideals_of_norm(E, ndE) - + isempty(detE) && return reps @vprintln :ZZLatWithIsom 1 "All possible ideal dets: $(length(detE))" - signatures = _possible_signatures(s1, s2, E, rk, fix_root) - + signatures = _possible_signatures(s2, E, rk, fix_root) + isempty(signatures) && return reps @vprintln :ZZLatWithIsom 1 "All possible signatures: $(length(signatures))" + for dd in detE, sign in signatures - append!(gene, hermitian_genera(E, rk, sign, dd; min_scale = inv(DE), max_scale = numerator(dd)*DE)) + append!(gene, hermitian_genera(E, rk, sign, dd; min_scale=inv(DE), max_scale=numerator(dd)*DE)) end unique!(gene) @vprintln :ZZLatWithIsom 1 "All possible genera: $(length(gene))" for g in gene - @vprintln :ZZLatWithIsom 1 "g = $g" - H = representative(g) - if !is_integral(DE*scale(H)) + if is_integral(G) && !is_integral(DE*scale(g)) continue end - if is_even(Lf) && !is_integral(different(fixed_ring(H))*norm(H)) + if is_even(G) && !is_integral(DK*norm(g)) continue end - @vprintln :ZZLatWithIsom 1 "$H" + @v_do :ZZLatWithIsom 3 Base.show(stdout, MIME"text/plain"(), g) + @vprintln :ZZLatWithIsom 1 "" + + H = representative(g) M, fM = trace_lattice_with_isometry(H) - det(M) == d || continue - MfM = integer_lattice_with_isometry(M, fM; check = false) + genus(M) != G && continue + + MfM = integer_lattice_with_isometry(M, fM; check=false) @hassert :ZZLatWithIsom 1 is_of_hermitian_type(MfM) - @hassert :ZZLatWithIsom 1 order_of_isometry(MfM) == nm - if is_even(M) != is_even(Lf) - continue - end - if !is_of_same_type(MfM^m, Lf) - continue - end + gr = genus_representatives(H) for HH in gr M, fM = trace_lattice_with_isometry(HH) - push!(reps, integer_lattice_with_isometry(M, fM; check = false)) + push!(reps, integer_lattice_with_isometry(M, fM; check=false)) end end return reps end -@doc raw""" - representatives_of_hermitian_type(G::ZZGenus, m::Int) -> Vector{ZZLatWithIsom} - representatives_of_hermitian_type(L::ZZLat, m::Int) -> Vector{ZZLatWithIsom} - -Given an non-empty genus of integer lattices $G$, return a list of -representatives of isomorphic classes of pairs $(L, f)$ consisting of a lattice -$L$ in $G$ and $f \in O(L)$ is an isometry of minimal polynomial $\Phi_m(X)$, -the $m-$th cyclotomic polynomial. - -If $m = 1,2$, this goes back to enumerate $G$ as a genus of integer lattices. - -One can also provide directly a representative $L$ of $G$ instead. -""" -representatives_of_hermitian_type(::Union{ZZGenus, ZZLat}, ::Int) - -function representatives_of_hermitian_type(G::ZZGenus, m::Int, fix_root::Bool = false) - Lf = integer_lattice_with_isometry(representative(G)) - return representatives_of_hermitian_type(Lf, m, fix_root) -end - -function representatives_of_hermitian_type(L::ZZLat, m::Int, fix_root::Bool = false) - Lf = integer_lattice_with_isometry(L) - return representatives_of_hermitian_type(Lf, m, fix_root) -end +representatives_of_hermitian_type(L::ZZLat, chi::Union{ZZPolyRingElem, QQPolyRingElem}, fix_root::Bool = false) = representatives_of_hermitian_type(genus(L), chi, fix_root) @doc raw""" splitting_of_hermitian_prime_power(Lf::ZZLatWithIsom, p::Int) -> Vector{ZZLatWithIsom} -Given a lattice with isometry $(L, f)$ of hermitian type with $f$ of order $q^e$ +Given an even lattice with isometry $(L, f)$ of hermitian type with $f$ of order $q^e$ for some prime number $q$, and given another prime number $p \neq q$, return a set of representatives of the isomorphism classes of lattices with isometry $(M, g)$ such that the type of $(M, g^p)$ is equal to the type of $(L, f)$. @@ -599,6 +631,7 @@ function splitting_of_hermitian_prime_power(Lf::ZZLatWithIsom, p::IntegerUnion; fix_root::Bool = false) rank(Lf) == 0 && return ZZLatWithIsom[Lf] + @req iseven(Lf) "Lattice must be even" @req is_prime(p) "p must be a prime number" @req is_of_hermitian_type(Lf) "Lf must be of hermitian type" @@ -616,11 +649,9 @@ function splitting_of_hermitian_prime_power(Lf::ZZLatWithIsom, p::IntegerUnion; @vprintln :ZZLatWithIsom 1 "$(length(atp)) admissible triple(s)" while !is_empty(atp) A, B = pop!(atp) - LB = integer_lattice_with_isometry(representative(B)) - RB = representatives_of_hermitian_type(LB, p*q^e, fix_root) + RB = representatives_of_hermitian_type(B, p*q^e, fix_root) is_empty(RB) && continue - LA = integer_lattice_with_isometry(representative(A)) - RA = representatives_of_hermitian_type(LA, q^e) + RA = representatives_of_hermitian_type(A, q^e) is_empty(RA) && continue for L1 in RA, L2 in RB E = admissible_equivariant_primitive_extensions(L1, L2, Lf, p; check = false) @@ -634,7 +665,7 @@ end splitting_of_prime_power(Lf::ZZLatWithIsom, p::Int, b::Int = 0) -> Vector{ZZLatWithIsom} -Given a lattice with isometry $(L, f)$ with $f$ of order $q^e$ for some +Given an even lattice with isometry $(L, f)$ with $f$ of order $q^e$ for some prime number $q$, a prime number $p \neq q$ and an integer $b = 0, 1$, return a set of representatives of the isomorphism classes of lattices with isometry $(M, g)$ such that the type of $(M, g^p)$ is equal to the type of $(L, f)$. @@ -671,8 +702,9 @@ function splitting_of_prime_power(Lf::ZZLatWithIsom, p::IntegerUnion, b::Int = 0 return ZZLatWithIsom[] end + @req iseven(Lf) "Lattice must be even" @req is_prime(p) "p must be a prime number" - @req b in [0, 1] "b must be an integer equal to 0 or 1" + @req b == 0 || b == 1 "b must be an integer equal to 0 or 1" ord = order_of_isometry(Lf) @req ord isa Int "Order of isometry must be finite" @@ -685,7 +717,7 @@ function splitting_of_prime_power(Lf::ZZLatWithIsom, p::IntegerUnion, b::Int = 0 reps = ZZLatWithIsom[] if e == 0 - reps = splitting_of_hermitian_prime_power(Lf, p; pA = p_inv, pB, fix_root) + reps = splitting_of_hermitian_prime_power(Lf, p; pA=p_inv, pB, fix_root) (b == 1) && filter!(M -> order_of_isometry(M) == p, reps) return reps end @@ -712,7 +744,7 @@ end splitting_of_pure_mixed_prime_power(Lf::ZZLatWithIsom, p::Int) -> Vector{ZZLatWithIsom} -Given a lattice with isometry $(L, f)$ and a prime number $p$, such that +Given an even lattice with isometry $(L, f)$ and a prime number $p$, such that $\prod_{i=0}^e\Phi_{p^dq^i}(f)$ is trivial for some $d > 0$ and $e \geq 0$, return a set of representatives of the isomorphism classes of lattices with isometry $(M, g)$ such that the type of $(M, g^p)$ is equal to the type @@ -726,6 +758,8 @@ function splitting_of_pure_mixed_prime_power(Lf::ZZLatWithIsom, _p::IntegerUnion fix_root::Bool = false) rank(Lf) == 0 && return ZZLatWithIsom[Lf] + @req iseven(Lf) "Lattice must be even" + n = order_of_isometry(Lf) @req is_finite(n) "Isometry must be of finite order" @@ -748,7 +782,7 @@ function splitting_of_pure_mixed_prime_power(Lf::ZZLatWithIsom, _p::IntegerUnion end phi = minimal_polynomial(Lf) - chi = prod(cyclotomic_polynomial(p^d*q^i, parent(phi)) for i=0:e; init = zero(phi)) + chi = prod(cyclotomic_polynomial(p^d*q^i, parent(phi)) for i=0:e; init = one(phi)) @req is_divisible_by(chi, phi) "Minimal polynomial is not of the correct form" @@ -759,7 +793,7 @@ function splitting_of_pure_mixed_prime_power(Lf::ZZLatWithIsom, _p::IntegerUnion end A0 = kernel_lattice(Lf, p^d*q^e) - if pB >= 0 && signature_tuple(A0)[3] != pB + if pB >= 0 && signature_tuple(A0)[1] != pB return reps end bool, r = divides(phi, cyclotomic_polynomial(p^d*q^e, parent(phi))) @@ -781,7 +815,7 @@ end splitting_of_mixed_prime_power(Lf::ZZLatWithIsom, p::Int, b::Int = 1) -> Vector{ZZLatWithIsom} -Given a lattice with isometry $(L, f)$ and a prime number $p$ such that +Given an even lattice with isometry $(L, f)$ and a prime number $p$ such that $f$ has order $p^dq^e$ for some prime number $q \neq p$, return a set of representatives of the isomorphism classes of lattices with isometry $(M, g)$ such that the type of $(M, g^p)$ is equal to the type of $(L, f)$. @@ -833,6 +867,7 @@ function splitting_of_mixed_prime_power(Lf::ZZLatWithIsom, p::IntegerUnion, b::I return ZZLatWithIsom[] end + @req iseven(Lf) "Lattice must be even" n = order_of_isometry(Lf) @req is_finite(n) "Isometry must be of finite order" @@ -879,10 +914,10 @@ lattices as an input - the function first computes a representative of $G$. Note that currently we support only orders which admit at most 2 prime divisors. """ function enumerate_classes_of_lattices_with_isometry(L::ZZLat, order::IntegerUnion) - @req is_even(L) "For now we support only the case where L is even" + @req iseven(L) "Lattice must be even" @req is_finite(order) && order >= 1 "order must be positive and finite" if order == 1 - reps = representatives_of_hermitian_type(integer_lattice_with_isometry(L)) + reps = representatives_of_hermitian_type(L, 1) return reps end pd = prime_divisors(order) diff --git a/experimental/QuadFormAndIsom/src/hermitian_miranda_morrison.jl b/experimental/QuadFormAndIsom/src/hermitian_miranda_morrison.jl index 081022e284d7..74498c2e6902 100644 --- a/experimental/QuadFormAndIsom/src/hermitian_miranda_morrison.jl +++ b/experimental/QuadFormAndIsom/src/hermitian_miranda_morrison.jl @@ -313,16 +313,12 @@ function _local_determinants_morphism(Lf::ZZLatWithIsom) # rank and then transport the generators along an appropriate map. qL, fqL = discriminant_group(Lf) OqL = orthogonal_group(qL) + if rank(Lf) != degree(Lf) - Lf2 = integer_lattice_with_isometry(integer_lattice(gram = gram_matrix(Lf)), isometry(Lf); ambient_representation = false, check = false) + Lf2 = integer_lattice_with_isometry(integer_lattice(; gram=gram_matrix(Lf)), isometry(Lf); ambient_representation=false, check=false) qL2, fqL2 = discriminant_group(Lf2) OqL2 = orthogonal_group(qL2) - ok, phi12 = is_isometric_with_isometry(qL, qL2) - @hassert :ZZLatWithIsom 1 ok - ok, g0 = is_conjugate_with_data(OqL, OqL(compose(phi12, compose(hom(fqL2), inv(phi12))); check = false), fqL) - @hassert :ZZLatWithIsom 1 ok - phi12 = compose(hom(OqL(g0)), phi12) - #@hassert :ZZLatWithIsom 1 matrix(compose(hom(fqL), phi12)) == matrix(compose(phi12, hom(fqL2))) + phi12 = hom(qL, qL2, identity_matrix(ZZ, ngens(qL))) @hassert :ZZLatWithIsom 1 is_isometry(phi12) else Lf2 = Lf @@ -339,6 +335,7 @@ function _local_determinants_morphism(Lf::ZZLatWithIsom) G, GinOqL = sub(OqL, gensG) @hassert :ZZLatWithIsom 1 fqL in G GtoG2 = hom(G, G2, gensG, gensG2; check = false) + @hassert :ZZLatWithIsom 1 GtoG2(fqL) == fqL2 # This is the associated hermitian O_E-lattice to (L, f): we want to make qL # (aka D_L) correspond to the quotient D^{-1}H^#/H by the trace construction, @@ -361,6 +358,7 @@ function _local_determinants_morphism(Lf::ZZLatWithIsom) # hermitian world in which H lives. In particular, the trace lattice of H2 # with respect to res will be exactly the dual of L. res = get_attribute(Lf2, :transfer_data) + # We want only the prime ideal in O_K which divides the quotient H2/H. For # this, we collect all the primes dividing DEQ or for which H is not locally # unimodular. Then, we check for which prime ideals p, the local quotient @@ -396,15 +394,23 @@ function _local_determinants_morphism(Lf::ZZLatWithIsom) # avoid computing unnecessary crt. This will hold for the rest of the code, we # for those particular objects, the `dlog` maps take vectors, corresponding to # finite adeles. + list_ker = eltype(S)[] Fdata = Tuple{AbsSimpleNumFieldOrderIdeal, Int}[] - for p in S + for _i in 1:length(S) + p = S[_i] if !_is_special(H, p) push!(Fdata, (p, 0)) + if Fsharpdata[_i][2] == 0 + push!(list_ker, p) + end else lp = prime_decomposition(OE, p) P = lp[1][1] e = valuation(DEK, P) push!(Fdata, (p, e)) + if Fsharpdata[_i][2] == e + push!(list_ker, p) + end end end @@ -436,6 +442,7 @@ function _local_determinants_morphism(Lf::ZZLatWithIsom) Q, mQ = quo(FmodFsharp, I) SQ, SQtoQ = snf(Q) + oSQ = order(SQ) function dlog(x::Vector) @hassert :ZZLatWithIsom 1 length(x) == length(Fsharpdata) @@ -452,7 +459,7 @@ function _local_determinants_morphism(Lf::ZZLatWithIsom) for g in gensG2 ds = elem_type(E)[] for p in S - if !_is_special(H, p) + if isone(oSQ) || p in list_ker push!(ds, one(E)) else lp = prime_decomposition(OE, p) @@ -470,7 +477,6 @@ function _local_determinants_morphism(Lf::ZZLatWithIsom) GSQ, SQtoGSQ, _ = Oscar._isomorphic_gap_group(SQ) f2 = hom(G2, GSQ, gensG2, SQtoGSQ.(imgs); check = false) f = compose(GtoG2, f2) - @hassert :ZZLatWithIsom 1 isone(f(fqL)) return f, GinOqL # Needs the second map to map the kernel of f into OqL end @@ -528,16 +534,10 @@ Oscar.canonical_unit(x::AbsSimpleNumFieldOrderQuoRingElem) = one(parent(x)) # (fixed by res). The new map we obtain should be a local invertible map with # integer (for the given local field at p) entries which defines an isometry of # D^{-1}H^# modulo H. - function _transfer_discriminant_isometry(res::AbstractSpaceRes, g::AutomorphismGroupElem{TorQuadModule}, Bp::T, - P::Hecke.RelNumFieldOrderIdeal, - BHp::T) where T <: MatrixElem{Hecke.RelSimpleNumFieldElem{AbsSimpleNumFieldElem}} - E = base_ring(codomain(res)) - Eabs, EabstoE = absolute_simple_field(E) - Pabs = EabstoE\P - OEabs = order(Pabs) + pr::T) where T <: MatrixElem{Hecke.RelSimpleNumFieldElem{AbsSimpleNumFieldElem}} q = domain(g) @hassert :ZZLatWithIsom 1 ambient_space(cover(q)) === domain(res) @@ -545,60 +545,38 @@ function _transfer_discriminant_isometry(res::AbstractSpaceRes, # action of g via res. B2 = zero(Bp) for i in 1:nrows(Bp) - B2[i, :] = res(lift(g(q(res\(vec(collect(Bp[i, :]))))))) - end - - # Here BHp is the inverse of a local basis matrix of H at p. Since we look for - # F such that F*Bp == B2 mod inv(BHp), we then transform the problem into - # finding a matrix F such that F*newBp == newB2 mod O_p. Then to ensure that F - # has integral coefficients, we multiplying newBp and newB2 by a big enough - # integer d so that they are both integral (all their entries are in OEabs, - # after passing to an absolute simple extension), we keep track of the - # P-valuation i of d, and we then map everything in OEabs/Pabs^i. There, there - # should be a modular solution KQ such that KQ*BpQ == B2Q. We lift this matrix - # in OEabs and map it back to OE. - Bpabs = map_entries(a -> EabstoE\a, Bp*BHp) - B2abs = map_entries(a -> EabstoE\a, B2*BHp) - - # Here d is not necessarily well defined in O_E, but as it is implemented, - # each of the denominator(a, O_E) return the smallest positive integer d such - # that d*a lies in O_E, while `a` might be a non-integral element in E. - d = lcm(lcm([denominator(a, OEabs) for a in Bpabs]), lcm([denominator(a, OEabs) for a in B2abs])) - Bpabs = change_base_ring(OEabs, d*Bpabs) - B2abs = change_base_ring(OEabs, d*B2abs) - - # We would need to solve the equation modulo OE, but we multiplied by d, so we - # need to keep track of d. Note that with the precaution we took earlier, the - # Pabs-valuation of d is necessarily positive, so this quotient cannot be - # trivial. - Q, p = quo(OEabs, Pabs^(valuation(d, Pabs))) - Bpabs = map_entries(p, Bpabs) - B2abs = map_entries(p, B2abs) - - # Our local modular solution we have to lift - 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 - # entries in the difference K*newBp-newB2 must have non-negative P-valuation. - # Since it is the case, then K satisfies K*Bp == B2 mod H locally at p. - @hassert :ZZLatWithIsom 1 _scale_valuation((K*Bp-B2)*BHp, P) >= 0 + B2[i, :] = res(lift(g(q(res\(vec(collect(Bp[i, :])))))))*pr + end + # We should have a global exact solution. For now it does not seem to be slow + # If for larger (quite large) examples it happens to be slow, then one could + # modify this a bit and try to look for an inexact approximation modulo H. + ok, K = can_solve_with_solution(Bp, B2; side=:left) + @hassert :ZZLatWithIsom 1 ok return K end # the minimum P-valuation among all the non-zero entries of M function _scale_valuation(M::T, P::Hecke.RelNumFieldOrderIdeal) where T <: MatrixElem{Hecke.RelSimpleNumFieldElem{AbsSimpleNumFieldElem}} - @hassert :ZZLatWithIsom 1 Hecke.nf(order(P)) === base_ring(M) + OE = order(P) + E = Hecke.nf(OE) + @hassert :ZZLatWithIsom 1 base_ring(M) === E iszero(M) && return inf - return minimum(valuation(v, P) for v in collect(M) if !iszero(v)) + O = fractional_ideal(OE, one(E)) + to_sum = [ M[i, j] * O for j in 1:nrows(M) for i in 1:j ] + d = length(to_sum) + for i in 1:d + push!(to_sum, involution(E)(to_sum[i])) + end + s = sum(to_sum; init=fractional_ideal(maximal_order(E), zero(E))) + return valuation(s, P) end # the minimum P-valuation among all the non-zero diagonal entries of M function _norm_valuation(M::T, P::Hecke.RelNumFieldOrderIdeal) where T <: MatrixElem{Hecke.RelSimpleNumFieldElem{AbsSimpleNumFieldElem}} - @hassert :ZZLatWithIsom 1 Hecke.nf(order(P)) === base_ring(M) - iszero(diagonal(M)) && return inf - r = minimum(valuation(v, P) for v in diagonal(M) if !iszero(v)) - return r + E = Hecke.nf(order(P)) + @hassert :ZZLatWithIsom 1 base_ring(M) === E + iszero(M) && return inf + return Hecke._get_norm_valuation_from_gram_matrix(M, P) end # This is algorithm 8 of BH23: under the good assumptions, then we can do a @@ -610,21 +588,28 @@ end # We use this method iteratively to lift isometries (along a surjective map), by # looking at better representatives until we reach a good enough precision for # our purpose. -function _local_hermitian_lifting(G::T, F::T, rho::Hecke.RelSimpleNumFieldElem, l::Int, P::Hecke.RelNumFieldOrderIdeal, e::Int, a::Int; check = true) where T <: MatrixElem{Hecke.RelSimpleNumFieldElem{AbsSimpleNumFieldElem}} +function _local_hermitian_lifting(G::T, F::T, rho::Hecke.RelSimpleNumFieldElem, l::Int, P::Hecke.RelNumFieldOrderIdeal, P2::Hecke.RelNumFieldOrderIdeal, split::Bool, e::Int, a::Int; check = true) where T <: MatrixElem{Hecke.RelSimpleNumFieldElem{AbsSimpleNumFieldElem}} @hassert :ZZLatWithIsom 1 trace(rho) == 1 E = base_ring(G) + s = involution(E) # G here is a local gram matrix - @hassert :ZZLatWithIsom 1 G == map_entries(involution(E), transpose(G)) + @hassert :ZZLatWithIsom 1 G == map_entries(s, transpose(G)) @hassert :ZZLatWithIsom 1 base_ring(F) === E # R represents the defect, how far F is to be an isometry of G - R = G - F*G*map_entries(involution(E), transpose(F)) + R = G - F*G*map_entries(s, transpose(F)) # These are the necessary conditions for the input of algorithm 8 in BH23 if check @hassert :ZZLatWithIsom 1 _scale_valuation(inv(G), P) >= 1+a @hassert :ZZLatWithIsom 1 _norm_valuation(inv(G), P) + valuation(rho, P) >= 1+a @hassert :ZZLatWithIsom 1 _scale_valuation(R, P) >= l-a @hassert :ZZLatWithIsom 1 _norm_valuation(R, P) + valuation(rho,P) >= l-a + if split + @hassert :ZZLatWithIsom 1 _scale_valuation(inv(G), P2) >= 1+a + @hassert :ZZLatWithIsom 1 _norm_valuation(inv(G), P2) + valuation(rho, P2) >= 1+a + @hassert :ZZLatWithIsom 1 _scale_valuation(R, P2) >= l-a + @hassert :ZZLatWithIsom 1 _norm_valuation(R, P2) + valuation(rho, P2) >= l-a + end end # R is s-symmetric, where s is the canonical involution of E/K. We split R @@ -637,19 +622,24 @@ function _local_hermitian_lifting(G::T, F::T, rho::Hecke.RelSimpleNumFieldElem, end end - diag = R - U - map_entries(involution(E), transpose(U)) + diag = R - U - map_entries(s, transpose(U)) - # this newF is suppose to be a better lift than F, i.e. it is congruent to F + # this newF is supposed to be a better lift than F, i.e. it is congruent to F # modulo P^{l+1} and the corresponding defect R2 has a higher P-valuation (so # P-adic, we are close to have a proper isometry) - newF = F + (U + rho*diag)*map_entries(involution(E), inv(transpose(F)))*inv(G) + newF = F + (U + rho*diag)*map_entries(s, inv(transpose(F)))*inv(G) l2 = 2*l+1 if check - @hassert :ZZLatWithIsom 1 _scale_valuation(F-newF, P) >= l+1 - R2 = G-newF*G*map_entries(involution(E), transpose(newF)) + @hassert :ZZLatWithIsom 1 minimum(valuation(m, P) for m in collect(F-newF) if !iszero(m)) >= l+1 + R2 = G-newF*G*map_entries(s, transpose(newF)) @hassert :ZZLatWithIsom 1 _scale_valuation(R2, P) >= l2-a @hassert :ZZLatWithIsom 1 _norm_valuation(R2, P) + valuation(rho, P) >= l2-a + if split + @hassert :ZZLatWithIsom 1 minimum(valuation(m, P2) for m in collect(F-newF) if !iszero(m)) >= l+1 + @hassert :ZZLatWithIsom 1 _scale_valuation(R2, P2) >= l2-a + @hassert :ZZLatWithIsom 1 _norm_valuation(R2, P2) + valuation(rho, P2) >= l2-a + end end return newF, l2 @@ -671,27 +661,29 @@ end # function _approximate_isometry(H::HermLat, H2::HermLat, g::AutomorphismGroupElem{TorQuadModule}, P::Hecke.RelNumFieldOrderIdeal, e::Int, a::Int, k::Int, res::AbstractSpaceRes) E = base_field(H) + s = involution(E) + P2 = s(P) + split = P2 != P + # In the split case, we need to check valuation at both primes above p + P2.is_prime = 1 @hassert :ZZLatWithIsom 1 Hecke.nf(order(P)) === E ok, b = is_modular(H, minimum(P)) if ok && b == -a return identity_matrix(E, 1) end - BHp = local_basis_matrix(H, minimum(P); type = :submodule) - BHp_inv = inv(BHp) - Bps = _local_basis_modular_submodules(H2, minimum(P), a, res) - Bp = reduce(vcat, Bps) - Gp = Bp*gram_matrix(ambient_space(H))*map_entries(involution(E), transpose(Bp)) - Fp = block_diagonal_matrix(typeof(Gp)[_transfer_discriminant_isometry(res, g, Bps[i], P, BHp_inv) for i in 1:length(Bps)]) + Bp, pr = _local_basis_matrix_and_projection(H2, minimum(P), a, res) + Gp = Bp*gram_matrix(ambient_space(H))*map_entries(s, transpose(Bp)) + Fp = _transfer_discriminant_isometry(res, g, Bp, pr) # This is the local defect. By default, it should have scale P-valuations -a # and norm P-valuation e-1-a - Rp = Gp - Fp*Gp*map_entries(involution(E), transpose(Fp)) + Rp = Gp - Fp*Gp*map_entries(s, transpose(Fp)) rho = _find_rho(P, e) l = 0 - while _scale_valuation(Rp, P) < 2*k+a - Fp, l = _local_hermitian_lifting(Gp, Fp, rho, l, P, e, a) - Rp = Gp - Fp*Gp*map_entries(involution(E), transpose(Fp)) + while _scale_valuation(Rp, P) < 2*k+a && (!split || _scale_valuation(Rp, P2) < 2*k+a) + Fp, l = _local_hermitian_lifting(Gp, Fp, rho, l, P, P2, split, e, a) + Rp = Gp - Fp*Gp*map_entries(s, transpose(Fp)) end return Fp @@ -700,7 +692,7 @@ end # We use this function compute a local basis matrix of H at p, whose integral # span defines a sublattice of H. If H has a P^{-a}-modular block at p, we remove # the corresponding basis vector(s) from the output to only keep the Jordan -# blocks of H_p which are of P-valuation different from -a +# blocks of H_p which are of P-valuation different from -a. # # In our context of use, -a is actually the biggest scale valuation for # D^{-1}H^#. Since we take care earlier to discard the cases where D^{-1}H^# is @@ -708,27 +700,45 @@ end # the jordan decomposition of D^{-1}H^# at p. From that point, we massage a bit # the basis matrices of the other jordan blocks to obtain local basis matrices # which span sublattices of D^{-1}H^#. -function _local_basis_modular_submodules(H::HermLat, p::AbsSimpleNumFieldOrderIdeal, a::Int, res::AbstractSpaceRes) - L = restrict_scalars(H, res) - B, _ , exps = jordan_decomposition(H, p) - if exps[end] == -a - pop!(B) - pop!(exps) - end - subs = eltype(B)[] - for b in B - H2 = lattice_in_same_ambient_space(H, b) - if !is_sublattice(H, H2) - L2 = restrict_scalars(H2, res) - L2 = intersect(L, L2) - B2 = basis_matrix(L2) - gene = Vector{elem_type(base_field(H))}[res(vec(collect(B2[i, :]))) for i in 1:nrows(B2)] - H2 = lattice(ambient_space(H), gene) - b = local_basis_matrix(H2, p; type = :submodule) +# +# If Hv is locally U + R where U if a Jordan block of scale P^{-a}, the matrix +# pr in output is the projection onto R. We multiply our local basis for R by +# pr to remove all residue from U: we use this map also to compute approximation +# of local isometries later. +function _local_basis_matrix_and_projection(Hv::HermLat, p::AbsSimpleNumFieldOrderIdeal, a::Int, res::AbstractSpaceRes) + B, _ , exps = jordan_decomposition(Hv, p) + pr = identity_matrix(base_field(Hv), rank(Hv)) + # If the last Jordan block U is P^{-a}-modular, then this part while + # vanish in the quotient Hv/H and we want to get rid of it. However + # we need to remember a decomposition Hv_p = R+U: for this + # we define the projection map Hv_p \to R so later we can + # remove any trace of U in our elements (for computing the first + # approximation of our isometries) + if expsv[end] == -a + for i in 1:nrows(Bv[end]) + pr[nrows(pr)-i+1, ncols(pr)-i+1] = 0 end - push!(subs, b) - end - return subs + subsv = Bv[1:end-1] + else + subsv = Bv + end + + # Now that we have a good looking local basis at p for R, we massage it + # a bit to make sure that globally it spans a sublattice of Hv. + Bp = reduce(vcat, subsv) + H2v = lattice_in_same_ambient_space(Hv, Bp) + if !is_sublattice(Hv, H2v) + Lv = restrict_scalars(Hv, res) + L2 = restrict_scalars(H2v, res) + L2 = intersect(Lv, L2) + B2 = basis_matrix(L2) + gene = Vector{elem_type(base_field(Hv))}[res(vec(collect(B2[i, :]))) for i in 1:nrows(B2)] + H2v = lattice(ambient_space(Hv), gene) + @hassert :ZZLatWithIsom 1 is_sublattice(Hv, H2v) + Bp = local_basis_matrix(H2v, p; type = :submodule) + end + @hassert :ZZLatWithIsom 1 rank(Bp) == rank(Bp*pr) + return Bp*pr, pr end # We need a special rho for Algorithm 8 of BH23: we construct such an element @@ -747,12 +757,15 @@ function _find_rho(P::Hecke.RelNumFieldOrderIdeal, e::Int) lp = prime_decomposition(OE, minimum(P)) dya = is_dyadic(P) if !dya - length(lp) == 1 && return E(1//2) - return gen(E) + rho = E(1//2) + @hassert :ZZLatWithIsom 1 trace(rho) == 1 + return rho end lp = prime_decomposition(OE, minimum(P)) if lp[1][2] == 1 - return Hecke._special_unit(P, minimum(P)) + rho = Hecke._special_unit(P, minimum(P)) + @hassert :ZZLatWithIsom 1 trace(rho) == 1 + return rho end K = base_field(E) Eabs, EabstoE = absolute_simple_field(E) diff --git a/experimental/QuadFormAndIsom/src/lattices_with_isometry.jl b/experimental/QuadFormAndIsom/src/lattices_with_isometry.jl index 1a3ef6f886a6..b7ad00678a9d 100644 --- a/experimental/QuadFormAndIsom/src/lattices_with_isometry.jl +++ b/experimental/QuadFormAndIsom/src/lattices_with_isometry.jl @@ -405,7 +405,7 @@ julia> minimum(Lf) ``` """ function minimum(Lf::ZZLatWithIsom) - @req is_positive_definite(Lf) "Underlying lattice must be positive definite" + @req is_definite(Lf) "Underlying lattice must be definite" return minimum(lattice(Lf)) end @@ -1452,7 +1452,7 @@ end is_of_hermitian_type(Lf::ZZLatWithIsom) -> Bool Given a lattice with isometry $(L, f)$, return whether the minimal polynomial of -the underlying isometry $f$ is irreducible. +the underlying isometry $f$ is irreducible and the associated order is maximal. Note that if $(L, f)$ is of hermitian type with $f$ of minimal polynomial $\chi$, then $L$ can be seen as a hermitian lattice over the order $\mathbb{Z}[\chi]$. @@ -1486,7 +1486,11 @@ true """ @attr function is_of_hermitian_type(Lf::ZZLatWithIsom) @req rank(Lf) > 0 "Underlying lattice must have positive rank" - return is_irreducible(minimal_polynomial(Lf)) + chi = minimal_polynomial(Lf) + !is_irreducible(chi) && return false + is_finite(order_of_isometry(Lf)) && return true + E = equation_order(number_field(chi; cached=false)[1]) + return is_maximal(E) end @doc raw""" @@ -1615,7 +1619,7 @@ function discriminant_group(Lf::ZZLatWithIsom) q = discriminant_group(L) f = hom(q, q, elem_type(q)[q(lift(t)*f) for t in gens(q)]) fq = gens(Oscar._orthogonal_group(q, ZZMatrix[matrix(f)]; check = false))[1] - return (q, fq) + return q, fq end @doc raw""" @@ -1726,6 +1730,7 @@ julia> order(G) disc = discriminant_representation(L, UL; check = false, ambient_representation = false) return image(disc) else + @req is_even(Lf) "Hermitian Miranda-Morrison currently available only for even lattices" # If L is indefinite of rank >=3, then we use the hermitian version of # Miranda-Morrison theory to compute the image of the centralizer f directly # in the centralizer of D_f. @@ -1750,49 +1755,8 @@ julia> order(G) psi = divs[end] M = kernel_lattice(Lf, psi) - qM, fqM = discriminant_group(M) - GM, _ = image_centralizer_in_Oq(M) - N = orthogonal_submodule(Lf, basis_matrix(M)) - qN, fqN = discriminant_group(N) - GN, _ = image_centralizer_in_Oq(N) - - phi, HMinqM, HNinqN = glue_map(L, lattice(M), lattice(N); check = false) - - # Since M and N are obtained by cutting some parts of `f \in O(L)`, the glue - # map should be equivariant! - @hassert :ZZLatWithIsom 1 is_invariant(fqM, HMinqM) - @hassert :ZZLatWithIsom 1 is_invariant(fqN, HNinqN) - @hassert :ZZLatWithIsom 1 matrix(compose(restrict_automorphism(fqM, HMinqM; check = false), phi)) == matrix(compose(phi, restrict_automorphism(fqN, HNinqN; check = false))) - - HM = domain(HMinqM) - OHM = orthogonal_group(HM) - - HN = domain(HNinqN) - OHN = orthogonal_group(HN) - - _, qMinD, qNinD, _, OqMinOD, OqNinOD = _sum_with_embeddings_orthogonal_groups(qM, qN) - HMinD = compose(HMinqM, qMinD) - HNinD = compose(HNinqN, qNinD) - - stabM, _ = stabilizer(GM, HMinqM) - stabN, _ = stabilizer(GN, HNinqN) - - actM = hom(stabM, OHM, elem_type(OHM)[OHM(restrict_automorphism(x, HMinqM; check = false)) for x in gens(stabM)]) - actN = hom(stabN, OHN, elem_type(OHN)[OHN(restrict_automorphism(x, HNinqN; check = false)) for x in gens(stabN)]) - - _, _, graph = _overlattice(phi, HMinD, HNinD, isometry(M), isometry(N); same_ambient = true) - disc, stab = _glue_stabilizers(phi, actM, actN, OqMinOD, OqNinOD, graph) - qL, fqL = discriminant_group(Lf) - OqL = orthogonal_group(qL) - phi = hom(qL, disc, TorQuadModuleElem[disc(lift(x)) for x in gens(qL)]) - @hassert :ZZLatWithIsom 1 is_isometry(phi) - @hassert :ZZLatWithIsom 1 qL == disc - - stab = sub(OqL, elem_type(OqL)[OqL(compose(phi, compose(g, inv(phi))); check = false) for g in stab]) - - @hassert :ZZLatWithIsom 1 fqL in stab[1] - return stab + return _glue_stabilizers(Lf, M, N) end end @@ -1874,8 +1838,7 @@ function signatures(Lf::ZZLatWithIsom) n = order_of_isometry(Lf) C = CalciumField() eig = eigenvalues(QQBar, f) - j = findfirst(z -> findfirst(k -> isone(z^k), 1:n) == n, eig) - lambda = C(eig[j]) + lambda = C(eig[1]) Sq = Int[i for i in 1:div(n,2) if gcd(i,n) == 1] D = Dict{Integer, Tuple{Int, Int}}() fC = change_base_ring(C, f) @@ -2272,12 +2235,14 @@ true x = gen(Qx) t = Dict{Integer, Tuple}() for l in divs - Hl = kernel_lattice(Lf, cyclotomic_polynomial(l)) - if !(order_of_isometry(Hl) in [-1,1,2]) - Hl = hermitian_structure(lattice(Hl), isometry(Hl); check = false, ambient_representation = false) - end Al = kernel_lattice(Lf, x^l-1) - t[l] = (genus(Hl), genus(Al)) + _Hl = kernel_lattice(Lf, cyclotomic_polynomial(l)) + if !(order_of_isometry(_Hl) in [-1,1,2]) + Hl = hermitian_structure(lattice(_Hl), isometry(_Hl); check = false, ambient_representation = false) + t[l] = (genus(Hl), genus(Al)) + else + t[l] = (genus(_Hl), genus(Al)) + end end return t end @@ -2310,14 +2275,16 @@ function is_of_type(L::ZZLatWithIsom, t::Dict) divs = sort(collect(keys(t))) x = gen(Hecke.Globals.Qx) for l in divs - Hl = kernel_lattice(L, cyclotomic_polynomial(l)) - if !(order_of_isometry(Hl) in [-1, 1, 2]) - t[l][1] isa HermGenus || return false - Hl = hermitian_structure(lattice(Hl), isometry(Hl); check = false, ambient_representation = false, E = base_field(t[l][1])) - end - genus(Hl) == t[l][1] || return false Al = kernel_lattice(L, x^l-1) genus(Al) == t[l][2] || return false + _Hl = kernel_lattice(L, cyclotomic_polynomial(l)) + if !(order_of_isometry(_Hl) in [-1, 1, 2]) + t[l][1] isa HermGenus || return false + Hl = hermitian_structure(lattice(_Hl), isometry(_Hl); check = false, ambient_representation = false, E = base_field(t[l][1])) + genus(Hl) == t[l][1] || return false + else + genus(_Hl) == t[l][1] || return false + end end return true end diff --git a/experimental/QuadFormAndIsom/src/spaces_with_isometry.jl b/experimental/QuadFormAndIsom/src/spaces_with_isometry.jl index 06388b9f3047..c53d4a7467f4 100644 --- a/experimental/QuadFormAndIsom/src/spaces_with_isometry.jl +++ b/experimental/QuadFormAndIsom/src/spaces_with_isometry.jl @@ -739,8 +739,8 @@ end @doc raw""" rational_spinor_norm(Vf::QuadSpaceWithIsom; b::Int = -1) -> QQFieldElem -Given a rational quadratic space with isometry $(V, b, f)$, return the real -spinor norm of the extension of $f$ to $V\otimes \mathbb{Q}$. +Given a rational quadratic space with isometry $(V, b, f)$, return the rational +spinor norm of $f$. If $\Phi$ is the form on $V$, then the spinor norm is computed with respect to $b\Phi$. diff --git a/experimental/QuadFormAndIsom/test/runtests.jl b/experimental/QuadFormAndIsom/test/runtests.jl index 940b57243b1c..52c86a8cf4fa 100644 --- a/experimental/QuadFormAndIsom/test/runtests.jl +++ b/experimental/QuadFormAndIsom/test/runtests.jl @@ -256,9 +256,8 @@ end @test order(ONf) == order(image_centralizer_in_Oq(N)[1]) E6 = root_lattice(:E, 6) - @test length(enumerate_classes_of_lattices_with_isometry(E6, 10)) == 3 @test length(enumerate_classes_of_lattices_with_isometry(E6, 20)) == 0 - @test length(enumerate_classes_of_lattices_with_isometry(E6, 18)) == 1 + @test length(enumerate_classes_of_lattices_with_isometry(E6, 9)) == 1 @test length(enumerate_classes_of_lattices_with_isometry(genus(E6), 1)) == 1 @test length(admissible_triples(E6, 2; pA=2)) == 2 @@ -266,6 +265,16 @@ end @test length(admissible_triples(E6, 3; pA=2, pB = 4)) == 1 end +@testset "Enumeration of hermitian lattices with isometry" begin + # Infinite isometry: chi is a Salem polynomial + G = genus(torsion_quadratic_module(QQ[0;]), (9, 1)) + _, x = QQ["x"] + chi = x^(10)+x^9-x^7-x^6-x^5-x^4-x^3+x+1 + rht = @inferred representatives_of_hermitian_type(G, chi) + @test !isempty(rht) + @test all(N -> !is_finite(order_of_isometry(N)), rht) +end + @testset "Primitive extensions and embeddings" begin # Compute orbits of short vectors k = integer_lattice(; gram=matrix(QQ,1,1,[4])) From 6a53af177609912e8b8f61fb246704521ac10f58 Mon Sep 17 00:00:00 2001 From: Max Horn Date: Fri, 23 Feb 2024 09:45:11 +0100 Subject: [PATCH 27/29] Tweak `exterior_algebra` tests (#3415) Do not just verify that certain `exterior_algebra` invocations don't error out; also check that the returned values satisfy certain properties. Also disable two `@test_broken` tests for now, because (a) the underlying issue is fixed in a Singular PR, but this causes OscarCI failures there.. (b) even if the underlying issue is fixed, those test were wrong, because `exterior_algebra` doesn't return a boolean, but the return value was used in a context where it must be boolean (namely as "argument" for `@test_broken`). --- experimental/ExteriorAlgebra/test/runtests.jl | 32 ++++++++++++------- 1 file changed, 20 insertions(+), 12 deletions(-) diff --git a/experimental/ExteriorAlgebra/test/runtests.jl b/experimental/ExteriorAlgebra/test/runtests.jl index bc52fcd5e425..2ad7c2069d7c 100644 --- a/experimental/ExteriorAlgebra/test/runtests.jl +++ b/experimental/ExteriorAlgebra/test/runtests.jl @@ -4,18 +4,26 @@ ######## CONSTRUCTOR TESTs @test_throws ArgumentError exterior_algebra(QQ, 0) - exterior_algebra(QQ, 1) # --> special case (is commutative) - exterior_algebra(QQ, 2) # --> first general case - exterior_algebra(QQ, 99) # --> Also tried with 999 indets, but takes a long time [~19s] - - exterior_algebra(GF(2), 2) # BUG?? not recognized as commutative!! - exterior_algebra(GF(3), 4) - exterior_algebra(residue_field(ZZ, 2)[1], 2) - exterior_algebra(residue_field(ZZ, 3)[1], 4) - ## exterior_algebra(GF(2), 1500); ## limit 1500 on my 32Gbyte machine (!NB printing requires a lot of space!) - - @test_broken exterior_algebra(GF(1180591620717411303449), 2) # --> ERROR prime too big (for GF) - @test_broken exterior_algebra(residue_field(ZZ, 1180591620717411303449)[1], 2) + @testset "exterior_algebra constructor" for (R,n) in [ + (QQ, 1) # --> special case (is commutative) + (QQ, 2) # --> first general case + (QQ, 99) # --> Also tried with 999 indets, but takes a long time [~19s] + + (GF(2), 2) # BUG?? not recognized as commutative!! + (GF(3), 4) + (residue_field(ZZ, 2)[1], 2) + (residue_field(ZZ, 3)[1], 4) + #(GF(1180591620717411303449), 2) + #(residue_field(ZZ, 1180591620717411303449)[1], 2) + ## (GF(2), 1500); ## limit 1500 on my 32Gbyte machine (!NB printing requires a lot of space!) + ] + A, g = exterior_algebra(R, n) + @test A isa PBWAlgQuo + @test g isa Vector{elem_type(A)} + @test length(g) == n + @test ngens(A) == n + @test gens(A) == g + end # Duplicate names are allowed exterior_algebra(QQ, ["x", "y", "x"]) From 1498d3588e53f3232b4c5071618f0904c4758867 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Lars=20G=C3=B6ttgens?= Date: Fri, 23 Feb 2024 10:07:05 +0100 Subject: [PATCH 28/29] Eliminate more spelling differences between American and British English (#3392) * `behaviour` -> `behavior` * `labelled` -> `labeled` * `modelled` -> `modeled` * `cancelled` -> `canceled` * `cancellation` -> `cancelation` * `regocnise` -> `recognize` * More `-ise-` -> `-ize-` * `-re` -> `-er` (cherry picked from commit 898f41af6ad35ce290e85dbf8cedd180607cf6c2) --- .../Schemes/CoveredSchemes.md | 2 +- .../FrameWorks/ring_localizations.md | 4 +- .../free_modules.md | 4 +- .../subquotients.md | 2 +- docs/src/CommutativeAlgebra/localizations.md | 2 +- docs/src/CommutativeAlgebra/rings.md | 2 +- docs/src/DeveloperDocumentation/debugging.md | 6 +- .../DeveloperDocumentation/serialization.md | 2 +- docs/src/Experimental/Singularities/intro.md | 2 +- .../PBWAlgebras/creation.md | 2 +- .../PBWAlgebras/quotients.md | 2 +- docs/src/Rings/integer.md | 6 +- examples/MatrixDisplay.jl | 10 +- examples/Timo.jl | 4 +- .../test/DoubleComplex.jl | 4 +- experimental/GaloisGrp/src/Solve.jl | 15 +- experimental/IntersectionTheory/src/Bott.jl | 2 +- .../LieAlgebras/test/WeylGroup-test.jl | 2 +- .../OrthogonalDiscriminants/gap/fix.g | 2 +- .../OrthogonalDiscriminants/src/utils.jl | 2 +- experimental/Schemes/CoherentSheaves.jl | 2 +- experimental/Schemes/elliptic_surface.jl | 4 +- .../AffineSchemes/Morphisms/Methods.jl | 2 +- .../AffineSchemes/Objects/Attributes.jl | 2 +- src/Groups/GAPGroups.jl | 2 +- src/Groups/MatrixDisplay.jl | 18 +-- src/Groups/group_characters.jl | 2 +- src/InvariantTheory/primary_invariants.jl | 6 +- src/Rings/AbelianClosure.jl | 2 +- src/Rings/AlgClosureFp.jl | 2 +- src/Rings/PBWAlgebraQuo.jl | 2 +- src/Rings/hilbert.jl | 2 +- src/Rings/mpolyquo-localizations.jl | 2 +- src/TropicalGeometry/curve.jl | 4 +- src/deprecations.jl | 2 + src/exports.jl | 2 +- .../Schemes/AffineSchemes.jl | 2 +- test/Groups/MatrixDisplay.jl | 150 +++++++++--------- 38 files changed, 144 insertions(+), 141 deletions(-) diff --git a/docs/src/AlgebraicGeometry/Schemes/CoveredSchemes.md b/docs/src/AlgebraicGeometry/Schemes/CoveredSchemes.md index 129612eee6e5..cade2cf0c97b 100644 --- a/docs/src/AlgebraicGeometry/Schemes/CoveredSchemes.md +++ b/docs/src/AlgebraicGeometry/Schemes/CoveredSchemes.md @@ -49,7 +49,7 @@ An `AbsCoveredScheme` may have different properties such as fiber_product(f::AbsCoveredSchemeMorphism, g::AbsCoveredSchemeMorphism) ``` -## The modeling of covered schemes and their expected behaviour +## The modeling of covered schemes and their expected behavior Any `AbsCoveredScheme` may possess several `Covering`s. This is necessary for several reasons; for instance, a morphism $f : X \to Y$ between `AbsCoveredScheme`s diff --git a/docs/src/CommutativeAlgebra/FrameWorks/ring_localizations.md b/docs/src/CommutativeAlgebra/FrameWorks/ring_localizations.md index 605392010c76..1efe854d74eb 100644 --- a/docs/src/CommutativeAlgebra/FrameWorks/ring_localizations.md +++ b/docs/src/CommutativeAlgebra/FrameWorks/ring_localizations.md @@ -8,7 +8,7 @@ end # A Framework for Localizing Rings For the convenience of the developer, we outline a general framework for creating concrete instances of localized rings in OSCAR, -addressing relevant abstract types as well as a standardized set of functions whose concrete behaviour must be implemented. +addressing relevant abstract types as well as a standardized set of functions whose concrete behavior must be implemented. We roughly follow the outline of the previous subsection on localizing multivariate rings which provides illustrating examples. With regard to notation, the name `Rloc` will refer to the localization of a commutative ring `R` with 1. @@ -45,7 +45,7 @@ to set `check = false`. For any concrete instance of type `AbsLocalizedRingElem`, methods for the functions `parent`, `numerator`, and `denominator` must be provided. Moreover, -if a cancellation function for the type of fractions under consideration is +if a cancelation function for the type of fractions under consideration is not yet available, such a function should be implemented and named `reduce_fraction`. diff --git a/docs/src/CommutativeAlgebra/ModulesOverMultivariateRings/free_modules.md b/docs/src/CommutativeAlgebra/ModulesOverMultivariateRings/free_modules.md index 2a2d7ea64b57..439dbb94c7ab 100644 --- a/docs/src/CommutativeAlgebra/ModulesOverMultivariateRings/free_modules.md +++ b/docs/src/CommutativeAlgebra/ModulesOverMultivariateRings/free_modules.md @@ -22,7 +22,7 @@ and homomorphisms between free modules by matrices. All OSCAR types for the modules considered here belong to the abstract type `ModuleFP{T}`, where `T` is the element type of the underlying ring. Graded or not, the free modules belong to the abstract subtype `AbstractFreeMod{T} <: ModuleFP{T}`, -they are modelled as objects of the concrete type `FreeMod{T} <: AbstractFreeMod{T}`. +they are modeled as objects of the concrete type `FreeMod{T} <: AbstractFreeMod{T}`. !!! note Canonical maps such us the canonical projection onto a quotient module arise in many @@ -98,7 +98,7 @@ degrees_of_generators(F::FreeMod) All OSCAR types for elements of the modules considered here belong to the abstract type `ModuleElemFP{T}`, where `T` is the element type of the underlying ring. The free modules belong to the abstract subtype `AbstractFreeModElem{T} <: ModuleFPElem{T}`. -They are modelled as objects of the concrete type `FreeModElem{T} <: AbstractFreeModElem{T}` +They are modeled as objects of the concrete type `FreeModElem{T} <: AbstractFreeModElem{T}` which implements an element $f$ of a free module $F$ as a sparse row, that is, as an object of type `SRow{T}`. This object specifies the coordinates of $f$ with respect to the basis of standard unit vectors of $F$. To create an element, enter its coordinates as a sparse row or a vector: diff --git a/docs/src/CommutativeAlgebra/ModulesOverMultivariateRings/subquotients.md b/docs/src/CommutativeAlgebra/ModulesOverMultivariateRings/subquotients.md index 6a35e3462e41..b2db2eca6355 100644 --- a/docs/src/CommutativeAlgebra/ModulesOverMultivariateRings/subquotients.md +++ b/docs/src/CommutativeAlgebra/ModulesOverMultivariateRings/subquotients.md @@ -52,7 +52,7 @@ and regard $M$ as a submodule of that ambient module, embedded in the natural wa All OSCAR types for the finitely presented modules considered here belong to the abstract type `ModuleFP{T}`, where `T` is the element type of the underlying ring. Graded or not, the subquotients belong to the abstract subtype `AbstractSubQuo{T} <: ModuleFP{T}`, -they are modelled as objects of the concrete type `SubquoModule{T} <: AbstractSubQuo{T}`. +they are modeled as objects of the concrete type `SubquoModule{T} <: AbstractSubQuo{T}`. !!! note Canonical maps such us the canonical projection onto a quotient module arise in many diff --git a/docs/src/CommutativeAlgebra/localizations.md b/docs/src/CommutativeAlgebra/localizations.md index d5a86733164d..ee4fa9be7251 100644 --- a/docs/src/CommutativeAlgebra/localizations.md +++ b/docs/src/CommutativeAlgebra/localizations.md @@ -290,7 +290,7 @@ internally represented by a pair `(r, u)` of elements of `R`, then - `parent(f)` refers to `RQL`, - `numerator(f)` to the image of `r` in `RQ`, and - `denominator(f)` to the image of `u` in `RQ`. -That is, the behaviour of the functions `numerator` and `denominator` reflects the mathematical viewpoint +That is, the behavior of the functions `numerator` and `denominator` reflects the mathematical viewpoint of representing `f` by pairs of elements of `RQ` and not the internal representation of `f` as pairs of elements of `R`. ##### Examples diff --git a/docs/src/CommutativeAlgebra/rings.md b/docs/src/CommutativeAlgebra/rings.md index 60c6d5f35e73..1b1b6aacbe52 100644 --- a/docs/src/CommutativeAlgebra/rings.md +++ b/docs/src/CommutativeAlgebra/rings.md @@ -228,7 +228,7 @@ we follow the former book. ### Types -Multivariate rings with gradings are modelled by objects of type +Multivariate rings with gradings are modeled by objects of type `MPolyDecRing{T, S} :< MPolyRing{T}`, with elements of type `MPolyRingElem_dec{T, S} :< MPolyRingElem{T}`. Here, `S` is the element type of the multivariate ring, and `T` is the element type of its coefficient ring as above. diff --git a/docs/src/DeveloperDocumentation/debugging.md b/docs/src/DeveloperDocumentation/debugging.md index 89568875aadd..a12a0f7475a1 100644 --- a/docs/src/DeveloperDocumentation/debugging.md +++ b/docs/src/DeveloperDocumentation/debugging.md @@ -3,7 +3,7 @@ ## Pitfalls: Mutable objects in OSCAR code Suppose you are having the following difficulties. Your code is exhibiting -inexplicable behaviour and values that should not be changing are changing in +inexplicable behavior and values that should not be changing are changing in seemingly random locations. To get to the bottom of these kind of issues it is necessary to be familiar with mutable objects in Julia and some of the relevant conventions in place in OSCAR. This section discusses these @@ -92,7 +92,7 @@ julia> evaluate(x) # x is now unchanged It is of course not true that all Julia functions take ownership of their arguments, but the GOP derives from the fact that this decision is an -implementation detail with performance consequences. The behaviour of a +implementation detail with performance consequences. The behavior of a function may be inconsistent across different types and versions of OSCAR. In the following two snippets, the GOP says both modifications of `a` are illegal since they have since been passed to a function. If `K = QQ`, the two @@ -161,7 +161,7 @@ julia> a 3 ``` -The preceding behaviour of the function `modular_proj` is an artifact of +The preceding behavior of the function `modular_proj` is an artifact of internal efficiency and may be desirable in certain circumstances. In other circumstances, the following `deepcopy`s may be necessary for your code to function correctly. diff --git a/docs/src/DeveloperDocumentation/serialization.md b/docs/src/DeveloperDocumentation/serialization.md index 441ad884e6ff..710cac635d42 100644 --- a/docs/src/DeveloperDocumentation/serialization.md +++ b/docs/src/DeveloperDocumentation/serialization.md @@ -1,6 +1,6 @@ # Serialization -This document summarises the serialization efforts of OSCAR, how it is supposed +This document summarizes the serialization efforts of OSCAR, how it is supposed to work, how it works and the overall goal. [Serialization](https://en.wikipedia.org/wiki/Serialization) broadly speaking is the process of reading and writing data. There are many reasons for this diff --git a/docs/src/Experimental/Singularities/intro.md b/docs/src/Experimental/Singularities/intro.md index c3dee6cfa299..20cfe37187ae 100644 --- a/docs/src/Experimental/Singularities/intro.md +++ b/docs/src/Experimental/Singularities/intro.md @@ -9,7 +9,7 @@ The singularities part of OSCAR provides functionality for handling - space germs - map germs -For readers' convenience, the documentation is organised by typical settings, +For readers' convenience, the documentation is organized by typical settings, This, on the other hand, implies that certain keywords may appear in several settings. In particular, there are overlaps between hypersurface singularities and curve singularities and between hypersurface singularities diff --git a/docs/src/NoncommutativeAlgebra/PBWAlgebras/creation.md b/docs/src/NoncommutativeAlgebra/PBWAlgebras/creation.md index d415965150dd..f410b760bb95 100644 --- a/docs/src/NoncommutativeAlgebra/PBWAlgebras/creation.md +++ b/docs/src/NoncommutativeAlgebra/PBWAlgebras/creation.md @@ -9,7 +9,7 @@ end ## Types -PBW-algebras are modelled by objects of type `PBWAlgRing{T, S} <: NCRing`, their elements are objects of type +PBW-algebras are modeled by objects of type `PBWAlgRing{T, S} <: NCRing`, their elements are objects of type `PBWAlgElem{T, S} <: NCRingElem`. Here, `T` is the element type of the field over which the PBW-algebra is defined (the type `S` is added for internal use). diff --git a/docs/src/NoncommutativeAlgebra/PBWAlgebras/quotients.md b/docs/src/NoncommutativeAlgebra/PBWAlgebras/quotients.md index c0272bb9415c..5cd23e827d74 100644 --- a/docs/src/NoncommutativeAlgebra/PBWAlgebras/quotients.md +++ b/docs/src/NoncommutativeAlgebra/PBWAlgebras/quotients.md @@ -16,7 +16,7 @@ functionality for dealing with quotients of PBW-algebras modulo two-sided ideals ## Types -GR-algebras are modelled by objects of type `PBWAlgQuo{T, S} <: NCRing`, their elements are objects of type +GR-algebras are modeled by objects of type `PBWAlgQuo{T, S} <: NCRing`, their elements are objects of type `PBWAlgQuoElem{T, S} <: NCRingElem`. Here, `T` is the element type of the field over which the GR-algebra is defined (the type `S` is added for internal use). diff --git a/docs/src/Rings/integer.md b/docs/src/Rings/integer.md index 34534d09cf9e..f4e735dff9e0 100644 --- a/docs/src/Rings/integer.md +++ b/docs/src/Rings/integer.md @@ -275,7 +275,7 @@ julia> ZZ(1)^(-2) !!! note In Julia `2^-2` is called a literal power. The value returned is a - floating point value. To get behaviour that agrees with OSCAR, one can + floating point value. To get behavior that agrees with OSCAR, one can write `2^Int(-2)`. The following is allowed for convenience. @@ -643,7 +643,7 @@ ERROR: 7 is not a factor of -1 * 5 * 2^2 * 3 !!! note The functions in this section that take `Int` arguments will return an `Int`, which may overflow or throw an error. Use the `ZZRingElem` versions if - this is not the desired behaviour. + this is not the desired behavior. ### Factorial @@ -753,7 +753,7 @@ julia> fibonacci(-2) !!! note The functions in this section that take `Int` arguments will return a `Int`, which may overflow or throw an error. Use the `ZZRingElem` versions if - this is not the desired behaviour. + this is not the desired behavior. ### Moebius mu function diff --git a/examples/MatrixDisplay.jl b/examples/MatrixDisplay.jl index c14e83b6941f..4284a713dd58 100644 --- a/examples/MatrixDisplay.jl +++ b/examples/MatrixDisplay.jl @@ -1,6 +1,6 @@ ############################################################################# ## -## functionality for displaying labelled matrices, +## functionality for displaying labeled matrices, ## that is, 2-dimensional arrays of strings ## together with row labels, columns labels, header, and footer ## @@ -47,7 +47,7 @@ function replace_TeX(str::String) end """ - labelled_matrix_formatted(io::IO, mat::Matrix{String}) + labeled_matrix_formatted(io::IO, mat::Matrix{String}) Output a formatted version of `mat` to `io`. The following attributes of `io` are supported. @@ -89,18 +89,18 @@ The following attributes of `io` are supported. (enter `0` for a line above the first row), - `:column_portions`: - array of column numbers after which a new labelled table shall be started; + array of column numbers after which a new labeled table shall be started; the default is to have just one portion in the `:TeX` case, and to create portions according to the screen width otherwise, - `:row_portions`: - array of row numbers after which a new labelled table shall be started; + array of row numbers after which a new labeled table shall be started; the default is to have just one portion. ## Examples: ... """ -function labelled_matrix_formatted(io::IO, mat::Matrix{String}) +function labeled_matrix_formatted(io::IO, mat::Matrix{String}) TeX = get(io, :TeX, false) subset_row = get(io, :subset_row, 1:size(mat, 1)) diff --git a/examples/Timo.jl b/examples/Timo.jl index 307476c0d74d..2492486179ec 100644 --- a/examples/Timo.jl +++ b/examples/Timo.jl @@ -8,9 +8,9 @@ function timo(f::QQPolyRingElem, p_all::Vector{Int}) all_g = [x for x = G] @show :aut - @time au = Oscar.SolveRadical.recognise(S, K, [K.pe^g for g = all_g]) + @time au = Oscar.SolveRadical.recognize(S, K, [K.pe^g for g = all_g]) # au = Hecke.closure([hom(k.fld, k.fld, x) for x = au]) -#recognise seems to be faster than closure - and keeps the link +#recognize seems to be faster than closure - and keeps the link #between the Galois group and the automorphisms @time au = [hom(K.fld, K.fld, x, check = false) for x = au] diff --git a/experimental/DoubleAndHyperComplexes/test/DoubleComplex.jl b/experimental/DoubleAndHyperComplexes/test/DoubleComplex.jl index 425fa4c4e66d..47ccd70e1786 100644 --- a/experimental/DoubleAndHyperComplexes/test/DoubleComplex.jl +++ b/experimental/DoubleAndHyperComplexes/test/DoubleComplex.jl @@ -90,7 +90,7 @@ @test matrix(map(tot_xyz, 2)) == R[-y z 0; -x 0 z; 0 -x y] @test matrix(map(tot_xyz, 3)) == R[x -y z] - # Test behaviour w.r.t zero entries + # Test behavior w.r.t zero entries Z = FreeMod(R, 0) Kx = ComplexOfMorphisms([hom(Z, R1, elem_type(R1)[]), hom(R1, R1, [x*R1[1]]), hom(R1, Z, [zero(Z)])], seed = -1) Ky = ComplexOfMorphisms([hom(Z, R1, elem_type(R1)[]), hom(R1, R1, [y*R1[1]]), hom(R1, Z, [zero(Z)])], seed = -1) @@ -206,7 +206,7 @@ end @test matrix(map(tot_xyz, 2)) == R[-y z 0; -x 0 z; 0 -x y] @test matrix(map(tot_xyz, 3)) == R[x -y z] - # Test behaviour w.r.t zero entries + # Test behavior w.r.t zero entries Z = FreeMod(R, 0) Kx = ComplexOfMorphisms([hom(Z, R1, elem_type(R1)[]), hom(R1, R1, [x*R1[1]]), hom(R1, Z, [zero(Z)])], seed = -1) Ky = ComplexOfMorphisms([hom(Z, R1, elem_type(R1)[]), hom(R1, R1, [y*R1[1]]), hom(R1, Z, [zero(Z)])], seed = -1) diff --git a/experimental/GaloisGrp/src/Solve.jl b/experimental/GaloisGrp/src/Solve.jl index 537506a661a9..f17886b250bc 100644 --- a/experimental/GaloisGrp/src/Solve.jl +++ b/experimental/GaloisGrp/src/Solve.jl @@ -8,6 +8,7 @@ function __init__() Hecke.add_assertion_scope(:SolveRadical) end +@deprecate recognise recognize mutable struct SubField coeff_field::Union{Nothing, SubField} @@ -376,13 +377,13 @@ function conjugates(C::GaloisCtx, S::SubField, a::QQFieldElem, pr::Int = 10) return [parent(rt[1])(a)] end -function recognise(C::GaloisCtx, S::SubField, I::SLPoly) - r = recognise(C, S, [I]) +function recognize(C::GaloisCtx, S::SubField, I::SLPoly) + r = recognize(C, S, [I]) r === nothing && return r return r[1] end -function recognise(C::GaloisCtx, S::SubField, J::Vector{<:SLPoly}, d=false) +function recognize(C::GaloisCtx, S::SubField, J::Vector{<:SLPoly}, d=false) if d != false B = d elseif isdefined(S, :ts) @@ -541,20 +542,20 @@ function Oscar.solve(f::ZZPolyRingElem; max_prec::Int=typemax(Int), show_radical cyclo = fld_arr[length(pp)+1] @vprint :SolveRadical 1 "finding roots-of-1...\n" - @vtime :SolveRadical 1 zeta = [recognise(C, cyclo, gens(parent(cyclo.pe))[i])//scale for i=pp] + @vtime :SolveRadical 1 zeta = [recognize(C, cyclo, gens(parent(cyclo.pe))[i])//scale for i=pp] @hassert :SolveRadical 1 all(i->isone(zeta[i]^lp[i]), 1:length(pp)) aut = [] @vprint :SolveRadical 1 "finding automorphisms...\n" for i=length(pp)+2:length(fld_arr) @vprint :SolveRadical 1 "..on level $(i-length(pp)-1)...\n" K = fld_arr[i] - @vtime :SolveRadical 1 push!(aut, hom(K.fld, K.fld, recognise(C, K, K.pe^K.conj[2]))) + @vtime :SolveRadical 1 push!(aut, hom(K.fld, K.fld, recognize(C, K, K.pe^K.conj[2]))) end for i=1:length(pp) fld_arr[i+1].fld.S = Symbol("z_$(lp[i])") end @vprint :SolveRadical 1 "find roots...\n" - @vtime :SolveRadical 1 R = recognise(C, All, gens(S)[rt]) + @vtime :SolveRadical 1 R = recognize(C, All, gens(S)[rt]) R = R .// scale #now, rewrite as radicals.. #the cyclos are fine: @@ -761,7 +762,7 @@ function galois_factor(C::GaloisCtx) end end z = _fixed_field(C, Gi, invar = I) - return recognise(C, z, x) + return recognize(C, z, x) end end # SolveRadical diff --git a/experimental/IntersectionTheory/src/Bott.jl b/experimental/IntersectionTheory/src/Bott.jl index d703c72460fa..16644def1b39 100644 --- a/experimental/IntersectionTheory/src/Bott.jl +++ b/experimental/IntersectionTheory/src/Bott.jl @@ -34,7 +34,7 @@ end # TnBundle, TnVariety - varieties with a torus action and equivariant bundles # # A Tⁿ-abstract_variety X is represented as the set of fixed points X.points, each -# labelled using some value of type P (e.g. an array), and has a multiplicity e +# labeled using some value of type P (e.g. an array), and has a multiplicity e # (orbifold multiplicity); # # A Tⁿ-equivariant bundle on X is represented by its localization/restriction diff --git a/experimental/LieAlgebras/test/WeylGroup-test.jl b/experimental/LieAlgebras/test/WeylGroup-test.jl index 9ffa1f51dde6..97e232b1c18c 100644 --- a/experimental/LieAlgebras/test/WeylGroup-test.jl +++ b/experimental/LieAlgebras/test/WeylGroup-test.jl @@ -188,7 +188,7 @@ include( @test word(s[1] * s[2] * s[1]) == UInt8[1, 2, 1] @test word(s[3] * s[2] * s[3]) == UInt8[2, 3, 2] - # test general multiplication behaviour + # test general multiplication behavior W = weyl_group(:B, 4) @test W(b4_w0) == W(b4_w0; normalize=false) diff --git a/experimental/OrthogonalDiscriminants/gap/fix.g b/experimental/OrthogonalDiscriminants/gap/fix.g index 1173f4469f70..1c2d6cde3afe 100644 --- a/experimental/OrthogonalDiscriminants/gap/fix.g +++ b/experimental/OrthogonalDiscriminants/gap/fix.g @@ -8,7 +8,7 @@ ############################################################################### ## -## Improve the behaviour of 'Indicator' in characteristic 2. +## Improve the behavior of 'Indicator' in characteristic 2. ## InstallMethod( IndicatorOp, "for a Brauer character table and = 2", diff --git a/experimental/OrthogonalDiscriminants/src/utils.jl b/experimental/OrthogonalDiscriminants/src/utils.jl index ea34ef6ac92a..396016bdde4f 100644 --- a/experimental/OrthogonalDiscriminants/src/utils.jl +++ b/experimental/OrthogonalDiscriminants/src/utils.jl @@ -402,7 +402,7 @@ function show_OD_info(tbl::Oscar.GAPGroupCharacterTable, io::IO = stdout) :separators_col => 0:(length(result[1])-1), ) - labelled_matrix_formatted(ioc, permutedims(reduce(hcat, result))) + labeled_matrix_formatted(ioc, permutedims(reduce(hcat, result))) println(io, "") end diff --git a/experimental/Schemes/CoherentSheaves.jl b/experimental/Schemes/CoherentSheaves.jl index 715fcb4b19fb..a2d8fbd12041 100644 --- a/experimental/Schemes/CoherentSheaves.jl +++ b/experimental/Schemes/CoherentSheaves.jl @@ -223,7 +223,7 @@ identifications given by the gluings in the `default_covering`. ### Lookup and production pattern for sheaves of modules # # When asked to produce a module on an open affine U, the functions - # below lead to the following behaviour. + # below lead to the following behavior. # # U₁ an `affine_chart` of `X` # _________/|\______________ (`patches` of `default_covering(X)`) diff --git a/experimental/Schemes/elliptic_surface.jl b/experimental/Schemes/elliptic_surface.jl index a4aa8147302e..c3a39cebb8ed 100644 --- a/experimental/Schemes/elliptic_surface.jl +++ b/experimental/Schemes/elliptic_surface.jl @@ -1704,7 +1704,7 @@ function _elliptic_parameter_conversion(X::EllipticSurface, u::VarietyFunctionFi eqn1 = numerator(f_trans) # According to # A. Kumar: "Elliptic Fibrations on a generic Jacobian Kummer surface" - # p. 45, l. 1 we expect the following cancellation to be possible: + # p. 45, l. 1 we expect the following cancelation to be possible: divisor_num = evaluate(numerator(x0), x2) divisor_den = evaluate(denominator(x0), x2) divisor = divisor_den * y2 - divisor_num @@ -1733,7 +1733,7 @@ function _elliptic_parameter_conversion(X::EllipticSurface, u::VarietyFunctionFi eqn1 = numerator(f_trans) # According to # A. Kumar: "Elliptic Fibrations on a generic Jacobian Kummer surface" - # p. 45, l. 15 we expect the following cancellation to be possible: + # p. 45, l. 15 we expect the following cancelation to be possible: success, eqn1 = divides(eqn1, y2) @assert success "equation did not come out in the anticipated form" return eqn1, phi diff --git a/src/AlgebraicGeometry/Schemes/AffineSchemes/Morphisms/Methods.jl b/src/AlgebraicGeometry/Schemes/AffineSchemes/Morphisms/Methods.jl index d2e952bfb1ee..6112f141be06 100644 --- a/src/AlgebraicGeometry/Schemes/AffineSchemes/Morphisms/Methods.jl +++ b/src/AlgebraicGeometry/Schemes/AffineSchemes/Morphisms/Methods.jl @@ -1,5 +1,5 @@ ########################################################### -# (1) The fibre product of two morphisms of affine schemes +# (1) The fiber product of two morphisms of affine schemes ########################################################### @doc raw""" diff --git a/src/AlgebraicGeometry/Schemes/AffineSchemes/Objects/Attributes.jl b/src/AlgebraicGeometry/Schemes/AffineSchemes/Objects/Attributes.jl index 4e777ca50dcb..79b2f1e928d6 100644 --- a/src/AlgebraicGeometry/Schemes/AffineSchemes/Objects/Attributes.jl +++ b/src/AlgebraicGeometry/Schemes/AffineSchemes/Objects/Attributes.jl @@ -828,7 +828,7 @@ If `X = Spec(R)` and `R` is... - a localized polynomial ring `R[U⁻¹]`, then this returns the zero ideal in that ring; - a quotient of a localized polynomial ring `(R[U⁻¹])/J`, then this returns the ideal `J` in the ring `R[U⁻¹]`. -This behaviour is streamlined with the return values of `modulus` on the algebraic side. +This behavior is streamlined with the return values of `modulus` on the algebraic side. If you are looking for an ideal `I` in the polynomial `ambient_ring` of `X` defining the closure of `X` in its `ambient_space`, use for instance `saturated_ideal(defining_ideal(X))`. ```jldoctest diff --git a/src/Groups/GAPGroups.jl b/src/Groups/GAPGroups.jl index f0c6ab20a73f..f6f442c7a799 100644 --- a/src/Groups/GAPGroups.jl +++ b/src/Groups/GAPGroups.jl @@ -1480,7 +1480,7 @@ false is_quasisimple(G::GAPGroup) Return whether `G` is a quasisimple group, -i.e., `G` is perfect such that the factor group modulo its centre is +i.e., `G` is perfect such that the factor group modulo its center is a non-abelian simple group. # Examples diff --git a/src/Groups/MatrixDisplay.jl b/src/Groups/MatrixDisplay.jl index 56f8d046c47f..ca96f3e69263 100644 --- a/src/Groups/MatrixDisplay.jl +++ b/src/Groups/MatrixDisplay.jl @@ -1,6 +1,6 @@ ############################################################################# ## -## Provide functionality for displaying labelled matrices, +## Provide functionality for displaying labeled matrices, ## that is, two-dimensional arrays of strings ## together with row labels, columns labels, header, and footer ## @@ -59,7 +59,7 @@ end """ - labelled_matrix_formatted(io::IO, mat::Matrix{String}) + labeled_matrix_formatted(io::IO, mat::Matrix{String}) Write a formatted version of `mat` to `io`. The following attributes of `io` are supported. @@ -108,11 +108,11 @@ The following attributes of `io` are supported. (enter `0` for a line in front of the first column), - `:portions_row`: - array of numbers of rows after which a new labelled table shall be started; + array of numbers of rows after which a new labeled table shall be started; the default is to have just one portion. - `:portions_col`: - array of numbers of column after which a new labelled table shall be started; + array of numbers of column after which a new labeled table shall be started; the default is to have just one portion in the `:TeX` case, and to create portions according to the screen width otherwise, @@ -131,7 +131,7 @@ julia> mat julia> io = IOBuffer(); # simply using `stdout` does not work in doctests julia> ioc = IOContext(io, - :header => ["", "a labelled matrix", ""], + :header => ["", "a labeled matrix", ""], :labels_row => [string(i) for i in 1:m], :labels_col => [string(j) for j in 1:n], :separators_row => [0], @@ -140,12 +140,12 @@ julia> ioc = IOContext(io, ); julia> Oscar.with_unicode() do - labelled_matrix_formatted(ioc, mat) + labeled_matrix_formatted(ioc, mat) end; julia> print(String(take!(io))) -a labelled matrix +a labeled matrix │ 1 2 3 4 ─┼─────────────────────────── @@ -165,7 +165,7 @@ julia> ioc = IOContext(io, ); julia> Oscar.with_unicode() do - labelled_matrix_formatted(ioc, mat) + labeled_matrix_formatted(ioc, mat) end; julia> print(String(take!(io))) @@ -189,7 +189,7 @@ julia> print(String(take!(io))) ``` """ -function labelled_matrix_formatted(io::IO, mat::Matrix{String}) +function labeled_matrix_formatted(io::IO, mat::Matrix{String}) TeX = get(io, :TeX, false) if Oscar.is_unicode_allowed() diff --git a/src/Groups/group_characters.jl b/src/Groups/group_characters.jl index 4d9530f965ac..aa84b833ee1d 100644 --- a/src/Groups/group_characters.jl +++ b/src/Groups/group_characters.jl @@ -942,7 +942,7 @@ function Base.show(io::IO, ::MIME"text/plain", tbl::GAPGroupCharacterTable) ) # print the table - labelled_matrix_formatted(ioc, mat) + labeled_matrix_formatted(ioc, mat) end diff --git a/src/InvariantTheory/primary_invariants.jl b/src/InvariantTheory/primary_invariants.jl index e769cbcbcb9c..bac9a6cb186f 100644 --- a/src/InvariantTheory/primary_invariants.jl +++ b/src/InvariantTheory/primary_invariants.jl @@ -258,11 +258,11 @@ An a priori known number $k \geq 1$ with $d_1\cdots d_n \geq k \cdot |G|$, where $G$ is the underlying group, can be specified by `degree_bound = k`. The default value is `degree_bound = 1`. In some situations, the runtime of the algorithm might be improved by assigning -a positive integer to `ensure_minimality`. This leads to an early cancellation of +a positive integer to `ensure_minimality`. This leads to an early cancelation of loops in the algorithm and the described minimality of the degrees is not guaranteed anymore. A smaller (positive) value of `ensure_minimality` corresponds -to an earlier cancellation. However, the default value `ensure_minimality = 0` -corresponds to no cancellation. +to an earlier cancelation. However, the default value `ensure_minimality = 0` +corresponds to no cancelation. # Examples ```jldoctest diff --git a/src/Rings/AbelianClosure.jl b/src/Rings/AbelianClosure.jl index c75b28e03c6b..c940c7a9aa3e 100644 --- a/src/Rings/AbelianClosure.jl +++ b/src/Rings/AbelianClosure.jl @@ -5,7 +5,7 @@ ############################################################################### # This is an implementation of Q^ab, the abelian closure of the rationals, -# which is modelled as the union of cyclotomic fields. +# which is modeled as the union of cyclotomic fields. # # We make Q^ab a singleton, similar to ZZ and QQ. Thus there will ever be only # one copy of Q^ab. In particular the elements do not have a parent stored. diff --git a/src/Rings/AlgClosureFp.jl b/src/Rings/AlgClosureFp.jl index afe60be3d290..38bf0aaaeeeb 100644 --- a/src/Rings/AlgClosureFp.jl +++ b/src/Rings/AlgClosureFp.jl @@ -5,7 +5,7 @@ ############################################################################### # This is an implementation of the algebraic closure of finite fields, -# which is modelled as the union of finite fields. +# which is modeled as the union of finite fields. module AlgClosureFp diff --git a/src/Rings/PBWAlgebraQuo.jl b/src/Rings/PBWAlgebraQuo.jl index 285f21c317e7..60dcdf9288e6 100644 --- a/src/Rings/PBWAlgebraQuo.jl +++ b/src/Rings/PBWAlgebraQuo.jl @@ -13,7 +13,7 @@ export PBWAlgQuo, PBWAlgQuoElem # achieve this a "new" pointer to the Singular ring is needed; # this pointer is a new data field (sring) in PBQAlgQuo. # -# To preserve the original behaviour the new field "sdata" in PBWAlgQuo +# To preserve the original behavior the new field "sdata" in PBWAlgQuo # is set to the same value as the field "sdata" in PBWAlg (unless # created by constructor for exterior_algebra. # diff --git a/src/Rings/hilbert.jl b/src/Rings/hilbert.jl index 53fd0fe3b173..2831438e020e 100644 --- a/src/Rings/hilbert.jl +++ b/src/Rings/hilbert.jl @@ -311,7 +311,7 @@ end ################################################################### # This function is also private/local to this file. -# Think of a graph where each vertex is labelled by an indeterminate. +# Think of a graph where each vertex is labeled by an indeterminate. # Each PP in the list L is interpreted as saying that all indeterminates # involved in that PP are "connected". The task is to find (minimal) # connected components of the entire graph. diff --git a/src/Rings/mpolyquo-localizations.jl b/src/Rings/mpolyquo-localizations.jl index bae23f57a234..d1073be4fde8 100644 --- a/src/Rings/mpolyquo-localizations.jl +++ b/src/Rings/mpolyquo-localizations.jl @@ -800,7 +800,7 @@ end ### Why are the `//`-methods not implemented? # Since a quotient ring Q = R/I of a polynomial ring R is not necessarily # factorial, it is difficult to decide, whether or not a and b have a -# common factor g that can be cancelled so that b'= b/g ∈ Q belongs +# common factor g that can be canceled so that b'= b/g ∈ Q belongs # to the multiplicative set. Moreover, this would be the case if any # lift of b' belonged to S + I where S ⊂ R is the original multiplicative # set. Such containment can not easily be checked based only on the diff --git a/src/TropicalGeometry/curve.jl b/src/TropicalGeometry/curve.jl index 521e84d67016..aa850c79989c 100644 --- a/src/TropicalGeometry/curve.jl +++ b/src/TropicalGeometry/curve.jl @@ -218,7 +218,7 @@ end # @doc raw""" # chip_firing_move(dtc::DivisorOnTropicalCurve, position::Int) -# Given a divisor `dtc` and vertex labelled `position`, compute the linearly equivalent divisor obtained by a chip firing move from the given vertex `position`. +# Given a divisor `dtc` and vertex labeled `position`, compute the linearly equivalent divisor obtained by a chip firing move from the given vertex `position`. # # Examples # ```jldoctest @@ -285,7 +285,7 @@ end # @doc raw""" # v_reduced(dtc::DivisorOnTropicalCurve, vertex::Int) -# Given a divisor `dtc` and vertex labelled `vertex`, compute the unique divisor reduced with repspect to `vertex` +# Given a divisor `dtc` and vertex labeled `vertex`, compute the unique divisor reduced with repspect to `vertex` # as defined in [BN07](@cite). # The divisor `dtc` must have positive coefficients apart from `vertex`. diff --git a/src/deprecations.jl b/src/deprecations.jl index eaaee4742b52..260154d3585b 100644 --- a/src/deprecations.jl +++ b/src/deprecations.jl @@ -91,3 +91,5 @@ end @deprecate subgroup_reps(G::T) where T <: Union{GAPGroup, FinGenAbGroup} map(representative, subgroup_classes(G)) @deprecate conjugacy_classes_maximal_subgroups(G::T) where T <: Union{GAPGroup, FinGenAbGroup} maximal_subgroup_classes(G) @deprecate conjugacy_classes_subgroups(G::T) where T <: Union{GAPGroup, FinGenAbGroup} subgroup_classes(G) + +@deprecate labelled_matrix_formatted labeled_matrix_formatted diff --git a/src/exports.jl b/src/exports.jl index df002cd2f7f0..f9ebe608bd4d 100644 --- a/src/exports.jl +++ b/src/exports.jl @@ -904,7 +904,7 @@ export known_class_fusions export koszul_complex export koszul_homology export koszul_matrix -export labelled_matrix_formatted +export labeled_matrix_formatted export lattice_points export lattice_volume export leading_coefficient diff --git a/test/AlgebraicGeometry/Schemes/AffineSchemes.jl b/test/AlgebraicGeometry/Schemes/AffineSchemes.jl index 2e778c6d91e6..a4e6f9165c63 100644 --- a/test/AlgebraicGeometry/Schemes/AffineSchemes.jl +++ b/test/AlgebraicGeometry/Schemes/AffineSchemes.jl @@ -288,7 +288,7 @@ end (a, b, c) = base_change(pr, inc_U) @test compose(a, inc_U) == compose(b, c) - # Behaviour for special types + # Behavior for special types U = PrincipalOpenSubset(IA2, y) UU, f = base_change(pr, U) @test UU isa PrincipalOpenSubset diff --git a/test/Groups/MatrixDisplay.jl b/test/Groups/MatrixDisplay.jl index ef2c318108d4..62ed81767f5e 100644 --- a/test/Groups/MatrixDisplay.jl +++ b/test/Groups/MatrixDisplay.jl @@ -3,11 +3,11 @@ using Documenter # # This module only exists to "host" a doctest used by the test suite. # -module AuxDocTest_labelled_matrix_formatted +module AuxDocTest_labeled_matrix_formatted @doc raw""" create the test matrix -```jldoctest labelled_matrix_formatted.test +```jldoctest labeled_matrix_formatted.test julia> using Oscar julia> m = 2; n = 2; mat = Array{String}(undef, m, n); @@ -19,16 +19,16 @@ text format no labels -```jldoctest labelled_matrix_formatted.test -julia> labelled_matrix_formatted(IOContext(stdout), mat) +```jldoctest labeled_matrix_formatted.test +julia> labeled_matrix_formatted(IOContext(stdout), mat) 1/1 1/2 2/1 2/2 ``` with header -```jldoctest labelled_matrix_formatted.test -julia> labelled_matrix_formatted(IOContext(stdout, +```jldoctest labeled_matrix_formatted.test +julia> labeled_matrix_formatted(IOContext(stdout, :header => ["header", ""]), mat) header @@ -38,8 +38,8 @@ header with footer -```jldoctest labelled_matrix_formatted.test -julia> labelled_matrix_formatted(IOContext(stdout, +```jldoctest labeled_matrix_formatted.test +julia> labeled_matrix_formatted(IOContext(stdout, :footer => ["footer"]), mat) 1/1 1/2 2/1 2/2 @@ -48,8 +48,8 @@ footer with row labels as vector -```jldoctest labelled_matrix_formatted.test -julia> labelled_matrix_formatted(IOContext(stdout, +```jldoctest labeled_matrix_formatted.test +julia> labeled_matrix_formatted(IOContext(stdout, :labels_row => [string(i)*":" for i in 1:m]), mat) 1: 1/1 1/2 2: 2/1 2/2 @@ -57,8 +57,8 @@ julia> labelled_matrix_formatted(IOContext(stdout, with row labels as matrix -```jldoctest labelled_matrix_formatted.test -julia> labelled_matrix_formatted(IOContext(stdout, +```jldoctest labeled_matrix_formatted.test +julia> labeled_matrix_formatted(IOContext(stdout, :labels_row => reshape([string(i)*":" for i in 1:m], m, 1)), mat) 1: 1/1 1/2 2: 2/1 2/2 @@ -66,8 +66,8 @@ julia> labelled_matrix_formatted(IOContext(stdout, with too wide row labels -```jldoctest labelled_matrix_formatted.test -julia> labelled_matrix_formatted(IOContext(stdout, +```jldoctest labeled_matrix_formatted.test +julia> labeled_matrix_formatted(IOContext(stdout, :labels_row => reshape(["_"^30*string(i)*":" for i in 1:m], m, 1), :displaysize => (52, 30)), mat) (row label part is too wide for the screen) @@ -75,8 +75,8 @@ julia> labelled_matrix_formatted(IOContext(stdout, with column labels as vector -```jldoctest labelled_matrix_formatted.test -julia> labelled_matrix_formatted(IOContext(stdout, +```jldoctest labeled_matrix_formatted.test +julia> labeled_matrix_formatted(IOContext(stdout, :labels_col => [string(j) for j in 1:n]), mat) 1 2 1/1 1/2 @@ -85,8 +85,8 @@ julia> labelled_matrix_formatted(IOContext(stdout, with column labels as matrix -```jldoctest labelled_matrix_formatted.test -julia> labelled_matrix_formatted(IOContext(stdout, +```jldoctest labeled_matrix_formatted.test +julia> labeled_matrix_formatted(IOContext(stdout, :labels_col => reshape([string(j) for j in 1:n], 1, n)), mat) 1 2 1/1 1/2 @@ -95,8 +95,8 @@ julia> labelled_matrix_formatted(IOContext(stdout, with row and column labels -```jldoctest labelled_matrix_formatted.test -julia> labelled_matrix_formatted(IOContext(stdout, +```jldoctest labeled_matrix_formatted.test +julia> labeled_matrix_formatted(IOContext(stdout, :labels_row => [string(i)*":" for i in 1:m], :labels_col => [string(j) for j in 1:n]), mat) 1 2 @@ -106,8 +106,8 @@ julia> labelled_matrix_formatted(IOContext(stdout, with row and column labels and corner as vector -```jldoctest labelled_matrix_formatted.test -julia> labelled_matrix_formatted(IOContext(stdout, +```jldoctest labeled_matrix_formatted.test +julia> labeled_matrix_formatted(IOContext(stdout, :labels_row => [string(i)*":" for i in 1:m], :labels_col => [string(j) for j in 1:n], :corner => ["(i,j)"]), mat) @@ -118,8 +118,8 @@ julia> labelled_matrix_formatted(IOContext(stdout, with row and column labels and corner as matrix -```jldoctest labelled_matrix_formatted.test -julia> labelled_matrix_formatted(IOContext(stdout, +```jldoctest labeled_matrix_formatted.test +julia> labeled_matrix_formatted(IOContext(stdout, :labels_row => [string(i)*":" for i in 1:m], :labels_col => [string(j) for j in 1:n], :corner => reshape(["(i,j)"], 1, 1)), mat) @@ -130,8 +130,8 @@ julia> labelled_matrix_formatted(IOContext(stdout, with a too wide column -```jldoctest labelled_matrix_formatted.test -julia> labelled_matrix_formatted(IOContext(stdout, +```jldoctest labeled_matrix_formatted.test +julia> labeled_matrix_formatted(IOContext(stdout, :labels_row => [string(i)*":" for i in 1:m], :labels_col => ["_"^30*string(j) for j in 1:n], :corner => reshape(["(i,j)"], 1, 1), @@ -147,9 +147,9 @@ julia> labelled_matrix_formatted(IOContext(stdout, with row separators but without column labels -```jldoctest labelled_matrix_formatted.test +```jldoctest labeled_matrix_formatted.test julia> Oscar.with_unicode() do - labelled_matrix_formatted(IOContext(stdout, + labeled_matrix_formatted(IOContext(stdout, :separators_row => [0, 1, 2]), mat) end ─────── @@ -157,7 +157,7 @@ julia> Oscar.with_unicode() do ─────── 2/1 2/2 ─────── -julia> labelled_matrix_formatted(IOContext(stdout, +julia> labeled_matrix_formatted(IOContext(stdout, :separators_row => [0, 1, 2]), mat) ------- 1/1 1/2 @@ -168,9 +168,9 @@ julia> labelled_matrix_formatted(IOContext(stdout, with row separators and column labels -```jldoctest labelled_matrix_formatted.test +```jldoctest labeled_matrix_formatted.test julia> Oscar.with_unicode() do - labelled_matrix_formatted(IOContext(stdout, + labeled_matrix_formatted(IOContext(stdout, :labels_col => [string(j) for j in 1:n], :separators_row => [0,1,2]), mat) end @@ -180,7 +180,7 @@ julia> Oscar.with_unicode() do ─────── 2/1 2/2 ─────── -julia> labelled_matrix_formatted(IOContext(stdout, +julia> labeled_matrix_formatted(IOContext(stdout, :labels_col => [string(j) for j in 1:n], :separators_row => [0,1,2]), mat) 1 2 @@ -193,14 +193,14 @@ julia> labelled_matrix_formatted(IOContext(stdout, with column separators but without row labels -```jldoctest labelled_matrix_formatted.test +```jldoctest labeled_matrix_formatted.test julia> Oscar.with_unicode() do - labelled_matrix_formatted(IOContext(stdout, + labeled_matrix_formatted(IOContext(stdout, :separators_col => [0, 1, 2]), mat) end │1/1│1/2│ │2/1│2/2│ -julia> labelled_matrix_formatted(IOContext(stdout, +julia> labeled_matrix_formatted(IOContext(stdout, :separators_col => [0, 1, 2]), mat) |1/1|1/2| |2/1|2/2| @@ -208,15 +208,15 @@ julia> labelled_matrix_formatted(IOContext(stdout, with column separators and row labels -```jldoctest labelled_matrix_formatted.test +```jldoctest labeled_matrix_formatted.test julia> Oscar.with_unicode() do - labelled_matrix_formatted(IOContext(stdout, + labeled_matrix_formatted(IOContext(stdout, :labels_row => [string(i)*":" for i in 1:m], :separators_col => [0, 1, 2]), mat) end 1:│1/1│1/2│ 2:│2/1│2/2│ -julia> labelled_matrix_formatted(IOContext(stdout, +julia> labeled_matrix_formatted(IOContext(stdout, :labels_row => [string(i)*":" for i in 1:m], :separators_col => [0, 1, 2]), mat) 1:|1/1|1/2| @@ -225,9 +225,9 @@ julia> labelled_matrix_formatted(IOContext(stdout, with row and column labels and separators -```jldoctest labelled_matrix_formatted.test +```jldoctest labeled_matrix_formatted.test julia> Oscar.with_unicode() do - labelled_matrix_formatted(IOContext(stdout, + labeled_matrix_formatted(IOContext(stdout, :labels_row => [string(i)*":" for i in 1:m], :labels_col => [string(j) for j in 1:n], :separators_row => [0, 1, 2], @@ -239,7 +239,7 @@ julia> Oscar.with_unicode() do ──┼───┼───┼ 2:│2/1│2/2│ ──┼───┼───┼ -julia> labelled_matrix_formatted(IOContext(stdout, +julia> labeled_matrix_formatted(IOContext(stdout, :labels_row => [string(i)*":" for i in 1:m], :labels_col => [string(j) for j in 1:n], :separators_row => [0, 1, 2], @@ -254,9 +254,9 @@ julia> labelled_matrix_formatted(IOContext(stdout, with row and column portions -```jldoctest labelled_matrix_formatted.test +```jldoctest labeled_matrix_formatted.test julia> Oscar.with_unicode() do - labelled_matrix_formatted(IOContext(stdout, + labeled_matrix_formatted(IOContext(stdout, :labels_row => [string(i)*":" for i in 1:m], :labels_col => [string(j) for j in 1:n], :separators_row => [0], @@ -279,7 +279,7 @@ julia> Oscar.with_unicode() do │ 2 ──┼─── 2:│2/2 -julia> labelled_matrix_formatted(IOContext(stdout, +julia> labeled_matrix_formatted(IOContext(stdout, :labels_row => [string(i)*":" for i in 1:m], :labels_col => [string(j) for j in 1:n], :separators_row => [0], @@ -305,7 +305,7 @@ julia> labelled_matrix_formatted(IOContext(stdout, LaTeX format -```jldoctest labelled_matrix_formatted.test +```jldoctest labeled_matrix_formatted.test julia> m = 2; n = 2; mat = Array{String}(undef, m, n); julia> for i in 1:m for j in 1:n mat[i,j] = string(i)*"/"*string(j); end; end; @@ -313,8 +313,8 @@ julia> for i in 1:m for j in 1:n mat[i,j] = string(i)*"/"*string(j); end; end; no labels -```jldoctest labelled_matrix_formatted.test -julia> labelled_matrix_formatted(IOContext(stdout, :TeX => true), mat) +```jldoctest labeled_matrix_formatted.test +julia> labeled_matrix_formatted(IOContext(stdout, :TeX => true), mat) $\begin{array}{rr} 1/1 & 1/2 \\ 2/1 & 2/2 \\ @@ -324,8 +324,8 @@ $ with header -```jldoctest labelled_matrix_formatted.test -julia> labelled_matrix_formatted(IOContext(stdout, :TeX => true, +```jldoctest labeled_matrix_formatted.test +julia> labeled_matrix_formatted(IOContext(stdout, :TeX => true, :header => ["header", ""]), mat) header @@ -338,8 +338,8 @@ $ with footer -```jldoctest labelled_matrix_formatted.test -julia> labelled_matrix_formatted(IOContext(stdout, :TeX => true, +```jldoctest labeled_matrix_formatted.test +julia> labeled_matrix_formatted(IOContext(stdout, :TeX => true, :footer => ["footer"]), mat) $\begin{array}{rr} 1/1 & 1/2 \\ @@ -354,8 +354,8 @@ $ with row labels as vector -```jldoctest labelled_matrix_formatted.test -julia> labelled_matrix_formatted(IOContext(stdout, :TeX => true, +```jldoctest labeled_matrix_formatted.test +julia> labeled_matrix_formatted(IOContext(stdout, :TeX => true, :labels_row => [string(i)*":" for i in 1:m]), mat) $\begin{array}{rrr} 1: & 1/1 & 1/2 \\ @@ -366,8 +366,8 @@ $ with row labels as matrix -```jldoctest labelled_matrix_formatted.test -julia> labelled_matrix_formatted(IOContext(stdout, :TeX => true, +```jldoctest labeled_matrix_formatted.test +julia> labeled_matrix_formatted(IOContext(stdout, :TeX => true, :labels_row => reshape([string(i)*":" for i in 1:m], m, 1)), mat) $\begin{array}{rrr} 1: & 1/1 & 1/2 \\ @@ -378,8 +378,8 @@ $ with column labels as vector -```jldoctest labelled_matrix_formatted.test -julia> labelled_matrix_formatted(IOContext(stdout, :TeX => true, +```jldoctest labeled_matrix_formatted.test +julia> labeled_matrix_formatted(IOContext(stdout, :TeX => true, :labels_col => [string(j) for j in 1:n]), mat) $\begin{array}{rr} 1 & 2 \\ @@ -391,8 +391,8 @@ $ with column labels as matrix -```jldoctest labelled_matrix_formatted.test -julia> labelled_matrix_formatted(IOContext(stdout, :TeX => true, +```jldoctest labeled_matrix_formatted.test +julia> labeled_matrix_formatted(IOContext(stdout, :TeX => true, :labels_col => reshape([string(j) for j in 1:n], 1, n)), mat) $\begin{array}{rr} 1 & 2 \\ @@ -404,8 +404,8 @@ $ with row and column labels -```jldoctest labelled_matrix_formatted.test -julia> labelled_matrix_formatted(IOContext(stdout, :TeX => true, +```jldoctest labeled_matrix_formatted.test +julia> labeled_matrix_formatted(IOContext(stdout, :TeX => true, :labels_row => [string(i)*":" for i in 1:m], :labels_col => [string(j) for j in 1:n]), mat) $\begin{array}{rrr} @@ -418,8 +418,8 @@ $ with row separators but without column labels -```jldoctest labelled_matrix_formatted.test -julia> labelled_matrix_formatted(IOContext(stdout, :TeX => true, +```jldoctest labeled_matrix_formatted.test +julia> labeled_matrix_formatted(IOContext(stdout, :TeX => true, :separators_row => [0, 1, 2]), mat) $\begin{array}{rr} \hline @@ -433,8 +433,8 @@ $ with row separators and column labels -```jldoctest labelled_matrix_formatted.test -julia> labelled_matrix_formatted(IOContext(stdout, :TeX => true, +```jldoctest labeled_matrix_formatted.test +julia> labeled_matrix_formatted(IOContext(stdout, :TeX => true, :labels_col => [string(j) for j in 1:n], :separators_row => [0,1,2]), mat) $\begin{array}{rr} @@ -450,8 +450,8 @@ $ with column separators but without row labels -```jldoctest labelled_matrix_formatted.test -julia> labelled_matrix_formatted(IOContext(stdout, :TeX => true, +```jldoctest labeled_matrix_formatted.test +julia> labeled_matrix_formatted(IOContext(stdout, :TeX => true, :separators_col => [0, 1, 2]), mat) $\begin{array}{|r|r|} 1/1 & 1/2 \\ @@ -462,8 +462,8 @@ $ with column separators and row labels -```jldoctest labelled_matrix_formatted.test -julia> labelled_matrix_formatted(IOContext(stdout, :TeX => true, +```jldoctest labeled_matrix_formatted.test +julia> labeled_matrix_formatted(IOContext(stdout, :TeX => true, :labels_row => [string(i)*":" for i in 1:m], :separators_col => [0, 1, 2]), mat) $\begin{array}{r|r|r|} @@ -475,8 +475,8 @@ $ with row and column labels and separators -```jldoctest labelled_matrix_formatted.test -julia> labelled_matrix_formatted(IOContext(stdout, :TeX => true, +```jldoctest labeled_matrix_formatted.test +julia> labeled_matrix_formatted(IOContext(stdout, :TeX => true, :labels_row => [string(i)*":" for i in 1:m], :labels_col => [string(j) for j in 1:n], :separators_row => [0, 1, 2], @@ -494,8 +494,8 @@ $ with row and column portions -```jldoctest labelled_matrix_formatted.test -julia> labelled_matrix_formatted(IOContext(stdout, :TeX => true, +```jldoctest labeled_matrix_formatted.test +julia> labeled_matrix_formatted(IOContext(stdout, :TeX => true, :labels_row => [string(i) for i in 1:m], :labels_col => [string(j) for j in 1:n], :separators_row => [0], @@ -535,7 +535,7 @@ end @testset "show and print formatted matrices" begin # temporarily disable GC logging to avoid glitches in the doctests VERSION >= v"1.8.0" && GC.enable_logging(false) - doctest(nothing, [AuxDocTest_labelled_matrix_formatted]) - #doctest(nothing, [AuxDocTest_labelled_matrix_formatted]; fix=true) + doctest(nothing, [AuxDocTest_labeled_matrix_formatted]) + #doctest(nothing, [AuxDocTest_labeled_matrix_formatted]; fix=true) VERSION >= v"1.8.0" && GC.enable_logging(true) end From 8dc43117428c80f3c1280ae207fb71a5b3ff81fa Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Lars=20G=C3=B6ttgens?= Date: Fri, 23 Feb 2024 12:02:06 +0100 Subject: [PATCH 29/29] Adapt interface for orthogonal and symplectic Lie algebras (#3391) * Small docs improvements * Adapt so interface * Add sp Lie algebra * Adapt to `vec` renaming * Don't assume anything about the kernel structure * Apply suggestions from code review Co-authored-by: Max Horn --------- Co-authored-by: Max Horn (cherry picked from commit db3dc1f663f5e90f1daf704e78ee9bfe78d30bea) --- .../LieAlgebras/docs/src/lie_algebras.md | 3 +- experimental/LieAlgebras/src/LieAlgebras.jl | 3 + .../LieAlgebras/src/LinearLieAlgebra.jl | 190 ++++++++++++++++-- .../LieAlgebras/test/LieAlgebraModule-test.jl | 8 +- .../LieAlgebras/test/LinearLieAlgebra-test.jl | 114 ++++++++++- .../LieAlgebras/test/iso_oscar_gap-test.jl | 1 + 6 files changed, 292 insertions(+), 27 deletions(-) diff --git a/experimental/LieAlgebras/docs/src/lie_algebras.md b/experimental/LieAlgebras/docs/src/lie_algebras.md index a40cda0b2a94..817ca4e30fde 100644 --- a/experimental/LieAlgebras/docs/src/lie_algebras.md +++ b/experimental/LieAlgebras/docs/src/lie_algebras.md @@ -87,7 +87,8 @@ lie_algebra abelian_lie_algebra(R::Field, n::Int) general_linear_lie_algebra(R::Field, n::Int) special_linear_lie_algebra(R::Field, n::Int) -special_orthogonal_lie_algebra(R::Field, n::Int) +special_orthogonal_lie_algebra +symplectic_lie_algebra ``` ## Relation to GAP Lie algebras diff --git a/experimental/LieAlgebras/src/LieAlgebras.jl b/experimental/LieAlgebras/src/LieAlgebras.jl index cd183c16fbc8..681994ac7709 100644 --- a/experimental/LieAlgebras/src/LieAlgebras.jl +++ b/experimental/LieAlgebras/src/LieAlgebras.jl @@ -18,6 +18,7 @@ import ..Oscar: _is_exterior_power, _is_tensor_product, _iso_oscar_gap, + _vec, action, basis_matrix, basis, @@ -181,6 +182,7 @@ export special_linear_lie_algebra export special_orthogonal_lie_algebra export standard_module export symmetric_power +export symplectic_lie_algebra export tensor_power export tensor_product_decomposition export trivial_module @@ -300,6 +302,7 @@ export special_linear_lie_algebra export special_orthogonal_lie_algebra export standard_module export symmetric_power +export symplectic_lie_algebra export tensor_power export tensor_product_decomposition export trivial_module diff --git a/experimental/LieAlgebras/src/LinearLieAlgebra.jl b/experimental/LieAlgebras/src/LinearLieAlgebra.jl index a05631973f01..9aeb2d7f54de 100644 --- a/experimental/LieAlgebras/src/LinearLieAlgebra.jl +++ b/experimental/LieAlgebras/src/LinearLieAlgebra.jl @@ -112,6 +112,8 @@ function _lie_algebra_type_to_string(type::Symbol, n::Int) return "Special linear Lie algebra of degree $n" elseif type == :special_orthogonal return "Special orthogonal Lie algebra of degree $n" + elseif type == :symplectic + return "Symplectic Lie algebra of degree $n" else return "Linear Lie algebra with $(n)x$(n) matrices" end @@ -191,7 +193,7 @@ end @doc raw""" lie_algebra(R::Field, n::Int, basis::Vector{<:MatElem{elem_type(R)}}, s::Vector{<:VarName}; cached::Bool) -> LinearLieAlgebra{elem_type(R)} -Construct the Lie algebra over the ring `R` with basis `basis` and basis element names +Construct the Lie algebra over the field `R` with basis `basis` and basis element names given by `s`. The basis elements must be square matrices of size `n`. We require `basis` to be linearly independent, and to contain the Lie bracket of any two basis elements in its span. @@ -225,7 +227,7 @@ end abelian_lie_algebra(::Type{LinearLieAlgebra}, R::Field, n::Int) -> LinearLieAlgebra{elem_type(R)} abelian_lie_algebra(::Type{AbstractLieAlgebra}, R::Field, n::Int) -> AbstractLieAlgebra{elem_type(R)} -Return the abelian Lie algebra of dimension `n` over the ring `R`. +Return the abelian Lie algebra of dimension `n` over the field `R`. The first argument can be optionally provided to specify the type of the returned Lie algebra. """ @@ -246,7 +248,8 @@ end @doc raw""" general_linear_lie_algebra(R::Field, n::Int) -> LinearLieAlgebra{elem_type(R)} -Return the general linear Lie algebra $\mathfrak{gl}_n(R)$. +Return the general linear Lie algebra $\mathfrak{gl}_n(R)$, +i.e., the Lie algebra of all $n \times n$ matrices over the field `R`. # Examples ```jldoctest @@ -281,7 +284,8 @@ end @doc raw""" special_linear_lie_algebra(R::Field, n::Int) -> LinearLieAlgebra{elem_type(R)} -Return the special linear Lie algebra $\mathfrak{sl}_n(R)$. +Return the special linear Lie algebra $\mathfrak{sl}_n(R)$, +i.e., the Lie algebra of all $n \times n$ matrices over the field `R` with trace zero. # Examples ```jldoctest @@ -317,37 +321,193 @@ function special_linear_lie_algebra(R::Field, n::Int) return L end +function _lie_algebra_basis_from_form(R::Field, n::Int, form::MatElem) + invform = inv(form) + eqs = zero_matrix(R, n^2, n^2) + for i in 1:n, j in 1:n + x = zero_matrix(R, n, n) + x[i, j] = 1 + eqs[(i-1) * n + j, :] = _vec(x + invform * transpose(x) * form) + end + ker = kernel(eqs) + rref!(ker) # we cannot assume anything about the kernel, but want to have a consistent output + dim = nrows(ker) + basis = [zero_matrix(R, n, n) for _ in 1:dim] + for i in 1:n + for k in 1:dim + basis[k][i, 1:n] = ker[k, (i-1) * n .+ (1:n)] + end + end + return basis +end + @doc raw""" special_orthogonal_lie_algebra(R::Field, n::Int) -> LinearLieAlgebra{elem_type(R)} + special_orthogonal_lie_algebra(R::Field, n::Int, gram::MatElem) -> LinearLieAlgebra{elem_type(R)} + special_orthogonal_lie_algebra(R::Field, n::Int, gram::Matrix) -> LinearLieAlgebra{elem_type(R)} Return the special orthogonal Lie algebra $\mathfrak{so}_n(R)$. +Given a non-degenerate symmetric bilinear form $f$ via its Gram matrix `gram`, +$\mathfrak{so}_n(R)$ is the Lie algebra of all $n \times n$ matrices $x$ over the field `R` +such that $f(xv, w) = -f(v, xw)$ for all $v, w \in R^n$. + +If `gram` is not provided, for $n = 2k$ the form defined by $\begin{matrix} 0 & I_k \\ -I_k & 0 \end{matrix}$ +is used, and for $n = 2k + 1$ the form defined by $\begin{matrix} 1 & 0 & 0 \\ 0 & 0 I_k \\ 0 & I_k & 0 \end{matrix}$. + # Examples ```jldoctest -julia> L = special_orthogonal_lie_algebra(QQ, 3) +julia> L1 = special_orthogonal_lie_algebra(QQ, 4) +Special orthogonal Lie algebra of degree 4 + of dimension 6 +over rational field + +julia> basis(L1) +6-element Vector{LinearLieAlgebraElem{QQFieldElem}}: + x_1 + x_2 + x_3 + x_4 + x_5 + x_6 + +julia> matrix_repr_basis(L1) +6-element Vector{QQMatrix}: + [1 0 0 0; 0 0 0 0; 0 0 -1 0; 0 0 0 0] + [0 1 0 0; 0 0 0 0; 0 0 0 0; 0 0 -1 0] + [0 0 0 1; 0 0 -1 0; 0 0 0 0; 0 0 0 0] + [0 0 0 0; 1 0 0 0; 0 0 0 -1; 0 0 0 0] + [0 0 0 0; 0 1 0 0; 0 0 0 0; 0 0 0 -1] + [0 0 0 0; 0 0 0 0; 0 1 0 0; -1 0 0 0] + +julia> L2 = special_orthogonal_lie_algebra(QQ, 3, identity_matrix(QQ, 3)) Special orthogonal Lie algebra of degree 3 of dimension 3 over rational field -julia> basis(L) +julia> basis(L2) 3-element Vector{LinearLieAlgebraElem{QQFieldElem}}: - x_1_2 - x_1_3 - x_2_3 + x_1 + x_2 + x_3 -julia> matrix_repr_basis(L) +julia> matrix_repr_basis(L2) 3-element Vector{QQMatrix}: [0 1 0; -1 0 0; 0 0 0] [0 0 1; 0 0 0; -1 0 0] [0 0 0; 0 0 1; 0 -1 0] ``` """ +special_orthogonal_lie_algebra + +function special_orthogonal_lie_algebra(R::Field, n::Int, gram::MatElem) + form = map_entries(R, gram) + @req size(form) == (n, n) "Invalid matrix dimensions" + @req is_symmetric(form) "Bilinear form must be symmetric" + @req is_invertible(form) "Bilinear form must be non-degenerate" + basis = _lie_algebra_basis_from_form(R, n, form) + dim = length(basis) + @assert characteristic(R) != 0 || dim == div(n^2 - n, 2) + s = ["x_$(i)" for i in 1:dim] + L = lie_algebra(R, n, basis, s; check=false) + set_attribute!(L, :type => :special_orthogonal, :form => form) + return L +end + +function special_orthogonal_lie_algebra(R::Field, n::Int, gram::Matrix) + return special_orthogonal_lie_algebra(R, n, matrix(R, gram)) +end + function special_orthogonal_lie_algebra(R::Field, n::Int) - basis = [ - (b = zero_matrix(R, n, n); b[i, j] = 1; b[j, i] = -1; b) for i in 1:n for j in (i + 1):n - ] - s = ["x_$(i)_$(j)" for i in 1:n for j in (i + 1):n] + if is_even(n) + k = div(n, 2) + form = zero_matrix(R, n, n) + form[1:k, k .+ (1:k)] = identity_matrix(R, k) + form[k .+ (1:k), 1:k] = identity_matrix(R, k) + else + k = div(n - 1, 2) + form = zero_matrix(R, n, n) + form[1, 1] = one(R) + form[1 .+ (1:k), 1 + k .+ (1:k)] = identity_matrix(R, k) + form[1 + k .+ (1:k), 1 .+ (1:k)] = identity_matrix(R, k) + end + return special_orthogonal_lie_algebra(R, n, form) +end + +@doc raw""" + symplectic_lie_algebra(R::Field, n::Int) -> LinearLieAlgebra{elem_type(R)} + symplectic_lie_algebra(R::Field, n::Int, gram::MatElem) -> LinearLieAlgebra{elem_type(R)} + symplectic_lie_algebra(R::Field, n::Int, gram::Matrix) -> LinearLieAlgebra{elem_type(R)} + +Return the symplectic Lie algebra $\mathfrak{sp}_n(R)$. + +Given a non-degenerate skew-symmetric bilinear form $f$ via its Gram matrix `gram`, +$\mathfrak{sp}_n(R)$ is the Lie algebra of all $n \times n$ matrices $x$ over the field `R` +such that $f(xv, w) = -f(v, xw)$ for all $v, w \in R^n$. + +If `gram` is not provided, for $n = 2k$ the form defined by $\begin{matrix} 0 & I_k \\ -I_k & 0 \end{matrix}$ +is used. +For odd $n$ there is no non-degenerate skew-symmetric bilinear form on $R^n$. + +# Examples +```jldoctest +julia> L = symplectic_lie_algebra(QQ, 4) +Symplectic Lie algebra of degree 4 + of dimension 10 +over rational field + +julia> basis(L) +10-element Vector{LinearLieAlgebraElem{QQFieldElem}}: + x_1 + x_2 + x_3 + x_4 + x_5 + x_6 + x_7 + x_8 + x_9 + x_10 + +julia> matrix_repr_basis(L) +10-element Vector{QQMatrix}: + [1 0 0 0; 0 0 0 0; 0 0 -1 0; 0 0 0 0] + [0 1 0 0; 0 0 0 0; 0 0 0 0; 0 0 -1 0] + [0 0 1 0; 0 0 0 0; 0 0 0 0; 0 0 0 0] + [0 0 0 1; 0 0 1 0; 0 0 0 0; 0 0 0 0] + [0 0 0 0; 1 0 0 0; 0 0 0 -1; 0 0 0 0] + [0 0 0 0; 0 1 0 0; 0 0 0 0; 0 0 0 -1] + [0 0 0 0; 0 0 0 1; 0 0 0 0; 0 0 0 0] + [0 0 0 0; 0 0 0 0; 1 0 0 0; 0 0 0 0] + [0 0 0 0; 0 0 0 0; 0 1 0 0; 1 0 0 0] + [0 0 0 0; 0 0 0 0; 0 0 0 0; 0 1 0 0] +``` +""" +symplectic_lie_algebra + +function symplectic_lie_algebra(R::Field, n::Int, gram::MatElem) + form = map_entries(R, gram) + @req size(form) == (n, n) "Invalid matrix dimensions" + @req is_skew_symmetric(form) "Bilinear form must be skew-symmetric" + @req is_even(n) && is_invertible(form) "Bilinear form must be non-degenerate" + basis = _lie_algebra_basis_from_form(R, n, form) + dim = length(basis) + @assert characteristic(R) != 0 || dim == div(n^2 + n, 2) + s = ["x_$(i)" for i in 1:dim] L = lie_algebra(R, n, basis, s; check=false) - set_attribute!(L, :type => :special_orthogonal) + set_attribute!(L, :type => :symplectic, :form => form) return L end + +function symplectic_lie_algebra(R::Field, n::Int, gram::Matrix) + return symplectic_lie_algebra(R, n, matrix(R, gram)) +end + +function symplectic_lie_algebra(R::Field, n::Int) + @req is_even(n) "Dimension must be even" + k = div(n, 2) + form = zero_matrix(R, n, n) + form[1:k, k .+ (1:k)] = identity_matrix(R, k) + form[k .+ (1:k), 1:k] = -identity_matrix(R, k) + return symplectic_lie_algebra(R, n, form) +end diff --git a/experimental/LieAlgebras/test/LieAlgebraModule-test.jl b/experimental/LieAlgebras/test/LieAlgebraModule-test.jl index 77701add151d..eb7d2798b2c3 100644 --- a/experimental/LieAlgebras/test/LieAlgebraModule-test.jl +++ b/experimental/LieAlgebras/test/LieAlgebraModule-test.jl @@ -69,8 +69,8 @@ lie_algebra_module_conformance_test(L, V) end - @testset "V of so_4(GF(2^3))" begin - L = special_orthogonal_lie_algebra(GF(2, 3), 4) + @testset "V of gl_4(GF(2^3))" begin + L = general_linear_lie_algebra(GF(2, 3), 4) V = standard_module(L) lie_algebra_module_conformance_test(L, V) end @@ -494,7 +494,7 @@ return struct_const_V end - L = special_orthogonal_lie_algebra(QQ, 3) + L = special_orthogonal_lie_algebra(QQ, 3, identity_matrix(QQ, 3)) struct_const_V = Matrix{Vector{Tuple{QQFieldElem,Int64}}}(undef, 3, 3) struct_const_V[1, :] = Vector{Tuple{QQFieldElem,Int64}}[[(QQ(-1), 2)], [(QQ(1), 1)], []] @@ -591,7 +591,7 @@ @test lie_algebra_module_struct_const(L, exterior_power(standard_module(L), 3)[1]) == struct_const_V - L = special_orthogonal_lie_algebra(QQ, 4) + L = special_orthogonal_lie_algebra(QQ, 4, identity_matrix(QQ, 4)) struct_const_V = Matrix{Vector{Tuple{QQFieldElem,Int64}}}(undef, 6, 4) struct_const_V[1, :] = Vector{Tuple{QQFieldElem,Int64}}[ diff --git a/experimental/LieAlgebras/test/LinearLieAlgebra-test.jl b/experimental/LieAlgebras/test/LinearLieAlgebra-test.jl index bfaac9e4b4c6..930f44737cdf 100644 --- a/experimental/LieAlgebras/test/LinearLieAlgebra-test.jl +++ b/experimental/LieAlgebras/test/LinearLieAlgebra-test.jl @@ -1,5 +1,5 @@ @testset "LieAlgebras.LinearLieAlgebra" begin - @testset "constructors for R=$R, n=$n" for R in [QQ, cyclotomic_field(4)[1]], n in 1:5 + @testset "constructors for R=$R, n=$n" for R in [QQ, cyclotomic_field(4)[1]], n in 1:6 L = general_linear_lie_algebra(R, n) @test dim(L) == n^2 @@ -8,6 +8,11 @@ L = special_orthogonal_lie_algebra(R, n) @test dim(L) == div(n^2 - n, 2) + + if is_even(n) + L = symplectic_lie_algebra(R, n) + @test dim(L) == div(n^2 + n, 2) + end end @testset "conformance tests" begin @@ -48,24 +53,94 @@ ) end + @testset "so_5(QQ)" begin + L = special_orthogonal_lie_algebra(QQ, 5) + lie_algebra_conformance_test( + L, LinearLieAlgebra{QQFieldElem}, LinearLieAlgebraElem{QQFieldElem} + ) + end + + @testset "so_4(QQ), #2" begin + L = special_orthogonal_lie_algebra(QQ, 4, identity_matrix(ZZ, 4)) + lie_algebra_conformance_test( + L, LinearLieAlgebra{QQFieldElem}, LinearLieAlgebraElem{QQFieldElem} + ) + end + + @testset "so_5(QQ), #2" begin + L = special_orthogonal_lie_algebra(QQ, 5, identity_matrix(ZZ, 5)) + lie_algebra_conformance_test( + L, LinearLieAlgebra{QQFieldElem}, LinearLieAlgebraElem{QQFieldElem} + ) + end + + @testset "sp_4(QQ)" begin + L = symplectic_lie_algebra(QQ, 4) + lie_algebra_conformance_test( + L, LinearLieAlgebra{QQFieldElem}, LinearLieAlgebraElem{QQFieldElem} + ) + end + @testset "gl_4(CF(4))" begin L = general_linear_lie_algebra(cyclotomic_field(4)[1], 4) lie_algebra_conformance_test( - L, LinearLieAlgebra{AbsSimpleNumFieldElem}, LinearLieAlgebraElem{AbsSimpleNumFieldElem} + L, + LinearLieAlgebra{AbsSimpleNumFieldElem}, + LinearLieAlgebraElem{AbsSimpleNumFieldElem}, ) end @testset "sl_4(CF(4))" begin L = special_linear_lie_algebra(cyclotomic_field(4)[1], 4) lie_algebra_conformance_test( - L, LinearLieAlgebra{AbsSimpleNumFieldElem}, LinearLieAlgebraElem{AbsSimpleNumFieldElem} + L, + LinearLieAlgebra{AbsSimpleNumFieldElem}, + LinearLieAlgebraElem{AbsSimpleNumFieldElem}, ) end @testset "so_4(CF(4))" begin L = special_orthogonal_lie_algebra(cyclotomic_field(4)[1], 4) lie_algebra_conformance_test( - L, LinearLieAlgebra{AbsSimpleNumFieldElem}, LinearLieAlgebraElem{AbsSimpleNumFieldElem} + L, + LinearLieAlgebra{AbsSimpleNumFieldElem}, + LinearLieAlgebraElem{AbsSimpleNumFieldElem}, + ) + end + + @testset "so_5(CF(4))" begin + L = special_orthogonal_lie_algebra(cyclotomic_field(4)[1], 5) + lie_algebra_conformance_test( + L, + LinearLieAlgebra{AbsSimpleNumFieldElem}, + LinearLieAlgebraElem{AbsSimpleNumFieldElem}, + ) + end + + @testset "so_4(CF(4)), #2" begin + L = special_orthogonal_lie_algebra(cyclotomic_field(4)[1], 4, identity_matrix(ZZ, 4)) + lie_algebra_conformance_test( + L, + LinearLieAlgebra{AbsSimpleNumFieldElem}, + LinearLieAlgebraElem{AbsSimpleNumFieldElem}, + ) + end + + @testset "so_5(CF(4)), #2" begin + L = special_orthogonal_lie_algebra(cyclotomic_field(4)[1], 5, identity_matrix(ZZ, 5)) + lie_algebra_conformance_test( + L, + LinearLieAlgebra{AbsSimpleNumFieldElem}, + LinearLieAlgebraElem{AbsSimpleNumFieldElem}, + ) + end + + @testset "sp_4(CF(4))" begin + L = symplectic_lie_algebra(cyclotomic_field(4)[1], 4) + lie_algebra_conformance_test( + L, + LinearLieAlgebra{AbsSimpleNumFieldElem}, + LinearLieAlgebraElem{AbsSimpleNumFieldElem}, ) end end @@ -83,14 +158,27 @@ return struct_const_L end - L = special_orthogonal_lie_algebra(QQ, 3) + L = special_orthogonal_lie_algebra(QQ, 3, identity_matrix(QQ, 3)) + @test matrix_repr_basis(L) == [ + matrix(QQ, [0 1 0; -1 0 0; 0 0 0]), + matrix(QQ, [0 0 1; 0 0 0; -1 0 0]), + matrix(QQ, [0 0 0; 0 0 1; 0 -1 0]), + ] struct_const_L = Matrix{Vector{Tuple{QQFieldElem,Int64}}}(undef, 3, 3) struct_const_L[1, :] = Vector{Tuple{QQFieldElem,Int64}}[[], [(QQ(-1), 3)], [(QQ(1), 2)]] struct_const_L[2, :] = Vector{Tuple{QQFieldElem,Int64}}[[(QQ(1), 3)], [], [(QQ(-1), 1)]] struct_const_L[3, :] = Vector{Tuple{QQFieldElem,Int64}}[[(QQ(-1), 2)], [(QQ(1), 1)], []] @test lie_algebra_struct_const(L) == struct_const_L - L = special_orthogonal_lie_algebra(QQ, 4) + L = special_orthogonal_lie_algebra(QQ, 4, identity_matrix(QQ, 4)) + @test matrix_repr_basis(L) == [ + matrix(QQ, [0 1 0 0; -1 0 0 0; 0 0 0 0; 0 0 0 0]), + matrix(QQ, [0 0 1 0; 0 0 0 0; -1 0 0 0; 0 0 0 0]), + matrix(QQ, [0 0 0 1; 0 0 0 0; 0 0 0 0; -1 0 0 0]), + matrix(QQ, [0 0 0 0; 0 0 1 0; 0 -1 0 0; 0 0 0 0]), + matrix(QQ, [0 0 0 0; 0 0 0 1; 0 0 0 0; 0 -1 0 0]), + matrix(QQ, [0 0 0 0; 0 0 0 0; 0 0 0 1; 0 0 -1 0]), + ] struct_const_L = Matrix{Vector{Tuple{QQFieldElem,Int64}}}(undef, 6, 6) struct_const_L[1, :] = Vector{Tuple{QQFieldElem,Int64}}[ [], [(QQ(-1), 4)], [(QQ(-1), 5)], [(QQ(1), 2)], [(QQ(1), 3)], [] @@ -112,7 +200,19 @@ ] @test lie_algebra_struct_const(L) == struct_const_L - L = special_orthogonal_lie_algebra(QQ, 5) + L = special_orthogonal_lie_algebra(QQ, 5, identity_matrix(QQ, 5)) + @test matrix_repr_basis(L) == [ + matrix(QQ, [0 1 0 0 0; -1 0 0 0 0; 0 0 0 0 0; 0 0 0 0 0; 0 0 0 0 0]), + matrix(QQ, [0 0 1 0 0; 0 0 0 0 0; -1 0 0 0 0; 0 0 0 0 0; 0 0 0 0 0]), + matrix(QQ, [0 0 0 1 0; 0 0 0 0 0; 0 0 0 0 0; -1 0 0 0 0; 0 0 0 0 0]), + matrix(QQ, [0 0 0 0 1; 0 0 0 0 0; 0 0 0 0 0; 0 0 0 0 0; -1 0 0 0 0]), + matrix(QQ, [0 0 0 0 0; 0 0 1 0 0; 0 -1 0 0 0; 0 0 0 0 0; 0 0 0 0 0]), + matrix(QQ, [0 0 0 0 0; 0 0 0 1 0; 0 0 0 0 0; 0 -1 0 0 0; 0 0 0 0 0]), + matrix(QQ, [0 0 0 0 0; 0 0 0 0 1; 0 0 0 0 0; 0 0 0 0 0; 0 -1 0 0 0]), + matrix(QQ, [0 0 0 0 0; 0 0 0 0 0; 0 0 0 1 0; 0 0 -1 0 0; 0 0 0 0 0]), + matrix(QQ, [0 0 0 0 0; 0 0 0 0 0; 0 0 0 0 1; 0 0 0 0 0; 0 0 -1 0 0]), + matrix(QQ, [0 0 0 0 0; 0 0 0 0 0; 0 0 0 0 0; 0 0 0 0 1; 0 0 0 -1 0]), + ] struct_const_L = Matrix{Vector{Tuple{QQFieldElem,Int64}}}(undef, 10, 5) struct_const_L[1, :] = Vector{Tuple{QQFieldElem,Int64}}[ [(QQ(-1), 2)], [(QQ(1), 1)], [], [], [] diff --git a/experimental/LieAlgebras/test/iso_oscar_gap-test.jl b/experimental/LieAlgebras/test/iso_oscar_gap-test.jl index 636142fbe587..f01c34998365 100644 --- a/experimental/LieAlgebras/test/iso_oscar_gap-test.jl +++ b/experimental/LieAlgebras/test/iso_oscar_gap-test.jl @@ -67,6 +67,7 @@ end general_linear_lie_algebra(RO, 2), special_linear_lie_algebra(RO, 3), special_orthogonal_lie_algebra(RO, 4), + symplectic_lie_algebra(RO, 6), ] @testset for LO in lie_algebras