From a915b162a9b210a79ed9753739aaa9c03406981b Mon Sep 17 00:00:00 2001 From: antonydellavecchia Date: Thu, 14 Dec 2023 10:12:04 +0100 Subject: [PATCH 001/128] init algebraic shifting --- experimental/AlgebraicShifting/README.md | 13 +++++ experimental/AlgebraicShifting/docs/doc.main | 8 +++ experimental/AlgebraicShifting/src/main.jl | 50 +++++++++++++++++++ .../AlgebraicShifting/test/runtests.jl | 4 ++ 4 files changed, 75 insertions(+) create mode 100644 experimental/AlgebraicShifting/README.md create mode 100644 experimental/AlgebraicShifting/docs/doc.main create mode 100644 experimental/AlgebraicShifting/src/main.jl create mode 100644 experimental/AlgebraicShifting/test/runtests.jl diff --git a/experimental/AlgebraicShifting/README.md b/experimental/AlgebraicShifting/README.md new file mode 100644 index 000000000000..91cd0ee3dba2 --- /dev/null +++ b/experimental/AlgebraicShifting/README.md @@ -0,0 +1,13 @@ +# An example template for the experimental section + +## Aims + +This is an example for a file structure to set up a new package +in the experimental section. All files you find here are part of the +minimum requirements. See also the official Oscar documentation. + +## Status + +We plan to also provide a function to automatically copy this template +for you to start your own package. + diff --git a/experimental/AlgebraicShifting/docs/doc.main b/experimental/AlgebraicShifting/docs/doc.main new file mode 100644 index 000000000000..c42ec6a31cee --- /dev/null +++ b/experimental/AlgebraicShifting/docs/doc.main @@ -0,0 +1,8 @@ +# An example documentation + +This is a sample text to outline the structure of the packages in the `Experimental` folder. +You can show docstrings like this: +```@docs + my_access_func(S::ExampleStruct) +``` + diff --git a/experimental/AlgebraicShifting/src/main.jl b/experimental/AlgebraicShifting/src/main.jl new file mode 100644 index 000000000000..aa1731531c49 --- /dev/null +++ b/experimental/AlgebraicShifting/src/main.jl @@ -0,0 +1,50 @@ +# Add your new types, functions, and methods here. +n = 5 +k = 3 +m = 4 + +Qx, x = polynomial_ring(QQ, :x => (1:n, 1:n)) + +X = matrix(fraction_field(Qx), hcat(x)) + +possible_m_sets = subsets(binomial(n, k), m) + +for i in 1:length(possible_m_sets) + K = sort(subsets(n, k)[possible_m_sets[i]]) + + sub_compound_matrix_rows = Vector{AbstractAlgebra.Generic.Frac}[] + for col_subset in sort(subsets(n, k)) + col_minors = [] + for row_subset in K + push!(col_minors, det(X[row_subset, col_subset])) + end + push!(sub_compound_matrix_rows, col_minors) + end + + A = reduce(hcat, sub_compound_matrix_rows) + _, _, _, U = lu(matrix(A)); + delta_K = Int[] + + row_index = 1 + row_bound = nrows(A) + for col_index in 1:ncols(A) + if !is_zero(U[row_index, col_index]) + push!(delta_K, col_index) + row_index += 1 + end + + row_index > row_bound && break + end + + println(delta_K) +end + +@doc raw""" + my_access_func(S::ExampleStruct) + +This is a dummy sample function to teach the use of docstrings. +""" +function my_access_func(S::ExampleStruct) + return S.i +end + diff --git a/experimental/AlgebraicShifting/test/runtests.jl b/experimental/AlgebraicShifting/test/runtests.jl new file mode 100644 index 000000000000..85a7ef3f1fa6 --- /dev/null +++ b/experimental/AlgebraicShifting/test/runtests.jl @@ -0,0 +1,4 @@ +@testset "Experimental template tests" begin + S = Oscar.ExampleStruct(5) + @test 5 == Oscar.my_access_func(S) +end From 1071a38ea6d2ad07ed381618700ab1cf3c69ff21 Mon Sep 17 00:00:00 2001 From: Antony Della Vecchia Date: Thu, 14 Dec 2023 17:09:16 +0100 Subject: [PATCH 002/128] copied from template --- .../src/AlgebraicShifting.jl | 44 +++++++++++++++++++ 1 file changed, 44 insertions(+) create mode 100644 experimental/AlgebraicShifting/src/AlgebraicShifting.jl diff --git a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl new file mode 100644 index 000000000000..ad376b9f9e29 --- /dev/null +++ b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl @@ -0,0 +1,44 @@ +function delta_ext(K::SimplicialComplex) + n = nvertices(K) + + cmp(S1, S2) = min(symdiff(S1, S2)...) in S1 + K_facets = sort(facets(K); lt=cmp) + + Qx, x = polynomial_ring(QQ, :x => (1:n, 1:n)) + X = matrix(fraction_field(Qx), hcat(x)) + sub_compound_matrix_rows = Vector{AbstractAlgebra.Generic.Frac}[] + + for col_subset in K_facets + col_minors = [] + for row_subset in K_facets + push!(col_minors, det(X[collect(row_subset), collect(col_subset)])) + end + push!(sub_compound_matrix_rows, col_minors) + end + + A = reduce(hcat, sub_compound_matrix_rows) + _, _, _, U = lu(matrix(A)); + delta_K = Int[] + + row_index = 1 + row_bound = nrows(A) + for col_index in 1:ncols(A) + if !is_zero(U[row_index, col_index]) + push!(delta_K, col_index) + row_index += 1 + end + + row_index > row_bound && break + end + println(K[delta_K]) +end + +#@doc raw""" +# my_access_func(S::ExampleStruct) +# +#This is a dummy sample function to teach the use of docstrings. +#""" +#function my_access_func(S::ExampleStruct) +# return S.i +#end + From 087ae2e1d0a00d2c1c2db06d131493280d1a7ead Mon Sep 17 00:00:00 2001 From: Antony Della Vecchia Date: Thu, 14 Dec 2023 17:09:31 +0100 Subject: [PATCH 003/128] copied from template --- experimental/AlgebraicShifting/src/main.jl | 50 ---------------------- src/Combinatorics/SimplicialComplexes.jl | 34 +++++++-------- src/deprecations.jl | 3 ++ src/exports.jl | 2 +- 4 files changed, 21 insertions(+), 68 deletions(-) delete mode 100644 experimental/AlgebraicShifting/src/main.jl diff --git a/experimental/AlgebraicShifting/src/main.jl b/experimental/AlgebraicShifting/src/main.jl deleted file mode 100644 index aa1731531c49..000000000000 --- a/experimental/AlgebraicShifting/src/main.jl +++ /dev/null @@ -1,50 +0,0 @@ -# Add your new types, functions, and methods here. -n = 5 -k = 3 -m = 4 - -Qx, x = polynomial_ring(QQ, :x => (1:n, 1:n)) - -X = matrix(fraction_field(Qx), hcat(x)) - -possible_m_sets = subsets(binomial(n, k), m) - -for i in 1:length(possible_m_sets) - K = sort(subsets(n, k)[possible_m_sets[i]]) - - sub_compound_matrix_rows = Vector{AbstractAlgebra.Generic.Frac}[] - for col_subset in sort(subsets(n, k)) - col_minors = [] - for row_subset in K - push!(col_minors, det(X[row_subset, col_subset])) - end - push!(sub_compound_matrix_rows, col_minors) - end - - A = reduce(hcat, sub_compound_matrix_rows) - _, _, _, U = lu(matrix(A)); - delta_K = Int[] - - row_index = 1 - row_bound = nrows(A) - for col_index in 1:ncols(A) - if !is_zero(U[row_index, col_index]) - push!(delta_K, col_index) - row_index += 1 - end - - row_index > row_bound && break - end - - println(delta_K) -end - -@doc raw""" - my_access_func(S::ExampleStruct) - -This is a dummy sample function to teach the use of docstrings. -""" -function my_access_func(S::ExampleStruct) - return S.i -end - diff --git a/src/Combinatorics/SimplicialComplexes.jl b/src/Combinatorics/SimplicialComplexes.jl index b42b73a195f3..5c59906f9db0 100644 --- a/src/Combinatorics/SimplicialComplexes.jl +++ b/src/Combinatorics/SimplicialComplexes.jl @@ -13,26 +13,26 @@ pm_object(K::SimplicialComplex) = K.pm_simplicialcomplex @doc raw""" - SimplicialComplex(generators::Union{Vector{Vector{Int}}, Vector{Set{Int}}}) + simplical_complex(generators::Union{Vector{Vector{Int}}, Vector{Set{Int}}}) Construct an abstract simplicial complex from a set of faces. While arbitrary non-negative integers are allowed as vertices, they will be relabeled to consecutive integers starting at 1. # Examples ```jldoctest -julia> K = SimplicialComplex([[1,2,3],[2,3,4]]) +julia> K = simplicial_complex([[1,2,3],[2,3,4]]) Abstract simplicial complex of dimension 2 on 4 vertices ``` Simplicial complex comprising the empty set only: ```jldoctest -julia> empty = SimplicialComplex(Vector{Set{Int}}([])) +julia> empty = simplicial_complex(Vector{Set{Int}}([])) Abstract simplicial complex of dimension -1 on 0 vertices ``` The original vertices can be recovered: ```jldoctest -julia> L = SimplicialComplex([[0,2,17],[2,17,90]]); +julia> L = simplicial_complex([[0,2,17],[2,17,90]]); julia> facets(L) 2-element Vector{Set{Int64}}: @@ -47,21 +47,21 @@ julia> vertexindices(L) 90 ``` """ -function SimplicialComplex(generators::Union{AbstractVector{<:AbstractVector{<:Base.Integer}}, AbstractVector{<:AbstractSet{<:Base.Integer}}}) - K = Polymake.topaz.SimplicialComplex(INPUT_FACES=generators) - SimplicialComplex(K) +function simplicial_complex(generators::Union{AbstractVector{<:AbstractVector{<:Base.Integer}}, AbstractVector{<:AbstractSet{<:Base.Integer}}}) + K = Polymake.topaz.SimplicialComplex(INPUT_FACES=generators) + SimplicialComplex(K) end -function SimplicialComplex(generators::IncidenceMatrix) - K = Polymake.@convert_to Array{Set} Polymake.common.rows(generators) - SimplicialComplex(K) +function simplicial_complex(generators::IncidenceMatrix) + K = Polymake.@convert_to Array{Set} Polymake.common.rows(generators) + SimplicialComplex(K) end # more efficient UNEXPORTED+UNDOCUMENTED version, which requires consecutive vertices, and facets as generators; # will produce errors / segfaults or worse if used improperly function _SimplicialComplex(generators::Union{Vector{Vector{Int}}, Vector{Set{Int}}}) - K = Polymake.topaz.SimplicialComplex(FACETS=generators) - SimplicialComplex(K) + K = Polymake.topaz.SimplicialComplex(FACETS=generators) + SimplicialComplex(K) end ################################################################################ @@ -207,7 +207,7 @@ Return `i`-th reduced integral cohomology group of `K`. # Examples ```jldoctest -julia> K = SimplicialComplex([[0,1],[1,2],[0,2]]); +julia> K = simplicial_complex([[0,1],[1,2],[0,2]]); julia> cohomology(K,1) GrpAb: Z @@ -222,7 +222,7 @@ Return the minimal non-faces of the abstract simplicial complex `K`. # Examples ```jldoctest -julia> K = SimplicialComplex([[1,2,3],[2,3,4]]); +julia> K = simplicial_complex([[1,2,3],[2,3,4]]); julia> minimal_nonfaces(K) 1-element Vector{Set{Int64}}: @@ -252,7 +252,7 @@ Return the Alexander dual of the abstract simplicial complex `K`. # Examples ```jldoctest -julia> K = SimplicialComplex([[1,2,3],[2,3,4]]); +julia> K = simplicial_complex([[1,2,3],[2,3,4]]); julia> alexander_dual(K) Abstract simplicial complex of dimension 1 on 2 vertices @@ -413,7 +413,7 @@ Return the star of the face `sigma` in the abstract simplicial complex `K`. # Examples ```jldoctest -julia> K = SimplicialComplex([[1,2,3],[2,3,4]]); +julia> K = simplicial_complex([[1,2,3],[2,3,4]]); julia> star_subcomplex(K,[1]) Abstract simplicial complex of dimension 2 on 3 vertices @@ -428,7 +428,7 @@ Return the link of the face `sigma` in the abstract simplicial complex `K`. # Examples ```jldoctest -julia> K = SimplicialComplex([[1,2,3],[2,3,4]]); +julia> K = simplical_complex ([[1,2,3],[2,3,4]]); julia> link_subcomplex(K,[2,3]) Abstract simplicial complex of dimension 0 on 2 vertices diff --git a/src/deprecations.jl b/src/deprecations.jl index 3ccde1445b02..3ef0c5d57646 100644 --- a/src/deprecations.jl +++ b/src/deprecations.jl @@ -508,3 +508,6 @@ end @deprecate normal_toric_variety(rays::AbstractCollection[RayVector], max_cones::IncidenceMatrix; non_redundant::Bool = false) normal_toric_variety(max_cones, rays; non_redundant) @deprecate components(X::AbsSpec) connected_components(X::AbsSpec) + +@deprecate SimplicialComplex(generators::Union{AbstractVector{<:AbstractVector{<:Base.Integer}}, AbstractVector{<:AbstractSet{<:Base.Integer}}}) simplicial_complex(generators) +@deprecate SimplicialComplex(generators::IncidenceMatrix) simplicial_complex(generators) diff --git a/src/exports.jl b/src/exports.jl index 60d3f4a6c873..f31f23cb0a84 100644 --- a/src/exports.jl +++ b/src/exports.jl @@ -158,7 +158,7 @@ export SchemeMor export SemidirectProductGroup export SesquilinearForm export SimpleGlueing -export SimplicialComplex +export SimplicialComplex, simplicial_complex export Singular export Sp export SpaceGerm From be2a95a3af77462c9ae7f30488874133840e04f0 Mon Sep 17 00:00:00 2001 From: antonydellavecchia Date: Fri, 15 Dec 2023 23:06:22 +0100 Subject: [PATCH 004/128] concrete function --- .../src/AlgebraicShifting.jl | 14 +++++--- src/Rings/mpoly-ideals.jl | 33 ++++++++++--------- 2 files changed, 26 insertions(+), 21 deletions(-) diff --git a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl index ad376b9f9e29..6716791e0745 100644 --- a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl +++ b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl @@ -4,14 +4,18 @@ function delta_ext(K::SimplicialComplex) cmp(S1, S2) = min(symdiff(S1, S2)...) in S1 K_facets = sort(facets(K); lt=cmp) + k = length(K_facets[1]) Qx, x = polynomial_ring(QQ, :x => (1:n, 1:n)) X = matrix(fraction_field(Qx), hcat(x)) - sub_compound_matrix_rows = Vector{AbstractAlgebra.Generic.Frac}[] - - for col_subset in K_facets + sub_compound_matrix_rows = Vector{FracElem{<:MPolyRingElem}}[] + nCk = sort(subsets(n, k)) + + for col_subset in nCk col_minors = [] for row_subset in K_facets - push!(col_minors, det(X[collect(row_subset), collect(col_subset)])) + ri = collect(row_subset) + ci = collect(col_subset) + push!(col_minors, det(X[ri, ci])) end push!(sub_compound_matrix_rows, col_minors) end @@ -30,7 +34,7 @@ function delta_ext(K::SimplicialComplex) row_index > row_bound && break end - println(K[delta_K]) + return simplicial_complex(nCk[delta_K]) end #@doc raw""" diff --git a/src/Rings/mpoly-ideals.jl b/src/Rings/mpoly-ideals.jl index 5b05a9eb0586..c5ae2c282bec 100644 --- a/src/Rings/mpoly-ideals.jl +++ b/src/Rings/mpoly-ideals.jl @@ -1521,22 +1521,23 @@ ideal(x[1, 2]*x[2, 2] + 6*x[2, 1]*x[1, 3] + x[1, 1]*x[2, 3]) """ 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) + 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 - return ideal(ring, converted_generators) + converted_g = finish(polynomial) + push!(converted_generators, converted_g) + end + return ideal(ring, converted_generators) end From b794172f4bcba6da18e748935b7f4bddb5c6c0e2 Mon Sep 17 00:00:00 2001 From: antonydellavecchia Date: Mon, 18 Dec 2023 09:52:31 +0100 Subject: [PATCH 005/128] fix for creating simplicial cmplex from from graph incidence matrix --- src/Combinatorics/SimplicialComplexes.jl | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/Combinatorics/SimplicialComplexes.jl b/src/Combinatorics/SimplicialComplexes.jl index 5c59906f9db0..41f2ff63866a 100644 --- a/src/Combinatorics/SimplicialComplexes.jl +++ b/src/Combinatorics/SimplicialComplexes.jl @@ -53,7 +53,7 @@ function simplicial_complex(generators::Union{AbstractVector{<:AbstractVector{<: end function simplicial_complex(generators::IncidenceMatrix) - K = Polymake.@convert_to Array{Set} Polymake.common.rows(generators) + K = Polymake.@convert_to Array{Set} Polymake.common.cols(generators) SimplicialComplex(K) end From 190d4865df9990a2b55ccdab9b9f0e15ef3cfa82 Mon Sep 17 00:00:00 2001 From: Antony Della Vecchia Date: Tue, 19 Dec 2023 18:30:04 +0100 Subject: [PATCH 006/128] use sparse matrices --- .../src/AlgebraicShifting.jl | 38 +++++++++++++------ 1 file changed, 27 insertions(+), 11 deletions(-) diff --git a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl index 6716791e0745..6de0163327bf 100644 --- a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl +++ b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl @@ -3,25 +3,41 @@ function delta_ext(K::SimplicialComplex) cmp(S1, S2) = min(symdiff(S1, S2)...) in S1 K_facets = sort(facets(K); lt=cmp) - + m = length(K_facets) k = length(K_facets[1]) + + K_min_non_faces = minimal_nonfaces(K) + Qx, x = polynomial_ring(QQ, :x => (1:n, 1:n)) - X = matrix(fraction_field(Qx), hcat(x)) - sub_compound_matrix_rows = Vector{FracElem{<:MPolyRingElem}}[] + F = fraction_field(Qx) + X = matrix(F, hcat(x)) nCk = sort(subsets(n, k)) - - for col_subset in nCk - col_minors = [] - for row_subset in K_facets + sub_compound_matrix = sparse_matrix(F, 0, 0) + + for row_subset in K_facets + row_minors = Tuple{Int, AbstractAlgebra.Generic.FracFieldElem}[] + + for (i, col_subset) in enumerate(nCk) + has_non_face = false + for non_face in K_min_non_faces + if is_subset(non_face, Set(col_subset)) + has_non_face = true + break + end + end + + if has_non_face + continue + end + ri = collect(row_subset) ci = collect(col_subset) - push!(col_minors, det(X[ri, ci])) + push!(row_minors, (i, det(X[ri, ci]))) end - push!(sub_compound_matrix_rows, col_minors) + push!(sub_compound_matrix, sparse_row(F, row_minors)) end - A = reduce(hcat, sub_compound_matrix_rows) - _, _, _, U = lu(matrix(A)); + @time _, _, _, U = lu(matrix(sub_compound_matrix)); delta_K = Int[] row_index = 1 From 324eee84b9cfa8d8c2dd497c309af4457d8b3b66 Mon Sep 17 00:00:00 2001 From: antonydellavecchia Date: Tue, 19 Dec 2023 21:00:13 +0100 Subject: [PATCH 007/128] computes correct result for octohedron --- .../src/AlgebraicShifting.jl | 27 ++++++++++--------- experimental/ModStd/ModStdQt.jl | 6 ++--- 2 files changed, 17 insertions(+), 16 deletions(-) diff --git a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl index 6de0163327bf..c9831c96ad35 100644 --- a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl +++ b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl @@ -9,22 +9,21 @@ function delta_ext(K::SimplicialComplex) K_min_non_faces = minimal_nonfaces(K) Qx, x = polynomial_ring(QQ, :x => (1:n, 1:n)) - F = fraction_field(Qx) - X = matrix(F, hcat(x)) + X = matrix(Qx, hcat(x)) nCk = sort(subsets(n, k)) - sub_compound_matrix = sparse_matrix(F, 0, 0) + sub_compound_matrix = sparse_matrix(Qx, 0, 0) for row_subset in K_facets - row_minors = Tuple{Int, AbstractAlgebra.Generic.FracFieldElem}[] + row_minors = Tuple{Int, MPolyRingElem}[] for (i, col_subset) in enumerate(nCk) has_non_face = false - for non_face in K_min_non_faces - if is_subset(non_face, Set(col_subset)) - has_non_face = true - break - end - end + #for non_face in K_min_non_faces + # if is_subset(non_face, Set(col_subset)) + # has_non_face = true + # break + # end + #end if has_non_face continue @@ -34,22 +33,24 @@ function delta_ext(K::SimplicialComplex) ci = collect(col_subset) push!(row_minors, (i, det(X[ri, ci]))) end - push!(sub_compound_matrix, sparse_row(F, row_minors)) + push!(sub_compound_matrix, sparse_row(Qx, row_minors)) end - @time _, _, _, U = lu(matrix(sub_compound_matrix)); + _, A = Oscar.ModStdQt.ref_ff_rc!(matrix(sub_compound_matrix)) + delta_K = Int[] row_index = 1 row_bound = nrows(A) for col_index in 1:ncols(A) - if !is_zero(U[row_index, col_index]) + if !is_zero(A[row_index, col_index]) push!(delta_K, col_index) row_index += 1 end row_index > row_bound && break end + nCk[delta_K] return simplicial_complex(nCk[delta_K]) end diff --git a/experimental/ModStd/ModStdQt.jl b/experimental/ModStd/ModStdQt.jl index 5ba7fc4231f5..096d606cea5b 100644 --- a/experimental/ModStd/ModStdQt.jl +++ b/experimental/ModStd/ModStdQt.jl @@ -515,7 +515,7 @@ function ref_ff_rc!(M::MatElem{<:MPolyRingElem}) break end if j > ncols(M) - return rk + return rk, M end rk += 1 @@ -523,13 +523,13 @@ function ref_ff_rc!(M::MatElem{<:MPolyRingElem}) if iszero(M[k, j]) continue end -# g, a, b = gcd_with_cofactors(M[k, j], M[i, j]) + g, a, b = gcd_with_cofactors(M[k, j], M[i, j]) M[k, :] = b*M[k, :] - a * M[i, :] M[k, :] = divexact(M[k, :], content(M[k, :])) end j += 1 end - return rk + return rk, M end #to, basically, make the doctest stable From 960fb0d84264289aee66f1344cda42ff3f9f24f1 Mon Sep 17 00:00:00 2001 From: antonydellavecchia Date: Tue, 19 Dec 2023 22:51:03 +0100 Subject: [PATCH 008/128] fixed function use --- experimental/AlgebraicShifting/src/AlgebraicShifting.jl | 4 ++-- experimental/ModStd/ModStdQt.jl | 4 ++-- 2 files changed, 4 insertions(+), 4 deletions(-) diff --git a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl index c9831c96ad35..1a2709299793 100644 --- a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl +++ b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl @@ -35,8 +35,8 @@ function delta_ext(K::SimplicialComplex) end push!(sub_compound_matrix, sparse_row(Qx, row_minors)) end - - _, A = Oscar.ModStdQt.ref_ff_rc!(matrix(sub_compound_matrix)) + A = matrix(sub_compound_matrix) + Oscar.ModStdQt.ref_ff_rc!(A) delta_K = Int[] diff --git a/experimental/ModStd/ModStdQt.jl b/experimental/ModStd/ModStdQt.jl index 096d606cea5b..a88d05ed3ab0 100644 --- a/experimental/ModStd/ModStdQt.jl +++ b/experimental/ModStd/ModStdQt.jl @@ -515,7 +515,7 @@ function ref_ff_rc!(M::MatElem{<:MPolyRingElem}) break end if j > ncols(M) - return rk, M + return rk end rk += 1 @@ -529,7 +529,7 @@ function ref_ff_rc!(M::MatElem{<:MPolyRingElem}) end j += 1 end - return rk, M + return rk end #to, basically, make the doctest stable From 5c6a3ae321e835cb326de04ae08315ef049a2fbd Mon Sep 17 00:00:00 2001 From: Antony Della Vecchia Date: Wed, 20 Dec 2023 18:39:01 +0100 Subject: [PATCH 009/128] started on delta_sym --- .../src/AlgebraicShifting.jl | 105 ++++++++++-------- 1 file changed, 57 insertions(+), 48 deletions(-) diff --git a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl index 1a2709299793..16eeab0aced3 100644 --- a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl +++ b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl @@ -1,65 +1,74 @@ +@doc raw""" + delta_ext(K::SimplicialComplex) + +Returns the exterior shift of `K` +""" function delta_ext(K::SimplicialComplex) n = nvertices(K) + dim_K = dim(K) cmp(S1, S2) = min(symdiff(S1, S2)...) in S1 K_facets = sort(facets(K); lt=cmp) - m = length(K_facets) - k = length(K_facets[1]) - - K_min_non_faces = minimal_nonfaces(K) - - Qx, x = polynomial_ring(QQ, :x => (1:n, 1:n)) - X = matrix(Qx, hcat(x)) - nCk = sort(subsets(n, k)) - sub_compound_matrix = sparse_matrix(Qx, 0, 0) - for row_subset in K_facets - row_minors = Tuple{Int, MPolyRingElem}[] + facet_dict = Dict( + (k => filter(f -> length(f) == k + 1, K_facets) for k in 1:dim_K ) + ) - for (i, col_subset) in enumerate(nCk) - has_non_face = false - #for non_face in K_min_non_faces - # if is_subset(non_face, Set(col_subset)) - # has_non_face = true - # break - # end - #end + for (dim_face, faces) in facet_dict + Qx, x = polynomial_ring(QQ, :x => (1:n, 1:n)) + X = matrix(Qx, hcat(x)) + nCk = sort(subsets(n, dim_face + 1)) + sub_compound_matrix = Vector{MPolyRingElem}[] - if has_non_face - continue + for col_subset in nCk + row_minors = MPolyRingElem[] + for row_subset in faces + ri = collect(row_subset) + ci = collect(col_subset) + push!(row_minors, det(X[ri, ci])) end - - ri = collect(row_subset) - ci = collect(col_subset) - push!(row_minors, (i, det(X[ri, ci]))) + push!(sub_compound_matrix, row_minors) end - push!(sub_compound_matrix, sparse_row(Qx, row_minors)) - end - A = matrix(sub_compound_matrix) - Oscar.ModStdQt.ref_ff_rc!(A) - delta_K = Int[] + A = matrix(Qx, sub_compound_matrix) + Oscar.ModStdQt.ref_ff_rc!(A) - row_index = 1 - row_bound = nrows(A) - for col_index in 1:ncols(A) - if !is_zero(A[row_index, col_index]) - push!(delta_K, col_index) - row_index += 1 - end + delta_k = Int[] + row_index = 1 + row_bound = nrows(A) + for col_index in 1:ncols(A) + if !is_zero(A[row_index, col_index]) + push!(delta_k, col_index) + row_index += 1 + end - row_index > row_bound && break + row_index > row_bound && break + end + facet_dict[dim_face] = map(Set, nCk[delta_k]) end - nCk[delta_K] - return simplicial_complex(nCk[delta_K]) + return simplicial_complex( + reduce(vcat, values(facet_dict)) + ) end -#@doc raw""" -# my_access_func(S::ExampleStruct) -# -#This is a dummy sample function to teach the use of docstrings. -#""" -#function my_access_func(S::ExampleStruct) -# return S.i -#end +@doc raw""" + delta_sym(K::SimplicialComplex) +Returns the symmetric shift of `K` +""" +function delta_sym(K::SimplicialComplex) + I_K = stanley_reisner_ideal(K) +end + + +function generic_initial_ideal(I::MPolyIdeal) + R = base_ring(I) + n = nvars(R) + Ry, y = polynomial_ring(R, :y => (1:n, 1:n)) + + for g in I_K + findall(x -> !is_zero(x[2]), exponents(g)) + map(e -> Y[:, ], exponents(g)) + end + +end From e3f3301ed90f9fd0eff8e5625ab36cf0adce4eb3 Mon Sep 17 00:00:00 2001 From: Antony Della Vecchia Date: Thu, 21 Dec 2023 17:42:38 +0100 Subject: [PATCH 010/128] some progress on delta sym --- .../src/AlgebraicShifting.jl | 29 +++++++++++++++---- 1 file changed, 23 insertions(+), 6 deletions(-) diff --git a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl index 16eeab0aced3..c1960d36cd4b 100644 --- a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl +++ b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl @@ -57,18 +57,35 @@ end Returns the symmetric shift of `K` """ function delta_sym(K::SimplicialComplex) - I_K = stanley_reisner_ideal(K) + R_K, quotient_map = stanley_reisner_ring(K) + Ry, y = polynomial_ring(R_K, :y => (1:n, 1:n)) + Y = matrix(Ry, hcat(y)) + y_1 = Y[1, :] * gens(R_K) + + collect(terms(y_1[1] * y_1[1])) end - function generic_initial_ideal(I::MPolyIdeal) R = base_ring(I) n = nvars(R) Ry, y = polynomial_ring(R, :y => (1:n, 1:n)) + Y = matrix(Ry, hcat(y)) + gens_R = gens(R) + generic_ini_gens = MPolyRingElem[] - for g in I_K - findall(x -> !is_zero(x[2]), exponents(g)) - map(e -> Y[:, ], exponents(g)) + for g in gens(I) + monomials = exponents(g) + non_zero_exp_indices = (findall(x -> !is_zero(x), m) for m in monomials) + generic_gen = zero(Ry) + for (m, e) in zip(monomials, non_zero_exp_indices) + degrees = m[e] + multinomials = Y[e, :] * gens_R + generic_monomial = prod(zip(multinomials, degrees)) do (multinomial, d) + multinomial^d + end + generic_gen += generic_monomial + end + push!(generic_ini_gens, generic_gen) end - + return ideal(generic_ini_gens) end From 40175f8ce3e3177b7fb51a41454d7d1c41e3b92d Mon Sep 17 00:00:00 2001 From: antonydellavecchia Date: Mon, 8 Jan 2024 09:34:26 +0100 Subject: [PATCH 011/128] ext and sym shifting work, return algebras still neds work --- .../src/AlgebraicShifting.jl | 157 +++++++++++------- 1 file changed, 101 insertions(+), 56 deletions(-) diff --git a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl index c1960d36cd4b..5024a662d767 100644 --- a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl +++ b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl @@ -1,22 +1,66 @@ +function independent_columns(A::MatElem) + col_indices = Int[] + row_index = 1 + row_bound = nrows(A) + for col_index in 1:ncols(A) + + if !is_zero(A[row_index, col_index]) + push!(col_indices, col_index) + row_index += 1 + end + row_index > row_bound && break + end + return col_indices +end + +function apply_on_facets(f::Function, K::SimplicialComplex) + dim_K = dim(K) + K_facets = facets(K) + facet_dict = Dict( + (k => filter(f -> length(f) == k + 1, K_facets) for k in 1:dim_K ) + ) + for (dim_face, faces) in facet_dict + facet_dict[dim_face] = Set.(f((dim_face, faces))) + end + + return simplicial_complex( + reduce(vcat, values(facet_dict)) + ) +end + +function shift_basis_ext(F::Field, K::SimplicialComplex) + n = nvertices(K) + shifted_K = Oscar.delta_ext(F, K) + lambda, _ = exterior_algebra(F, n) + x = gens(lambda) + + ker_gens = [ + reduce(*, lift.( + x[collect(f)] + )) for f in minimal_nonfaces(K) + ] + + lift_ring = base_ring(lambda) + J = two_sided_ideal(lift_ring, (ker_gens)) + A, _ = quo(lift_ring, J + modulus(lambda)) + x = gens(A) + basis = [reduce(*, x[collect(s)]) for s in facets(shifted_K)] + + return A, basis +end + @doc raw""" delta_ext(K::SimplicialComplex) Returns the exterior shift of `K` """ -function delta_ext(K::SimplicialComplex) +function delta_ext(F::Field, K::SimplicialComplex) n = nvertices(K) - dim_K = dim(K) - cmp(S1, S2) = min(symdiff(S1, S2)...) in S1 - K_facets = sort(facets(K); lt=cmp) - - facet_dict = Dict( - (k => filter(f -> length(f) == k + 1, K_facets) for k in 1:dim_K ) - ) - - for (dim_face, faces) in facet_dict - Qx, x = polynomial_ring(QQ, :x => (1:n, 1:n)) - X = matrix(Qx, hcat(x)) + Fx, x = polynomial_ring(F, :x => (1:n, 1:n)) + apply_on_facets(K) do (dim_face, faces) + sort!(faces; lt=cmp) + X = matrix(Fx, hcat(x)) nCk = sort(subsets(n, dim_face + 1)) sub_compound_matrix = Vector{MPolyRingElem}[] @@ -29,26 +73,11 @@ function delta_ext(K::SimplicialComplex) end push!(sub_compound_matrix, row_minors) end - - A = matrix(Qx, sub_compound_matrix) + A = matrix(Fx, sub_compound_matrix) Oscar.ModStdQt.ref_ff_rc!(A) - - delta_k = Int[] - row_index = 1 - row_bound = nrows(A) - for col_index in 1:ncols(A) - if !is_zero(A[row_index, col_index]) - push!(delta_k, col_index) - row_index += 1 - end - - row_index > row_bound && break - end - facet_dict[dim_face] = map(Set, nCk[delta_k]) + delta_k = independent_columns(A) + return nCk[delta_k] end - return simplicial_complex( - reduce(vcat, values(facet_dict)) - ) end @doc raw""" @@ -57,35 +86,51 @@ end Returns the symmetric shift of `K` """ function delta_sym(K::SimplicialComplex) - R_K, quotient_map = stanley_reisner_ring(K) - Ry, y = polynomial_ring(R_K, :y => (1:n, 1:n)) - Y = matrix(Ry, hcat(y)) - y_1 = Y[1, :] * gens(R_K) - - collect(terms(y_1[1] * y_1[1])) -end + n = nvertices(K) + Ry, y = polynomial_ring(QQ, :y => (1:n, 1:n)) + Ryx, x = polynomial_ring(Ry, n) -function generic_initial_ideal(I::MPolyIdeal) - R = base_ring(I) - n = nvars(R) - Ry, y = polynomial_ring(R, :y => (1:n, 1:n)) - Y = matrix(Ry, hcat(y)) - gens_R = gens(R) - generic_ini_gens = MPolyRingElem[] + # we use a different ring to generate monomial_basis, coefficients need to be a field, + # but we want to avoid using fraction field of Ry during row reduction + mb_ring, z = graded_polynomial_ring(QQ, n) + o = monomial_ordering(mb_ring, :lex) + cmp_order(a, b) = cmp(o, a, b) <= 0 + + apply_on_facets(K) do (dim_face, faces) + r = dim_face + 1 + mb = sort(monomial_basis(mb_ring, r); lt=cmp_order) + + R_K, _ = stanley_reisner_ring(Ryx, K) + Y = matrix(Ry, hcat(y)) + A = Vector{MPolyRingElem}[] + + for b in mb + transformed_monomial = evaluate(b, Y * gens(R_K)) + generic_col = collect(coefficients(lift(transformed_monomial))) + push!(A, generic_col) + end + C = matrix(Ry, reduce(hcat, A)) + Oscar.ModStdQt.ref_ff_rc!(C) + + smallest_basis_el = z[r]^r + smallest_index = findfirst(a -> a == smallest_basis_el, mb) + col_indices = filter(x -> x >= smallest_index, independent_columns(C)) + generic_monomial_exponents = first.(exponents.(mb[col_indices])) - for g in gens(I) - monomials = exponents(g) - non_zero_exp_indices = (findall(x -> !is_zero(x), m) for m in monomials) - generic_gen = zero(Ry) - for (m, e) in zip(monomials, non_zero_exp_indices) - degrees = m[e] - multinomials = Y[e, :] * gens_R - generic_monomial = prod(zip(multinomials, degrees)) do (multinomial, d) - multinomial^d + shifted_sets = Vector{Int}[] + for me in generic_monomial_exponents + shifted_set = Int[] + for (i, e) in enumerate(me) + if is_zero(e) + continue + else + for j in 1:e + push!(shifted_set, i - r + j) + end + end end - generic_gen += generic_monomial + push!(shifted_sets, shifted_set) end - push!(generic_ini_gens, generic_gen) + return shifted_sets end - return ideal(generic_ini_gens) end From ddd84b5dc866db5b837136c4916c8db3c6895419 Mon Sep 17 00:00:00 2001 From: Antony Della Vecchia Date: Mon, 8 Jan 2024 20:38:49 +0100 Subject: [PATCH 012/128] updtes to delta_sym --- .../src/#AlgebraicShifting.jl# | 142 ++++++++++++++++++ .../src/AlgebraicShifting.jl | 20 ++- 2 files changed, 155 insertions(+), 7 deletions(-) create mode 100644 experimental/AlgebraicShifting/src/#AlgebraicShifting.jl# diff --git a/experimental/AlgebraicShifting/src/#AlgebraicShifting.jl# b/experimental/AlgebraicShifting/src/#AlgebraicShifting.jl# new file mode 100644 index 000000000000..ef7832233faf --- /dev/null +++ b/experimental/AlgebraicShifting/src/#AlgebraicShifting.jl# @@ -0,0 +1,142 @@ +function independent_columns(A::MatElem) + col_indices = Int[] + row_index = 1 + row_bound = nrows(A) + for col_index in 1:ncols(A) + + if !is_zero(A[row_index, col_index]) + push!(col_indices, col_index) + row_index += 1 + end + row_index > row_bound && break + end + return col_indices +end + +# applies function on facets of equal dimension +function apply_on_facets(f::Function, K::SimplicialComplex) + dim_K = dim(K) + K_facets = facets(K) + facet_dict = Dict( + (k => filter(f -> length(f) == k + 1, K_facets) for k in 1:dim_K ) + ) + for (dim_face, faces) in facet_dict + facet_dict[dim_face] = Set.(f((dim_face, faces))) + end + return facet_dict +end + +function shift_basis_ext(F::Field, K::SimplicialComplex) + n = nvertices(K) + shifted_K = Oscar.delta_ext(F, K) + lambda, _ = exterior_algebra(F, n) + x = gens(lambda) + + ker_gens = [ + reduce(*, lift.( + x[collect(f)] + )) for f in minimal_nonfaces(K) + ] + + lift_ring = base_ring(lambda) + J = two_sided_ideal(lift_ring, (ker_gens)) + A, _ = quo(lift_ring, J + modulus(lambda)) + x = gens(A) + basis = [reduce(*, x[collect(s)]) for s in facets(shifted_K)] + + return A, basis +end + +@doc raw""" + delta_ext(K::SimplicialComplex) + +Returns the exterior shift of `K` +""" +function delta_ext(F::Field, K::SimplicialComplex) + n = nvertices(K) + cmp(S1, S2) = min(symdiff(S1, S2)...) in S1 + Fx, x = polynomial_ring(F, :x => (1:n, 1:n)) + facet_dict = apply_on_facets(K) do (dim_face, faces) + sort!(faces; lt=cmp) + X = matrix(Fx, hcat(x)) + nCk = sort(subsets(n, dim_face + 1)) + sub_compound_matrix = Vector{MPolyRingElem}[] + + for col_subset in nCk + row_minors = MPolyRingElem[] + for row_subset in faces + ri = collect(row_subset) + ci = collect(col_subset) + push!(row_minors, det(X[ri, ci])) + end + push!(sub_compound_matrix, row_minors) + end + A = matrix(Fx, sub_compound_matrix) + Oscar.ModStdQt.ref_ff_rc!(A) + delta_k = independent_columns(A) + return nCk[delta_k] + end + + return simplicial_complex( + reduce(vcat, values(facet_dict)) + ) +end + +@doc raw""" + delta_sym(K::SimplicialComplex) + +Returns the symmetric shift of `K` +""" +function delta_sym(F::Field, K::SimplicialComplex) + n = nvertices(K) + Fy, y = polynomial_ring(F, :y => (1:n, 1:n)) + Fyx, x = polynomial_ring(Fy, n) + + # we use a different ring to generate monomial_basis, coefficients need to be a field, + # but we want to avoid using fraction field of Ry during row reduction + mb_ring, z = graded_polynomial_ring(F, n) + o = monomial_ordering(mb_ring, :lex) + cmp_order(a, b) = cmp(o, a, b) > 0 + + facet_dict = apply_on_facets(K) do (dim_face, faces) + r = dim_face + 1 + mb = sort(monomial_basis(mb_ring, r); lt=cmp_order) + + R_K, _ = stanley_reisner_ring(Ryx, K) + Y = matrix(Ry, hcat(y)) + A = Vector{MPolyRingElem}[] + + for b in mb + transformed_monomial = evaluate(b, Y * gens(R_K)) + generic_col = collect(coefficients(lift(transformed_monomial))) + push!(A, generic_col) + end + C = matrix(Ry, reduce(hcat, A)) + Oscar.ModStdQt.ref_ff_rc!(C) + + smallest_basis_el = z[r]^r + smallest_index = findfirst(a -> a == smallest_basis_el, mb) + col_indices = filter(x -> x >= smallest_index, independent_columns(C)) + generic_monomial_exponents = first.(exponents.(mb[col_indices])) + + shifted_sets = Vector{Int}[] + for me in generic_monomial_exponents + shifted_set = Int[] + for (i, e) in enumerate(me) + if is_zero(e) + continue + else + for j in 1:e + push!(shifted_set, i - r + j) + end + end + end + push!(shifted_sets, shifted_set) + end + return shifted_sets + end + + return simplicial_complex( + reduce(vcat, values(facet_dict)) + ) +end diff --git a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl index 5024a662d767..43f4556e4d9f 100644 --- a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl +++ b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl @@ -13,6 +13,7 @@ function independent_columns(A::MatElem) return col_indices end +# applies function on facets of equal dimension function apply_on_facets(f::Function, K::SimplicialComplex) dim_K = dim(K) K_facets = facets(K) @@ -22,10 +23,7 @@ function apply_on_facets(f::Function, K::SimplicialComplex) for (dim_face, faces) in facet_dict facet_dict[dim_face] = Set.(f((dim_face, faces))) end - - return simplicial_complex( - reduce(vcat, values(facet_dict)) - ) + return facet_dict end function shift_basis_ext(F::Field, K::SimplicialComplex) @@ -58,7 +56,7 @@ function delta_ext(F::Field, K::SimplicialComplex) n = nvertices(K) cmp(S1, S2) = min(symdiff(S1, S2)...) in S1 Fx, x = polynomial_ring(F, :x => (1:n, 1:n)) - apply_on_facets(K) do (dim_face, faces) + facet_dict = apply_on_facets(K) do (dim_face, faces) sort!(faces; lt=cmp) X = matrix(Fx, hcat(x)) nCk = sort(subsets(n, dim_face + 1)) @@ -78,6 +76,10 @@ function delta_ext(F::Field, K::SimplicialComplex) delta_k = independent_columns(A) return nCk[delta_k] end + + return simplicial_complex( + reduce(vcat, values(facet_dict)) + ) end @doc raw""" @@ -94,9 +96,9 @@ function delta_sym(K::SimplicialComplex) # but we want to avoid using fraction field of Ry during row reduction mb_ring, z = graded_polynomial_ring(QQ, n) o = monomial_ordering(mb_ring, :lex) - cmp_order(a, b) = cmp(o, a, b) <= 0 + cmp_order(a, b) = cmp(o, a, b) > 0 - apply_on_facets(K) do (dim_face, faces) + facet_dict = apply_on_facets(K) do (dim_face, faces) r = dim_face + 1 mb = sort(monomial_basis(mb_ring, r); lt=cmp_order) @@ -133,4 +135,8 @@ function delta_sym(K::SimplicialComplex) end return shifted_sets end + + return simplicial_complex( + reduce(vcat, values(facet_dict)) + ) end From dccec997e09216966665792089935a8b18658bd7 Mon Sep 17 00:00:00 2001 From: antonydellavecchia Date: Wed, 10 Jan 2024 10:07:47 +0100 Subject: [PATCH 013/128] added field for sym shift --- .../src/#AlgebraicShifting.jl# | 142 ------------------ .../src/AlgebraicShifting.jl | 15 +- 2 files changed, 7 insertions(+), 150 deletions(-) delete mode 100644 experimental/AlgebraicShifting/src/#AlgebraicShifting.jl# diff --git a/experimental/AlgebraicShifting/src/#AlgebraicShifting.jl# b/experimental/AlgebraicShifting/src/#AlgebraicShifting.jl# deleted file mode 100644 index ef7832233faf..000000000000 --- a/experimental/AlgebraicShifting/src/#AlgebraicShifting.jl# +++ /dev/null @@ -1,142 +0,0 @@ -function independent_columns(A::MatElem) - col_indices = Int[] - row_index = 1 - row_bound = nrows(A) - for col_index in 1:ncols(A) - - if !is_zero(A[row_index, col_index]) - push!(col_indices, col_index) - row_index += 1 - end - row_index > row_bound && break - end - return col_indices -end - -# applies function on facets of equal dimension -function apply_on_facets(f::Function, K::SimplicialComplex) - dim_K = dim(K) - K_facets = facets(K) - facet_dict = Dict( - (k => filter(f -> length(f) == k + 1, K_facets) for k in 1:dim_K ) - ) - for (dim_face, faces) in facet_dict - facet_dict[dim_face] = Set.(f((dim_face, faces))) - end - return facet_dict -end - -function shift_basis_ext(F::Field, K::SimplicialComplex) - n = nvertices(K) - shifted_K = Oscar.delta_ext(F, K) - lambda, _ = exterior_algebra(F, n) - x = gens(lambda) - - ker_gens = [ - reduce(*, lift.( - x[collect(f)] - )) for f in minimal_nonfaces(K) - ] - - lift_ring = base_ring(lambda) - J = two_sided_ideal(lift_ring, (ker_gens)) - A, _ = quo(lift_ring, J + modulus(lambda)) - x = gens(A) - basis = [reduce(*, x[collect(s)]) for s in facets(shifted_K)] - - return A, basis -end - -@doc raw""" - delta_ext(K::SimplicialComplex) - -Returns the exterior shift of `K` -""" -function delta_ext(F::Field, K::SimplicialComplex) - n = nvertices(K) - cmp(S1, S2) = min(symdiff(S1, S2)...) in S1 - Fx, x = polynomial_ring(F, :x => (1:n, 1:n)) - facet_dict = apply_on_facets(K) do (dim_face, faces) - sort!(faces; lt=cmp) - X = matrix(Fx, hcat(x)) - nCk = sort(subsets(n, dim_face + 1)) - sub_compound_matrix = Vector{MPolyRingElem}[] - - for col_subset in nCk - row_minors = MPolyRingElem[] - for row_subset in faces - ri = collect(row_subset) - ci = collect(col_subset) - push!(row_minors, det(X[ri, ci])) - end - push!(sub_compound_matrix, row_minors) - end - A = matrix(Fx, sub_compound_matrix) - Oscar.ModStdQt.ref_ff_rc!(A) - delta_k = independent_columns(A) - return nCk[delta_k] - end - - return simplicial_complex( - reduce(vcat, values(facet_dict)) - ) -end - -@doc raw""" - delta_sym(K::SimplicialComplex) - -Returns the symmetric shift of `K` -""" -function delta_sym(F::Field, K::SimplicialComplex) - n = nvertices(K) - Fy, y = polynomial_ring(F, :y => (1:n, 1:n)) - Fyx, x = polynomial_ring(Fy, n) - - # we use a different ring to generate monomial_basis, coefficients need to be a field, - # but we want to avoid using fraction field of Ry during row reduction - mb_ring, z = graded_polynomial_ring(F, n) - o = monomial_ordering(mb_ring, :lex) - cmp_order(a, b) = cmp(o, a, b) > 0 - - facet_dict = apply_on_facets(K) do (dim_face, faces) - r = dim_face + 1 - mb = sort(monomial_basis(mb_ring, r); lt=cmp_order) - - R_K, _ = stanley_reisner_ring(Ryx, K) - Y = matrix(Ry, hcat(y)) - A = Vector{MPolyRingElem}[] - - for b in mb - transformed_monomial = evaluate(b, Y * gens(R_K)) - generic_col = collect(coefficients(lift(transformed_monomial))) - push!(A, generic_col) - end - C = matrix(Ry, reduce(hcat, A)) - Oscar.ModStdQt.ref_ff_rc!(C) - - smallest_basis_el = z[r]^r - smallest_index = findfirst(a -> a == smallest_basis_el, mb) - col_indices = filter(x -> x >= smallest_index, independent_columns(C)) - generic_monomial_exponents = first.(exponents.(mb[col_indices])) - - shifted_sets = Vector{Int}[] - for me in generic_monomial_exponents - shifted_set = Int[] - for (i, e) in enumerate(me) - if is_zero(e) - continue - else - for j in 1:e - push!(shifted_set, i - r + j) - end - end - end - push!(shifted_sets, shifted_set) - end - return shifted_sets - end - - return simplicial_complex( - reduce(vcat, values(facet_dict)) - ) -end diff --git a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl index 43f4556e4d9f..3209e44eb18e 100644 --- a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl +++ b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl @@ -3,7 +3,6 @@ function independent_columns(A::MatElem) row_index = 1 row_bound = nrows(A) for col_index in 1:ncols(A) - if !is_zero(A[row_index, col_index]) push!(col_indices, col_index) row_index += 1 @@ -87,14 +86,14 @@ end Returns the symmetric shift of `K` """ -function delta_sym(K::SimplicialComplex) +function delta_sym(F::Field, K::SimplicialComplex) n = nvertices(K) - Ry, y = polynomial_ring(QQ, :y => (1:n, 1:n)) - Ryx, x = polynomial_ring(Ry, n) + Fy, y = polynomial_ring(F, :y => (1:n, 1:n)) + Fyx, x = polynomial_ring(Fy, n) # we use a different ring to generate monomial_basis, coefficients need to be a field, # but we want to avoid using fraction field of Ry during row reduction - mb_ring, z = graded_polynomial_ring(QQ, n) + mb_ring, z = graded_polynomial_ring(F, n) o = monomial_ordering(mb_ring, :lex) cmp_order(a, b) = cmp(o, a, b) > 0 @@ -102,8 +101,8 @@ function delta_sym(K::SimplicialComplex) r = dim_face + 1 mb = sort(monomial_basis(mb_ring, r); lt=cmp_order) - R_K, _ = stanley_reisner_ring(Ryx, K) - Y = matrix(Ry, hcat(y)) + R_K, _ = stanley_reisner_ring(Fyx, K) + Y = matrix(Fy, hcat(y)) A = Vector{MPolyRingElem}[] for b in mb @@ -111,7 +110,7 @@ function delta_sym(K::SimplicialComplex) generic_col = collect(coefficients(lift(transformed_monomial))) push!(A, generic_col) end - C = matrix(Ry, reduce(hcat, A)) + C = matrix(Fy, reduce(hcat, A)) Oscar.ModStdQt.ref_ff_rc!(C) smallest_basis_el = z[r]^r From 295fcffc01039d26aa51538f2812830ae4a854e6 Mon Sep 17 00:00:00 2001 From: Antony Della Vecchia Date: Wed, 10 Jan 2024 19:05:14 +0100 Subject: [PATCH 014/128] fixed apply on facets --- .../src/AlgebraicShifting.jl | 32 ++++++++++++------- 1 file changed, 20 insertions(+), 12 deletions(-) diff --git a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl index 3209e44eb18e..f93349e252a7 100644 --- a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl +++ b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl @@ -13,16 +13,28 @@ function independent_columns(A::MatElem) end # applies function on facets of equal dimension -function apply_on_facets(f::Function, K::SimplicialComplex) +function apply_on_faces(f::Function, K::SimplicialComplex) dim_K = dim(K) K_facets = facets(K) facet_dict = Dict( - (k => filter(f -> length(f) == k + 1, K_facets) for k in 1:dim_K ) + (k => Set(filter(f -> length(f) == k + 1, K_facets)) for k in 1:dim_K ) ) + + for facet in K_facets + dim_facet = length(facet) - 1 + + for subset_size in 2:dim_facet + for subset in subsets(facet, subset_size) + push!(facet_dict[subset_size - 1], subset) + end + end + end + + input_faces = Vector{Int}[] for (dim_face, faces) in facet_dict - facet_dict[dim_face] = Set.(f((dim_face, faces))) + input_faces = vcat(input_faces, f((dim_face, collect.(faces)))) end - return facet_dict + return input_faces end function shift_basis_ext(F::Field, K::SimplicialComplex) @@ -55,7 +67,7 @@ function delta_ext(F::Field, K::SimplicialComplex) n = nvertices(K) cmp(S1, S2) = min(symdiff(S1, S2)...) in S1 Fx, x = polynomial_ring(F, :x => (1:n, 1:n)) - facet_dict = apply_on_facets(K) do (dim_face, faces) + input_faces = apply_on_faces(K) do (dim_face, faces) sort!(faces; lt=cmp) X = matrix(Fx, hcat(x)) nCk = sort(subsets(n, dim_face + 1)) @@ -76,9 +88,7 @@ function delta_ext(F::Field, K::SimplicialComplex) return nCk[delta_k] end - return simplicial_complex( - reduce(vcat, values(facet_dict)) - ) + return simplicial_complex(input_faces) end @doc raw""" @@ -97,7 +107,7 @@ function delta_sym(F::Field, K::SimplicialComplex) o = monomial_ordering(mb_ring, :lex) cmp_order(a, b) = cmp(o, a, b) > 0 - facet_dict = apply_on_facets(K) do (dim_face, faces) + input_faces = apply_on_faces(K) do (dim_face, faces) r = dim_face + 1 mb = sort(monomial_basis(mb_ring, r); lt=cmp_order) @@ -135,7 +145,5 @@ function delta_sym(F::Field, K::SimplicialComplex) return shifted_sets end - return simplicial_complex( - reduce(vcat, values(facet_dict)) - ) + return simplicial_complex(input_faces) end From 27c72c0a024e86ac8ec19911edb01eb1065628f2 Mon Sep 17 00:00:00 2001 From: antonydellavecchia Date: Wed, 10 Jan 2024 23:19:28 +0100 Subject: [PATCH 015/128] delta_sym bug fixed --- .../src/AlgebraicShifting.jl | 19 +++++++++---------- 1 file changed, 9 insertions(+), 10 deletions(-) diff --git a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl index f93349e252a7..88725a991902 100644 --- a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl +++ b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl @@ -106,18 +106,19 @@ function delta_sym(F::Field, K::SimplicialComplex) mb_ring, z = graded_polynomial_ring(F, n) o = monomial_ordering(mb_ring, :lex) cmp_order(a, b) = cmp(o, a, b) > 0 + R_K, _ = stanley_reisner_ring(Fyx, K) input_faces = apply_on_faces(K) do (dim_face, faces) r = dim_face + 1 mb = sort(monomial_basis(mb_ring, r); lt=cmp_order) - - R_K, _ = stanley_reisner_ring(Fyx, K) Y = matrix(Fy, hcat(y)) A = Vector{MPolyRingElem}[] - + for b in mb transformed_monomial = evaluate(b, Y * gens(R_K)) - generic_col = collect(coefficients(lift(transformed_monomial))) + # this part will need to be adjusted for finite fields + non_zero_terms = filter(x -> !is_zero(R_K(x)), collect(terms(lift(transformed_monomial)))) + generic_col = first.(coefficients.(non_zero_terms)) push!(A, generic_col) end C = matrix(Fy, reduce(hcat, A)) @@ -131,13 +132,11 @@ function delta_sym(F::Field, K::SimplicialComplex) shifted_sets = Vector{Int}[] for me in generic_monomial_exponents shifted_set = Int[] + index_count = 1 for (i, e) in enumerate(me) - if is_zero(e) - continue - else - for j in 1:e - push!(shifted_set, i - r + j) - end + for j in 1:e + push!(shifted_set, i - (r - index_count)) + index_count += 1 end end push!(shifted_sets, shifted_set) From 398d1f94c4884053c53357042a5296222ff40afd Mon Sep 17 00:00:00 2001 From: antonydellavecchia Date: Tue, 16 Jan 2024 23:22:53 +0100 Subject: [PATCH 016/128] added fix for delta_sym with finite fields --- experimental/AlgebraicShifting/src/AlgebraicShifting.jl | 5 +++-- 1 file changed, 3 insertions(+), 2 deletions(-) diff --git a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl index 88725a991902..1314aebbe0a7 100644 --- a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl +++ b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl @@ -116,8 +116,9 @@ function delta_sym(F::Field, K::SimplicialComplex) for b in mb transformed_monomial = evaluate(b, Y * gens(R_K)) - # this part will need to be adjusted for finite fields - non_zero_terms = filter(x -> !is_zero(R_K(x)), collect(terms(lift(transformed_monomial)))) + # this can be moved outside loop at some point + non_zero_terms = filter(x -> !is_zero(R_K(x)), + collect(monomials(lift(transformed_monomial)))) generic_col = first.(coefficients.(non_zero_terms)) push!(A, generic_col) end From 3762f5a000e839ad18eda1fbad8f1792915583eb Mon Sep 17 00:00:00 2001 From: antonydellavecchia Date: Wed, 17 Jan 2024 15:07:04 +0100 Subject: [PATCH 017/128] Revert "added fix for delta_sym with finite fields" This reverts commit 398d1f94c4884053c53357042a5296222ff40afd. --- experimental/AlgebraicShifting/src/AlgebraicShifting.jl | 5 ++--- 1 file changed, 2 insertions(+), 3 deletions(-) diff --git a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl index 1314aebbe0a7..88725a991902 100644 --- a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl +++ b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl @@ -116,9 +116,8 @@ function delta_sym(F::Field, K::SimplicialComplex) for b in mb transformed_monomial = evaluate(b, Y * gens(R_K)) - # this can be moved outside loop at some point - non_zero_terms = filter(x -> !is_zero(R_K(x)), - collect(monomials(lift(transformed_monomial)))) + # this part will need to be adjusted for finite fields + non_zero_terms = filter(x -> !is_zero(R_K(x)), collect(terms(lift(transformed_monomial)))) generic_col = first.(coefficients.(non_zero_terms)) push!(A, generic_col) end From 33d59f3ae261d0f0edcc7b90b226f47fa1778ffc Mon Sep 17 00:00:00 2001 From: antonydellavecchia Date: Wed, 24 Jan 2024 11:36:50 +0100 Subject: [PATCH 018/128] name changes --- .../AlgebraicShifting/src/AlgebraicShifting.jl | 11 ++++++----- 1 file changed, 6 insertions(+), 5 deletions(-) diff --git a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl index 88725a991902..9a07770edb39 100644 --- a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl +++ b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl @@ -12,7 +12,7 @@ function independent_columns(A::MatElem) return col_indices end -# applies function on facets of equal dimension +# applies function on faces of equal dimension function apply_on_faces(f::Function, K::SimplicialComplex) dim_K = dim(K) K_facets = facets(K) @@ -59,15 +59,16 @@ function shift_basis_ext(F::Field, K::SimplicialComplex) end @doc raw""" - delta_ext(K::SimplicialComplex) + exterior_shift(K::SimplicialComplex) Returns the exterior shift of `K` """ -function delta_ext(F::Field, K::SimplicialComplex) +function exterior_shift(F::Field, K::SimplicialComplex) n = nvertices(K) cmp(S1, S2) = min(symdiff(S1, S2)...) in S1 Fx, x = polynomial_ring(F, :x => (1:n, 1:n)) input_faces = apply_on_faces(K) do (dim_face, faces) + println("shifting faces of dim $dim_face") sort!(faces; lt=cmp) X = matrix(Fx, hcat(x)) nCk = sort(subsets(n, dim_face + 1)) @@ -92,11 +93,11 @@ function delta_ext(F::Field, K::SimplicialComplex) end @doc raw""" - delta_sym(K::SimplicialComplex) + symmetric_shift(K::SimplicialComplex) Returns the symmetric shift of `K` """ -function delta_sym(F::Field, K::SimplicialComplex) +function symmetric_shift(F::Field, K::SimplicialComplex) n = nvertices(K) Fy, y = polynomial_ring(F, :y => (1:n, 1:n)) Fyx, x = polynomial_ring(Fy, n) From be99cbdc4f3b25ed0b4ed8e1a034d913b1622a8c Mon Sep 17 00:00:00 2001 From: Antony Della Vecchia Date: Tue, 13 Feb 2024 15:27:59 +0100 Subject: [PATCH 019/128] optional change_of_basis --- .../src/AlgebraicShifting.jl | 38 +++++++++++++------ 1 file changed, 27 insertions(+), 11 deletions(-) diff --git a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl index 9a07770edb39..e1b900b05764 100644 --- a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl +++ b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl @@ -59,32 +59,48 @@ function shift_basis_ext(F::Field, K::SimplicialComplex) end @doc raw""" - exterior_shift(K::SimplicialComplex) + exterior_shift(F::Field, K::SimplicialComplex) Returns the exterior shift of `K` """ -function exterior_shift(F::Field, K::SimplicialComplex) +function exterior_shift(F::Field, K::SimplicialComplex; + change_of_basis::T = nothing) where T <: Union{Nothing, MatrixGroupElem} n = nvertices(K) + if isnothing(change_of_basis) + Fx, x = polynomial_ring(F, :x => (1:n, 1:n)) + change_of_basis = matrix(Fx, hcat(x)) + matrix_base = Fx + else + change_of_basis = matrix(change_of_basis) + matrix_base = base_ring(change_of_basis) + end + cmp(S1, S2) = min(symdiff(S1, S2)...) in S1 - Fx, x = polynomial_ring(F, :x => (1:n, 1:n)) + input_faces = apply_on_faces(K) do (dim_face, faces) - println("shifting faces of dim $dim_face") sort!(faces; lt=cmp) - X = matrix(Fx, hcat(x)) nCk = sort(subsets(n, dim_face + 1)) - sub_compound_matrix = Vector{MPolyRingElem}[] + entry_type = elem_type(matrix_base) + + sub_compound_matrix = Vector{entry_type}[] for col_subset in nCk - row_minors = MPolyRingElem[] + row_minors = entry_type[] for row_subset in faces ri = collect(row_subset) ci = collect(col_subset) - push!(row_minors, det(X[ri, ci])) + push!(row_minors, det(change_of_basis[ri, ci])) end push!(sub_compound_matrix, row_minors) end - A = matrix(Fx, sub_compound_matrix) - Oscar.ModStdQt.ref_ff_rc!(A) + + A = matrix(matrix_base, sub_compound_matrix) + + if isnothing(change_of_basis) + Oscar.ModStdQt.ref_ff_rc!(A) + else + rref!(A) + end delta_k = independent_columns(A) return nCk[delta_k] end @@ -93,7 +109,7 @@ function exterior_shift(F::Field, K::SimplicialComplex) end @doc raw""" - symmetric_shift(K::SimplicialComplex) + symmetric_shift(F::Field, K::SimplicialComplex) Returns the symmetric shift of `K` """ From 163b843305e0559a7d26eda3ca46ecb96b2ebb57 Mon Sep 17 00:00:00 2001 From: Antony Della Vecchia Date: Wed, 14 Feb 2024 10:35:45 +0100 Subject: [PATCH 020/128] fix regression --- experimental/AlgebraicShifting/src/AlgebraicShifting.jl | 5 ++--- 1 file changed, 2 insertions(+), 3 deletions(-) diff --git a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl index e1b900b05764..f1e21b96d6ca 100644 --- a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl +++ b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl @@ -64,14 +64,13 @@ end Returns the exterior shift of `K` """ function exterior_shift(F::Field, K::SimplicialComplex; - change_of_basis::T = nothing) where T <: Union{Nothing, MatrixGroupElem} + change_of_basis::T = nothing) where T <: Union{Nothing, MatElem} n = nvertices(K) if isnothing(change_of_basis) Fx, x = polynomial_ring(F, :x => (1:n, 1:n)) change_of_basis = matrix(Fx, hcat(x)) matrix_base = Fx else - change_of_basis = matrix(change_of_basis) matrix_base = base_ring(change_of_basis) end @@ -96,7 +95,7 @@ function exterior_shift(F::Field, K::SimplicialComplex; A = matrix(matrix_base, sub_compound_matrix) - if isnothing(change_of_basis) + if matrix_base == Fx Oscar.ModStdQt.ref_ff_rc!(A) else rref!(A) From 02c134ffcbaa9560be3a9eae2f471298424c13f6 Mon Sep 17 00:00:00 2001 From: antonydellavecchia Date: Wed, 14 Feb 2024 16:08:21 +0100 Subject: [PATCH 021/128] added some comments --- experimental/AlgebraicShifting/src/AlgebraicShifting.jl | 6 ++++++ 1 file changed, 6 insertions(+) diff --git a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl index 9a07770edb39..4a12b1125550 100644 --- a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl +++ b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl @@ -107,6 +107,8 @@ function symmetric_shift(F::Field, K::SimplicialComplex) mb_ring, z = graded_polynomial_ring(F, n) o = monomial_ordering(mb_ring, :lex) cmp_order(a, b) = cmp(o, a, b) > 0 + + # the generators of the stanley reisner ideal are combinations of [x_1, ..., x_n] R_K, _ = stanley_reisner_ring(Fyx, K) input_faces = apply_on_faces(K) do (dim_face, faces) @@ -119,6 +121,10 @@ function symmetric_shift(F::Field, K::SimplicialComplex) transformed_monomial = evaluate(b, Y * gens(R_K)) # this part will need to be adjusted for finite fields non_zero_terms = filter(x -> !is_zero(R_K(x)), collect(terms(lift(transformed_monomial)))) + + # coefficients is a function for polynomials but since we are looking at the terms + # i.e. we are seperating by monomials already, we know the first coefficient is just + # the coefficient of the monomial generic_col = first.(coefficients.(non_zero_terms)) push!(A, generic_col) end From 79bced65152e29efc268dacbe1237bd5e07b3a83 Mon Sep 17 00:00:00 2001 From: antonydellavecchia Date: Wed, 14 Feb 2024 21:42:51 +0100 Subject: [PATCH 022/128] cond fix --- experimental/AlgebraicShifting/src/AlgebraicShifting.jl | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl index a9461d36102c..5561be53fe35 100644 --- a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl +++ b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl @@ -95,7 +95,7 @@ function exterior_shift(F::Field, K::SimplicialComplex; A = matrix(matrix_base, sub_compound_matrix) - if matrix_base == Fx + if matrix_base isa MPolyRing Oscar.ModStdQt.ref_ff_rc!(A) else rref!(A) From 251ceaa87ec0ffaa8373f0930e1d8c936a791afd Mon Sep 17 00:00:00 2001 From: antonydellavecchia Date: Tue, 20 Feb 2024 16:45:14 +0100 Subject: [PATCH 023/128] adds comments --- .../src/AlgebraicShifting.jl | 24 ++++++++++++++++--- 1 file changed, 21 insertions(+), 3 deletions(-) diff --git a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl index 5561be53fe35..a301e6f924e3 100644 --- a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl +++ b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl @@ -19,6 +19,8 @@ function apply_on_faces(f::Function, K::SimplicialComplex) facet_dict = Dict( (k => Set(filter(f -> length(f) == k + 1, K_facets)) for k in 1:dim_K ) ) + + # look into hasse diagram from polymake for facet in K_facets dim_facet = length(facet) - 1 @@ -65,8 +67,13 @@ Returns the exterior shift of `K` """ function exterior_shift(F::Field, K::SimplicialComplex; change_of_basis::T = nothing) where T <: Union{Nothing, MatElem} + # the exterior shifting works in a different algebra that lends + # itself to an easier implementation n = nvertices(K) + is_generic = false if isnothing(change_of_basis) + is_generic = true + # generic change of basis Fx, x = polynomial_ring(F, :x => (1:n, 1:n)) change_of_basis = matrix(Fx, hcat(x)) matrix_base = Fx @@ -74,10 +81,11 @@ function exterior_shift(F::Field, K::SimplicialComplex; matrix_base = base_ring(change_of_basis) end + # might not be needed cmp(S1, S2) = min(symdiff(S1, S2)...) in S1 input_faces = apply_on_faces(K) do (dim_face, faces) - sort!(faces; lt=cmp) + # look into why there is sort here nCk = sort(subsets(n, dim_face + 1)) entry_type = elem_type(matrix_base) @@ -95,7 +103,7 @@ function exterior_shift(F::Field, K::SimplicialComplex; A = matrix(matrix_base, sub_compound_matrix) - if matrix_base isa MPolyRing + if is_generic Oscar.ModStdQt.ref_ff_rc!(A) else rref!(A) @@ -111,12 +119,14 @@ end symmetric_shift(F::Field, K::SimplicialComplex) Returns the symmetric shift of `K` + +see survey on algebraic shifting Gil Kalai (properly cite at some point) """ function symmetric_shift(F::Field, K::SimplicialComplex) n = nvertices(K) Fy, y = polynomial_ring(F, :y => (1:n, 1:n)) Fyx, x = polynomial_ring(Fy, n) - + # the computation is a over the field of fractions Fyx # we use a different ring to generate monomial_basis, coefficients need to be a field, # but we want to avoid using fraction field of Ry during row reduction mb_ring, z = graded_polynomial_ring(F, n) @@ -128,13 +138,21 @@ function symmetric_shift(F::Field, K::SimplicialComplex) input_faces = apply_on_faces(K) do (dim_face, faces) r = dim_face + 1 + + # look into sorts mb = sort(monomial_basis(mb_ring, r); lt=cmp_order) Y = matrix(Fy, hcat(y)) A = Vector{MPolyRingElem}[] for b in mb + # need to compare with some alternatives transformed_monomial = evaluate(b, Y * gens(R_K)) + + # double check this line + # is stanley reisner ring over Z needed to then reduce later + # stanley reisner over F is cheaper # this part will need to be adjusted for finite fields + # there should be no lifting non_zero_terms = filter(x -> !is_zero(R_K(x)), collect(terms(lift(transformed_monomial)))) # coefficients is a function for polynomials but since we are looking at the terms From 055513378e7c83a8148f34e6085276fdb5cf18e8 Mon Sep 17 00:00:00 2001 From: Antony Della Vecchia Date: Tue, 20 Feb 2024 17:13:25 +0100 Subject: [PATCH 024/128] starting tests --- experimental/AlgebraicShifting/test/runtests.jl | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/experimental/AlgebraicShifting/test/runtests.jl b/experimental/AlgebraicShifting/test/runtests.jl index 85a7ef3f1fa6..a81a23a62d75 100644 --- a/experimental/AlgebraicShifting/test/runtests.jl +++ b/experimental/AlgebraicShifting/test/runtests.jl @@ -1,4 +1,4 @@ -@testset "Experimental template tests" begin - S = Oscar.ExampleStruct(5) - @test 5 == Oscar.my_access_func(S) +@testset "Exterior Shift" begin + K = simplicial_complex([[1, 2, 3], [1, 4]]) + end From f6149981d062ff7caf896a07bd17ca5f60fbb2ef Mon Sep 17 00:00:00 2001 From: Antony Della Vecchia Date: Tue, 20 Feb 2024 18:46:58 +0100 Subject: [PATCH 025/128] oscar updates --- experimental/AlgebraicShifting/src/AlgebraicShifting.jl | 6 +++--- experimental/AlgebraicShifting/test/runtests.jl | 5 +++-- 2 files changed, 6 insertions(+), 5 deletions(-) diff --git a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl index 5561be53fe35..1e5f9f196476 100644 --- a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl +++ b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl @@ -38,7 +38,7 @@ function apply_on_faces(f::Function, K::SimplicialComplex) end function shift_basis_ext(F::Field, K::SimplicialComplex) - n = nvertices(K) + n = n_vertices(K) shifted_K = Oscar.delta_ext(F, K) lambda, _ = exterior_algebra(F, n) x = gens(lambda) @@ -65,7 +65,7 @@ Returns the exterior shift of `K` """ function exterior_shift(F::Field, K::SimplicialComplex; change_of_basis::T = nothing) where T <: Union{Nothing, MatElem} - n = nvertices(K) + n = n_vertices(K) if isnothing(change_of_basis) Fx, x = polynomial_ring(F, :x => (1:n, 1:n)) change_of_basis = matrix(Fx, hcat(x)) @@ -113,7 +113,7 @@ end Returns the symmetric shift of `K` """ function symmetric_shift(F::Field, K::SimplicialComplex) - n = nvertices(K) + n = n_vertices(K) Fy, y = polynomial_ring(F, :y => (1:n, 1:n)) Fyx, x = polynomial_ring(Fy, n) diff --git a/experimental/AlgebraicShifting/test/runtests.jl b/experimental/AlgebraicShifting/test/runtests.jl index a81a23a62d75..4f9023ad7bef 100644 --- a/experimental/AlgebraicShifting/test/runtests.jl +++ b/experimental/AlgebraicShifting/test/runtests.jl @@ -1,4 +1,5 @@ -@testset "Exterior Shift" begin +@testset "Algebraic Shifting" begin K = simplicial_complex([[1, 2, 3], [1, 4]]) - + k_ext = Oscar.exterior_shift(GF(2), K) + k_sym = Oscar.symmetric_shift(QQ, K) end From e05fb2ff0a22acac40ed9c4138e122ad4b33a79a Mon Sep 17 00:00:00 2001 From: antonydellavecchia Date: Thu, 22 Feb 2024 15:20:45 +0100 Subject: [PATCH 026/128] fixes change of basis matrix --- experimental/AlgebraicShifting/src/AlgebraicShifting.jl | 3 +-- 1 file changed, 1 insertion(+), 2 deletions(-) diff --git a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl index a301e6f924e3..20a52b414e9a 100644 --- a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl +++ b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl @@ -100,8 +100,7 @@ function exterior_shift(F::Field, K::SimplicialComplex; end push!(sub_compound_matrix, row_minors) end - - A = matrix(matrix_base, sub_compound_matrix) + A = reduce(hcat, sub_compound_matrix) if is_generic Oscar.ModStdQt.ref_ff_rc!(A) From 3d57d241f5d3fb4f93fbdb695bdfdc2056e2bb58 Mon Sep 17 00:00:00 2001 From: antonydellavecchia Date: Thu, 22 Feb 2024 20:17:01 +0100 Subject: [PATCH 027/128] fix for exterior shift --- experimental/AlgebraicShifting/src/AlgebraicShifting.jl | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl index 20a52b414e9a..2a2dce763d76 100644 --- a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl +++ b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl @@ -100,7 +100,7 @@ function exterior_shift(F::Field, K::SimplicialComplex; end push!(sub_compound_matrix, row_minors) end - A = reduce(hcat, sub_compound_matrix) + A = matrix(reduce(hcat, sub_compound_matrix)) if is_generic Oscar.ModStdQt.ref_ff_rc!(A) From 56f50f146549d8ab2de9f28310bd7e7f0b682ef3 Mon Sep 17 00:00:00 2001 From: antonydellavecchia Date: Thu, 22 Feb 2024 20:41:50 +0100 Subject: [PATCH 028/128] update for n_vertices --- experimental/AlgebraicShifting/src/AlgebraicShifting.jl | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl index 2a2dce763d76..7e456e13c8bb 100644 --- a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl +++ b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl @@ -40,7 +40,7 @@ function apply_on_faces(f::Function, K::SimplicialComplex) end function shift_basis_ext(F::Field, K::SimplicialComplex) - n = nvertices(K) + n = n_vertices(K) shifted_K = Oscar.delta_ext(F, K) lambda, _ = exterior_algebra(F, n) x = gens(lambda) @@ -69,7 +69,7 @@ function exterior_shift(F::Field, K::SimplicialComplex; change_of_basis::T = nothing) where T <: Union{Nothing, MatElem} # the exterior shifting works in a different algebra that lends # itself to an easier implementation - n = nvertices(K) + n = n_vertices(K) is_generic = false if isnothing(change_of_basis) is_generic = true @@ -122,7 +122,7 @@ Returns the symmetric shift of `K` see survey on algebraic shifting Gil Kalai (properly cite at some point) """ function symmetric_shift(F::Field, K::SimplicialComplex) - n = nvertices(K) + n = n_vertices(K) Fy, y = polynomial_ring(F, :y => (1:n, 1:n)) Fyx, x = polynomial_ring(Fy, n) # the computation is a over the field of fractions Fyx From 6a70d42b5e3d60c0c2a325af11013a7cebeeee83 Mon Sep 17 00:00:00 2001 From: antonydellavecchia Date: Thu, 22 Feb 2024 21:14:14 +0100 Subject: [PATCH 029/128] needed for serialization of results --- src/Serialization/containers.jl | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/src/Serialization/containers.jl b/src/Serialization/containers.jl index 6f656c6f11d9..10c4a7a681b6 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 From 07bcbd9e4a217117ebf62bec29af6edd4a2da5d3 Mon Sep 17 00:00:00 2001 From: antonydellavecchia Date: Fri, 1 Mar 2024 13:21:09 +0100 Subject: [PATCH 030/128] fixes loading polymake simplicial complex and other types --- src/Serialization/polymake.jl | 14 ++++++++------ 1 file changed, 8 insertions(+), 6 deletions(-) diff --git a/src/Serialization/polymake.jl b/src/Serialization/polymake.jl index 1ba57c2aa897..6cd3c562248d 100644 --- a/src/Serialization/polymake.jl +++ b/src/Serialization/polymake.jl @@ -36,13 +36,15 @@ 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)) - if T <: PolyhedralObject{QQFieldElem} - return T(inner_object) - elseif T <: PolyhedralObject{Float64} - return T(inner_object, AbstractAlgebra.Floats{Float64}()) - else + if T <: PolyhedralObject{Float64} + return T(inner_object, AbstractAlgebra.Floats{Float64}()) + else + try + return T(inner_object) + catch e error("Unsupported object type $T for loading polymake object") - end + end + end end From c35125005ce32f30fd9e721b65a1fbfa3493c3c5 Mon Sep 17 00:00:00 2001 From: antonydellavecchia Date: Fri, 1 Mar 2024 13:24:05 +0100 Subject: [PATCH 031/128] adds test case --- test/Serialization/polymake/runtests.jl | 50 ++-- .../Serialization/polymake/simplicial.complex | 251 ++++++++++++++++++ 2 files changed, 279 insertions(+), 22 deletions(-) create mode 100644 test/Serialization/polymake/simplicial.complex diff --git a/test/Serialization/polymake/runtests.jl b/test/Serialization/polymake/runtests.jl index 8a2136b36ecb..92c8d8e5177e 100644 --- a/test/Serialization/polymake/runtests.jl +++ b/test/Serialization/polymake/runtests.jl @@ -1,28 +1,34 @@ @testset "polymake" begin - - @testset "loading polymake objects" begin - s = load(joinpath(@__DIR__, "square.poly")) - @test s isa Polyhedron{QQFieldElem} - @test n_vertices(s) == 4 - @test n_facets(s) == 4 + + @testset "loading polymake objects" begin + s = load(joinpath(@__DIR__, "square.poly")) + @test s isa Polyhedron{QQFieldElem} + @test n_vertices(s) == 4 + @test n_facets(s) == 4 - nf = load(joinpath(@__DIR__, "nf_square.fan")) - @test nf isa PolyhedralFan{QQFieldElem} - @test n_rays(nf) == 4 - @test number_of_maximal_cones(nf) == 4 + nf = load(joinpath(@__DIR__, "nf_square.fan")) + @test nf isa PolyhedralFan{QQFieldElem} + @test n_rays(nf) == 4 + @test number_of_maximal_cones(nf) == 4 - g = load(joinpath(@__DIR__, "square_graph.graph")) - @test g isa Graph{Undirected} - @test n_edges(g) == 4 + g = load(joinpath(@__DIR__, "square_graph.graph")) + @test g isa Graph{Undirected} + @test n_edges(g) == 4 - um = nothing - @test_logs (:warn, r"No function for converting the deserialized Polymake type to Oscar") um = load(joinpath(@__DIR__, "um5.mat")) - @test um isa Polymake.PropertyValueAllocated + um = nothing + @test_logs (:warn, r"No function for converting the deserialized Polymake type to Oscar") um = load(joinpath(@__DIR__, "um5.mat")) + @test um isa Polymake.PropertyValueAllocated - i = load(joinpath(@__DIR__, "ideal.mv")) - @test i isa Oscar.Ideal - @test map(collect, map(coefficients, gens(i))) == [[1, 1], [1, -4]] - @test map(collect, map(exponents, gens(i))) == - [[[2, 0], [0, 1]], [[3, 0], [0, 1]]] - end + i = load(joinpath(@__DIR__, "ideal.mv")) + @test i isa Oscar.Ideal + @test map(collect, map(coefficients, gens(i))) == [[1, 1], [1, -4]] + @test map(collect, map(exponents, gens(i))) == + [[[2, 0], [0, 1]], [[3, 0], [0, 1]]] + + s = load(joinpath(@__DIR__, "simplicial.complex")) + @test s isa SimplicialComplex + @test n_vertices(s) == 5 + @test n_facets(s) == 3 + + end end diff --git a/test/Serialization/polymake/simplicial.complex b/test/Serialization/polymake/simplicial.complex new file mode 100644 index 000000000000..737e4cfce1f8 --- /dev/null +++ b/test/Serialization/polymake/simplicial.complex @@ -0,0 +1,251 @@ +{ + "DIM": 2, + "_ns": { + "polymake": [ + "https://polymake.org", + "4.11" + ] + }, + "VERTEX_INDICES": [ + 1, + 2, + 3, + 4 + ], + "_id": "44.pm", + "FACETS": [ + [ + 0, + 1, + 2 + ], + [ + 0, + 1, + 3 + ], + [ + 2, + 3 + ] + ], + "PURE": false, + "HASSE_DIAGRAM": { + "TOP_NODE": 0, + "ADJACENCY": [ + [], + [ + 0 + ], + [ + 0 + ], + [ + 0 + ], + [ + 1, + 2 + ], + [ + 1 + ], + [ + 1 + ], + [ + 2 + ], + [ + 2 + ], + [ + 3, + 5, + 6 + ], + [ + 3, + 7, + 8 + ], + [ + 4, + 5, + 7 + ], + [ + 4, + 6, + 8 + ], + [ + 9, + 10, + 11, + 12 + ] + ], + "INVERSE_RANK_MAP": [ + { + "0": [ + 13 + ], + "1": [ + 9, + 10, + 11, + 12 + ], + "2": [ + 3, + 4, + 5, + 6, + 7, + 8 + ], + "3": [ + 1, + 2 + ], + "4": [ + 0 + ] + } + ], + "DECORATION": [ + [ + [ + -1 + ], + 4 + ], + [ + [ + 0, + 1, + 2 + ], + 3 + ], + [ + [ + 0, + 1, + 3 + ], + 3 + ], + [ + [ + 2, + 3 + ], + 2 + ], + [ + [ + 0, + 1 + ], + 2 + ], + [ + [ + 0, + 2 + ], + 2 + ], + [ + [ + 1, + 2 + ], + 2 + ], + [ + [ + 0, + 3 + ], + 2 + ], + [ + [ + 1, + 3 + ], + 2 + ], + [ + [ + 2 + ], + 1 + ], + [ + [ + 3 + ], + 1 + ], + [ + [ + 0 + ], + 1 + ], + [ + [ + 1 + ], + 1 + ], + [ + [], + 0 + ] + ], + "BOTTOM_NODE": 13 + }, + "INPUT_FACES": [ + [ + 1, + 2, + 3 + ], + [ + 1, + 2, + 4 + ], + [ + 1, + 2 + ], + [ + 1, + 3 + ], + [ + 1, + 4 + ], + [ + 2, + 3 + ], + [ + 2, + 4 + ], + [ + 3, + 4 + ] + ], + "_type": "topaz::SimplicialComplex", + "N_VERTICES": 4 +} From 41de5bc7a0201bb7dac297bce45b822334744b86 Mon Sep 17 00:00:00 2001 From: antonydellavecchia Date: Fri, 1 Mar 2024 13:27:04 +0100 Subject: [PATCH 032/128] removing unnecessary else --- src/Serialization/polymake.jl | 12 +++++------- 1 file changed, 5 insertions(+), 7 deletions(-) diff --git a/src/Serialization/polymake.jl b/src/Serialization/polymake.jl index 6cd3c562248d..08be2ae60866 100644 --- a/src/Serialization/polymake.jl +++ b/src/Serialization/polymake.jl @@ -38,16 +38,14 @@ function load_from_polymake(::Type{T}, jsondict::Dict{Symbol, Any}) where { inner_object = Polymake.call_function(:common, :deserialize_json_string, json(jsondict)) if T <: PolyhedralObject{Float64} return T(inner_object, AbstractAlgebra.Floats{Float64}()) - else - try - return T(inner_object) - catch e - error("Unsupported object type $T for loading polymake object") - end + end + try + return T(inner_object) + catch e + error("Unsupported object type $T for loading polymake object") end end - # Distinguish between the various polymake datatypes. function load_from_polymake(jsondict::Dict{Symbol, Any}) typename = jsondict[:_type] From 8fdc000115b3d1f93ff0f4d85748ac99c6cbe177 Mon Sep 17 00:00:00 2001 From: antonydellavecchia Date: Fri, 1 Mar 2024 13:36:21 +0100 Subject: [PATCH 033/128] fix test --- test/Serialization/polymake/runtests.jl | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/test/Serialization/polymake/runtests.jl b/test/Serialization/polymake/runtests.jl index 92c8d8e5177e..2398563cf272 100644 --- a/test/Serialization/polymake/runtests.jl +++ b/test/Serialization/polymake/runtests.jl @@ -27,8 +27,8 @@ s = load(joinpath(@__DIR__, "simplicial.complex")) @test s isa SimplicialComplex - @test n_vertices(s) == 5 - @test n_facets(s) == 3 + @test n_vertices(s) == 4 + @test length(facets(s)) == 3 end end From c6423600e34017415baa82f73d0862350dfe2797 Mon Sep 17 00:00:00 2001 From: antonydellavecchia Date: Mon, 4 Mar 2024 09:27:17 +0100 Subject: [PATCH 034/128] allow change of basis to be generic + comment about sort --- experimental/AlgebraicShifting/src/AlgebraicShifting.jl | 8 +++++++- 1 file changed, 7 insertions(+), 1 deletion(-) diff --git a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl index 7e456e13c8bb..7b453d21eca3 100644 --- a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl +++ b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl @@ -79,13 +79,19 @@ function exterior_shift(F::Field, K::SimplicialComplex; matrix_base = Fx else matrix_base = base_ring(change_of_basis) + if matrix_base isa MPolyRing + is_generic = true + end end # might not be needed cmp(S1, S2) = min(symdiff(S1, S2)...) in S1 input_faces = apply_on_faces(K) do (dim_face, faces) - # look into why there is sort here + # is needed here since otherwise the sets are not + # in lex order, seubsets is being called from Hecke, + # maybe we should look into this and see if polymake's + # is preffered? nCk = sort(subsets(n, dim_face + 1)) entry_type = elem_type(matrix_base) From 8adf1ea5be8bfa2be330f627388b95d40e87a812 Mon Sep 17 00:00:00 2001 From: Antony Della Vecchia Date: Mon, 4 Mar 2024 14:25:28 +0100 Subject: [PATCH 035/128] adds some functions for simplicial complexes from polymake --- src/Combinatorics/SimplicialComplexes.jl | 53 ++++++++++++++++++++++++ src/exports.jl | 1 + 2 files changed, 54 insertions(+) diff --git a/src/Combinatorics/SimplicialComplexes.jl b/src/Combinatorics/SimplicialComplexes.jl index 476a7f4747bb..5994f4ea8706 100644 --- a/src/Combinatorics/SimplicialComplexes.jl +++ b/src/Combinatorics/SimplicialComplexes.jl @@ -570,3 +570,56 @@ function is_isomorphic(K1::SimplicialComplex, K2::SimplicialComplex) return Polymake.topaz.isomorphic(pm_object(K1), pm_object(K2))::Bool end +############################################################################### +### helpful functions +############################################################################### + +@doc raw""" + connected_sum(K1::SimplicialComplex, K2::SimplicialComplex, f1::Int=0, f2::Int=0) + +Compute the connected sum of two complexes. Parameters f1 and f2 specify which facet + of the first and second complex correspondingly are glued together. Default is the +0-th facet of both. The vertices in the selected facets are identified with each +other according to their order in the facet (that is, in icreasing index order). + +# Examples +```jldoctest +julia> K1 = torus(); + +julia> K2 = torus(); + +julia> surface_genus_2 = connected(K1, K2) + +julia> homology(surface_genus_2, 1) +Z^4 + +julia> is_manifold(surface_genus_2) +true +``` +""" +function connected_sum(K1::SimplicialComplex, K2::SimplicialComplex, f1::Int=0, f2::Int=0) + return SimplicialComplex(Polymake.topaz.connected_sum(pm_object(K1), pm_object(K2), f1, f2)) +end + +@doc raw""" + deletion(K::SimplicialComplex, face::Set{Int}) + +Remove the given face and all the faces containing it. + +# Examples +```jldoctest +julia> K = simpicial_complex([[1, 2, 3], [2, 3, 4]]); + +julia> K_with_deletion = deletion(K, Set([1, 2])); + +julia> facets(K_with_deletion) +2-element Vector{Set{Int64}}: + Set([3, 1]) + Set([4, 2, 3]) +``` +""" +function deletion(K::SimplicialComplex, face::Set{Int}) + pm_set = Polymake.convert_to_pm_type(Set{Int}) + pm_face = convert(pm_set, Polymake.to_zero_based_indexing(face)) + return SimplicialComplex(Polymake.topaz.deletion(Oscar.pm_object(K), pm_face)) +end diff --git a/src/exports.jl b/src/exports.jl index 2f6755040a91..53f06fa07831 100644 --- a/src/exports.jl +++ b/src/exports.jl @@ -379,6 +379,7 @@ export conjugate export conjugate_group export conjugate_transpose export connected_components +export connected_sum export connectivity_function export contains export continued_fraction_hirzebruch_jung From 6f70071405ac3489e215e546f37ba3bf48fe9d3f Mon Sep 17 00:00:00 2001 From: Antony Della Vecchia Date: Tue, 5 Mar 2024 12:58:46 +0100 Subject: [PATCH 036/128] get rid of monomial sort --- experimental/AlgebraicShifting/src/AlgebraicShifting.jl | 5 ++--- 1 file changed, 2 insertions(+), 3 deletions(-) diff --git a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl index 7e456e13c8bb..c97dae25eda6 100644 --- a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl +++ b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl @@ -130,7 +130,6 @@ function symmetric_shift(F::Field, K::SimplicialComplex) # but we want to avoid using fraction field of Ry during row reduction mb_ring, z = graded_polynomial_ring(F, n) o = monomial_ordering(mb_ring, :lex) - cmp_order(a, b) = cmp(o, a, b) > 0 # the generators of the stanley reisner ideal are combinations of [x_1, ..., x_n] R_K, _ = stanley_reisner_ring(Fyx, K) @@ -138,8 +137,7 @@ function symmetric_shift(F::Field, K::SimplicialComplex) input_faces = apply_on_faces(K) do (dim_face, faces) r = dim_face + 1 - # look into sorts - mb = sort(monomial_basis(mb_ring, r); lt=cmp_order) + mb = reverse(monomial_basis(mb_ring, r)) Y = matrix(Fy, hcat(y)) A = Vector{MPolyRingElem}[] @@ -154,6 +152,7 @@ function symmetric_shift(F::Field, K::SimplicialComplex) # there should be no lifting non_zero_terms = filter(x -> !is_zero(R_K(x)), collect(terms(lift(transformed_monomial)))) + # coefficients is a function for polynomials but since we are looking at the terms # i.e. we are seperating by monomials already, we know the first coefficient is just # the coefficient of the monomial From 393962ae3172ace5e2d4c50ef17cb8ee89828d1e Mon Sep 17 00:00:00 2001 From: Antony Della Vecchia Date: Tue, 5 Mar 2024 15:26:31 +0100 Subject: [PATCH 037/128] cleans up symmetric shift a bit --- .../src/AlgebraicShifting.jl | 20 +++++-------------- 1 file changed, 5 insertions(+), 15 deletions(-) diff --git a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl index f25aedf6bbd6..4307f794b229 100644 --- a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl +++ b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl @@ -138,7 +138,7 @@ function symmetric_shift(F::Field, K::SimplicialComplex) o = monomial_ordering(mb_ring, :lex) # the generators of the stanley reisner ideal are combinations of [x_1, ..., x_n] - R_K, _ = stanley_reisner_ring(Fyx, K) + I_K = stanley_reisner_ideal(Fyx, K) input_faces = apply_on_faces(K) do (dim_face, faces) r = dim_face + 1 @@ -149,22 +149,12 @@ function symmetric_shift(F::Field, K::SimplicialComplex) for b in mb # need to compare with some alternatives - transformed_monomial = evaluate(b, Y * gens(R_K)) - - # double check this line - # is stanley reisner ring over Z needed to then reduce later - # stanley reisner over F is cheaper - # this part will need to be adjusted for finite fields - # there should be no lifting - non_zero_terms = filter(x -> !is_zero(R_K(x)), collect(terms(lift(transformed_monomial)))) - - - # coefficients is a function for polynomials but since we are looking at the terms - # i.e. we are seperating by monomials already, we know the first coefficient is just - # the coefficient of the monomial - generic_col = first.(coefficients.(non_zero_terms)) + transformed_monomial = evaluate(b, Y * gens(Fyx)) + generic_col = collect(coefficients.(normal_form(transformed_monomial, I_K))) + push!(A, generic_col) end + C = matrix(Fy, reduce(hcat, A)) Oscar.ModStdQt.ref_ff_rc!(C) From e74021917213a772029eaaea3420ad7abb74fdca Mon Sep 17 00:00:00 2001 From: Antony Della Vecchia Date: Tue, 5 Mar 2024 17:07:34 +0100 Subject: [PATCH 038/128] adds gb details to stanley reisner ideal --- src/Combinatorics/SimplicialComplexes.jl | 8 ++++++-- 1 file changed, 6 insertions(+), 2 deletions(-) diff --git a/src/Combinatorics/SimplicialComplexes.jl b/src/Combinatorics/SimplicialComplexes.jl index 476a7f4747bb..cb06fd838364 100644 --- a/src/Combinatorics/SimplicialComplexes.jl +++ b/src/Combinatorics/SimplicialComplexes.jl @@ -327,8 +327,12 @@ Ideal generated by ``` """ function stanley_reisner_ideal(R::MPolyRing, K::SimplicialComplex) - mnf = minimal_nonfaces(IncidenceMatrix, K) - return ideal([ R([1], [Vector{Int}(mnf[i,:])]) for i in 1:Polymake.nrows(mnf) ]) + mnf = minimal_nonfaces(IncidenceMatrix, K) + gens = [ R([1], [Vector{Int}(mnf[i,:])]) for i in 1:Polymake.nrows(mnf) ] + # I is actually a universal groebner basis but I am not sure if there is a way + # to set that? + I = IdealGens(R, gens, default_ordering(R); isGB=true, isReduced=true) + return ideal(I) end @doc raw""" From e46d1ef48205699192564c657f08adceb826ec38 Mon Sep 17 00:00:00 2001 From: Antony Della Vecchia Date: Tue, 5 Mar 2024 17:51:48 +0100 Subject: [PATCH 039/128] symmetric shift working over finite characteristic --- .../AlgebraicShifting/src/AlgebraicShifting.jl | 16 ++++++++++++---- 1 file changed, 12 insertions(+), 4 deletions(-) diff --git a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl index 4307f794b229..3c25ad1de8ec 100644 --- a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl +++ b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl @@ -135,10 +135,9 @@ function symmetric_shift(F::Field, K::SimplicialComplex) # we use a different ring to generate monomial_basis, coefficients need to be a field, # but we want to avoid using fraction field of Ry during row reduction mb_ring, z = graded_polynomial_ring(F, n) - o = monomial_ordering(mb_ring, :lex) # the generators of the stanley reisner ideal are combinations of [x_1, ..., x_n] - I_K = stanley_reisner_ideal(Fyx, K) + R_K, _ = stanley_reisner_ring(Fyx, K) input_faces = apply_on_faces(K) do (dim_face, faces) r = dim_face + 1 @@ -146,11 +145,20 @@ function symmetric_shift(F::Field, K::SimplicialComplex) mb = reverse(monomial_basis(mb_ring, r)) Y = matrix(Fy, hcat(y)) A = Vector{MPolyRingElem}[] + mb_exponents = first.(collect.(exponents.(mb))) # gets monomial exponents for b in mb # need to compare with some alternatives - transformed_monomial = evaluate(b, Y * gens(Fyx)) - generic_col = collect(coefficients.(normal_form(transformed_monomial, I_K))) + transformed_monomial = evaluate(b, Y * gens(R_K)) + + # we need to iterate through exponents here since the functions terms, coefficients or exponents + # do not return 0 terms and we need to make sure the generic col aligns with the others + # this is needed for the case when the field has finite characteristic + # we use the lift because currently there is no function for get the coeff of + # a MPolyQuoRingElem, which means we also need to check if it's zero before adding the coefficient + generic_col = [ + !is_zero(R_K(monomial(Fyx, e))) ? coeff(lift(transformed_monomial), e) : Fy(0) + for e in mb_exponents] push!(A, generic_col) end From df8279e7f396b63d82e148caa9dd99a4eab25a71 Mon Sep 17 00:00:00 2001 From: Antony Della Vecchia Date: Wed, 6 Mar 2024 14:45:42 +0100 Subject: [PATCH 040/128] set description on john solid files --- data/JohnsonSolids/j09.mrdi | 2 +- data/JohnsonSolids/j10.mrdi | 2 +- data/JohnsonSolids/j13.mrdi | 2 +- data/JohnsonSolids/j16.mrdi | 2 +- data/JohnsonSolids/j17.mrdi | 2 +- data/JohnsonSolids/j18.mrdi | 2 +- data/JohnsonSolids/j20.mrdi | 2 +- data/JohnsonSolids/j21.mrdi | 2 +- data/JohnsonSolids/j22.mrdi | 2 +- data/JohnsonSolids/j23.mrdi | 2 +- data/JohnsonSolids/j24.mrdi | 2 +- data/JohnsonSolids/j25.mrdi | 2 +- data/JohnsonSolids/j30.mrdi | 2 +- data/JohnsonSolids/j32.mrdi | 2 +- data/JohnsonSolids/j33.mrdi | 2 +- data/JohnsonSolids/j34.mrdi | 2 +- data/JohnsonSolids/j35.mrdi | 2 +- data/JohnsonSolids/j36.mrdi | 2 +- data/JohnsonSolids/j38.mrdi | 2 +- data/JohnsonSolids/j39.mrdi | 2 +- data/JohnsonSolids/j40.mrdi | 2 +- data/JohnsonSolids/j41.mrdi | 2 +- data/JohnsonSolids/j42.mrdi | 2 +- data/JohnsonSolids/j43.mrdi | 2 +- data/JohnsonSolids/j44.mrdi | 2 +- data/JohnsonSolids/j45.mrdi | 2 +- data/JohnsonSolids/j46.mrdi | 2 +- data/JohnsonSolids/j47.mrdi | 2 +- data/JohnsonSolids/j48.mrdi | 2 +- data/JohnsonSolids/j49.mrdi | 2 +- data/JohnsonSolids/j50.mrdi | 2 +- data/JohnsonSolids/j51.mrdi | 2 +- data/JohnsonSolids/j52.mrdi | 2 +- data/JohnsonSolids/j53.mrdi | 2 +- data/JohnsonSolids/j54.mrdi | 2 +- data/JohnsonSolids/j55.mrdi | 2 +- data/JohnsonSolids/j56.mrdi | 2 +- data/JohnsonSolids/j57.mrdi | 2 +- data/JohnsonSolids/j58.mrdi | 2 +- data/JohnsonSolids/j59.mrdi | 2 +- data/JohnsonSolids/j60.mrdi | 2 +- data/JohnsonSolids/j61.mrdi | 2 +- data/JohnsonSolids/j64.mrdi | 2 +- data/JohnsonSolids/j68.mrdi | 2 +- data/JohnsonSolids/j69.mrdi | 2 +- data/JohnsonSolids/j70.mrdi | 2 +- data/JohnsonSolids/j71.mrdi | 2 +- data/JohnsonSolids/j72.mrdi | 2 +- data/JohnsonSolids/j73.mrdi | 2 +- data/JohnsonSolids/j74.mrdi | 2 +- data/JohnsonSolids/j75.mrdi | 2 +- data/JohnsonSolids/j77.mrdi | 2 +- data/JohnsonSolids/j78.mrdi | 2 +- data/JohnsonSolids/j79.mrdi | 2 +- data/JohnsonSolids/j82.mrdi | 2 +- data/JohnsonSolids/j84.mrdi | 2 +- data/JohnsonSolids/j85.mrdi | 2 +- data/JohnsonSolids/j86.mrdi | 2 +- data/JohnsonSolids/j87.mrdi | 2 +- data/JohnsonSolids/j88.mrdi | 2 +- data/JohnsonSolids/j89.mrdi | 2 +- data/JohnsonSolids/j90.mrdi | 2 +- data/JohnsonSolids/j92.mrdi | 2 +- .../src/AlgebraicShifting.jl | 2 +- .../Polyhedron/standard_constructions.jl | 72 +++---------------- src/Serialization/polymake.jl | 9 +++ test/PolyhedralGeometry/polyhedron.jl | 3 +- 67 files changed, 82 insertions(+), 130 deletions(-) diff --git a/data/JohnsonSolids/j09.mrdi b/data/JohnsonSolids/j09.mrdi index b788f63ad90f..9725f6ff81b8 100644 --- a/data/JohnsonSolids/j09.mrdi +++ b/data/JohnsonSolids/j09.mrdi @@ -1 +1 @@ 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-3f 1279a749 -5a","0 0 0 0"],["8f1bbcdcbfa53e0b -3e 1c9f25c9 -5b","0 0 0 0"]]}}},"5911afe5-d882-4d64-bef3-559bbdd78f5c":{"_type":"PolyRing","data":{"base_ring":{"_type":"QQField"},"symbols":["x"]}}}} \ No newline at end of file diff --git a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl index 4307f794b229..3d431be9441e 100644 --- a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl +++ b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl @@ -151,7 +151,7 @@ function symmetric_shift(F::Field, K::SimplicialComplex) # need to compare with some alternatives transformed_monomial = evaluate(b, Y * gens(Fyx)) generic_col = collect(coefficients.(normal_form(transformed_monomial, I_K))) - + println(generic_col) push!(A, generic_col) end diff --git a/src/PolyhedralGeometry/Polyhedron/standard_constructions.jl b/src/PolyhedralGeometry/Polyhedron/standard_constructions.jl index aca35c61ff0c..cb71b6c55975 100644 --- a/src/PolyhedralGeometry/Polyhedron/standard_constructions.jl +++ b/src/PolyhedralGeometry/Polyhedron/standard_constructions.jl @@ -242,69 +242,13 @@ Construct the regular icosahedron, one out of two exceptional Platonic solids. """ icosahedron() = polyhedron(Polymake.polytope.icosahedron()); -const _johnson_names = Dict{Int, String}((9 => "Johnson solid J9: Elongated pentagonal pyramid"), - (10 => "Johnson solid J10: Gyroelongated square pyramid"), - (13 => "Johnson solid J13: Pentagonal bipyramid"), - (16 => "Johnson solid J16: Elongated pentagonal bipyramid"), - (17 => "Johnson solid J17: Gyroelongated square bipyramid"), - (18 => "Johnson solid J18: Elongated triangular cupola"), - (20 => "Johnson solid J20: Elongated pentagonal cupola"), - (21 => "Johnson solid J21: Elongated pentagonal rotunda"), - (22 => "Johnson solid J22: Gyroelongated triangular cupola"), - (23 => "Johnson solid J23: Gyroelongated square cupola"), - (24 => "Johnson solid J24: Gyroelongated pentagonal cupola"), - (25 => "Johnson solid J25: Gyroelongated pentagonal rotunda"), - (30 => "Johnson solid J30: Pentagonal orthobicupola"), - (32 => "Johnson solid J32: Pentagonal orthocupolarotunda"), - (33 => "Johnson solid J33: Pentagonal gyrocupolarotunda"), - (34 => "Johnson solid J34: Pentagonal orthobirotunda"), - (35 => "Johnson solid J35: Elongated triangular orthobicupola"), - (36 => "Johnson solid J36: Elongated triangular gyrobicupola"), - (38 => "Johnson solid J38: Elongated pentagonal orthobicupola"), - (39 => "Johnson solid J39: Elongated pentagonal gyrobicupola"), - (40 => "Johnson solid J40: Elongated pentagonal orthocupolarotunda"), - (41 => "Johnson solid J41: Elongated pentagonal gyrocupolarotunda"), - (42 => "Johnson solid J42: Elongated pentagonal orthobirotunda"), - (43 => "Johnson solid J43: Elongated pentagonal gyrobirotunda"), - (44 => "Johnson solid J44: Gyroelongated triangular bicupola"), - (45 => "Johnson solid J45: Gyroelongated square bicupola"), - (46 => "Johnson solid J46: Gyroelongated pentagonal bicupola"), - (47 => "Johnson solid J47: Gyroelongated pentagonal cupolarotunda"), - (48 => "Johnson solid J48: Gyroelongated pentagonal birotunda"), - (49 => "Johnson solid J49: Augmented triangular prism"), - (50 => "Johnson solid J50: Biaugmented triangular prism"), - (51 => "Johnson solid J51: Triaugmented triangular prism"), - (52 => "Johnson solid J52: Augmented pentagonal prism"), - (53 => "Johnson solid J53: Biaugmented pentagonal prism"), - (54 => "Johnson solid J54: Augmented hexagonal prism"), - (55 => "Johnson solid J55: Parabiaugmented hexagonal prism"), - (56 => "Johnson solid J56: Metabiaugmented hexagonal prism"), - (57 => "Johnson solid J57: Triaugmented hexagonal prism"), - (58 => "Johnson solid J58: Augmented dodecahedron"), - (59 => "Johnson solid J59: Parabiaugmented dodecahedron"), - (60 => "Johnson solid J60: Metabiaugmented dodecahedron"), - (61 => "Johnson solid J61: Triaugmented dodecahedron"), - (64 => "Johnson solid J64: Augmented tridiminished icosahedron"), - (68 => "Johnson solid J68: Augmented truncated dodecahedron"), - (69 => "Johnson solid J69: Parabiaugmented truncated dodecahedron"), - (70 => "Johnson solid J70: Metabiaugmented truncated dodecahedron"), - (71 => "Johnson solid J71: Triaugmented truncated dodecahedron"), - (72 => "Johnson solid J72: Gyrate rhombicosidodecahedron"), - (73 => "Johnson solid J73: Parabigyrate rhombicosidodecahedron"), - (74 => "Johnson solid J74: Metabigyrate rhombicosidodecahedron"), - (75 => "Johnson solid J75: Trigyrate rhombicosidodecahedron"), - (77 => "Johnson solid J77: Paragyrate diminished rhombicosidodecahedron"), - (78 => "Johnson solid J78: Metagyrate diminished rhombicosidodecahedron"), - (79 => "Johnson solid J79: Bigyrate diminished rhombicosidodecahedron"), - (82 => "Johnson solid J82: Gyrate bidiminished rhombicosidodecahedron"), - (84 => "Johnson solid J84: Snub disphenoid"), - (85 => "Johnson solid J85: Snub square antiprism"), - (86 => "Johnson solid J86: Sphenocorona"), - (87 => "Johnson solid J87: Augmented sphenocorona"), - (88 => "Johnson solid J88: Sphenomegacorona"), - (89 => "Johnson solid J89: Hebesphenomegacorona"), - (90 => "Johnson solid J90: Disphenocingulum"), - (92 => "Johnson solid J92: Triangular hebesphenorotunda")) +const _johnson_names = Set{Int}([9, 10, 13, 16, 17, 18, 20, 21, 22, 23, 24, + 25, 30, 32, 33, 34, 35, 36, 38, 39, 40, + 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, + 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, + 61, 64, 68, 69, 70, 71, 72, 73, 74, 75, + 77, 78, 79, 82, 84, 85, 86, 87, 88, 89, + 90, 92]) @doc raw""" johnson_solid(i::Int) @@ -315,7 +259,7 @@ A Johnson solid is a 3-polytope whose facets are regular polygons, of various go It is proper if it is not an Archimedean solid. Up to scaling there are exactly 92 proper Johnson solids. """ function johnson_solid(index::Int) - if haskey(_johnson_names, index) + if index in _johnson_names # code used for generation of loaded files can be found at: # https://github.com/dmg-lab/JohnsonSrc str_index = lpad(index, 2, '0') diff --git a/src/Serialization/polymake.jl b/src/Serialization/polymake.jl index 08be2ae60866..545074066253 100644 --- a/src/Serialization/polymake.jl +++ b/src/Serialization/polymake.jl @@ -126,6 +126,11 @@ function _bigobject_to_dict(bo::Polymake.BigObject, coeff::Field) end end end + description = Polymake.getdescription(bo) + + if !isempty(description) + data["_description"] = String(description) + end data end @@ -148,6 +153,10 @@ function _load_bigobject_from_dict!(obj::Polymake.BigObject, dict::Dict, parent_ Polymake.take(obj, key_str, convert(Polymake.PolymakeType, v)) end end + if haskey(dict, "_description") + Polymake.setdescription!(obj, dict["_description"]) + end + return obj end function _dict_to_bigobject(dict::Dict{String, Any}) diff --git a/test/PolyhedralGeometry/polyhedron.jl b/test/PolyhedralGeometry/polyhedron.jl index c2f3000ec46f..9c921f2c0db7 100644 --- a/test/PolyhedralGeometry/polyhedron.jl +++ b/test/PolyhedralGeometry/polyhedron.jl @@ -584,10 +584,9 @@ end @testset "Johnson solids" begin - for i in keys(Oscar._johnson_names) + for i in 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 From bbb4e656a0e0b060b6b83863defad9a5b384099a Mon Sep 17 00:00:00 2001 From: Antony Della Vecchia Date: Wed, 6 Mar 2024 14:55:32 +0100 Subject: [PATCH 041/128] Revert "set description on john solid files" This reverts commit df8279e7f396b63d82e148caa9dd99a4eab25a71. --- data/JohnsonSolids/j09.mrdi | 2 +- data/JohnsonSolids/j10.mrdi | 2 +- data/JohnsonSolids/j13.mrdi | 2 +- data/JohnsonSolids/j16.mrdi | 2 +- data/JohnsonSolids/j17.mrdi | 2 +- data/JohnsonSolids/j18.mrdi | 2 +- data/JohnsonSolids/j20.mrdi | 2 +- data/JohnsonSolids/j21.mrdi | 2 +- data/JohnsonSolids/j22.mrdi | 2 +- data/JohnsonSolids/j23.mrdi | 2 +- data/JohnsonSolids/j24.mrdi | 2 +- data/JohnsonSolids/j25.mrdi | 2 +- data/JohnsonSolids/j30.mrdi | 2 +- data/JohnsonSolids/j32.mrdi | 2 +- data/JohnsonSolids/j33.mrdi | 2 +- data/JohnsonSolids/j34.mrdi | 2 +- data/JohnsonSolids/j35.mrdi | 2 +- data/JohnsonSolids/j36.mrdi | 2 +- data/JohnsonSolids/j38.mrdi | 2 +- data/JohnsonSolids/j39.mrdi | 2 +- data/JohnsonSolids/j40.mrdi | 2 +- data/JohnsonSolids/j41.mrdi | 2 +- data/JohnsonSolids/j42.mrdi | 2 +- data/JohnsonSolids/j43.mrdi | 2 +- data/JohnsonSolids/j44.mrdi | 2 +- data/JohnsonSolids/j45.mrdi | 2 +- data/JohnsonSolids/j46.mrdi | 2 +- data/JohnsonSolids/j47.mrdi | 2 +- data/JohnsonSolids/j48.mrdi | 2 +- data/JohnsonSolids/j49.mrdi | 2 +- data/JohnsonSolids/j50.mrdi | 2 +- data/JohnsonSolids/j51.mrdi | 2 +- data/JohnsonSolids/j52.mrdi | 2 +- data/JohnsonSolids/j53.mrdi | 2 +- data/JohnsonSolids/j54.mrdi | 2 +- data/JohnsonSolids/j55.mrdi | 2 +- data/JohnsonSolids/j56.mrdi | 2 +- data/JohnsonSolids/j57.mrdi | 2 +- data/JohnsonSolids/j58.mrdi | 2 +- data/JohnsonSolids/j59.mrdi | 2 +- data/JohnsonSolids/j60.mrdi | 2 +- data/JohnsonSolids/j61.mrdi | 2 +- data/JohnsonSolids/j64.mrdi | 2 +- data/JohnsonSolids/j68.mrdi | 2 +- data/JohnsonSolids/j69.mrdi | 2 +- data/JohnsonSolids/j70.mrdi | 2 +- data/JohnsonSolids/j71.mrdi | 2 +- data/JohnsonSolids/j72.mrdi | 2 +- data/JohnsonSolids/j73.mrdi | 2 +- data/JohnsonSolids/j74.mrdi | 2 +- data/JohnsonSolids/j75.mrdi | 2 +- data/JohnsonSolids/j77.mrdi | 2 +- data/JohnsonSolids/j78.mrdi | 2 +- data/JohnsonSolids/j79.mrdi | 2 +- data/JohnsonSolids/j82.mrdi | 2 +- data/JohnsonSolids/j84.mrdi | 2 +- data/JohnsonSolids/j85.mrdi | 2 +- data/JohnsonSolids/j86.mrdi | 2 +- data/JohnsonSolids/j87.mrdi | 2 +- data/JohnsonSolids/j88.mrdi | 2 +- data/JohnsonSolids/j89.mrdi | 2 +- data/JohnsonSolids/j90.mrdi | 2 +- data/JohnsonSolids/j92.mrdi | 2 +- .../src/AlgebraicShifting.jl | 2 +- .../Polyhedron/standard_constructions.jl | 72 ++++++++++++++++--- src/Serialization/polymake.jl | 9 --- test/PolyhedralGeometry/polyhedron.jl | 3 +- 67 files changed, 130 insertions(+), 82 deletions(-) diff --git a/data/JohnsonSolids/j09.mrdi b/data/JohnsonSolids/j09.mrdi index 9725f6ff81b8..b788f63ad90f 100644 --- a/data/JohnsonSolids/j09.mrdi +++ b/data/JohnsonSolids/j09.mrdi @@ -1 +1 @@ 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a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl +++ b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl @@ -151,7 +151,7 @@ function symmetric_shift(F::Field, K::SimplicialComplex) # need to compare with some alternatives transformed_monomial = evaluate(b, Y * gens(Fyx)) generic_col = collect(coefficients.(normal_form(transformed_monomial, I_K))) - println(generic_col) + push!(A, generic_col) end diff --git a/src/PolyhedralGeometry/Polyhedron/standard_constructions.jl b/src/PolyhedralGeometry/Polyhedron/standard_constructions.jl index cb71b6c55975..aca35c61ff0c 100644 --- a/src/PolyhedralGeometry/Polyhedron/standard_constructions.jl +++ b/src/PolyhedralGeometry/Polyhedron/standard_constructions.jl @@ -242,13 +242,69 @@ Construct the regular icosahedron, one out of two exceptional Platonic solids. """ icosahedron() = polyhedron(Polymake.polytope.icosahedron()); -const _johnson_names = Set{Int}([9, 10, 13, 16, 17, 18, 20, 21, 22, 23, 24, - 25, 30, 32, 33, 34, 35, 36, 38, 39, 40, - 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, - 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, - 61, 64, 68, 69, 70, 71, 72, 73, 74, 75, - 77, 78, 79, 82, 84, 85, 86, 87, 88, 89, - 90, 92]) +const _johnson_names = Dict{Int, String}((9 => "Johnson solid J9: Elongated pentagonal pyramid"), + (10 => "Johnson solid J10: Gyroelongated square pyramid"), + (13 => "Johnson solid J13: Pentagonal bipyramid"), + (16 => "Johnson solid J16: Elongated pentagonal bipyramid"), + (17 => "Johnson solid J17: Gyroelongated square bipyramid"), + (18 => "Johnson solid J18: Elongated triangular cupola"), + (20 => "Johnson solid J20: Elongated pentagonal cupola"), + (21 => "Johnson solid J21: Elongated pentagonal rotunda"), + (22 => "Johnson solid J22: Gyroelongated triangular cupola"), + (23 => "Johnson solid J23: Gyroelongated square cupola"), + (24 => "Johnson solid J24: Gyroelongated pentagonal cupola"), + (25 => "Johnson solid J25: Gyroelongated pentagonal rotunda"), + (30 => "Johnson solid J30: Pentagonal orthobicupola"), + (32 => "Johnson solid J32: Pentagonal orthocupolarotunda"), + (33 => "Johnson solid J33: Pentagonal gyrocupolarotunda"), + (34 => "Johnson solid J34: Pentagonal orthobirotunda"), + (35 => "Johnson solid J35: Elongated triangular orthobicupola"), + (36 => "Johnson solid J36: Elongated triangular gyrobicupola"), + (38 => "Johnson solid J38: Elongated pentagonal orthobicupola"), + (39 => "Johnson solid J39: Elongated pentagonal gyrobicupola"), + (40 => "Johnson solid J40: Elongated pentagonal orthocupolarotunda"), + (41 => "Johnson solid J41: Elongated pentagonal gyrocupolarotunda"), + (42 => "Johnson solid J42: Elongated pentagonal orthobirotunda"), + (43 => "Johnson solid J43: Elongated pentagonal gyrobirotunda"), + (44 => "Johnson solid J44: Gyroelongated triangular bicupola"), + (45 => "Johnson solid J45: Gyroelongated square bicupola"), + (46 => "Johnson solid J46: Gyroelongated pentagonal bicupola"), + (47 => "Johnson solid J47: Gyroelongated pentagonal cupolarotunda"), + (48 => "Johnson solid J48: Gyroelongated pentagonal birotunda"), + (49 => "Johnson solid J49: Augmented triangular prism"), + (50 => "Johnson solid J50: Biaugmented triangular prism"), + (51 => "Johnson solid J51: Triaugmented triangular prism"), + (52 => "Johnson solid J52: Augmented pentagonal prism"), + (53 => "Johnson solid J53: Biaugmented pentagonal prism"), + (54 => "Johnson solid J54: Augmented hexagonal prism"), + (55 => "Johnson solid J55: Parabiaugmented hexagonal prism"), + (56 => "Johnson solid J56: Metabiaugmented hexagonal prism"), + (57 => "Johnson solid J57: Triaugmented hexagonal prism"), + (58 => "Johnson solid J58: Augmented dodecahedron"), + (59 => "Johnson solid J59: Parabiaugmented dodecahedron"), + (60 => "Johnson solid J60: Metabiaugmented dodecahedron"), + (61 => "Johnson solid J61: Triaugmented dodecahedron"), + (64 => "Johnson solid J64: Augmented tridiminished icosahedron"), + (68 => "Johnson solid J68: Augmented truncated dodecahedron"), + (69 => "Johnson solid J69: Parabiaugmented truncated dodecahedron"), + (70 => "Johnson solid J70: Metabiaugmented truncated dodecahedron"), + (71 => "Johnson solid J71: Triaugmented truncated dodecahedron"), + (72 => "Johnson solid J72: Gyrate rhombicosidodecahedron"), + (73 => "Johnson solid J73: Parabigyrate rhombicosidodecahedron"), + (74 => "Johnson solid J74: Metabigyrate rhombicosidodecahedron"), + (75 => "Johnson solid J75: Trigyrate rhombicosidodecahedron"), + (77 => "Johnson solid J77: Paragyrate diminished rhombicosidodecahedron"), + (78 => "Johnson solid J78: Metagyrate diminished rhombicosidodecahedron"), + (79 => "Johnson solid J79: Bigyrate diminished rhombicosidodecahedron"), + (82 => "Johnson solid J82: Gyrate bidiminished rhombicosidodecahedron"), + (84 => "Johnson solid J84: Snub disphenoid"), + (85 => "Johnson solid J85: Snub square antiprism"), + (86 => "Johnson solid J86: Sphenocorona"), + (87 => "Johnson solid J87: Augmented sphenocorona"), + (88 => "Johnson solid J88: Sphenomegacorona"), + (89 => "Johnson solid J89: Hebesphenomegacorona"), + (90 => "Johnson solid J90: Disphenocingulum"), + (92 => "Johnson solid J92: Triangular hebesphenorotunda")) @doc raw""" johnson_solid(i::Int) @@ -259,7 +315,7 @@ A Johnson solid is a 3-polytope whose facets are regular polygons, of various go It is proper if it is not an Archimedean solid. Up to scaling there are exactly 92 proper Johnson solids. """ function johnson_solid(index::Int) - if index in _johnson_names + if haskey(_johnson_names, index) # code used for generation of loaded files can be found at: # https://github.com/dmg-lab/JohnsonSrc str_index = lpad(index, 2, '0') diff --git a/src/Serialization/polymake.jl b/src/Serialization/polymake.jl index 545074066253..08be2ae60866 100644 --- a/src/Serialization/polymake.jl +++ b/src/Serialization/polymake.jl @@ -126,11 +126,6 @@ function _bigobject_to_dict(bo::Polymake.BigObject, coeff::Field) end end end - description = Polymake.getdescription(bo) - - if !isempty(description) - data["_description"] = String(description) - end data end @@ -153,10 +148,6 @@ function _load_bigobject_from_dict!(obj::Polymake.BigObject, dict::Dict, parent_ Polymake.take(obj, key_str, convert(Polymake.PolymakeType, v)) end end - if haskey(dict, "_description") - Polymake.setdescription!(obj, dict["_description"]) - end - return obj end function _dict_to_bigobject(dict::Dict{String, Any}) diff --git a/test/PolyhedralGeometry/polyhedron.jl b/test/PolyhedralGeometry/polyhedron.jl index 9c921f2c0db7..c2f3000ec46f 100644 --- a/test/PolyhedralGeometry/polyhedron.jl +++ b/test/PolyhedralGeometry/polyhedron.jl @@ -584,9 +584,10 @@ end @testset "Johnson solids" begin - for i in Oscar._johnson_names + 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 From 4f56b91329f51c3f333e4b2d569f9ee05bed094c Mon Sep 17 00:00:00 2001 From: Antony Della Vecchia Date: Wed, 6 Mar 2024 15:09:43 +0100 Subject: [PATCH 042/128] updates for symmetric shift --- .../src/AlgebraicShifting.jl | 53 ++++++++++++------- 1 file changed, 35 insertions(+), 18 deletions(-) diff --git a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl index 3c25ad1de8ec..cda394d249ee 100644 --- a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl +++ b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl @@ -84,9 +84,6 @@ function exterior_shift(F::Field, K::SimplicialComplex; end end - # might not be needed - cmp(S1, S2) = min(symdiff(S1, S2)...) in S1 - input_faces = apply_on_faces(K) do (dim_face, faces) # is needed here since otherwise the sets are not # in lex order, seubsets is being called from Hecke, @@ -127,52 +124,72 @@ Returns the symmetric shift of `K` see survey on algebraic shifting Gil Kalai (properly cite at some point) """ -function symmetric_shift(F::Field, K::SimplicialComplex) +function symmetric_shift(F::Field, K::SimplicialComplex; + change_of_basis::T = nothing) where T <: Union{Nothing, MatElem} + n = n_vertices(K) - Fy, y = polynomial_ring(F, :y => (1:n, 1:n)) - Fyx, x = polynomial_ring(Fy, n) + is_generic = false + if isnothing(change_of_basis) + is_generic = true + # generic change of basis + Fy, y = polynomial_ring(F, :y => (1:n, 1:n)) + change_of_basis = matrix(Fy, hcat(y)) + matrix_base = Fy + else + matrix_base = base_ring(change_of_basis) + if matrix_base isa MPolyRing + is_generic = true + end + end + + Rx, x = polynomial_ring(matrix_base, n) + # the generators of the stanley reisner ideal are combinations of [x_1, ..., x_n] + R_K, _ = stanley_reisner_ring(Rx, K) + # the computation is a over the field of fractions Fyx # we use a different ring to generate monomial_basis, coefficients need to be a field, # but we want to avoid using fraction field of Ry during row reduction mb_ring, z = graded_polynomial_ring(F, n) - # the generators of the stanley reisner ideal are combinations of [x_1, ..., x_n] - R_K, _ = stanley_reisner_ring(Fyx, K) input_faces = apply_on_faces(K) do (dim_face, faces) r = dim_face + 1 mb = reverse(monomial_basis(mb_ring, r)) - Y = matrix(Fy, hcat(y)) - A = Vector{MPolyRingElem}[] + A = Vector{elem_type(matrix_base)}[] mb_exponents = first.(collect.(exponents.(mb))) # gets monomial exponents for b in mb # need to compare with some alternatives - transformed_monomial = evaluate(b, Y * gens(R_K)) + transformed_monomial = evaluate(b, change_of_basis * gens(R_K)) # we need to iterate through exponents here since the functions terms, coefficients or exponents # do not return 0 terms and we need to make sure the generic col aligns with the others # this is needed for the case when the field has finite characteristic # we use the lift because currently there is no function for get the coeff of # a MPolyQuoRingElem, which means we also need to check if it's zero before adding the coefficient - generic_col = [ - !is_zero(R_K(monomial(Fyx, e))) ? coeff(lift(transformed_monomial), e) : Fy(0) + col = [ + !is_zero(R_K(monomial(Rx, e))) ? coeff(lift(transformed_monomial), e) : matrix_base(0) for e in mb_exponents] - push!(A, generic_col) + push!(A, col) end - C = matrix(Fy, reduce(hcat, A)) - Oscar.ModStdQt.ref_ff_rc!(C) + C = matrix(matrix_base, reduce(hcat, A)) + + if is_generic + Oscar.ModStdQt.ref_ff_rc!(C) + else + rref!(C) + end smallest_basis_el = z[r]^r smallest_index = findfirst(a -> a == smallest_basis_el, mb) col_indices = filter(x -> x >= smallest_index, independent_columns(C)) - generic_monomial_exponents = first.(exponents.(mb[col_indices])) + monomial_exponents = first.(exponents.(mb[col_indices])) shifted_sets = Vector{Int}[] - for me in generic_monomial_exponents + for me in monomial_exponents shifted_set = Int[] index_count = 1 for (i, e) in enumerate(me) From d17cfab97e88f26659c8194c1fe4e3ce481708bc Mon Sep 17 00:00:00 2001 From: antonydellavecchia Date: Thu, 7 Mar 2024 09:57:57 +0100 Subject: [PATCH 043/128] adds functionality for automorphisms of simplicial complexes --- src/Combinatorics/SimplicialComplexes.jl | 30 +++++++++++++++++++++++ test/Combinatorics/SimplicialComplexes.jl | 9 +++++++ 2 files changed, 39 insertions(+) diff --git a/src/Combinatorics/SimplicialComplexes.jl b/src/Combinatorics/SimplicialComplexes.jl index 8298ff379264..0f4ad6b7a3f1 100644 --- a/src/Combinatorics/SimplicialComplexes.jl +++ b/src/Combinatorics/SimplicialComplexes.jl @@ -621,3 +621,33 @@ function deletion(K::SimplicialComplex, face::Union{<:AbstractSet{Int},<:Abstrac zero_based = Polymake.to_zero_based_indexing(face) return SimplicialComplex(Polymake.topaz.deletion(pm_object(K), zero_based)) end + +@doc raw""" + automorphism_group(K::SimplicialComplex) + +Given a simplicial complex `K` return its automorphism group as a `PermGroup`. +The action of the group can be either on vertices or on the facets of `K`. + +# Examples +```jldoctest +julia> K = simplicial_complex([[1, 2, 3], [2, 3, 4]]) +Abstract simplicial complex of dimension 2 on 4 vertices + +julia> automorphism_group(K; action=:on_vertices) +Permutation group of degree 4 + +julia> automorphism_group(K; action=:on_facets) +Permutation group of degree 1 +``` +""" +function automorphism_group(K::SimplicialComplex; action=:on_vertices) + I = minimal_nonfaces(IncidenceMatrix, K) + + if action == :on_vertices + return automorphism_group(I; action=:on_cols) + end + + if action == :on_facets + return automorphism_group(I; action=:on_rows) + end +end diff --git a/test/Combinatorics/SimplicialComplexes.jl b/test/Combinatorics/SimplicialComplexes.jl index 611809b746a0..6abdf05a3fb8 100644 --- a/test/Combinatorics/SimplicialComplexes.jl +++ b/test/Combinatorics/SimplicialComplexes.jl @@ -65,4 +65,13 @@ K2 = simplicial_complex([[1, 2], [2, 3]]) @test is_isomorphic(K1, K2) end + + @testset "automorphism groups" begin + K = simplicial_complex([[1, 2], [2, 3]]) + G = automorphism_group(K) + @test G == permutation_group(3, [cperm([1, 3])]) + + G = automorphism_group(K; action=:on_facets) + @test is_trivial(G) + end end From 29d9d024f614fa067795a3f039d8c516aa49641e Mon Sep 17 00:00:00 2001 From: antonydellavecchia Date: Thu, 7 Mar 2024 10:01:12 +0100 Subject: [PATCH 044/128] adds docs + missing docs for the other recently added functions --- docs/src/Combinatorics/simplicialcomplexes.md | 3 +++ src/Combinatorics/SimplicialComplexes.jl | 2 +- 2 files changed, 4 insertions(+), 1 deletion(-) diff --git a/docs/src/Combinatorics/simplicialcomplexes.md b/docs/src/Combinatorics/simplicialcomplexes.md index 1e9243f63013..32e9c9a7e9aa 100644 --- a/docs/src/Combinatorics/simplicialcomplexes.md +++ b/docs/src/Combinatorics/simplicialcomplexes.md @@ -98,6 +98,9 @@ stanley_reisner_ring(R::MPolyRing, K::SimplicialComplex) ```@docs is_isomorphic(K1::SimplicialComplex, K2::SimplicialComplex) +connected_sum(K1::SimplicialComplex, K2::SimplicialComplex, f1::Int=0, f2::Int=0) +deletion(K::SimplicialComplex, face::Union{<:AbstractSet{Int},<:AbstractVector{Int}}) +automorphism_group(K::SimplicialComplex; action=:on_vertices) ``` ## Saving and loading diff --git a/src/Combinatorics/SimplicialComplexes.jl b/src/Combinatorics/SimplicialComplexes.jl index 0f4ad6b7a3f1..cc31c9abaa13 100644 --- a/src/Combinatorics/SimplicialComplexes.jl +++ b/src/Combinatorics/SimplicialComplexes.jl @@ -640,7 +640,7 @@ julia> automorphism_group(K; action=:on_facets) Permutation group of degree 1 ``` """ -function automorphism_group(K::SimplicialComplex; action=:on_vertices) +function automorphism_group(K::SimplicialComplex; action=:on_vertices) I = minimal_nonfaces(IncidenceMatrix, K) if action == :on_vertices From 9c22f09463970b48998ca2e0f8b0577b4d90878e Mon Sep 17 00:00:00 2001 From: antonydellavecchia Date: Thu, 7 Mar 2024 10:14:54 +0100 Subject: [PATCH 045/128] adjustments to the docs --- src/Combinatorics/SimplicialComplexes.jl | 5 +++-- 1 file changed, 3 insertions(+), 2 deletions(-) diff --git a/src/Combinatorics/SimplicialComplexes.jl b/src/Combinatorics/SimplicialComplexes.jl index cc31c9abaa13..afa6bbc9b8ed 100644 --- a/src/Combinatorics/SimplicialComplexes.jl +++ b/src/Combinatorics/SimplicialComplexes.jl @@ -623,10 +623,11 @@ function deletion(K::SimplicialComplex, face::Union{<:AbstractSet{Int},<:Abstrac end @doc raw""" - automorphism_group(K::SimplicialComplex) + automorphism_group(K::SimplicialComplex; action=:on_vertices) Given a simplicial complex `K` return its automorphism group as a `PermGroup`. -The action of the group can be either on vertices or on the facets of `K`. +The action of the group can be either on the vertices by passing `:on_vertices` to the +`action` keyword argument or on the facets by passing `:on_facets`. # Examples ```jldoctest From 592f7c0f454bb90a0677f78380f1936dd57e2b28 Mon Sep 17 00:00:00 2001 From: antonydellavecchia Date: Thu, 7 Mar 2024 11:30:26 +0100 Subject: [PATCH 046/128] adds n_facets + uses combinatorial symmetries from polymake --- docs/src/Combinatorics/simplicialcomplexes.md | 1 + src/Combinatorics/SimplicialComplexes.jl | 35 ++++++++++++------- test/Combinatorics/SimplicialComplexes.jl | 4 +-- 3 files changed, 25 insertions(+), 15 deletions(-) diff --git a/docs/src/Combinatorics/simplicialcomplexes.md b/docs/src/Combinatorics/simplicialcomplexes.md index 32e9c9a7e9aa..676b88cba41b 100644 --- a/docs/src/Combinatorics/simplicialcomplexes.md +++ b/docs/src/Combinatorics/simplicialcomplexes.md @@ -46,6 +46,7 @@ complex_projective_plane() ```@docs n_vertices(K::SimplicialComplex) +n_facets(K::SimplicialComplex) dim(K::SimplicialComplex) f_vector(K::SimplicialComplex) h_vector(K::SimplicialComplex) diff --git a/src/Combinatorics/SimplicialComplexes.jl b/src/Combinatorics/SimplicialComplexes.jl index afa6bbc9b8ed..f935187e061b 100644 --- a/src/Combinatorics/SimplicialComplexes.jl +++ b/src/Combinatorics/SimplicialComplexes.jl @@ -120,6 +120,13 @@ julia> n_vertices(torus()) """ n_vertices(K::SimplicialComplex) = pm_object(K).N_VERTICES::Int +@doc raw""" + n_facets(K::SimplicialComplex) + +Return the number of facets of the abstract simplicial complex `K`. +""" +n_facets(K::SimplicialComplex) = pm_object(K).N_FACETS::Int + @doc raw""" facets(K::SimplicialComplex) @@ -626,29 +633,31 @@ end automorphism_group(K::SimplicialComplex; action=:on_vertices) Given a simplicial complex `K` return its automorphism group as a `PermGroup`. -The action of the group can be either on the vertices by passing `:on_vertices` to the -`action` keyword argument or on the facets by passing `:on_facets`. +The group can be returned as a subgroup of the permutation group of the vertices +by passing `:on_vertices` to the `action` keyword argument or on the facets + by passing `:on_facets`. # Examples ```jldoctest julia> K = simplicial_complex([[1, 2, 3], [2, 3, 4]]) Abstract simplicial complex of dimension 2 on 4 vertices -julia> automorphism_group(K; action=:on_vertices) +julia> automorphism_group(K) Permutation group of degree 4 - -julia> automorphism_group(K; action=:on_facets) -Permutation group of degree 1 ``` """ function automorphism_group(K::SimplicialComplex; action=:on_vertices) - I = minimal_nonfaces(IncidenceMatrix, K) - + pm_K = Oscar.pm_object(K) + Polymake.topaz.combinatorial_symmetries(pm_K) if action == :on_vertices - return automorphism_group(I; action=:on_cols) - end - - if action == :on_facets - return automorphism_group(I; action=:on_rows) + gens_G = Polymake.to_one_based_indexing(pm_K.GROUP.RAYS_ACTION.GENERATORS) + n = n_vertices(K) + return permutation_group(n, cperm.(gens_G)) + elseif action == :on_facets + gens_G = Polymake.to_one_based_indexing(pm_K.GROUP.FACETS_ACTION.GENERATORS) + n = n_facets(K) + return permutation_group(n, cperm.(gens_G)) + else + error("unsupported keyword passed to action") end end diff --git a/test/Combinatorics/SimplicialComplexes.jl b/test/Combinatorics/SimplicialComplexes.jl index 6abdf05a3fb8..1ee6fa99086f 100644 --- a/test/Combinatorics/SimplicialComplexes.jl +++ b/test/Combinatorics/SimplicialComplexes.jl @@ -69,9 +69,9 @@ @testset "automorphism groups" begin K = simplicial_complex([[1, 2], [2, 3]]) G = automorphism_group(K) - @test G == permutation_group(3, [cperm([1, 3])]) + @test G == permutation_group(3, cperm.([[1, 2, 3], [1, 3, 2]])) G = automorphism_group(K; action=:on_facets) - @test is_trivial(G) + @test G == permutation_group(2, [cperm([1, 2])]) end end From 5acb531baa5d1ec7fdf4bee629377242f1b6f716 Mon Sep 17 00:00:00 2001 From: antonydellavecchia Date: Thu, 7 Mar 2024 16:45:03 +0100 Subject: [PATCH 047/128] acts on_simplicial_complex --- docs/src/Combinatorics/simplicialcomplexes.md | 1 + src/Combinatorics/SimplicialComplexes.jl | 27 +++++++++++++++++++ src/exports.jl | 1 + test/Combinatorics/SimplicialComplexes.jl | 4 +++ 4 files changed, 33 insertions(+) diff --git a/docs/src/Combinatorics/simplicialcomplexes.md b/docs/src/Combinatorics/simplicialcomplexes.md index 676b88cba41b..487bdcc039f8 100644 --- a/docs/src/Combinatorics/simplicialcomplexes.md +++ b/docs/src/Combinatorics/simplicialcomplexes.md @@ -102,6 +102,7 @@ is_isomorphic(K1::SimplicialComplex, K2::SimplicialComplex) connected_sum(K1::SimplicialComplex, K2::SimplicialComplex, f1::Int=0, f2::Int=0) deletion(K::SimplicialComplex, face::Union{<:AbstractSet{Int},<:AbstractVector{Int}}) automorphism_group(K::SimplicialComplex; action=:on_vertices) +on_simplicial_complex(K::SimplicialComplex, g::PermGroupElem) ``` ## Saving and loading diff --git a/src/Combinatorics/SimplicialComplexes.jl b/src/Combinatorics/SimplicialComplexes.jl index f935187e061b..364c223086be 100644 --- a/src/Combinatorics/SimplicialComplexes.jl +++ b/src/Combinatorics/SimplicialComplexes.jl @@ -661,3 +661,30 @@ function automorphism_group(K::SimplicialComplex; action=:on_vertices) error("unsupported keyword passed to action") end end + +@doc raw""" + on_simplicial_complex(K::SimplicialComplex, g::PermGroupElem) + +Given a simplicial complex `K` return the simplicial complex corresponding +to a permutation on it's vertices given by `g`. + +# Examples +```jldoctest +julia> K = simplicial_complex([[1, 2, 3], [2, 3, 4]]) +Abstract simplicial complex of dimension 2 on 4 vertices + +julia> G = automorphism_group(K) +Permutation group of degree 4 + +julia> g = collect(G)[2] +(1,5,4,2,3) + +julia> on_simplicial_complex(K, g) +Abstract simplicial complex of dimension 2 on 5 vertices +``` +""" +function on_simplicial_complex(K::SimplicialComplex, g::PermGroupElem) + @req order(parent(g)) == n_vertices(K) "g needs to be an element of the permutation group on the vertices" + new_facets = on_sets_sets(Set(facets(K)), g) + simplicial_complex(collect(new_facets)) +end diff --git a/src/exports.jl b/src/exports.jl index 4ee2c6f2169b..2e9c88c77f78 100644 --- a/src/exports.jl +++ b/src/exports.jl @@ -1110,6 +1110,7 @@ export on_indeterminates export on_lines export on_sets export on_sets_sets +export on_simplicial_complex export on_subgroups export on_tuples export one! diff --git a/test/Combinatorics/SimplicialComplexes.jl b/test/Combinatorics/SimplicialComplexes.jl index 1ee6fa99086f..ffd22bc1d753 100644 --- a/test/Combinatorics/SimplicialComplexes.jl +++ b/test/Combinatorics/SimplicialComplexes.jl @@ -71,6 +71,10 @@ G = automorphism_group(K) @test G == permutation_group(3, cperm.([[1, 2, 3], [1, 3, 2]])) + g = collect(G)[2] + G_K = on_simplicial_complex(K, g) + @test facets(simplicial_complex([[1, 3], [2, 3]])) == facets(G_K) + G = automorphism_group(K; action=:on_facets) @test G == permutation_group(2, [cperm([1, 2])]) end From e74d373da6c16cadad87d8d5b3b6a07268835244 Mon Sep 17 00:00:00 2001 From: Antony Della Vecchia Date: Mon, 11 Mar 2024 11:35:42 +0100 Subject: [PATCH 048/128] fixes for docstrings --- src/Combinatorics/SimplicialComplexes.jl | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/src/Combinatorics/SimplicialComplexes.jl b/src/Combinatorics/SimplicialComplexes.jl index 364c223086be..8785707e55bc 100644 --- a/src/Combinatorics/SimplicialComplexes.jl +++ b/src/Combinatorics/SimplicialComplexes.jl @@ -677,10 +677,10 @@ julia> G = automorphism_group(K) Permutation group of degree 4 julia> g = collect(G)[2] -(1,5,4,2,3) +(1,2)(3,4) julia> on_simplicial_complex(K, g) -Abstract simplicial complex of dimension 2 on 5 vertices +Abstract simplicial complex of dimension 2 on 4 vertices ``` """ function on_simplicial_complex(K::SimplicialComplex, g::PermGroupElem) From fa7f6f411d7415e1d2cdf4c22fd776896ced7c02 Mon Sep 17 00:00:00 2001 From: antonydellavecchia Date: Wed, 13 Mar 2024 10:20:51 +0100 Subject: [PATCH 049/128] warning --- src/Combinatorics/SimplicialComplexes.jl | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/Combinatorics/SimplicialComplexes.jl b/src/Combinatorics/SimplicialComplexes.jl index 3a9f79fc633c..9282dd28a144 100644 --- a/src/Combinatorics/SimplicialComplexes.jl +++ b/src/Combinatorics/SimplicialComplexes.jl @@ -688,7 +688,7 @@ Abstract simplicial complex of dimension 2 on 5 vertices ``` """ function on_simplicial_complex(K::SimplicialComplex, g::PermGroupElem) - @req order(parent(g)) == n_vertices(K) "g needs to be an element of the permutation group on the vertices" + @req degree(parent(g)) == n_vertices(K) "g needs to be an element of the permutation group on the vertices" new_facets = on_sets_sets(Set(facets(K)), g) simplicial_complex(collect(new_facets)) end From f49653f0f28e4dc7c61335e9fa70db70a5666aa9 Mon Sep 17 00:00:00 2001 From: Antony Della Vecchia Date: Tue, 19 Mar 2024 12:11:26 +0100 Subject: [PATCH 050/128] fixes require check --- src/Combinatorics/SimplicialComplexes.jl | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/Combinatorics/SimplicialComplexes.jl b/src/Combinatorics/SimplicialComplexes.jl index 8785707e55bc..3fc438ba717f 100644 --- a/src/Combinatorics/SimplicialComplexes.jl +++ b/src/Combinatorics/SimplicialComplexes.jl @@ -684,7 +684,7 @@ Abstract simplicial complex of dimension 2 on 4 vertices ``` """ function on_simplicial_complex(K::SimplicialComplex, g::PermGroupElem) - @req order(parent(g)) == n_vertices(K) "g needs to be an element of the permutation group on the vertices" + @req degree(parent(g)) == n_vertices(K) "g needs to be an element of the permutation group on the vertices" new_facets = on_sets_sets(Set(facets(K)), g) simplicial_complex(collect(new_facets)) end From 1addc98607eb0b48aca7b9cd9e4da47f96dc684b Mon Sep 17 00:00:00 2001 From: antonydellavecchia Date: Mon, 6 May 2024 13:29:54 +0200 Subject: [PATCH 051/128] add missing vertices --- experimental/AlgebraicShifting/src/AlgebraicShifting.jl | 5 ++++- 1 file changed, 4 insertions(+), 1 deletion(-) diff --git a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl index cda394d249ee..15276e09f298 100644 --- a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl +++ b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl @@ -114,7 +114,10 @@ function exterior_shift(F::Field, K::SimplicialComplex; return nCk[delta_k] end - return simplicial_complex(input_faces) + # add missing vertices + vertices_in_edges = reduce(union, input_faces) + missing_vertices = [[missing_v] for missing_v in symdiff(Set(1:n), vertices_in_edges)] + return simplicial_complex([input_faces..., missing_vertices...]) end @doc raw""" From a82180c9ebe9fff32ffd8b70170146d955064ff9 Mon Sep 17 00:00:00 2001 From: antonydellavecchia Date: Mon, 5 Aug 2024 08:35:19 +0200 Subject: [PATCH 052/128] simplicial product --- src/Combinatorics/SimplicialComplexes.jl | 4 ++++ src/exports.jl | 1 + 2 files changed, 5 insertions(+) diff --git a/src/Combinatorics/SimplicialComplexes.jl b/src/Combinatorics/SimplicialComplexes.jl index bc2faae31403..b4f115f53626 100644 --- a/src/Combinatorics/SimplicialComplexes.jl +++ b/src/Combinatorics/SimplicialComplexes.jl @@ -693,3 +693,7 @@ function on_simplicial_complex(K::SimplicialComplex, g::PermGroupElem) new_facets = on_sets_sets(Set(facets(K)), g) simplicial_complex(collect(new_facets)) end + +function simplicial_product(K1::SimplicialComplex, K2::SimplicialComplex) + return SimplicialComplex(Polymake.topaz.simplicial_product(pm_object(K1), pm_object(K2))) +end diff --git a/src/exports.jl b/src/exports.jl index e67c2f9fbc8e..917e1a96c379 100644 --- a/src/exports.jl +++ b/src/exports.jl @@ -1364,6 +1364,7 @@ export signed_incidence_matrix export signed_permutahedron export simplex export simplicial_complex +export simplicial_product export simplified_fp_group export simplify export simplify! From d61a096bcefef058aebafb326f4e079fc3e04f0c Mon Sep 17 00:00:00 2001 From: Antony Della Vecchia Date: Fri, 9 Aug 2024 20:13:31 +0200 Subject: [PATCH 053/128] added link_subcomplex --- src/Combinatorics/SimplicialComplexes.jl | 5 +++++ 1 file changed, 5 insertions(+) diff --git a/src/Combinatorics/SimplicialComplexes.jl b/src/Combinatorics/SimplicialComplexes.jl index b4f115f53626..6ca4a015ea1d 100644 --- a/src/Combinatorics/SimplicialComplexes.jl +++ b/src/Combinatorics/SimplicialComplexes.jl @@ -697,3 +697,8 @@ end function simplicial_product(K1::SimplicialComplex, K2::SimplicialComplex) return SimplicialComplex(Polymake.topaz.simplicial_product(pm_object(K1), pm_object(K2))) end + +function link_subcomplex(K::SimplicialComplex, face::Union{<:AbstractSet{Int},<:AbstractVector{Int}}) + zero_based_face = Polymake.to_zero_based_indexing(face) + return SimplicialComplex(Polymake.link_subcomplex(pm_object(K), zero_based_face)) +end From 14b61a1b1697500550dd3060f4710dae843e82cc Mon Sep 17 00:00:00 2001 From: Antony Della Vecchia Date: Tue, 20 Aug 2024 17:14:17 +0200 Subject: [PATCH 054/128] reduce over quotients --- experimental/AlgebraicShifting/src/AlgebraicShifting.jl | 4 ++++ 1 file changed, 4 insertions(+) diff --git a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl index 15276e09f298..6ccfadde87c5 100644 --- a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl +++ b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl @@ -107,6 +107,10 @@ function exterior_shift(F::Field, K::SimplicialComplex; if is_generic Oscar.ModStdQt.ref_ff_rc!(A) + elseif matrix_base isa MPolyQuoRing + A_lift = lift.(A) + A = matrix_base.(Oscar.ModStdQt.ref_ff_rc!(A_lift)) + simplify!.(A) else rref!(A) end From d28bfb692fc80a4715ec1bec4b12dc47a79edb5c Mon Sep 17 00:00:00 2001 From: Antony Della Vecchia Date: Mon, 26 Aug 2024 20:50:57 +0200 Subject: [PATCH 055/128] barycentric sub div --- src/Combinatorics/SimplicialComplexes.jl | 4 ++++ src/exports.jl | 1 + 2 files changed, 5 insertions(+) diff --git a/src/Combinatorics/SimplicialComplexes.jl b/src/Combinatorics/SimplicialComplexes.jl index 6ca4a015ea1d..07a067f49d75 100644 --- a/src/Combinatorics/SimplicialComplexes.jl +++ b/src/Combinatorics/SimplicialComplexes.jl @@ -702,3 +702,7 @@ function link_subcomplex(K::SimplicialComplex, face::Union{<:AbstractSet{Int},<: zero_based_face = Polymake.to_zero_based_indexing(face) return SimplicialComplex(Polymake.link_subcomplex(pm_object(K), zero_based_face)) end + +function barycentric_subdivision(K::SimplicialComplex) + return SimplicialComplex(Polymake.topaz.barycentric_subdivision(pm_object(K))) +end diff --git a/src/exports.jl b/src/exports.jl index 64d75660015e..f2534c8169af 100644 --- a/src/exports.jl +++ b/src/exports.jl @@ -273,6 +273,7 @@ export bases export basis_of_global_sections export basis_of_global_sections_via_homogeneous_component export basis_of_global_sections_via_rational_functions +export barycentric_subdivision export bell export betti export betti_number From 33e463bef2cc23eb100f1194b9cfd2f4e339d9d9 Mon Sep 17 00:00:00 2001 From: Antony Della Vecchia Date: Thu, 29 Aug 2024 19:27:09 +0200 Subject: [PATCH 056/128] json -> JSON3.write --- src/Serialization/Combinatorics.jl | 8 ++++---- src/Serialization/PolyhedralGeometry.jl | 2 +- src/Serialization/main.jl | 6 +++--- src/Serialization/polymake.jl | 8 ++++---- 4 files changed, 12 insertions(+), 12 deletions(-) diff --git a/src/Serialization/Combinatorics.jl b/src/Serialization/Combinatorics.jl index 0c38256629a1..1207efa0e071 100644 --- a/src/Serialization/Combinatorics.jl +++ b/src/Serialization/Combinatorics.jl @@ -15,7 +15,7 @@ end function load_object(s::DeserializerState, g::Type{Graph{T}}) where T <: Union{Directed, Undirected} - smallobj = Polymake.call_function(:common, :deserialize_json_string, json(s.obj)) + smallobj = Polymake.call_function(:common, :deserialize_json_string, JSON3.write(s.obj)) return g(smallobj) end @@ -56,7 +56,7 @@ function save_object(s::SerializerState, IM::IncidenceMatrix) end function load_object(s::DeserializerState, ::Type{<: IncidenceMatrix}) - IM = Polymake.call_function(:common, :deserialize_json_string, json(s.obj)) + IM = Polymake.call_function(:common, :deserialize_json_string, JSON3.write(s.obj)) return IM end @@ -71,7 +71,7 @@ function save_object(s::SerializerState, K::SimplicialComplex) end function load_object(s::DeserializerState, K::Type{SimplicialComplex}) - bigobject = Polymake.call_function(:common, :deserialize_json_string, json(s.obj)) + bigobject = Polymake.call_function(:common, :deserialize_json_string, JSON3.write(s.obj)) return K(bigobject) end @@ -85,6 +85,6 @@ function save_object(s::SerializerState, PT::PhylogeneticTree) end function load_object(s::DeserializerState, T::Type{PhylogeneticTree}, dict::Dict) - bigobject = Polymake.call_function(:common, :deserialize_json_string, json(dict)) + bigobject = Polymake.call_function(:common, :deserialize_json_string, JSON3.write(dict)) return T(bigobject) end diff --git a/src/Serialization/PolyhedralGeometry.jl b/src/Serialization/PolyhedralGeometry.jl index 883ab3a84b9d..b377a04db931 100644 --- a/src/Serialization/PolyhedralGeometry.jl +++ b/src/Serialization/PolyhedralGeometry.jl @@ -21,7 +21,7 @@ end function load_object(s::DeserializerState, ::Type{Polymake.BigObject}) dict = Dict{Symbol, Any}(s.obj) - bigobject = Polymake.call_function(:common, :deserialize_json_string, json(dict)) + bigobject = Polymake.call_function(:common, :deserialize_json_string, JSON3.write(dict)) return bigobject end diff --git a/src/Serialization/main.jl b/src/Serialization/main.jl index 2de3cf9a271c..0b229de2d1a0 100644 --- a/src/Serialization/main.jl +++ b/src/Serialization/main.jl @@ -543,7 +543,7 @@ function save(io::IO, obj::T; metadata::Union{MetaData, Nothing}=nothing, end if !isnothing(metadata) - save_json(s, json(metadata), :meta) + save_json(s, JSON3.write(metadata), :meta) end end serializer_close(s) @@ -653,9 +653,9 @@ function load(io::IO; params::Any = nothing, type::Any = nothing, end if file_version < VERSION_NUMBER - jsondict = JSON.parse(json(s.obj), dicttype=Dict{Symbol, Any}) + jsondict = JSON.parse(JSON3.write(s.obj), dicttype=Dict{Symbol, Any}) jsondict = upgrade(file_version, jsondict) - s.obj = JSON3.read(json(jsondict)) + s.obj = JSON3.read(JSON2.write(jsondict)) if haskey(s.obj, refs_key) s.refs = s.obj[refs_key] diff --git a/src/Serialization/polymake.jl b/src/Serialization/polymake.jl index 012346ab1f28..432b58706a77 100644 --- a/src/Serialization/polymake.jl +++ b/src/Serialization/polymake.jl @@ -8,12 +8,12 @@ Load a graph stored in JSON format, given the filename as input. """ function load_from_polymake(::Type{Graph{T}}, jsondict::Dict{Symbol, Any}) where {T <: Union{Directed, Undirected}} - polymake_object = Polymake.call_function(:common, :deserialize_json_string, json(jsondict)) + polymake_object = Polymake.call_function(:common, :deserialize_json_string, JSON3.write(jsondict)) return Graph{T}(polymake_object) end function load_from_polymake(::Type{PhylogeneticTree{T}}, jsondict::Dict{Symbol, Any}) where {T <: Union{Float64, Int, QQFieldElem}} - polymake_object = Polymake.call_function(:common, :deserialize_json_string, json(jsondict)) + polymake_object = Polymake.call_function(:common, :deserialize_json_string, JSON3.write(jsondict)) return PhylogeneticTree{T}(polymake_object) end @@ -35,7 +35,7 @@ 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)) + inner_object = Polymake.call_function(:common, :deserialize_json_string, JSON3.write(jsondict)) if T <: PolyhedralObject{Float64} return T(inner_object, AbstractAlgebra.Floats{Float64}()) end @@ -54,7 +54,7 @@ function load_from_polymake(jsondict::Dict{Symbol, Any}) return load_from_polymake(oscar_type, jsondict) else # We just try to default to something from Polymake.jl - deserialized = Polymake.call_function(:common, :deserialize_json_string, json(jsondict)) + deserialized = Polymake.call_function(:common, :deserialize_json_string, JSON3.write(jsondict)) if !isa(deserialized, Polymake.BigObject) @warn "No function for converting the deserialized Polymake type to Oscar type: $(typeof(deserialized))" return deserialized From 2c9a7171e81fc3b9e6678d888f36b61ea2a425b3 Mon Sep 17 00:00:00 2001 From: Benjamin Lorenz Date: Thu, 29 Aug 2024 19:41:18 +0200 Subject: [PATCH 057/128] Update src/Serialization/main.jl --- src/Serialization/main.jl | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/Serialization/main.jl b/src/Serialization/main.jl index 0b229de2d1a0..502c8f812357 100644 --- a/src/Serialization/main.jl +++ b/src/Serialization/main.jl @@ -655,7 +655,7 @@ function load(io::IO; params::Any = nothing, type::Any = nothing, if file_version < VERSION_NUMBER jsondict = JSON.parse(JSON3.write(s.obj), dicttype=Dict{Symbol, Any}) jsondict = upgrade(file_version, jsondict) - s.obj = JSON3.read(JSON2.write(jsondict)) + s.obj = JSON3.read(JSON3.write(jsondict)) if haskey(s.obj, refs_key) s.refs = s.obj[refs_key] From a1a5a8a6e09845181657186587d4f833060bcc36 Mon Sep 17 00:00:00 2001 From: antonydellavecchia Date: Fri, 30 Aug 2024 13:57:06 +0200 Subject: [PATCH 058/128] fixes upgrade scripts --- src/Serialization/Upgrades/0.12.2.jl | 4 +++- src/Serialization/Upgrades/main.jl | 11 +++++++++-- src/Serialization/main.jl | 9 ++++----- src/Serialization/serializers.jl | 2 +- 4 files changed, 17 insertions(+), 9 deletions(-) diff --git a/src/Serialization/Upgrades/0.12.2.jl b/src/Serialization/Upgrades/0.12.2.jl index 6a7f00f00c30..f367dd3f19bc 100644 --- a/src/Serialization/Upgrades/0.12.2.jl +++ b/src/Serialization/Upgrades/0.12.2.jl @@ -23,6 +23,7 @@ push!(upgrade_scripts_set, UpgradeScript( v"0.12.2", function upgrade_0_12_2(s::UpgradeState, dict::Dict) + s.nested_level += 1 # moves down tree to point where type exists in dict # since we are only doing updates based on certain types # no :type key implies the dict is data @@ -133,7 +134,8 @@ push!(upgrade_scripts_set, UpgradeScript( merge!(s.id_to_dict, local_refs) end - if !isempty(s.id_to_dict) + s.nested_level -= 1 + if !isempty(s.id_to_dict) && s.nested_level == 0 upgraded_dict[:refs] = s.id_to_dict end diff --git a/src/Serialization/Upgrades/main.jl b/src/Serialization/Upgrades/main.jl index 8f16414cc99c..bb168ddbe6ee 100644 --- a/src/Serialization/Upgrades/main.jl +++ b/src/Serialization/Upgrades/main.jl @@ -41,12 +41,13 @@ function script(upgrade_script::UpgradeScript) return upgrade_script.script end -struct UpgradeState +mutable struct UpgradeState id_to_dict::Dict{Symbol, Any} + nested_level::Int end function UpgradeState() - return UpgradeState(Dict{Symbol, Any}()) + return UpgradeState(Dict{Symbol, Any}(), 0) end (u_s::UpgradeScript)(s::UpgradeState, @@ -63,6 +64,7 @@ recursing on the tree structure. It is independent of any particular file format version and can be used in any upgrade script. """ function upgrade_data(upgrade::Function, s::UpgradeState, dict::Dict) + s.nested_level += 1 # file comes from polymake haskey(dict, :_ns) && haskey(dict[:_ns], :polymake) && return dict @@ -71,19 +73,24 @@ function upgrade_data(upgrade::Function, s::UpgradeState, dict::Dict) if dict_value isa String || dict_value isa Int64 || dict_value isa Bool upgraded_dict[key] = dict_value elseif dict_value isa Dict + s.nested_level += 1 upgraded_dict[key] = upgrade(s, dict_value) + s.nested_level -= 1 else # not a string or a dictionary, so must be a vector new_value = [] for v in dict_value if v isa String push!(new_value, v) else + s.nested_level += 1 push!(new_value, upgrade(s, v)) + s.nested_level -= 1 end end upgraded_dict[key] = new_value end end + s.nested_level -= 1 return upgraded_dict end diff --git a/src/Serialization/main.jl b/src/Serialization/main.jl index 502c8f812357..abf5b85c979d 100644 --- a/src/Serialization/main.jl +++ b/src/Serialization/main.jl @@ -655,11 +655,10 @@ function load(io::IO; params::Any = nothing, type::Any = nothing, if file_version < VERSION_NUMBER jsondict = JSON.parse(JSON3.write(s.obj), dicttype=Dict{Symbol, Any}) jsondict = upgrade(file_version, jsondict) - s.obj = JSON3.read(JSON3.write(jsondict)) - - if haskey(s.obj, refs_key) - s.refs = s.obj[refs_key] - end + jsondict_str = JSON3.write(jsondict) + s = state(deserializer_open(jsondict_str, + serializer_type, + with_attrs ? type_attr_map : Dict{String, Vector{Symbol}}())) end try diff --git a/src/Serialization/serializers.jl b/src/Serialization/serializers.jl index 2466707c0711..c637f5643c25 100644 --- a/src/Serialization/serializers.jl +++ b/src/Serialization/serializers.jl @@ -224,7 +224,7 @@ function serializer_open( end function deserializer_open( - io::IO, + io::Union{IO, String}, T::Type{JSONSerializer}, type_attr_map::S) where S <:Union{Dict{String, Vector{Symbol}}, Nothing} From caa5530044ec9c75e9744bda56f190b298f54617 Mon Sep 17 00:00:00 2001 From: antonydellavecchia Date: Fri, 30 Aug 2024 14:25:42 +0200 Subject: [PATCH 059/128] Update src/Serialization/main.jl but, s.obj should always be from JSON3, at least until we change something Co-authored-by: Benjamin Lorenz --- src/Serialization/main.jl | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/src/Serialization/main.jl b/src/Serialization/main.jl index abf5b85c979d..05d6955feba7 100644 --- a/src/Serialization/main.jl +++ b/src/Serialization/main.jl @@ -653,7 +653,8 @@ function load(io::IO; params::Any = nothing, type::Any = nothing, end if file_version < VERSION_NUMBER - jsondict = JSON.parse(JSON3.write(s.obj), dicttype=Dict{Symbol, Any}) + # we need a mutable dictionary + jsondict = copy(s.obj) jsondict = upgrade(file_version, jsondict) jsondict_str = JSON3.write(jsondict) s = state(deserializer_open(jsondict_str, From c8b95701f72045bd5984162d2f06cda71683045f Mon Sep 17 00:00:00 2001 From: Antony Della Vecchia Date: Mon, 9 Sep 2024 10:09:29 +0200 Subject: [PATCH 060/128] use io instead of string --- src/Serialization/main.jl | 2 +- src/Serialization/serializers.jl | 2 +- 2 files changed, 2 insertions(+), 2 deletions(-) diff --git a/src/Serialization/main.jl b/src/Serialization/main.jl index 05d6955feba7..b7a331776e42 100644 --- a/src/Serialization/main.jl +++ b/src/Serialization/main.jl @@ -657,7 +657,7 @@ function load(io::IO; params::Any = nothing, type::Any = nothing, jsondict = copy(s.obj) jsondict = upgrade(file_version, jsondict) jsondict_str = JSON3.write(jsondict) - s = state(deserializer_open(jsondict_str, + s = state(deserializer_open(IOBufer(jsondict_str), serializer_type, with_attrs ? type_attr_map : Dict{String, Vector{Symbol}}())) end diff --git a/src/Serialization/serializers.jl b/src/Serialization/serializers.jl index c637f5643c25..2466707c0711 100644 --- a/src/Serialization/serializers.jl +++ b/src/Serialization/serializers.jl @@ -224,7 +224,7 @@ function serializer_open( end function deserializer_open( - io::Union{IO, String}, + io::IO, T::Type{JSONSerializer}, type_attr_map::S) where S <:Union{Dict{String, Vector{Symbol}}, Nothing} From 96fcaf03bb897c58c67857d53cb5533b210592a4 Mon Sep 17 00:00:00 2001 From: Antony Della Vecchia Date: Mon, 9 Sep 2024 10:24:37 +0200 Subject: [PATCH 061/128] typo --- src/Serialization/main.jl | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/Serialization/main.jl b/src/Serialization/main.jl index b7a331776e42..bd32b0515e8b 100644 --- a/src/Serialization/main.jl +++ b/src/Serialization/main.jl @@ -657,7 +657,7 @@ function load(io::IO; params::Any = nothing, type::Any = nothing, jsondict = copy(s.obj) jsondict = upgrade(file_version, jsondict) jsondict_str = JSON3.write(jsondict) - s = state(deserializer_open(IOBufer(jsondict_str), + s = state(deserializer_open(IOBuffer(jsondict_str), serializer_type, with_attrs ? type_attr_map : Dict{String, Vector{Symbol}}())) end From 13b1e26cc0e5b8a508dea43fc2c9a2a20feb481a Mon Sep 17 00:00:00 2001 From: Antony Della Vecchia Date: Mon, 9 Sep 2024 11:46:29 +0200 Subject: [PATCH 062/128] fix arguments to deserializer_open --- src/Serialization/main.jl | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/Serialization/main.jl b/src/Serialization/main.jl index 6571d63b7bdf..a2072d132194 100644 --- a/src/Serialization/main.jl +++ b/src/Serialization/main.jl @@ -660,7 +660,7 @@ function load(io::IO; params::Any = nothing, type::Any = nothing, jsondict_str = JSON3.write(jsondict) s = state(deserializer_open(IOBuffer(jsondict_str), serializer_type, - with_attrs ? type_attr_map : Dict{String, Vector{Symbol}}())) + with_attrs)) end try From 973d9e867853ae0b60d6feb1717143d2b059c927 Mon Sep 17 00:00:00 2001 From: Antony Della Vecchia Date: Tue, 10 Sep 2024 10:55:30 +0200 Subject: [PATCH 063/128] remove white space --- src/Serialization/main.jl | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/Serialization/main.jl b/src/Serialization/main.jl index a2072d132194..7bac5fbdd626 100644 --- a/src/Serialization/main.jl +++ b/src/Serialization/main.jl @@ -710,7 +710,7 @@ function load(io::IO; params::Any = nothing, type::Any = nothing, using Oscar version $VERSION_NUMBER """ end - + if contains(string(file_version), "DEV") commit = split(string(file_version), "-")[end] @warn "Attempted loading file stored using a DEV version with commit $commit" From 00e1ffb3afa3821963c6141df89b5021091a836a Mon Sep 17 00:00:00 2001 From: Antony Della Vecchia Date: Tue, 10 Sep 2024 11:40:46 +0200 Subject: [PATCH 064/128] no need for key when serializing weyl group --- experimental/LieAlgebras/src/serialization.jl | 6 ++---- 1 file changed, 2 insertions(+), 4 deletions(-) diff --git a/experimental/LieAlgebras/src/serialization.jl b/experimental/LieAlgebras/src/serialization.jl index 9d74c7a26357..d4c9f076504c 100644 --- a/experimental/LieAlgebras/src/serialization.jl +++ b/experimental/LieAlgebras/src/serialization.jl @@ -313,13 +313,11 @@ end @register_serialization_type WeylGroup uses_id function save_object(s::SerializerState, W::WeylGroup) - save_data_dict(s) do - save_typed_object(s, root_system(W), :root_system) - end + save_object(s, root_system(W)) end function load_object(s::DeserializerState, ::Type{WeylGroup}) - R = load_typed_object(s, :root_system) + R = load_object(s, RootSystem) return weyl_group(R) end From 00cb3fc7e0a5820eae8397402996861c45a63bd7 Mon Sep 17 00:00:00 2001 From: Antony Della Vecchia Date: Tue, 10 Sep 2024 11:49:41 +0200 Subject: [PATCH 065/128] root system uses ref --- experimental/LieAlgebras/src/serialization.jl | 5 +++-- 1 file changed, 3 insertions(+), 2 deletions(-) diff --git a/experimental/LieAlgebras/src/serialization.jl b/experimental/LieAlgebras/src/serialization.jl index d4c9f076504c..f19d98c2e8ba 100644 --- a/experimental/LieAlgebras/src/serialization.jl +++ b/experimental/LieAlgebras/src/serialization.jl @@ -313,11 +313,12 @@ end @register_serialization_type WeylGroup uses_id function save_object(s::SerializerState, W::WeylGroup) - save_object(s, root_system(W)) + RS_ref = save_as_ref(s, root_system(W)) + save_object(s, RS_ref) end function load_object(s::DeserializerState, ::Type{WeylGroup}) - R = load_object(s, RootSystem) + R = load_ref(s) return weyl_group(R) end From 944ac0c3d4aa81978108882c62f3812fac336c04 Mon Sep 17 00:00:00 2001 From: Antony Della Vecchia Date: Thu, 10 Oct 2024 16:05:35 +0200 Subject: [PATCH 066/128] unifiying the exterior shift function --- .../src/AlgebraicShifting.jl | 119 +------------- .../AlgebraicShifting/src/PartialShift.jl | 146 ++++++++++++++++++ .../src/UniformHypergraph.jl | 49 ++++++ 3 files changed, 203 insertions(+), 111 deletions(-) create mode 100644 experimental/AlgebraicShifting/src/PartialShift.jl create mode 100644 experimental/AlgebraicShifting/src/UniformHypergraph.jl diff --git a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl index 6ccfadde87c5..7b314a129d79 100644 --- a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl +++ b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl @@ -1,3 +1,11 @@ +include("UniformHypergraph.jl") +include("PartialShift.jl") + +export PartialExtShift +export UniformHypergraph + +export uniform_hypergraph + function independent_columns(A::MatElem) col_indices = Int[] row_index = 1 @@ -12,117 +20,6 @@ function independent_columns(A::MatElem) return col_indices end -# applies function on faces of equal dimension -function apply_on_faces(f::Function, K::SimplicialComplex) - dim_K = dim(K) - K_facets = facets(K) - facet_dict = Dict( - (k => Set(filter(f -> length(f) == k + 1, K_facets)) for k in 1:dim_K ) - ) - - # look into hasse diagram from polymake - - for facet in K_facets - dim_facet = length(facet) - 1 - - for subset_size in 2:dim_facet - for subset in subsets(facet, subset_size) - push!(facet_dict[subset_size - 1], subset) - end - end - end - - input_faces = Vector{Int}[] - for (dim_face, faces) in facet_dict - input_faces = vcat(input_faces, f((dim_face, collect.(faces)))) - end - return input_faces -end - -function shift_basis_ext(F::Field, K::SimplicialComplex) - n = n_vertices(K) - shifted_K = Oscar.delta_ext(F, K) - lambda, _ = exterior_algebra(F, n) - x = gens(lambda) - - ker_gens = [ - reduce(*, lift.( - x[collect(f)] - )) for f in minimal_nonfaces(K) - ] - - lift_ring = base_ring(lambda) - J = two_sided_ideal(lift_ring, (ker_gens)) - A, _ = quo(lift_ring, J + modulus(lambda)) - x = gens(A) - basis = [reduce(*, x[collect(s)]) for s in facets(shifted_K)] - - return A, basis -end - -@doc raw""" - exterior_shift(F::Field, K::SimplicialComplex) - -Returns the exterior shift of `K` -""" -function exterior_shift(F::Field, K::SimplicialComplex; - change_of_basis::T = nothing) where T <: Union{Nothing, MatElem} - # the exterior shifting works in a different algebra that lends - # itself to an easier implementation - n = n_vertices(K) - is_generic = false - if isnothing(change_of_basis) - is_generic = true - # generic change of basis - Fx, x = polynomial_ring(F, :x => (1:n, 1:n)) - change_of_basis = matrix(Fx, hcat(x)) - matrix_base = Fx - else - matrix_base = base_ring(change_of_basis) - if matrix_base isa MPolyRing - is_generic = true - end - end - - input_faces = apply_on_faces(K) do (dim_face, faces) - # is needed here since otherwise the sets are not - # in lex order, seubsets is being called from Hecke, - # maybe we should look into this and see if polymake's - # is preffered? - nCk = sort(subsets(n, dim_face + 1)) - entry_type = elem_type(matrix_base) - - sub_compound_matrix = Vector{entry_type}[] - - for col_subset in nCk - row_minors = entry_type[] - for row_subset in faces - ri = collect(row_subset) - ci = collect(col_subset) - push!(row_minors, det(change_of_basis[ri, ci])) - end - push!(sub_compound_matrix, row_minors) - end - A = matrix(reduce(hcat, sub_compound_matrix)) - - if is_generic - Oscar.ModStdQt.ref_ff_rc!(A) - elseif matrix_base isa MPolyQuoRing - A_lift = lift.(A) - A = matrix_base.(Oscar.ModStdQt.ref_ff_rc!(A_lift)) - simplify!.(A) - else - rref!(A) - end - delta_k = independent_columns(A) - return nCk[delta_k] - end - - # add missing vertices - vertices_in_edges = reduce(union, input_faces) - missing_vertices = [[missing_v] for missing_v in symdiff(Set(1:n), vertices_in_edges)] - return simplicial_complex([input_faces..., missing_vertices...]) -end @doc raw""" symmetric_shift(F::Field, K::SimplicialComplex) diff --git a/experimental/AlgebraicShifting/src/PartialShift.jl b/experimental/AlgebraicShifting/src/PartialShift.jl new file mode 100644 index 000000000000..a9ef72ce1898 --- /dev/null +++ b/experimental/AlgebraicShifting/src/PartialShift.jl @@ -0,0 +1,146 @@ +################################################################################ +# helpful functions for Partial Shifts +################################################################################ + +const ComplexOrHypergraph = Union{UniformHypergraph, SimplicialComplex} + +################################################################################ +# Matrix construction helper functions +function inversions(g::PermGroupElem) + return [(i,j) for j in 2:degree(parent(g)) for i in 1:j-1 if g(i) > g(j)] +end + +""" Given `K` checks if index can be set to zero (B- invariance)""" +function is_zero_entry(K::SimplicialComplex, indices::Tuple{Int, Int}) + K_facets = Set{Set{Int}}(facets(K)) + for facet in K_facets + # need a comment for this line + !(indices[1] in facet) && continue + # swap indices[1] with indices[2] in facet + S = push!(delete!(copy(facet), indices[1]), indices[2]) + !any(is_subset(S, check_facet) for check_facet in K_facets) && return false + end + return true +end + +is_zero_entry(K::UniformHypergraph, indices::Tuple{Int, Int}) = is_zero_entry(simplicial_complex(K), indices) + +function generic_unipotent_matrix(R::MPolyRing) + x = gens(R) + n_vars = length(x) + @req is_square(n_vars) "indeterminants should come from a square matrix" + n = Int(sqrt(n_vars)) + x = matrix(R, reshape(x, n, n)) + u = identity_matrix(R, n) + # make unipotent matrix + for i in 1:n + for j in i + 1:n + u[i, j] = x[i, j] + end + end + return u +end + +function generic_unipotent_matrix(F::Field, n::Int) + Fx, x = polynomial_ring(F, :x => (1:n, 1:n)) + return generic_unipotent_matrix(Fx) +end + +raw""" Returns the matrix ``\frU(w)``. """ +function generic_unipotent_matrix(F::Field, w::WeylGroupElem) + n = rank(root_system(parent(w)))+1 + Fx, x = polynomial_ring(F, :x => (1:n, 1:n)) + u = identity_matrix(Fx, n) + for (i, j) in inversions(perm(w)) + u[i, j] = x[i, j] + end + return u +end + +""" The `K`-indexed rows of the `k`th compound matrix of a square matrix `X`, where `K` is `k`-homogeneous. """ +function compound_matrix(m::MatElem, K::Vector{Vector{Int}}) + @req size(m,1) == size(m,2) "Only valid for square matrices" + @req length(Set(map(length, K))) == 1 "All entries in K must have the same size." + n = size(m, 1) + k = collect(Set(map(length, K)))[1] + @req all(1 <= i <= n for s in K for i in s) "All entries in K must represent $k-element subsets of [n]." + nCk = sort(subsets(n, k)) + return matrix(base_ring(m), [det(m[row, col]) for row in K, col in nCk]) +end + +compound_matrix(m::MatElem, k::Int) = compound_matrix(m, sort(subsets(size(m, 1), k))) +compound_matrix(p::PermGroupElem, k::Int) = compound_matrix(permutation_matrix(ZZ, p), k) +compound_matrix(w::WeylGroupElem, k::Int) = compound_matrix(perm(w), k) + +############################################################################### +# Exterior shift +############################################################################### +raw""" exterior_shift(K::UniformHypergraph, g::MatElem) + +Computes the exterior shift ``\Delta_g(K)`` of ``K`` w.r.t. the invertible matrix ``g``. +""" +function exterior_shift(K::UniformHypergraph, g::MatElem{}) + # the exterior shifting works in a different algebra that lends + # itself to an easier implementation + @req size(g, 1) == size(g, 2) "Change of basis matrix must be square." + @req size(g, 1) == n_vertices(K) "Matrix size does not match K." + matrix_base = base_ring(g) + nCk = sort!(subsets(n_vertices(K), face_size(K))) + c = compound_matrix(g, faces(K)) + if matrix_base isa MPolyRing + Oscar.ModStdQt.ref_ff_rc!(c) + elseif matrix_base isa MPolyQuoRing + lifted_c = lift.(c) + Oscar.ModStdQt.ref_ff_rc!(lifted_c) + c = simplify.(matrix_base.(lifted_c)) + else + rref!(c) + end + return uniform_hypergraph(nCk[independent_columns(c)], n_vertices(K), face_size(K)) +end + +function exterior_shift(K::SimplicialComplex, g::MatElem) + return simplicial_complex([ + (exterior_shift(faces(uniform_hypergraph(K, k), g)) for k in 1:dim(K)+1)...; + [[i] for i in 1:n_vertices(K)] # Make sure result is a complex on n vertices + ]) +end + +raw""" exterior_shift(K::ComplexOrHypergraph, w :: WeylGroupElem = nothing; field :: Field = QQ) + +Computes the (partial) generic exterior shift of ``K`` w.r.t. the Weyl group element ``w``. + +With ``w = w_0`` the longest word in the Weyl group (default), this is the generic exterior shift of ``K``. + +# Example +Compute the exterior generic shift of the real projective plane: +``` +julia> K = real_projective_plane() +julia> is_shifted(K) +julia> L = exterior_shift2(K) +julia> is_shifted(L) +julia> betti_numbers(K) == betti_numbers(L) +``` +Apply the partial generic shift w.r.t. a permutation ``w``: +``` +julia> W = weyl_group(:A, 5) +julia> s = gens(W) +julia> w = s[1] * s[2] * s[1] +julia> L = exterior_shift(K, w) +``` +""" +function exterior_shift(F::Field, K::ComplexOrHypergraph, w::WeylGroupElem) + n = n_vertices(K) + @req n == rank(root_system(parent(w))) + 1 "number of vertices - 1 should equal the rank of the root system" + + # set certain entries to zero, see B-invariance (probably needs a better name) + bool_mat = matrix(F, [is_zero_entry(K, (i, j) for i in 1:n, j in 1:n)]) + M = bool_mat .* generic_unipotent_matrix(F, w) + return exterior_shift(K, M * permutation_matrix(F, perm(w))) +end + +function exterior_shift(F::Field, K::ComplexOrHypergraph) + n = n_vertices(K) + W = weyl_group(:A, n - 1) + return exterior_shift(F, K, longest_element(W)) +end diff --git a/experimental/AlgebraicShifting/src/UniformHypergraph.jl b/experimental/AlgebraicShifting/src/UniformHypergraph.jl new file mode 100644 index 000000000000..46efcc7a0263 --- /dev/null +++ b/experimental/AlgebraicShifting/src/UniformHypergraph.jl @@ -0,0 +1,49 @@ +struct UniformHypergraph + n_vertices :: Int + k :: Int + faces :: Vector{Vector{Int}} +end + +function uniform_hypergraph(faces :: Vector{Vector{Int}}, n :: Int, k :: Int) + faces = sort(collect(Set(sort.(collect.(Set.(faces)))))) + @req all(length(f) == k && 1 <= minimum(f) && maximum(f) <= n for f in faces) "Parameters don't define a uniform hypergraph." + return UniformHypergraph(n, k, faces) +end + +function uniform_hypergraph(faces :: Vector{Vector{Int}}, n :: Int) + return uniform_hypergraph(faces, n, only(Set(length.(faces)))) +end + +function uniform_hypergraph(faces :: Vector{Vector{Int}}) + return uniform_hypergraph(faces, maximum(maximum.(faces))) +end + +function uniform_hypergraph(K :: SimplicialComplex, k :: Int) + return uniform_hypergraph(complex_faces(K, k-1), n_vertices(K), k) +end + +import Oscar: n_vertices, simplicial_complex + +function simplicial_complex(K :: UniformHypergraph) + return simplicial_complex([[[i] for i in 1:n_vertices(K)]; faces(K)]) +end + +function n_vertices(K :: UniformHypergraph) + return K.n_vertices +end + +faces(K::UniformHypergraph) = K.faces +face_size(K::UniformHypergraph) = K.k + +function Base.hash(K :: UniformHypergraph, u :: UInt) + return hash(K.n_vertices, hash(K.k, hash(K.faces, u))) +end + +function Base.:(==)(K :: UniformHypergraph, L :: UniformHypergraph) + return K.n_vertices == L.n_vertices && K.k == L.k && K.faces == L.faces +end + +raw""" Alexander dual, seen as bijection ``\binom{[n]}{k} \to \binom{[n]}{n-k}`` """ +function alexander_dual(K :: UniformHypergraph) + return uniform_hypergraph(alexander_dual(simplicial_complex([[[i] for i in 1:K.n_vertices]; K.faces])), K.n_vertices - K.k) +end From c6fccd55506e6613cc2316d3685b6e9e5f9fe235 Mon Sep 17 00:00:00 2001 From: Antony Della Vecchia Date: Mon, 14 Oct 2024 12:15:08 +0200 Subject: [PATCH 067/128] things are starting to work --- .../src/AlgebraicShifting.jl | 3 +- experimental/Experimental.jl | 1 + experimental/LieAlgebras/src/LieAlgebras.jl | 3 + experimental/LieAlgebras/src/WeylGroup.jl | 127 ++++++++++++++---- 4 files changed, 107 insertions(+), 27 deletions(-) diff --git a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl index 7b314a129d79..b1bae0dedbf9 100644 --- a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl +++ b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl @@ -1,9 +1,10 @@ include("UniformHypergraph.jl") include("PartialShift.jl") -export PartialExtShift export UniformHypergraph +export compound_matrix +export generic_unipotent_matrix export uniform_hypergraph function independent_columns(A::MatElem) diff --git a/experimental/Experimental.jl b/experimental/Experimental.jl index ee49a3e16a0e..f6c1a044b711 100644 --- a/experimental/Experimental.jl +++ b/experimental/Experimental.jl @@ -8,6 +8,7 @@ const expdir = joinpath(@__DIR__, "../experimental") const orderedpkgs = [ "LieAlgebras", "BasisLieHighestWeight", # needs code from LieAlgebras + "AlgebraicShifting", # Needs code form Lie Algebras (Weyl Groups specifically) "SetPartitions", "PartitionedPermutations", # needs code from SetPartitions "Schemes", diff --git a/experimental/LieAlgebras/src/LieAlgebras.jl b/experimental/LieAlgebras/src/LieAlgebras.jl index 81726acad82b..9f16e14786e4 100644 --- a/experimental/LieAlgebras/src/LieAlgebras.jl +++ b/experimental/LieAlgebras/src/LieAlgebras.jl @@ -70,6 +70,8 @@ import ..Oscar: ngens, order, parent_type, + perm, + permutation_matrix, rank, root, roots, @@ -315,6 +317,7 @@ export negative_roots export number_of_positive_roots, n_positive_roots # alias lives in a submodule export number_of_roots, n_roots # alias lives in a submodule export number_of_simple_roots, n_simple_roots # alias lives in a submodule +export perm, permutation_matrix export positive_coroot export positive_coroots export positive_root diff --git a/experimental/LieAlgebras/src/WeylGroup.jl b/experimental/LieAlgebras/src/WeylGroup.jl index accc823ddf8f..4a2d376d667f 100644 --- a/experimental/LieAlgebras/src/WeylGroup.jl +++ b/experimental/LieAlgebras/src/WeylGroup.jl @@ -251,32 +251,32 @@ Returns whether `x` is smaller than `y` with respect to the Bruhat order, i.e., whether some (not necessarily connected) subexpression of a reduced decomposition of `y`, is a reduced decomposition of `x`. """ -function Base.:(<)(x::WeylGroupElem, y::WeylGroupElem) - @req parent(x) === parent(y) "$x, $y must belong to the same Weyl group" - - if length(x) >= length(y) - return false - elseif isone(x) - return true - end - - tx = deepcopy(x) - for i in 1:length(y) - b, j, _ = explain_lmul(tx, y[i]) - if !b - deleteat!(word(tx), j) - if isone(tx) - return true - end - end - - if length(tx) > length(y) - i - return false - end - end - - return false -end +#function Base.:(<)(x::WeylGroupElem, y::WeylGroupElem) +# @req parent(x) === parent(y) "$x, $y must belong to the same Weyl group" +# +# if length(x) >= length(y) +# return false +# elseif isone(x) +# return true +# end +# +# tx = deepcopy(x) +# for i in 1:length(y) +# b, j, _ = explain_lmul(tx, y[i]) +# if !b +# deleteat!(word(tx), j) +# if isone(tx) +# return true +# end +# end +# +# if length(tx) > length(y) - i +# return false +# end +# end +# +# return false +#end function Base.:(==)(x::WeylGroupElem, y::WeylGroupElem) return parent(x) === parent(y) && word(x) == word(y) @@ -649,3 +649,78 @@ function Base.iterate(iter::WeylOrbitIterator, state::WeylIteratorNoCopyState) (wt, _), state = it return deepcopy(wt), state end + +################################################################################ +# converting to permutations + +function perm(w::WeylGroupElem) + coxeter_type, n = root_system_type(root_system(parent(w)))[1] + @req coxeter_type == :A "Weyl group is not the symmetric group" + G = symmetric_group(n + 1) + return reduce(*, [cperm(G, [i, i + 1]) for i in word(w)]; init = cperm(G)) +end + +function (W::WeylGroup)(p::PermGroupElem) + coxeter_type, n = root_system_type(root_system(W))[1] + @req coxeter_type == :A && degree(parent(p)) == n+1 "Weyl group is not Sym($(n+1))." + word = UInt8[] + for cycle in cycles(p) + transpositions = [ + sort([c, cycle[i + 1]]) for (i, c) in enumerate(cycle) if i < length(cycle)] + for t in transpositions + word = reduce(vcat, [ + [i for i in t[1]:t[2] - 1], + [i for i in reverse(t[1]:t[2] - 2)], + word]) + end + end + return W(word) +end + +permutation_matrix(R::Ring, w::WeylGroupElem) = permutation_matrix(R, perm(w)) + +################################################################################ +# Bruhat Strong order + +# BJORNER, Brenti, Theorem 2.1.5 +function bruhat_leq(v::PermGroupElem, w::PermGroupElem) + @req parent(v) == parent(w) "Can only compare elements of symmetric group of same size." + n = degree(parent(v)) + + bracket = (u, i, j) -> count(true for a in 1:i if u(a) >= j) + return all(bracket(v, i, j) <= bracket(w, i, j) for i in 1:n for j in 1:n) +end + +# not sure if we need to bring in these * functions +function Base.:(*)(w::WeylGroupElem, m::MatElem) + return permutation_matrix(base_ring(m), w) * m +end + +function Base.:(*)(m::MatElem, w::WeylGroupElem) + return m * permutation_matrix(base_ring(m), w) +end + +# not sure if it's a good idea to make <= the strong order +function Base.:(<=)(x::WeylGroupElem, y::WeylGroupElem) + coxeter_type_x, _ = root_system_type(root_system(parent(x)))[1] + coxeter_type_y, _ = root_system_type(root_system(parent(y)))[1] + if coxeter_type_x == coxeter_type_y == :A + return bruhat_leq(perm(x), perm(y)) + else + error("unimplemented") + end +end + +function Base.:(<)(x::WeylGroupElem, y::WeylGroupElem) + coxeter_type_x, _ = root_system_type(root_system(parent(x)))[1] + coxeter_type_y, _ = root_system_type(root_system(parent(y)))[1] + if coxeter_type_x == coxeter_type_y == :A + return x != y && bruhat_leq(perm(x), perm(y)) + else + error("unimplemented") + end +end + +function isless(w::WeylGroupElem, v::WeylGroupElem) + return w < v +end From 50be74ba297256f2662c983229fe509e52903ac9 Mon Sep 17 00:00:00 2001 From: Antony Della Vecchia Date: Tue, 22 Oct 2024 16:54:38 +0200 Subject: [PATCH 068/128] partial shift graph --- .../src/AlgebraicShifting.jl | 4 + .../AlgebraicShifting/src/PartialShift.jl | 9 +- .../src/PartialShiftGraph.jl | 124 ++++++++++++++++++ .../src/UniformHypergraph.jl | 6 + .../AlgebraicShifting/test/runtests.jl | 10 +- 5 files changed, 146 insertions(+), 7 deletions(-) create mode 100644 experimental/AlgebraicShifting/src/PartialShiftGraph.jl diff --git a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl index b1bae0dedbf9..fb5204d555e6 100644 --- a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl +++ b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl @@ -1,9 +1,13 @@ include("UniformHypergraph.jl") include("PartialShift.jl") +include("PartialShiftGraph.jl") export UniformHypergraph export compound_matrix +export exterior_shift +export partial_shift_graph_nodes +export partial_shift_graph export generic_unipotent_matrix export uniform_hypergraph diff --git a/experimental/AlgebraicShifting/src/PartialShift.jl b/experimental/AlgebraicShifting/src/PartialShift.jl index a9ef72ce1898..3bf4be4d52f3 100644 --- a/experimental/AlgebraicShifting/src/PartialShift.jl +++ b/experimental/AlgebraicShifting/src/PartialShift.jl @@ -79,7 +79,7 @@ raw""" exterior_shift(K::UniformHypergraph, g::MatElem) Computes the exterior shift ``\Delta_g(K)`` of ``K`` w.r.t. the invertible matrix ``g``. """ -function exterior_shift(K::UniformHypergraph, g::MatElem{}) +function exterior_shift(K::UniformHypergraph, g::MatElem) # the exterior shifting works in a different algebra that lends # itself to an easier implementation @req size(g, 1) == size(g, 2) "Change of basis matrix must be square." @@ -101,12 +101,13 @@ end function exterior_shift(K::SimplicialComplex, g::MatElem) return simplicial_complex([ - (exterior_shift(faces(uniform_hypergraph(K, k), g)) for k in 1:dim(K)+1)...; + (faces(exterior_shift(uniform_hypergraph(K, k), g)) for k in 1:dim(K)+1)...; [[i] for i in 1:n_vertices(K)] # Make sure result is a complex on n vertices ]) end -raw""" exterior_shift(K::ComplexOrHypergraph, w :: WeylGroupElem = nothing; field :: Field = QQ) +raw""" exterior_shift(F::Field, K::ComplexOrHypergraph, w::WeylGroupElem) + exterior_shift(K::ComplexOrHypergraph, w::WeylGroupElem) Computes the (partial) generic exterior shift of ``K`` w.r.t. the Weyl group element ``w``. @@ -134,7 +135,7 @@ function exterior_shift(F::Field, K::ComplexOrHypergraph, w::WeylGroupElem) @req n == rank(root_system(parent(w))) + 1 "number of vertices - 1 should equal the rank of the root system" # set certain entries to zero, see B-invariance (probably needs a better name) - bool_mat = matrix(F, [is_zero_entry(K, (i, j) for i in 1:n, j in 1:n)]) + bool_mat = matrix(F, [is_zero_entry(K, (i, j)) for i in 1:n, j in 1:n]) M = bool_mat .* generic_unipotent_matrix(F, w) return exterior_shift(K, M * permutation_matrix(F, perm(w))) end diff --git a/experimental/AlgebraicShifting/src/PartialShiftGraph.jl b/experimental/AlgebraicShifting/src/PartialShiftGraph.jl new file mode 100644 index 000000000000..a10d1189b709 --- /dev/null +++ b/experimental/AlgebraicShifting/src/PartialShiftGraph.jl @@ -0,0 +1,124 @@ +""" + Discovers the nodes of partial shift graph starting from `K`. +""" +function partial_shift_graph_nodes(F::Field, K::SimplicialComplex, W::Vector{WeylGroupElem};) + current_node = K + visited_nodes = Set([current_node]) + + function adjacent_shifts(K::SimplicialComplex) + shifts_of_K = [exterior_shift(F, K, w) for w in W] + adjacent_nodes = Set(filter(x -> !isequal(K, x), shifts_of_K)) + return shifts_of_K + end + + unvisited_nodes = adjacent_shifts(current_node) + + while(!isempty(unvisited_nodes)) + current_node = pop!(unvisited_nodes) + push!(visited_nodes, current_node) + shifts = adjacent_shifts(current_node) + # dont visit things twice + unvisited_nodes = union(unvisited_nodes, setdiff(shifts, visited_nodes)) + end + + return sort(collect(visited_nodes)) +end + + +""" Compute the multi edges, that is, for each complex K compute which + other complexes can be reached by applying the partial shifts `deltas` + to K, and store the shift matrices that give rise to each edge.""" +function multi_edges(F::Field, + W::WeylGroup, + complexes::Vector{Tuple{Int,T}}, + complex_labels::Dict{T, Int} +) :: Dict{Tuple{Int, Int}, Vector{WeylGroupElem}} where T <: ComplexOrHypergraph + # For each complex K with index i, compute the shifted complex Δ of K by w for each w ∈ W. + # For nontrivial Δ, place (i, Δ) → w in a singleton dictionary, and eventually merge all dictionaries + # to obtain a dictionary (i, Δ) → [w that yield the shift K → Δ] + reduce( + (d1, d2) -> mergewith!(vcat, d1, d2), + ( + Dict((i, complex_labels[Δ]) => [w]) + for (i, K) in complexes + for (w, Δ) in ((w, exterior_shift2(K, w; field=F)) for w in W) + if Δ != K + ); + init=Dict{Tuple{Int, Int}, Vector{WeylGroupElem}}() + ) +end + + +""" construct_full_graph(complexes :: Vector{T} where T <: ComplexOrHypergraph; ...) :: Tuple{Graph{Directed}, EdgeLabels} + +Constructs the partial shift graph on `complexes`. + +Returns a tuple `(G, D)`, where `G` is a directed graph whose vertices correspond to the `complexes`, +such that there is an edge `K → L` if there exists a shift matrix `w` such that `L` is the partial generic shift of `K` by `w`. +If `K` and `K` are the `i`th and `j`th entry of `complexes`, resp., +`D[i,j]` contains all `w ∈ W` such that `L` is the partial generic shift of `K` by `w`. + +# Arguments +- `complexes`: A vector of simplicial complexes of uniform hypergraphs (all belonging to the same ``Γ(n, k, l)``). +- `parallel :: Bool` (default: `false`) run the process in parrallel using the `Distributed` package; the setup is left to the user. +- `W`: The user may provide a list `W` of Weyl group elements to be used to construct the shifts. + `W` must be a subset the (same instance of the) symmetric group of the same order as the complexes. + If `W` is not provided, the function will use the symmetric group of the same order as the complexes. + +# Examples +``` +julia> Γ(n,k,l) = uniform_hypergraph.(subsets(subsets(n, k), l), n) +julia> Ks = Γ(4,2,5) +julia> G, D = construct_full_graph(Ks) +``` +""" +function partial_shift_graph(F::Field, complexes :: Vector{T} where T <: ComplexOrHypergraph; + parallel :: Bool = false, W = nothing) :: Tuple{Graph{Directed}, EdgeLabels} + # Deal with trivial case + if length(complexes) <= 1 + return (graph_from_adjacency_matrix(Directed, zeros(length(complexes),length(complexes))), EdgeLabels()) + end + + ns_vertices = Set(n_vertices.(complexes)) + @req length(ns_vertices) == 1 "All complexes are required to have the same number of vertices." + n = collect(ns_vertices)[1] + + # inverse lookup K → index of K in complexes + complex_labels = Dict(K => index for (index, K) in enumerate(complexes)) + + # set the weyl group to be used to construct the shifts + if isnothing(W) + W = weyl_group(:A, n - 1); + else + W2 = only(unique(parent.(W))) + T = root_system_type(root_system(W2)) + @req T[1][1] == :A && T[1][2] == n - 1 "The Weyl group should be of type A_$(n-1) and not $(T[1])." + end + + task_size = 1 + map_function = map + if parallel + # setup parallel parameters + channels = Oscar.params_channels(Union{RootSystem, WeylGroup, Vector{SimplicialComplex}, Vector{UniformHypergraph}}) + # setup parents needed to be sent to each process + Oscar.put_params(channels, root_system(W)) + Oscar.put_params(channels, W) + map_function = pmap + end + + # Basically, the following does the same as the following, but with a progress indicator: + # edge_tuples = multi_edges(W, collect(enumerate(complexes)), complex_labels) + edge_labels = reduce( + (d1, d2) -> mergewith!(vcat, d1, d2), + # a progress bar here would be nice for the users, but this requires adding a dependency to Oscar + # @showprogress map_function( + map_function( + Ks -> multi_edges(F, W, Ks, complex_labels), + Iterators.partition(enumerate(complexes), task_size) + ) + ) + + graph = graph_from_edges(Directed, [[i,j] for (i,j) in keys(edge_labels)]) + return (graph, edge_labels) +end + diff --git a/experimental/AlgebraicShifting/src/UniformHypergraph.jl b/experimental/AlgebraicShifting/src/UniformHypergraph.jl index 46efcc7a0263..9ae9d3a9c3bd 100644 --- a/experimental/AlgebraicShifting/src/UniformHypergraph.jl +++ b/experimental/AlgebraicShifting/src/UniformHypergraph.jl @@ -1,3 +1,9 @@ +# this might not be necessary if we can use polymake hasse diagram functionality? +function complex_faces(K :: SimplicialComplex, d :: Int) :: Vector{Vector{Int}} + return sort(union(subsets.(sort.(collect.(facets(K))), d+1)...)) + # return union(subsets.(facets(K), d+1)...) +end + struct UniformHypergraph n_vertices :: Int k :: Int diff --git a/experimental/AlgebraicShifting/test/runtests.jl b/experimental/AlgebraicShifting/test/runtests.jl index 4f9023ad7bef..e19a26cb801c 100644 --- a/experimental/AlgebraicShifting/test/runtests.jl +++ b/experimental/AlgebraicShifting/test/runtests.jl @@ -1,5 +1,9 @@ @testset "Algebraic Shifting" begin - K = simplicial_complex([[1, 2, 3], [1, 4]]) - k_ext = Oscar.exterior_shift(GF(2), K) - k_sym = Oscar.symmetric_shift(QQ, K) + K = simplicial_complex([[1, 2, 3], [2, 4]]) + + @testset "Partial Shift Graph" begin + n = n_vertices(K) + W = weyl_group(:A, n - 1) + partial_shift_graph_nodes(QQ, K, collect(W)) + end end From fd089a733fbba5c41c40a3594cf213afa9d65b77 Mon Sep 17 00:00:00 2001 From: Antony Della Vecchia Date: Wed, 23 Oct 2024 14:53:03 +0200 Subject: [PATCH 069/128] tests passing --- .../src/AlgebraicShifting.jl | 2 +- .../AlgebraicShifting/src/PartialShift.jl | 4 +- .../src/PartialShiftGraph.jl | 60 ++++++++++--------- .../src/UniformHypergraph.jl | 2 + .../AlgebraicShifting/test/runtests.jl | 8 ++- 5 files changed, 43 insertions(+), 33 deletions(-) diff --git a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl index fb5204d555e6..75ea97973e74 100644 --- a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl +++ b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl @@ -6,7 +6,7 @@ export UniformHypergraph export compound_matrix export exterior_shift -export partial_shift_graph_nodes +export partial_shift_graph_vertices export partial_shift_graph export generic_unipotent_matrix export uniform_hypergraph diff --git a/experimental/AlgebraicShifting/src/PartialShift.jl b/experimental/AlgebraicShifting/src/PartialShift.jl index 3bf4be4d52f3..f916d49ffe5b 100644 --- a/experimental/AlgebraicShifting/src/PartialShift.jl +++ b/experimental/AlgebraicShifting/src/PartialShift.jl @@ -15,9 +15,9 @@ function is_zero_entry(K::SimplicialComplex, indices::Tuple{Int, Int}) K_facets = Set{Set{Int}}(facets(K)) for facet in K_facets # need a comment for this line - !(indices[1] in facet) && continue + !(indices[2] in facet) && continue # swap indices[1] with indices[2] in facet - S = push!(delete!(copy(facet), indices[1]), indices[2]) + S = push!(delete!(copy(facet), indices[2]), indices[1]) !any(is_subset(S, check_facet) for check_facet in K_facets) && return false end return true diff --git a/experimental/AlgebraicShifting/src/PartialShiftGraph.jl b/experimental/AlgebraicShifting/src/PartialShiftGraph.jl index a10d1189b709..45390c4dae8c 100644 --- a/experimental/AlgebraicShifting/src/PartialShiftGraph.jl +++ b/experimental/AlgebraicShifting/src/PartialShiftGraph.jl @@ -1,7 +1,11 @@ +const EdgeLabels = Dict{Tuple{Int, Int}, Vector{WeylGroupElem}} + """ Discovers the nodes of partial shift graph starting from `K`. """ -function partial_shift_graph_nodes(F::Field, K::SimplicialComplex, W::Vector{WeylGroupElem};) +function partial_shift_graph_vertices(F::Field, + K::SimplicialComplex, + W::Union{WeylGroup, Vector{WeylGroupElem}};) current_node = K visited_nodes = Set([current_node]) @@ -31,25 +35,24 @@ end function multi_edges(F::Field, W::WeylGroup, complexes::Vector{Tuple{Int,T}}, - complex_labels::Dict{T, Int} -) :: Dict{Tuple{Int, Int}, Vector{WeylGroupElem}} where T <: ComplexOrHypergraph - # For each complex K with index i, compute the shifted complex Δ of K by w for each w ∈ W. - # For nontrivial Δ, place (i, Δ) → w in a singleton dictionary, and eventually merge all dictionaries - # to obtain a dictionary (i, Δ) → [w that yield the shift K → Δ] + complex_labels::Dict{Set{Set{Int}}, Int} +) :: Dict{Tuple{Int, Int}, Vector{WeylGroupElem}} where T <: ComplexOrHypergraph; + # For each complex K with index i, compute the shifted complex delta of K by w for each w ∈ W. + # For nontrivial delta, place (i, delta) → w in a singleton dictionary, and eventually merge all dictionaries + # to obtain a dictionary (i, delta) → [w that yield the shift K → delta] reduce( - (d1, d2) -> mergewith!(vcat, d1, d2), - ( - Dict((i, complex_labels[Δ]) => [w]) - for (i, K) in complexes - for (w, Δ) in ((w, exterior_shift2(K, w; field=F)) for w in W) - if Δ != K - ); + (d1, d2) -> mergewith!(vcat, d1, d2), + ( + Dict((i, complex_labels[Set(facets(delta))]) => [w]) + for (i, K) in complexes + for (w, delta) in ((w, exterior_shift(F, K, w)) for w in W) + if Set(facets(delta)) != Set(facets(K))); init=Dict{Tuple{Int, Int}, Vector{WeylGroupElem}}() ) end -""" construct_full_graph(complexes :: Vector{T} where T <: ComplexOrHypergraph; ...) :: Tuple{Graph{Directed}, EdgeLabels} +""" partial_shift_graph(complexes :: Vector{T} where T <: ComplexOrHypergraph; ...) :: Tuple{Graph{Directed}, EdgeLabels} Constructs the partial shift graph on `complexes`. @@ -72,8 +75,8 @@ julia> Ks = Γ(4,2,5) julia> G, D = construct_full_graph(Ks) ``` """ -function partial_shift_graph(F::Field, complexes :: Vector{T} where T <: ComplexOrHypergraph; - parallel :: Bool = false, W = nothing) :: Tuple{Graph{Directed}, EdgeLabels} +function partial_shift_graph(F::Field, complexes::Vector{T}; + parallel::Bool = false, W = nothing) :: Tuple{Graph{Directed}, EdgeLabels} where T <: ComplexOrHypergraph; # Deal with trivial case if length(complexes) <= 1 return (graph_from_adjacency_matrix(Directed, zeros(length(complexes),length(complexes))), EdgeLabels()) @@ -84,15 +87,15 @@ function partial_shift_graph(F::Field, complexes :: Vector{T} where T <: Complex n = collect(ns_vertices)[1] # inverse lookup K → index of K in complexes - complex_labels = Dict(K => index for (index, K) in enumerate(complexes)) + complex_labels = Dict(Set(facets(K)) => index for (index, K) in enumerate(complexes)) # set the weyl group to be used to construct the shifts if isnothing(W) W = weyl_group(:A, n - 1); else W2 = only(unique(parent.(W))) - T = root_system_type(root_system(W2)) - @req T[1][1] == :A && T[1][2] == n - 1 "The Weyl group should be of type A_$(n-1) and not $(T[1])." + sys_type = root_system_type(root_system(W2)) + @req sys_type[1][1] == :A && sys_type[1][2] == n - 1 "Only Weyl groups type A_$(n-1) are currently support and received type $(T[1])." end task_size = 1 @@ -108,15 +111,16 @@ function partial_shift_graph(F::Field, complexes :: Vector{T} where T <: Complex # Basically, the following does the same as the following, but with a progress indicator: # edge_tuples = multi_edges(W, collect(enumerate(complexes)), complex_labels) - edge_labels = reduce( - (d1, d2) -> mergewith!(vcat, d1, d2), - # a progress bar here would be nice for the users, but this requires adding a dependency to Oscar - # @showprogress map_function( - map_function( - Ks -> multi_edges(F, W, Ks, complex_labels), - Iterators.partition(enumerate(complexes), task_size) - ) - ) + edge_labels = multi_edges(F, W, collect(enumerate(complexes)), complex_labels) + #edge_labels = reduce( + # (d1, d2) -> mergewith!(vcat, d1, d2), + # # a progress bar here would be nice for the users, but this requires adding a dependency to Oscar + # # @showprogress map_function( + # map_function( + # Ks -> multi_edges(F, W, Ks, complex_labels), + # Iterators.partition(enumerate(complexes), task_size) + # ) + #) graph = graph_from_edges(Directed, [[i,j] for (i,j) in keys(edge_labels)]) return (graph, edge_labels) diff --git a/experimental/AlgebraicShifting/src/UniformHypergraph.jl b/experimental/AlgebraicShifting/src/UniformHypergraph.jl index 9ae9d3a9c3bd..286ec50b1637 100644 --- a/experimental/AlgebraicShifting/src/UniformHypergraph.jl +++ b/experimental/AlgebraicShifting/src/UniformHypergraph.jl @@ -39,6 +39,8 @@ function n_vertices(K :: UniformHypergraph) end faces(K::UniformHypergraph) = K.faces +# added for covenience when writting functions for Simplicial complex and Uniform Hypergraph +facets(K::UniformHypergraph) = K.faces face_size(K::UniformHypergraph) = K.k function Base.hash(K :: UniformHypergraph, u :: UInt) diff --git a/experimental/AlgebraicShifting/test/runtests.jl b/experimental/AlgebraicShifting/test/runtests.jl index e19a26cb801c..2fa316dc8bf1 100644 --- a/experimental/AlgebraicShifting/test/runtests.jl +++ b/experimental/AlgebraicShifting/test/runtests.jl @@ -1,9 +1,13 @@ @testset "Algebraic Shifting" begin - K = simplicial_complex([[1, 2, 3], [2, 4]]) + K = simplicial_complex([[1, 3] , [2, 3]]) @testset "Partial Shift Graph" begin n = n_vertices(K) W = weyl_group(:A, n - 1) - partial_shift_graph_nodes(QQ, K, collect(W)) + s = gens(W) + vertices = partial_shift_graph_vertices(QQ, K, W) + directed_graph, edge_labels = partial_shift_graph(QQ, vertices) + @test collect(edges(directed_graph)) == [Edge(t...) for t in [[2, 1], [3, 1], [3, 2]]] + @test word.(edge_labels[2, 1]) == word.([s[1], s[1] * s[2], s[1] * s[2] * s[1], s[2] * s[1]]) end end From ca861b048c026a8e6f318a7549fbb700c7bfaeb3 Mon Sep 17 00:00:00 2001 From: Antony Della Vecchia Date: Wed, 23 Oct 2024 15:46:11 +0200 Subject: [PATCH 070/128] still need partial graph vertices to work properly --- .../AlgebraicShifting/src/PartialShiftGraph.jl | 16 +++++++++++----- 1 file changed, 11 insertions(+), 5 deletions(-) diff --git a/experimental/AlgebraicShifting/src/PartialShiftGraph.jl b/experimental/AlgebraicShifting/src/PartialShiftGraph.jl index 45390c4dae8c..76158c7d9465 100644 --- a/experimental/AlgebraicShifting/src/PartialShiftGraph.jl +++ b/experimental/AlgebraicShifting/src/PartialShiftGraph.jl @@ -11,8 +11,12 @@ function partial_shift_graph_vertices(F::Field, function adjacent_shifts(K::SimplicialComplex) shifts_of_K = [exterior_shift(F, K, w) for w in W] - adjacent_nodes = Set(filter(x -> !isequal(K, x), shifts_of_K)) - return shifts_of_K + # we do this so that we don't introduce an isequal for simplicial complexes + # in oscar since there isn't a canonical definition of when two simplicial complexes + # are equal + facets_adjacent_nodes = unique( + facets.(filter(x -> Set(facets(K)) != Set(facets(x)), shifts_of_K))) + return simplicial_complex.(adjacent_nodes) end unvisited_nodes = adjacent_shifts(current_node) @@ -22,10 +26,12 @@ function partial_shift_graph_vertices(F::Field, push!(visited_nodes, current_node) shifts = adjacent_shifts(current_node) # dont visit things twice - unvisited_nodes = union(unvisited_nodes, setdiff(shifts, visited_nodes)) + unvisited_nodes = union( + unvisited_nodes, + filter(x -> !(Set(facets(x)) in Set.(facets.(visited_nodes))), + shifts)) end - - return sort(collect(visited_nodes)) + return sort(collect(visited_nodes); lt= (x, y) -> Set(facets(x)) < Set(facets(y))) end From a5a434ba340a54a89b5985343da3838eee26877a Mon Sep 17 00:00:00 2001 From: antonydellavecchia Date: Thu, 24 Oct 2024 10:49:33 +0200 Subject: [PATCH 071/128] tests passing and correct for partial shift graph --- .../src/PartialShiftGraph.jl | 21 +++++++++++++++++-- 1 file changed, 19 insertions(+), 2 deletions(-) diff --git a/experimental/AlgebraicShifting/src/PartialShiftGraph.jl b/experimental/AlgebraicShifting/src/PartialShiftGraph.jl index 76158c7d9465..1dffaddb5180 100644 --- a/experimental/AlgebraicShifting/src/PartialShiftGraph.jl +++ b/experimental/AlgebraicShifting/src/PartialShiftGraph.jl @@ -1,5 +1,22 @@ const EdgeLabels = Dict{Tuple{Int, Int}, Vector{WeylGroupElem}} +""" + Given two simplicial complexes `K1`, `K2` return true if + `K1` is lexicographically less than `K2` +""" +function isless_lex(K1::SimplicialComplex, K2::SimplicialComplex) + K1_facet_set = Set(facets(K1)) + K2_facet_set = Set(facets(K2)) + S = collect(symdiff(K1_facet_set, K2_facet_set)) + set_cmp(S1, S2) = min(symdiff(S1, S2)...) in S1 + + if isempty(S) + return false + end + + return sort(S;lt=set_cmp)[1] in K1_facet_set +end + """ Discovers the nodes of partial shift graph starting from `K`. """ @@ -16,7 +33,7 @@ function partial_shift_graph_vertices(F::Field, # are equal facets_adjacent_nodes = unique( facets.(filter(x -> Set(facets(K)) != Set(facets(x)), shifts_of_K))) - return simplicial_complex.(adjacent_nodes) + return simplicial_complex.(facets_adjacent_nodes) end unvisited_nodes = adjacent_shifts(current_node) @@ -31,7 +48,7 @@ function partial_shift_graph_vertices(F::Field, filter(x -> !(Set(facets(x)) in Set.(facets.(visited_nodes))), shifts)) end - return sort(collect(visited_nodes); lt= (x, y) -> Set(facets(x)) < Set(facets(y))) + return sort(collect(visited_nodes); lt=isless_lex) end From eda808f835a6c2fc8891e4acda75a116cc123f6b Mon Sep 17 00:00:00 2001 From: Antony Della Vecchia Date: Thu, 24 Oct 2024 15:28:17 +0200 Subject: [PATCH 072/128] comparing speed with old code --- .../src/PartialShiftGraph.jl | 27 ++++++++++--------- src/Combinatorics/SimplicialComplexes.jl | 4 +++ 2 files changed, 19 insertions(+), 12 deletions(-) diff --git a/experimental/AlgebraicShifting/src/PartialShiftGraph.jl b/experimental/AlgebraicShifting/src/PartialShiftGraph.jl index 1dffaddb5180..6fc4f2886a3f 100644 --- a/experimental/AlgebraicShifting/src/PartialShiftGraph.jl +++ b/experimental/AlgebraicShifting/src/PartialShiftGraph.jl @@ -1,5 +1,16 @@ const EdgeLabels = Dict{Tuple{Int, Int}, Vector{WeylGroupElem}} +function isless_lex(S1::Set{Set{Int}}, S2::Set{Set{Int}}) + S_diff = collect(symdiff(S1, S2)) + set_cmp(a, b) = min(symdiff(a, b)...) in a + + if isempty(S_diff) + return false + end + + return sort(S_diff;lt=set_cmp)[1] in S1 +end + """ Given two simplicial complexes `K1`, `K2` return true if `K1` is lexicographically less than `K2` @@ -7,14 +18,7 @@ const EdgeLabels = Dict{Tuple{Int, Int}, Vector{WeylGroupElem}} function isless_lex(K1::SimplicialComplex, K2::SimplicialComplex) K1_facet_set = Set(facets(K1)) K2_facet_set = Set(facets(K2)) - S = collect(symdiff(K1_facet_set, K2_facet_set)) - set_cmp(S1, S2) = min(symdiff(S1, S2)...) in S1 - - if isempty(S) - return false - end - - return sort(S;lt=set_cmp)[1] in K1_facet_set + return isless_lex(K1_facet_set, K2_facet_set) end """ @@ -27,13 +31,12 @@ function partial_shift_graph_vertices(F::Field, visited_nodes = Set([current_node]) function adjacent_shifts(K::SimplicialComplex) - shifts_of_K = [exterior_shift(F, K, w) for w in W] + unique_w = unique(w -> facets(exterior_shift(F, K, w)), W) + # we do this so that we don't introduce an isequal for simplicial complexes # in oscar since there isn't a canonical definition of when two simplicial complexes # are equal - facets_adjacent_nodes = unique( - facets.(filter(x -> Set(facets(K)) != Set(facets(x)), shifts_of_K))) - return simplicial_complex.(facets_adjacent_nodes) + return sort([exterior_shift(F, K, w) for w in unique_w]; lt=isless_lex) end unvisited_nodes = adjacent_shifts(current_node) diff --git a/src/Combinatorics/SimplicialComplexes.jl b/src/Combinatorics/SimplicialComplexes.jl index 07a067f49d75..656e2bf11deb 100644 --- a/src/Combinatorics/SimplicialComplexes.jl +++ b/src/Combinatorics/SimplicialComplexes.jl @@ -59,6 +59,10 @@ function simplicial_complex(generators::Union{AbstractVector{<:AbstractVector{<: SimplicialComplex(K) end +function simplicial_complex(generators::Union{Set{<:AbstractVector{<:Base.Integer}}, Set{<:AbstractSet{<:Base.Integer}}}) + return simplicial_complex(collect(generators)) +end + function simplicial_complex(generators::IncidenceMatrix) K = Polymake.@convert_to Array{Set} Polymake.common.rows(generators) simplicial_complex(K) From f50ecc70515fa7d95dbd2ae8231b40aaf836738f Mon Sep 17 00:00:00 2001 From: Antony Della Vecchia Date: Thu, 24 Oct 2024 17:50:21 +0200 Subject: [PATCH 073/128] still trying to not count things twice --- experimental/AlgebraicShifting/src/PartialShift.jl | 4 ++-- .../AlgebraicShifting/src/PartialShiftGraph.jl | 13 ++++++------- experimental/AlgebraicShifting/test/runtests.jl | 2 +- 3 files changed, 9 insertions(+), 10 deletions(-) diff --git a/experimental/AlgebraicShifting/src/PartialShift.jl b/experimental/AlgebraicShifting/src/PartialShift.jl index f916d49ffe5b..2bbd3c7cd7b9 100644 --- a/experimental/AlgebraicShifting/src/PartialShift.jl +++ b/experimental/AlgebraicShifting/src/PartialShift.jl @@ -135,8 +135,8 @@ function exterior_shift(F::Field, K::ComplexOrHypergraph, w::WeylGroupElem) @req n == rank(root_system(parent(w))) + 1 "number of vertices - 1 should equal the rank of the root system" # set certain entries to zero, see B-invariance (probably needs a better name) - bool_mat = matrix(F, [is_zero_entry(K, (i, j)) for i in 1:n, j in 1:n]) - M = bool_mat .* generic_unipotent_matrix(F, w) + #bool_mat = matrix(F, [is_zero_entry(K, (i, j)) for i in 1:n, j in 1:n]) + M = generic_unipotent_matrix(F, w) return exterior_shift(K, M * permutation_matrix(F, perm(w))) end diff --git a/experimental/AlgebraicShifting/src/PartialShiftGraph.jl b/experimental/AlgebraicShifting/src/PartialShiftGraph.jl index 6fc4f2886a3f..87741392bd93 100644 --- a/experimental/AlgebraicShifting/src/PartialShiftGraph.jl +++ b/experimental/AlgebraicShifting/src/PartialShiftGraph.jl @@ -31,12 +31,12 @@ function partial_shift_graph_vertices(F::Field, visited_nodes = Set([current_node]) function adjacent_shifts(K::SimplicialComplex) - unique_w = unique(w -> facets(exterior_shift(F, K, w)), W) - # we do this so that we don't introduce an isequal for simplicial complexes # in oscar since there isn't a canonical definition of when two simplicial complexes # are equal - return sort([exterior_shift(F, K, w) for w in unique_w]; lt=isless_lex) + unique_shift_facets = unique(sort( + [Set(facets(exterior_shift(F, K, w))) for w in W]; lt=isless_lex)) + return simplicial_complex.(unique_shift_facets) end unvisited_nodes = adjacent_shifts(current_node) @@ -46,10 +46,9 @@ function partial_shift_graph_vertices(F::Field, push!(visited_nodes, current_node) shifts = adjacent_shifts(current_node) # dont visit things twice - unvisited_nodes = union( - unvisited_nodes, - filter(x -> !(Set(facets(x)) in Set.(facets.(visited_nodes))), - shifts)) + new_nodes = filter(x -> !(x in Set.(facets.(visited_nodes))), Set.(facets.(shifts))) + unvisited_nodes = simplicial_complex.( + union(Set.(facets.(unvisited_nodes)), Set.(new_nodes))) end return sort(collect(visited_nodes); lt=isless_lex) end diff --git a/experimental/AlgebraicShifting/test/runtests.jl b/experimental/AlgebraicShifting/test/runtests.jl index 2fa316dc8bf1..ba55b73cfc90 100644 --- a/experimental/AlgebraicShifting/test/runtests.jl +++ b/experimental/AlgebraicShifting/test/runtests.jl @@ -5,7 +5,7 @@ n = n_vertices(K) W = weyl_group(:A, n - 1) s = gens(W) - vertices = partial_shift_graph_vertices(QQ, K, W) + all_shifts = partial_shift_graph_vertices(QQ, K, W) directed_graph, edge_labels = partial_shift_graph(QQ, vertices) @test collect(edges(directed_graph)) == [Edge(t...) for t in [[2, 1], [3, 1], [3, 2]]] @test word.(edge_labels[2, 1]) == word.([s[1], s[1] * s[2], s[1] * s[2] * s[1], s[2] * s[1]]) From 07187d7102de030b8d86d2d79b27d948ddd857d9 Mon Sep 17 00:00:00 2001 From: Antony Della Vecchia Date: Fri, 25 Oct 2024 11:39:48 +0200 Subject: [PATCH 074/128] started docs --- experimental/AlgebraicShifting/docs/doc.main | 13 ++++--- .../AlgebraicShifting/src/PartialShift.jl | 14 ++++--- .../src/PartialShiftGraph.jl | 37 ++++++++----------- .../AlgebraicShifting/test/runtests.jl | 2 +- 4 files changed, 31 insertions(+), 35 deletions(-) diff --git a/experimental/AlgebraicShifting/docs/doc.main b/experimental/AlgebraicShifting/docs/doc.main index c42ec6a31cee..f266625127d1 100644 --- a/experimental/AlgebraicShifting/docs/doc.main +++ b/experimental/AlgebraicShifting/docs/doc.main @@ -1,8 +1,9 @@ -# An example documentation +[ + "Algebraic Shifting" => [ + "introduction.md", + "exterior_shifting.md", + "partial_shift_graph.md" + ] +] -This is a sample text to outline the structure of the packages in the `Experimental` folder. -You can show docstrings like this: -```@docs - my_access_func(S::ExampleStruct) -``` diff --git a/experimental/AlgebraicShifting/src/PartialShift.jl b/experimental/AlgebraicShifting/src/PartialShift.jl index 2bbd3c7cd7b9..9cb398e24eeb 100644 --- a/experimental/AlgebraicShifting/src/PartialShift.jl +++ b/experimental/AlgebraicShifting/src/PartialShift.jl @@ -10,14 +10,16 @@ function inversions(g::PermGroupElem) return [(i,j) for j in 2:degree(parent(g)) for i in 1:j-1 if g(i) > g(j)] end -""" Given `K` checks if index can be set to zero (B- invariance)""" +""" Given `K` checks if index can be set to zero B- invariance)""" function is_zero_entry(K::SimplicialComplex, indices::Tuple{Int, Int}) + row, col = indices + row == col && return false K_facets = Set{Set{Int}}(facets(K)) for facet in K_facets # need a comment for this line - !(indices[2] in facet) && continue - # swap indices[1] with indices[2] in facet - S = push!(delete!(copy(facet), indices[2]), indices[1]) + !(col in facet) && continue + # replace index from row with index from col in facet + S = push!(delete!(copy(facet), col), row) !any(is_subset(S, check_facet) for check_facet in K_facets) && return false end return true @@ -135,8 +137,8 @@ function exterior_shift(F::Field, K::ComplexOrHypergraph, w::WeylGroupElem) @req n == rank(root_system(parent(w))) + 1 "number of vertices - 1 should equal the rank of the root system" # set certain entries to zero, see B-invariance (probably needs a better name) - #bool_mat = matrix(F, [is_zero_entry(K, (i, j)) for i in 1:n, j in 1:n]) - M = generic_unipotent_matrix(F, w) + bool_mat = matrix(F, [!is_zero_entry(K, (i, j)) for i in 1:n, j in 1:n]) + M = bool_mat .* generic_unipotent_matrix(F, w) return exterior_shift(K, M * permutation_matrix(F, perm(w))) end diff --git a/experimental/AlgebraicShifting/src/PartialShiftGraph.jl b/experimental/AlgebraicShifting/src/PartialShiftGraph.jl index 87741392bd93..f7eef41e740f 100644 --- a/experimental/AlgebraicShifting/src/PartialShiftGraph.jl +++ b/experimental/AlgebraicShifting/src/PartialShiftGraph.jl @@ -2,12 +2,9 @@ const EdgeLabels = Dict{Tuple{Int, Int}, Vector{WeylGroupElem}} function isless_lex(S1::Set{Set{Int}}, S2::Set{Set{Int}}) S_diff = collect(symdiff(S1, S2)) + isempty(S_diff) && return false set_cmp(a, b) = min(symdiff(a, b)...) in a - if isempty(S_diff) - return false - end - return sort(S_diff;lt=set_cmp)[1] in S1 end @@ -16,9 +13,7 @@ end `K1` is lexicographically less than `K2` """ function isless_lex(K1::SimplicialComplex, K2::SimplicialComplex) - K1_facet_set = Set(facets(K1)) - K2_facet_set = Set(facets(K2)) - return isless_lex(K1_facet_set, K2_facet_set) + return isless_lex(Set(facets(K1)), Set(facets(K2))) end """ @@ -29,22 +24,19 @@ function partial_shift_graph_vertices(F::Field, W::Union{WeylGroup, Vector{WeylGroupElem}};) current_node = K visited_nodes = Set([current_node]) - - function adjacent_shifts(K::SimplicialComplex) - # we do this so that we don't introduce an isequal for simplicial complexes - # in oscar since there isn't a canonical definition of when two simplicial complexes - # are equal - unique_shift_facets = unique(sort( - [Set(facets(exterior_shift(F, K, w))) for w in W]; lt=isless_lex)) - return simplicial_complex.(unique_shift_facets) - end - - unvisited_nodes = adjacent_shifts(current_node) + # by properties of algebraic shifting + # we know that K we be the last in this list since it is sorted + unvisited_nodes = unique( + x -> Set(facets(x)), + sort([exterior_shift(F, K, w) for w in W]; lt=isless_lex))[1:end - 1] while(!isempty(unvisited_nodes)) current_node = pop!(unvisited_nodes) push!(visited_nodes, current_node) - shifts = adjacent_shifts(current_node) + shifts = unique( + x -> Set(facets(x)), + sort([exterior_shift(F, K, w) for w in W]; lt=isless_lex))[1:end - 1] + # dont visit things twice new_nodes = filter(x -> !(x in Set.(facets.(visited_nodes))), Set.(facets.(shifts))) unvisited_nodes = simplicial_complex.( @@ -134,12 +126,13 @@ function partial_shift_graph(F::Field, complexes::Vector{T}; map_function = pmap end - # Basically, the following does the same as the following, but with a progress indicator: - # edge_tuples = multi_edges(W, collect(enumerate(complexes)), complex_labels) edge_labels = multi_edges(F, W, collect(enumerate(complexes)), complex_labels) + # a progress bar here would be nice for the users, but this requires adding a dependency to Oscar + # Basically, the following does the same as the line above, but with a progress indicator: + # edge_tuples = multi_edges(W, collect(enumerate(complexes)), complex_labels) #edge_labels = reduce( # (d1, d2) -> mergewith!(vcat, d1, d2), - # # a progress bar here would be nice for the users, but this requires adding a dependency to Oscar + # # @showprogress map_function( # map_function( # Ks -> multi_edges(F, W, Ks, complex_labels), diff --git a/experimental/AlgebraicShifting/test/runtests.jl b/experimental/AlgebraicShifting/test/runtests.jl index ba55b73cfc90..25e3adca9eb1 100644 --- a/experimental/AlgebraicShifting/test/runtests.jl +++ b/experimental/AlgebraicShifting/test/runtests.jl @@ -6,7 +6,7 @@ W = weyl_group(:A, n - 1) s = gens(W) all_shifts = partial_shift_graph_vertices(QQ, K, W) - directed_graph, edge_labels = partial_shift_graph(QQ, vertices) + directed_graph, edge_labels = partial_shift_graph(QQ, all_shifts) @test collect(edges(directed_graph)) == [Edge(t...) for t in [[2, 1], [3, 1], [3, 2]]] @test word.(edge_labels[2, 1]) == word.([s[1], s[1] * s[2], s[1] * s[2] * s[1], s[2] * s[1]]) end From 9373abec5b941dbce64a769941099421f10d7aa2 Mon Sep 17 00:00:00 2001 From: Antony Della Vecchia Date: Fri, 25 Oct 2024 18:04:56 +0200 Subject: [PATCH 075/128] more docs --- docs/oscar_references.bib | 19 ++++++++++++ experimental/AlgebraicShifting/docs/doc.main | 1 - .../docs/src/exterior_shifting.md | 12 +++++++ .../docs/src/introduction.md | 24 ++++++++++++++ .../AlgebraicShifting/src/PartialShift.jl | 31 ++++++------------- .../src/PartialShiftGraph.jl | 13 ++++---- 6 files changed, 71 insertions(+), 29 deletions(-) create mode 100644 experimental/AlgebraicShifting/docs/src/exterior_shifting.md create mode 100644 experimental/AlgebraicShifting/docs/src/introduction.md diff --git a/docs/oscar_references.bib b/docs/oscar_references.bib index 21d4e03c6cb0..298fdb4db17a 100644 --- a/docs/oscar_references.bib +++ b/docs/oscar_references.bib @@ -1530,6 +1530,25 @@ @InCollection{KL91 doi = {10.1007/3-540-54522-0_108} } + +@InProceedings {KAL02, + author = {Kalai, Gil}, + title = {Algebraic shifting}, + booktitle = {Computational commutative algebra and combinatorics}, + editor = {Hibi, Takayuki}, + venue = {Osaka}, + eventdate={1999}, + series = {Advanced Studies in Pure Mathematics}, + shortseries = {Adv. Stud. Pure Math.}, + number = {33}, + pages = {121--163}, + publisher = {Mathematical Society of Japan}, + shortpublisher = {Math. Soc. Japan}, + location = {Tokyo}, + year = {2002}, + dor = {10.2969/aspm/03310121}, +} + @InProceedings{KLT20, author = {Kaluba, Marek and Lorenz, Benjamin and Timme, Sascha}, title = {Polymake.jl: A New Interface to polymake}, diff --git a/experimental/AlgebraicShifting/docs/doc.main b/experimental/AlgebraicShifting/docs/doc.main index f266625127d1..bd183bbd137a 100644 --- a/experimental/AlgebraicShifting/docs/doc.main +++ b/experimental/AlgebraicShifting/docs/doc.main @@ -6,4 +6,3 @@ ] ] - diff --git a/experimental/AlgebraicShifting/docs/src/exterior_shifting.md b/experimental/AlgebraicShifting/docs/src/exterior_shifting.md new file mode 100644 index 000000000000..afcb3bb30ead --- /dev/null +++ b/experimental/AlgebraicShifting/docs/src/exterior_shifting.md @@ -0,0 +1,12 @@ +```@meta +CurrentModule = Oscar +DocTestSetup = Oscar.doctestsetup() +``` + +# Exterior Shifting + +## Helpful Matrix constructions + +```@docs +generic_unipotent_matrix +``` diff --git a/experimental/AlgebraicShifting/docs/src/introduction.md b/experimental/AlgebraicShifting/docs/src/introduction.md new file mode 100644 index 000000000000..bb2f4a6ff870 --- /dev/null +++ b/experimental/AlgebraicShifting/docs/src/introduction.md @@ -0,0 +1,24 @@ +```@meta +CurrentModule = Oscar +DocTestSetup = Oscar.doctestsetup() +``` + + +# Introduction + +This project aims to provide functionality for Algebraic Shifting, for some background on the subject we refer to [KAL02](@cite). + + +## Status + +This part of OSCAR is in an experimental state; please see [Adding new projects to experimental](@ref) for what this means. + +## Contact + +Please direct questions about this part of OSCAR to the following people: +* [Antony Della Vecchia](https://antonydellavecchia.github.io) + + +You can ask questions in the [OSCAR Slack](https://www.oscar-system.org/community/#slack). + +Alternatively, you can [raise an issue on github](https://www.oscar-system.org/community/#how-to-report-issues). diff --git a/experimental/AlgebraicShifting/src/PartialShift.jl b/experimental/AlgebraicShifting/src/PartialShift.jl index 9cb398e24eeb..2eb2467a5ff1 100644 --- a/experimental/AlgebraicShifting/src/PartialShift.jl +++ b/experimental/AlgebraicShifting/src/PartialShift.jl @@ -10,23 +10,6 @@ function inversions(g::PermGroupElem) return [(i,j) for j in 2:degree(parent(g)) for i in 1:j-1 if g(i) > g(j)] end -""" Given `K` checks if index can be set to zero B- invariance)""" -function is_zero_entry(K::SimplicialComplex, indices::Tuple{Int, Int}) - row, col = indices - row == col && return false - K_facets = Set{Set{Int}}(facets(K)) - for facet in K_facets - # need a comment for this line - !(col in facet) && continue - # replace index from row with index from col in facet - S = push!(delete!(copy(facet), col), row) - !any(is_subset(S, check_facet) for check_facet in K_facets) && return false - end - return true -end - -is_zero_entry(K::UniformHypergraph, indices::Tuple{Int, Int}) = is_zero_entry(simplicial_complex(K), indices) - function generic_unipotent_matrix(R::MPolyRing) x = gens(R) n_vars = length(x) @@ -48,7 +31,15 @@ function generic_unipotent_matrix(F::Field, n::Int) return generic_unipotent_matrix(Fx) end -raw""" Returns the matrix ``\frU(w)``. """ +@doc raw""" + generic_unipotent_matrix(R::MPolyRing) + generic_unipotent_matrix(F::Field, n::Int) + generic_unipotent_matrix(F::Field, w::WeylGroupElem) + +Constructs a unipotent matrix with entries in a polynomial ring `R`. +Alternatively one can provide a field `F` and a square integer `n`, + +""" function generic_unipotent_matrix(F::Field, w::WeylGroupElem) n = rank(root_system(parent(w)))+1 Fx, x = polynomial_ring(F, :x => (1:n, 1:n)) @@ -136,9 +127,7 @@ function exterior_shift(F::Field, K::ComplexOrHypergraph, w::WeylGroupElem) n = n_vertices(K) @req n == rank(root_system(parent(w))) + 1 "number of vertices - 1 should equal the rank of the root system" - # set certain entries to zero, see B-invariance (probably needs a better name) - bool_mat = matrix(F, [!is_zero_entry(K, (i, j)) for i in 1:n, j in 1:n]) - M = bool_mat .* generic_unipotent_matrix(F, w) + M = generic_unipotent_matrix(F, w) return exterior_shift(K, M * permutation_matrix(F, perm(w))) end diff --git a/experimental/AlgebraicShifting/src/PartialShiftGraph.jl b/experimental/AlgebraicShifting/src/PartialShiftGraph.jl index f7eef41e740f..5d47e2b98f4c 100644 --- a/experimental/AlgebraicShifting/src/PartialShiftGraph.jl +++ b/experimental/AlgebraicShifting/src/PartialShiftGraph.jl @@ -13,7 +13,9 @@ end `K1` is lexicographically less than `K2` """ function isless_lex(K1::SimplicialComplex, K2::SimplicialComplex) - return isless_lex(Set(facets(K1)), Set(facets(K2))) + K1_facet_set = Set(facets(K1)) + K2_facet_set = Set(facets(K2)) + return isless_lex(K1_facet_set, K2_facet_set) end """ @@ -45,7 +47,6 @@ function partial_shift_graph_vertices(F::Field, return sort(collect(visited_nodes); lt=isless_lex) end - """ Compute the multi edges, that is, for each complex K compute which other complexes can be reached by applying the partial shifts `deltas` to K, and store the shift matrices that give rise to each edge.""" @@ -68,7 +69,6 @@ function multi_edges(F::Field, ) end - """ partial_shift_graph(complexes :: Vector{T} where T <: ComplexOrHypergraph; ...) :: Tuple{Graph{Directed}, EdgeLabels} Constructs the partial shift graph on `complexes`. @@ -126,13 +126,12 @@ function partial_shift_graph(F::Field, complexes::Vector{T}; map_function = pmap end - edge_labels = multi_edges(F, W, collect(enumerate(complexes)), complex_labels) - # a progress bar here would be nice for the users, but this requires adding a dependency to Oscar - # Basically, the following does the same as the line above, but with a progress indicator: + # Basically, the following does the same as the following, but with a progress indicator: # edge_tuples = multi_edges(W, collect(enumerate(complexes)), complex_labels) + edge_labels = multi_edges(F, W, collect(enumerate(complexes)), complex_labels) #edge_labels = reduce( # (d1, d2) -> mergewith!(vcat, d1, d2), - + # # a progress bar here would be nice for the users, but this requires adding a dependency to Oscar # # @showprogress map_function( # map_function( # Ks -> multi_edges(F, W, Ks, complex_labels), From deb41d780e0527e2201281050ec30bc46f18140a Mon Sep 17 00:00:00 2001 From: Antony Della Vecchia Date: Tue, 29 Oct 2024 11:18:21 +0100 Subject: [PATCH 076/128] working as it should now --- .../AlgebraicShifting/src/PartialShift.jl | 21 +++++++++- .../src/PartialShiftGraph.jl | 42 +++++++++---------- 2 files changed, 40 insertions(+), 23 deletions(-) diff --git a/experimental/AlgebraicShifting/src/PartialShift.jl b/experimental/AlgebraicShifting/src/PartialShift.jl index 2eb2467a5ff1..795e198b1803 100644 --- a/experimental/AlgebraicShifting/src/PartialShift.jl +++ b/experimental/AlgebraicShifting/src/PartialShift.jl @@ -38,7 +38,6 @@ end Constructs a unipotent matrix with entries in a polynomial ring `R`. Alternatively one can provide a field `F` and a square integer `n`, - """ function generic_unipotent_matrix(F::Field, w::WeylGroupElem) n = rank(root_system(parent(w)))+1 @@ -65,6 +64,23 @@ compound_matrix(m::MatElem, k::Int) = compound_matrix(m, sort(subsets(size(m, 1) compound_matrix(p::PermGroupElem, k::Int) = compound_matrix(permutation_matrix(ZZ, p), k) compound_matrix(w::WeylGroupElem, k::Int) = compound_matrix(perm(w), k) +""" Given `K` checks if matrix entry can be set to zero zero """ +function _set_to_zero(K::SimplicialComplex, indices::Tuple{Int, Int}) + row, col = indices + row == col && return false + K_facets = facets(K) + for facet in K_facets + # if column index is not in face there is nothing to do + !(col in facet) && continue + # replace index from row with index from col in facet + S = push!(delete!(copy(facet), col), row) + !any(is_subset(S, check_facet) for check_facet in K_facets) && return false + end + return true +end + +_set_to_zero(K::UniformHypergraph, indices::Tuple{Int, Int}) = _set_to_zero(simplicial_complex(K), indices) + ############################################################################### # Exterior shift ############################################################################### @@ -127,6 +143,9 @@ function exterior_shift(F::Field, K::ComplexOrHypergraph, w::WeylGroupElem) n = n_vertices(K) @req n == rank(root_system(parent(w))) + 1 "number of vertices - 1 should equal the rank of the root system" + # set certain entries to zero, (pre-computation row reduction) + #bool_mat = matrix(F, [!set_to_zero(K, (i, j)) for i in 1:n, j in 1:n]) + #M = bool_mat .* generic_unipotent_matrix(F, w) M = generic_unipotent_matrix(F, w) return exterior_shift(K, M * permutation_matrix(F, perm(w))) end diff --git a/experimental/AlgebraicShifting/src/PartialShiftGraph.jl b/experimental/AlgebraicShifting/src/PartialShiftGraph.jl index 5d47e2b98f4c..60a3f19bb6eb 100644 --- a/experimental/AlgebraicShifting/src/PartialShiftGraph.jl +++ b/experimental/AlgebraicShifting/src/PartialShiftGraph.jl @@ -12,11 +12,7 @@ end Given two simplicial complexes `K1`, `K2` return true if `K1` is lexicographically less than `K2` """ -function isless_lex(K1::SimplicialComplex, K2::SimplicialComplex) - K1_facet_set = Set(facets(K1)) - K2_facet_set = Set(facets(K2)) - return isless_lex(K1_facet_set, K2_facet_set) -end +isless_lex(K1::SimplicialComplex, K2::SimplicialComplex) = isless_lex(Set(facets(K1)), Set(facets(K2))) """ Discovers the nodes of partial shift graph starting from `K`. @@ -24,30 +20,30 @@ end function partial_shift_graph_vertices(F::Field, K::SimplicialComplex, W::Union{WeylGroup, Vector{WeylGroupElem}};) - current_node = K - visited_nodes = Set([current_node]) + current = K + visited = [current] # by properties of algebraic shifting # we know that K we be the last in this list since it is sorted - unvisited_nodes = unique( + unvisited = unique( x -> Set(facets(x)), sort([exterior_shift(F, K, w) for w in W]; lt=isless_lex))[1:end - 1] - while(!isempty(unvisited_nodes)) - current_node = pop!(unvisited_nodes) - push!(visited_nodes, current_node) + while(!isempty(unvisited)) + current = pop!(unvisited) + push!(visited, current) shifts = unique( x -> Set(facets(x)), - sort([exterior_shift(F, K, w) for w in W]; lt=isless_lex))[1:end - 1] + sort([exterior_shift(F, current, w) for w in W]; lt=isless_lex))[1:end - 1] # dont visit things twice - new_nodes = filter(x -> !(x in Set.(facets.(visited_nodes))), Set.(facets.(shifts))) - unvisited_nodes = simplicial_complex.( - union(Set.(facets.(unvisited_nodes)), Set.(new_nodes))) + new_facets = filter(x -> !(x in Set.(facets.(visited))), Set.(facets.(shifts))) + unvisited = simplicial_complex.( + union(Set.(facets.(unvisited)), new_facets)) end - return sort(collect(visited_nodes); lt=isless_lex) + return sort(collect(visited); lt=isless_lex) end -""" Compute the multi edges, that is, for each complex K compute which +""" Compute the multi edges, that is, for each complex `K` compute which other complexes can be reached by applying the partial shifts `deltas` to K, and store the shift matrices that give rise to each edge.""" function multi_edges(F::Field, @@ -69,7 +65,9 @@ function multi_edges(F::Field, ) end -""" partial_shift_graph(complexes :: Vector{T} where T <: ComplexOrHypergraph; ...) :: Tuple{Graph{Directed}, EdgeLabels} +@doc raw""" + partial_shift_graph(complexes::Vector{Simplicialcomplex}) + partial_shift_graph(complexes::Vector{Uniformhypergraph}) Constructs the partial shift graph on `complexes`. @@ -92,8 +90,8 @@ julia> Ks = Γ(4,2,5) julia> G, D = construct_full_graph(Ks) ``` """ -function partial_shift_graph(F::Field, complexes::Vector{T}; - parallel::Bool = false, W = nothing) :: Tuple{Graph{Directed}, EdgeLabels} where T <: ComplexOrHypergraph; +function partial_shift_graph(F::Field, complexes::Vector{T}, W::Union{Nothing, WeylGroup, Vector{WeylGroupElem}} = nothing; + parallel::Bool = false) :: Tuple{Graph{Directed}, EdgeLabels} where T <: ComplexOrHypergraph; # Deal with trivial case if length(complexes) <= 1 return (graph_from_adjacency_matrix(Directed, zeros(length(complexes),length(complexes))), EdgeLabels()) @@ -111,8 +109,8 @@ function partial_shift_graph(F::Field, complexes::Vector{T}; W = weyl_group(:A, n - 1); else W2 = only(unique(parent.(W))) - sys_type = root_system_type(root_system(W2)) - @req sys_type[1][1] == :A && sys_type[1][2] == n - 1 "Only Weyl groups type A_$(n-1) are currently support and received type $(T[1])." + rs_type = root_system_type(root_system(W2)) + @req rs_type[1][1] == :A && rs_type[1][2] == n - 1 "Only Weyl groups type A_$(n-1) are currently support and received type $(T[1])." end task_size = 1 From 8b226a6798010125f92b5de2a67e031faa731bf9 Mon Sep 17 00:00:00 2001 From: Antony Della Vecchia Date: Tue, 29 Oct 2024 14:52:18 +0100 Subject: [PATCH 077/128] progress on docs --- docs/oscar_references.bib | 2 +- .../docs/src/exterior_shifting.md | 1 + .../docs/src/partial_shift_graph.md | 1 + .../src/AlgebraicShifting.jl | 3 +- .../AlgebraicShifting/src/PartialShift.jl | 68 +++++++++++++++---- 5 files changed, 59 insertions(+), 16 deletions(-) create mode 100644 experimental/AlgebraicShifting/docs/src/partial_shift_graph.md diff --git a/docs/oscar_references.bib b/docs/oscar_references.bib index 298fdb4db17a..3d49b1cd5551 100644 --- a/docs/oscar_references.bib +++ b/docs/oscar_references.bib @@ -1531,7 +1531,7 @@ @InCollection{KL91 } -@InProceedings {KAL02, +@InProceedings{KAL02, author = {Kalai, Gil}, title = {Algebraic shifting}, booktitle = {Computational commutative algebra and combinatorics}, diff --git a/experimental/AlgebraicShifting/docs/src/exterior_shifting.md b/experimental/AlgebraicShifting/docs/src/exterior_shifting.md index afcb3bb30ead..1f042a510f47 100644 --- a/experimental/AlgebraicShifting/docs/src/exterior_shifting.md +++ b/experimental/AlgebraicShifting/docs/src/exterior_shifting.md @@ -9,4 +9,5 @@ DocTestSetup = Oscar.doctestsetup() ```@docs generic_unipotent_matrix +rothe_matrix ``` diff --git a/experimental/AlgebraicShifting/docs/src/partial_shift_graph.md b/experimental/AlgebraicShifting/docs/src/partial_shift_graph.md new file mode 100644 index 000000000000..26ed10b84dab --- /dev/null +++ b/experimental/AlgebraicShifting/docs/src/partial_shift_graph.md @@ -0,0 +1 @@ +# Partial Shift Graph diff --git a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl index 75ea97973e74..cd6dbe0dd914 100644 --- a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl +++ b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl @@ -6,9 +6,10 @@ export UniformHypergraph export compound_matrix export exterior_shift +export generic_unipotent_matrix export partial_shift_graph_vertices export partial_shift_graph -export generic_unipotent_matrix +export rothe_matrix export uniform_hypergraph function independent_columns(A::MatElem) diff --git a/experimental/AlgebraicShifting/src/PartialShift.jl b/experimental/AlgebraicShifting/src/PartialShift.jl index 795e198b1803..b82bc70d4037 100644 --- a/experimental/AlgebraicShifting/src/PartialShift.jl +++ b/experimental/AlgebraicShifting/src/PartialShift.jl @@ -34,19 +34,52 @@ end @doc raw""" generic_unipotent_matrix(R::MPolyRing) generic_unipotent_matrix(F::Field, n::Int) - generic_unipotent_matrix(F::Field, w::WeylGroupElem) Constructs a unipotent matrix with entries in a polynomial ring `R`. -Alternatively one can provide a field `F` and a square integer `n`, +One can also provide a field `F` and an integer `n`, +then the entries of the unipotent matrix will lie in a multi variate +polynomial ring over `F` with `n^2` variables. + +# Examples +```jldoctest + +julia> R, x = polynomial_ring(QQ, :x=> (1:2, 1:2)) +(Multivariate polynomial ring in 4 variables over QQ, QQMPolyRingElem[x[1, 1] x[1, 2]; x[2, 1] x[2, 2]]) + +julia> generic_unipotent_matrix(R) +[1 x[1, 2]] +[0 1] + +julia> generic_unipotent_matrix(GF(2), 2) +[1 x[1, 2]] +[0 1] +``` """ -function generic_unipotent_matrix(F::Field, w::WeylGroupElem) + +@doc raw""" + rothe_matrix(F::Field, w::WeylGroupElem; K::Union{SimplicialComplex, Nothing} = nothing) + +For a base field `F` and a weyl group element `w` return the matrix with entries in the +multivariate polynomial ring `R` with `n^2` many indeterminants where `n - 1` is the rank of the +root system of the weyl group. +We know that since `general_linear_group(n^2, R)` has a Bruhat decomposition, and element lies in some double coset $BwB$. +The \emph{Rothe matrix} is a normal form for a the matrix on the left of a representative for the double coset corresponding to `w`. +We use the name \emph{Rothe matrix} because of its resemblance with a \emph{Rothe diagram} (add ref?) + +# Examples +```jldoctest + +``` +""" + +function rothe_matrix(F::Field, w::WeylGroupElem) n = rank(root_system(parent(w)))+1 Fx, x = polynomial_ring(F, :x => (1:n, 1:n)) u = identity_matrix(Fx, n) for (i, j) in inversions(perm(w)) u[i, j] = x[i, j] end - return u + return u * permutation_matrix(F, perm(w)) end """ The `K`-indexed rows of the `k`th compound matrix of a square matrix `X`, where `K` is `k`-homogeneous. """ @@ -115,19 +148,22 @@ function exterior_shift(K::SimplicialComplex, g::MatElem) ]) end -raw""" exterior_shift(F::Field, K::ComplexOrHypergraph, w::WeylGroupElem) - exterior_shift(K::ComplexOrHypergraph, w::WeylGroupElem) +@doc raw""" + exterior_shift(F::Field, K::ComplexOrHypergraph, w::WeylGroupElem) + exterior_shift(K::ComplexOrHypergraph, w::WeylGroupElem) + exterior_shift(K::ComplexOrHypergraph) -Computes the (partial) generic exterior shift of ``K`` w.r.t. the Weyl group element ``w``. +Computes the (partial) exterior shift of a simplical complex or uniform hypergraph `K` with respect to the Weyl group element `w` and the field `F`. +If the field is not given then `QQ` is used during the computation. +If `w` is not given then `longest_element(weyl_group(:A, n_vertices(K) - 1))` is used -With ``w = w_0`` the longest word in the Weyl group (default), this is the generic exterior shift of ``K``. # Example Compute the exterior generic shift of the real projective plane: ``` julia> K = real_projective_plane() julia> is_shifted(K) -julia> L = exterior_shift2(K) +julia> L = exterior_shift(K) julia> is_shifted(L) julia> betti_numbers(K) == betti_numbers(L) ``` @@ -143,11 +179,13 @@ function exterior_shift(F::Field, K::ComplexOrHypergraph, w::WeylGroupElem) n = n_vertices(K) @req n == rank(root_system(parent(w))) + 1 "number of vertices - 1 should equal the rank of the root system" - # set certain entries to zero, (pre-computation row reduction) - #bool_mat = matrix(F, [!set_to_zero(K, (i, j)) for i in 1:n, j in 1:n]) - #M = bool_mat .* generic_unipotent_matrix(F, w) - M = generic_unipotent_matrix(F, w) - return exterior_shift(K, M * permutation_matrix(F, perm(w))) + # in some cases this provides a speed up, not extremely important, we can chose to omit + # these lines + # handle some pre computation row reduction of compound matrix + #bool_mat = matrix(F, [!_set_to_zero(K, (i, j)) for i in 1:n, j in 1:n]) + #M = (bool_mat * permutation_matrix(F, perm(w))) .* + + return exterior_shift(K, rothe_matrix(F, w)) end function exterior_shift(F::Field, K::ComplexOrHypergraph) @@ -155,3 +193,5 @@ function exterior_shift(F::Field, K::ComplexOrHypergraph) W = weyl_group(:A, n - 1) return exterior_shift(F, K, longest_element(W)) end + +exterior_shift(K::ComplexOrHypergraph) = exterior_shift(QQ, K) From 901dc91d827154500bf3531a4f79b432026be7d2 Mon Sep 17 00:00:00 2001 From: Antony Della Vecchia Date: Tue, 29 Oct 2024 15:14:53 +0100 Subject: [PATCH 078/128] adds is_shifted --- experimental/AlgebraicShifting/src/UniformHypergraph.jl | 4 +++- src/Combinatorics/SimplicialComplexes.jl | 4 ++++ src/exports.jl | 1 + 3 files changed, 8 insertions(+), 1 deletion(-) diff --git a/experimental/AlgebraicShifting/src/UniformHypergraph.jl b/experimental/AlgebraicShifting/src/UniformHypergraph.jl index 286ec50b1637..e79e8a455b7d 100644 --- a/experimental/AlgebraicShifting/src/UniformHypergraph.jl +++ b/experimental/AlgebraicShifting/src/UniformHypergraph.jl @@ -52,6 +52,8 @@ function Base.:(==)(K :: UniformHypergraph, L :: UniformHypergraph) end raw""" Alexander dual, seen as bijection ``\binom{[n]}{k} \to \binom{[n]}{n-k}`` """ -function alexander_dual(K :: UniformHypergraph) +function alexander_dual(K::UniformHypergraph) return uniform_hypergraph(alexander_dual(simplicial_complex([[[i] for i in 1:K.n_vertices]; K.faces])), K.n_vertices - K.k) end + +is_shifted(K::UniformHypergraph) = is_shifted(simplicial_complex(K)) diff --git a/src/Combinatorics/SimplicialComplexes.jl b/src/Combinatorics/SimplicialComplexes.jl index d0dd8bbe61b8..6aa1ed554af7 100644 --- a/src/Combinatorics/SimplicialComplexes.jl +++ b/src/Combinatorics/SimplicialComplexes.jl @@ -710,3 +710,7 @@ end function barycentric_subdivision(K::SimplicialComplex) return SimplicialComplex(Polymake.topaz.barycentric_subdivision(pm_object(K))) end + +function is_shifted(K::SimplicialComplex) + return pm_object(K).SHIFTED +end diff --git a/src/exports.jl b/src/exports.jl index 576e33847950..2cd0483b0e19 100644 --- a/src/exports.jl +++ b/src/exports.jl @@ -899,6 +899,7 @@ export is_right export is_semiregular export is_semisimple export is_semistandard +export is_shifted export is_simple, has_is_simple, set_is_simple export is_simplicial export is_singular From dbf2651c0e1a7945cdfd6cd3fecb0182b2effb71 Mon Sep 17 00:00:00 2001 From: Antony Della Vecchia Date: Tue, 29 Oct 2024 17:37:13 +0100 Subject: [PATCH 079/128] docs almost done --- .../docs/src/exterior_shifting.md | 11 ++ .../docs/src/partial_shift_graph.md | 9 + .../src/AlgebraicShifting.jl | 1 + .../AlgebraicShifting/src/PartialShift.jl | 157 ++++++++++++++---- .../src/PartialShiftGraph.jl | 78 ++++++--- .../src/UniformHypergraph.jl | 54 ++++-- 6 files changed, 244 insertions(+), 66 deletions(-) diff --git a/experimental/AlgebraicShifting/docs/src/exterior_shifting.md b/experimental/AlgebraicShifting/docs/src/exterior_shifting.md index 1f042a510f47..95038fc36f52 100644 --- a/experimental/AlgebraicShifting/docs/src/exterior_shifting.md +++ b/experimental/AlgebraicShifting/docs/src/exterior_shifting.md @@ -5,9 +5,20 @@ DocTestSetup = Oscar.doctestsetup() # Exterior Shifting +## Uniform Hypergraphs +```@docs +uniform_hypergraph +``` + ## Helpful Matrix constructions ```@docs generic_unipotent_matrix rothe_matrix +compound_matrix +``` + +## Exterior (Partial) Shifting +```@docs +exterior_shift ``` diff --git a/experimental/AlgebraicShifting/docs/src/partial_shift_graph.md b/experimental/AlgebraicShifting/docs/src/partial_shift_graph.md index 26ed10b84dab..c1de71984bd0 100644 --- a/experimental/AlgebraicShifting/docs/src/partial_shift_graph.md +++ b/experimental/AlgebraicShifting/docs/src/partial_shift_graph.md @@ -1 +1,10 @@ +```@meta +CurrentModule = Oscar +DocTestSetup = Oscar.doctestsetup() +``` + # Partial Shift Graph + +```@docs +partial_shift_graph_vertices +``` diff --git a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl index cd6dbe0dd914..b1a0a4f7efb9 100644 --- a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl +++ b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl @@ -6,6 +6,7 @@ export UniformHypergraph export compound_matrix export exterior_shift +export face_size export generic_unipotent_matrix export partial_shift_graph_vertices export partial_shift_graph diff --git a/experimental/AlgebraicShifting/src/PartialShift.jl b/experimental/AlgebraicShifting/src/PartialShift.jl index b82bc70d4037..8d8242ce5227 100644 --- a/experimental/AlgebraicShifting/src/PartialShift.jl +++ b/experimental/AlgebraicShifting/src/PartialShift.jl @@ -26,11 +26,6 @@ function generic_unipotent_matrix(R::MPolyRing) return u end -function generic_unipotent_matrix(F::Field, n::Int) - Fx, x = polynomial_ring(F, :x => (1:n, 1:n)) - return generic_unipotent_matrix(Fx) -end - @doc raw""" generic_unipotent_matrix(R::MPolyRing) generic_unipotent_matrix(F::Field, n::Int) @@ -55,6 +50,10 @@ julia> generic_unipotent_matrix(GF(2), 2) [0 1] ``` """ +function generic_unipotent_matrix(F::Field, n::Int) + Fx, x = polynomial_ring(F, :x => (1:n, 1:n)) + return generic_unipotent_matrix(Fx) +end @doc raw""" rothe_matrix(F::Field, w::WeylGroupElem; K::Union{SimplicialComplex, Nothing} = nothing) @@ -62,16 +61,34 @@ julia> generic_unipotent_matrix(GF(2), 2) For a base field `F` and a weyl group element `w` return the matrix with entries in the multivariate polynomial ring `R` with `n^2` many indeterminants where `n - 1` is the rank of the root system of the weyl group. -We know that since `general_linear_group(n^2, R)` has a Bruhat decomposition, and element lies in some double coset $BwB$. -The \emph{Rothe matrix} is a normal form for a the matrix on the left of a representative for the double coset corresponding to `w`. -We use the name \emph{Rothe matrix} because of its resemblance with a \emph{Rothe diagram} (add ref?) +We know that since `general_linear_group(n^2, R)` has a Bruhat decomposition, any element lies in some double coset $BwB$. +The Rothe matrix is a normal form for the matrix on the left of a representative for the double coset corresponding to `w`. +(this might need to be explained further and reference the preprint) +We use the name Rothe matrix because of its resemblance with a Rothe diagram. (add ref?) # Examples ```jldoctest + julia> W = weyl_group(:A, 4) +Weyl group for root system defined by Cartan matrix [2 -1 0 0; -1 2 -1 0; 0 -1 2 -1; 0 0 -1 2] + +julia> s = gens(W) +4-element Vector{WeylGroupElem}: + s1 + s2 + s3 + s4 +julia> w = s[2] * s[3] * s[4] +s2 * s3 * s4 + +julia> rothe_matrix(GF(2), w) +[1 0 0 0 0] +[0 x[2, 3] x[2, 4] x[2, 5] 1] +[0 1 0 0 0] +[0 0 1 0 0] +[0 0 0 1 0] ``` """ - function rothe_matrix(F::Field, w::WeylGroupElem) n = rank(root_system(parent(w)))+1 Fx, x = polynomial_ring(F, :x => (1:n, 1:n)) @@ -82,22 +99,66 @@ function rothe_matrix(F::Field, w::WeylGroupElem) return u * permutation_matrix(F, perm(w)) end -""" The `K`-indexed rows of the `k`th compound matrix of a square matrix `X`, where `K` is `k`-homogeneous. """ -function compound_matrix(m::MatElem, K::Vector{Vector{Int}}) +@doc raw""" + compound_matrix(m::MatElem, k::Int) + compound_matrix(p::PermGroupElem, k::Int) + compound_matrix(w::WeylGroupElem, k::Int) + compound_matrix(m::MatElem, K::Vector{Vector{Int}}) + +Given a matrix `m` return the matrix where each entry is a `k` minor of `m`. +The entries of the compound matrix are ordered with respect to the lexicographic order on sets. +When passed a `PermGroupElem` or `WeylGroupElem`, return the copound matrix for their +permutation matrix representation. + +Alternatively, passing a `UniformHypergraph` `K` will return the compound matrix with entries the `face_size(K)` minors, and restrict the rows to the rows corresponding to `K` + +# Examples +```jldoctest + +julia> M = generic_unipotent_matrix(QQ, 3) +[1 x[1, 2] x[1, 3]] +[0 1 x[2, 3]] +[0 0 1] + +julia> compound_matrix(M, 2) +[1 x[2, 3] x[1, 2]*x[2, 3] - x[1, 3]] +[0 1 x[1, 2]] +[0 0 1] + +julia> compound_matrix(perm([1, 3, 2]), 2) +[0 1 0] +[1 0 0] +[0 0 -1] + +julia> W = weyl_group(:A, 2) +Weyl group for root system defined by Cartan matrix [2 -1; -1 2] + +julia> compound_matrix(longest_element(W), 2) +[ 0 0 -1] +[ 0 -1 0] +[-1 0 0] + +julia> K = uniform_hypergraph([[1, 2], [2, 3]]) +UniformHypergraph(3, 2, [[1, 2], [2, 3]]) + +julia> compound_matrix(M, K) +[1 x[2, 3] x[1, 2]*x[2, 3] - x[1, 3]] +[0 0 1] +``` +""" +function compound_matrix(m::MatElem, K::UniformHypergraph) @req size(m,1) == size(m,2) "Only valid for square matrices" - @req length(Set(map(length, K))) == 1 "All entries in K must have the same size." n = size(m, 1) - k = collect(Set(map(length, K)))[1] - @req all(1 <= i <= n for s in K for i in s) "All entries in K must represent $k-element subsets of [n]." + k = face_size(K) nCk = sort(subsets(n, k)) - return matrix(base_ring(m), [det(m[row, col]) for row in K, col in nCk]) + return matrix(base_ring(m), [det(m[row, col]) for row in faces(K), col in nCk]) end -compound_matrix(m::MatElem, k::Int) = compound_matrix(m, sort(subsets(size(m, 1), k))) +compound_matrix(m::MatElem, k::Int) = compound_matrix(m, uniform_hypergraph(sort(subsets(size(m, 1), k)))) compound_matrix(p::PermGroupElem, k::Int) = compound_matrix(permutation_matrix(ZZ, p), k) compound_matrix(w::WeylGroupElem, k::Int) = compound_matrix(perm(w), k) -""" Given `K` checks if matrix entry can be set to zero zero """ +# this might be removed (currently is not used) function _set_to_zero(K::SimplicialComplex, indices::Tuple{Int, Int}) row, col = indices row == col && return false @@ -128,7 +189,7 @@ function exterior_shift(K::UniformHypergraph, g::MatElem) @req size(g, 1) == n_vertices(K) "Matrix size does not match K." matrix_base = base_ring(g) nCk = sort!(subsets(n_vertices(K), face_size(K))) - c = compound_matrix(g, faces(K)) + c = compound_matrix(g, K) if matrix_base isa MPolyRing Oscar.ModStdQt.ref_ff_rc!(c) elseif matrix_base isa MPolyQuoRing @@ -149,30 +210,60 @@ function exterior_shift(K::SimplicialComplex, g::MatElem) end @doc raw""" - exterior_shift(F::Field, K::ComplexOrHypergraph, w::WeylGroupElem) - exterior_shift(K::ComplexOrHypergraph, w::WeylGroupElem) - exterior_shift(K::ComplexOrHypergraph) + exterior_shift(F::Field, K::SimplicialComplex, w::WeylGroupElem) + exterior_shift(F::Field, K::UniformHypergraph, w::WeylGroupElem) + exterior_shift(K::SimplicialComplex, w::WeylGroupElem) + exterior_shift(K::UniformHypergraph, w::WeylGroupElem) + exterior_shift(K::SimplicialComplex) + exterior_shift(K::UniformHypergraph) Computes the (partial) exterior shift of a simplical complex or uniform hypergraph `K` with respect to the Weyl group element `w` and the field `F`. If the field is not given then `QQ` is used during the computation. If `w` is not given then `longest_element(weyl_group(:A, n_vertices(K) - 1))` is used - -# Example -Compute the exterior generic shift of the real projective plane: -``` -julia> K = real_projective_plane() +# Examples +```jldoctest julia> is_shifted(K) +false + julia> L = exterior_shift(K) +Abstract simplicial complex of dimension 2 on 6 vertices + +julia> facets(L) +10-element Vector{Set{Int64}}: + Set([2, 3, 1]) + Set([4, 2, 1]) + Set([5, 2, 1]) + Set([6, 2, 1]) + Set([4, 3, 1]) + Set([5, 3, 1]) + Set([6, 3, 1]) + Set([5, 4, 1]) + Set([4, 6, 1]) + Set([5, 6, 1]) + julia> is_shifted(L) -julia> betti_numbers(K) == betti_numbers(L) -``` -Apply the partial generic shift w.r.t. a permutation ``w``: -``` -julia> W = weyl_group(:A, 5) +true + +julia> betti_numbers(L) == betti_numbers(K) +true + +julia> W = weyl_group(:A, n_vertices(K) - 1) +Weyl group for root system defined by Cartan matrix [2 -1 0 0 0; -1 2 -1 0 0; 0 -1 2 -1 0; 0 0 -1 2 -1; 0 0 0 -1 2] + julia> s = gens(W) -julia> w = s[1] * s[2] * s[1] -julia> L = exterior_shift(K, w) +5-element Vector{WeylGroupElem}: + s1 + s2 + s3 + s4 + s5 + +julia> w = s[2] * s[3] * s[4] +s2 * s3 * s4 + +julia> L = exterior_shift(GF(2), K, w) +Abstract simplicial complex of dimension 2 on 6 vertices ``` """ function exterior_shift(F::Field, K::ComplexOrHypergraph, w::WeylGroupElem) diff --git a/experimental/AlgebraicShifting/src/PartialShiftGraph.jl b/experimental/AlgebraicShifting/src/PartialShiftGraph.jl index 60a3f19bb6eb..543c0b5348c9 100644 --- a/experimental/AlgebraicShifting/src/PartialShiftGraph.jl +++ b/experimental/AlgebraicShifting/src/PartialShiftGraph.jl @@ -14,8 +14,36 @@ end """ isless_lex(K1::SimplicialComplex, K2::SimplicialComplex) = isless_lex(Set(facets(K1)), Set(facets(K2))) -""" - Discovers the nodes of partial shift graph starting from `K`. +@doc raw""" + partial_shift_graph_vertices(F::Field,::SimplicialComplex, W::Union{WeylGroup, Vector{WeylGroupElem}};) + +Given a field `F` discover the vertices of the partial shift graph starting from `K` +using exterior partial shifts corresponding to elements in `W`. +Returns a `Vector{SimplicialCompplex}` ordered lexicographically. + +#Example +```jldoctest +julia> K = simplicial_complex([[1, 2], [2, 3], [3, 4]]) +Abstract simplicial complex of dimension 1 on 4 vertices + +julia> shifts = partial_shift_graph_vertices(QQ, K, weyl_group(:A, 3)) +6-element Vector{SimplicialComplex}: + Abstract simplicial complex of dimension 1 on 4 vertices + Abstract simplicial complex of dimension 1 on 4 vertices + Abstract simplicial complex of dimension 1 on 4 vertices + Abstract simplicial complex of dimension 1 on 4 vertices + Abstract simplicial complex of dimension 1 on 4 vertices + Abstract simplicial complex of dimension 1 on 4 vertices + +julia> facets.(shifts) +6-element Vector{Vector{Set{Int64}}}: + [Set([3, 1]), Set([4, 1]), Set([2, 1])] + [Set([3, 1]), Set([2, 3]), Set([2, 1]), Set([4])] + [Set([3, 1]), Set([4, 2]), Set([2, 1])] + [Set([4, 3]), Set([3, 1]), Set([2, 1])] + [Set([2, 1]), Set([2, 3]), Set([4, 2])] + [Set([2, 1]), Set([2, 3]), Set([4, 3])] +``` """ function partial_shift_graph_vertices(F::Field, K::SimplicialComplex, @@ -23,7 +51,7 @@ function partial_shift_graph_vertices(F::Field, current = K visited = [current] # by properties of algebraic shifting - # we know that K we be the last in this list since it is sorted + # we know that K we be the last in this sorted list unvisited = unique( x -> Set(facets(x)), sort([exterior_shift(F, K, w) for w in W]; lt=isless_lex))[1:end - 1] @@ -66,31 +94,36 @@ function multi_edges(F::Field, end @doc raw""" - partial_shift_graph(complexes::Vector{Simplicialcomplex}) - partial_shift_graph(complexes::Vector{Uniformhypergraph}) + partial_shift_graph(F::Field, complexes::Vector{Simplicialcomplex}; parallel=false) + partial_shift_graph(F::Field, complexes::Vector{Uniformhypergraph}; parallel=false) + partial_shift_graph(F::Field, complexes::Vector{Simplicialcomplex}, W::Union{WeylGroup, Vector{WeylGroupElem}}; parallel=false) + partial_shift_graph(F::Field, complexes::Vector{Uniformhypergraph}, W::Union{WeylGroup, Vector{WeylGroupElem}}; parallel=false) + Constructs the partial shift graph on `complexes`. Returns a tuple `(G, D)`, where `G` is a directed graph whose vertices correspond to the `complexes`, such that there is an edge `K → L` if there exists a shift matrix `w` such that `L` is the partial generic shift of `K` by `w`. -If `K` and `K` are the `i`th and `j`th entry of `complexes`, resp., +If `K` and `L` are the `i`th and `j`th entry of `complexes`, resp., `D[i,j]` contains all `w ∈ W` such that `L` is the partial generic shift of `K` by `w`. # Arguments - `complexes`: A vector of simplicial complexes of uniform hypergraphs (all belonging to the same ``Γ(n, k, l)``). -- `parallel :: Bool` (default: `false`) run the process in parrallel using the `Distributed` package; the setup is left to the user. +- `parallel :: Bool` (default: `false`) run the process in parrallel using the `Distributed` package; make sure to do `@everywhere using Oscar`. - `W`: The user may provide a list `W` of Weyl group elements to be used to construct the shifts. `W` must be a subset the (same instance of the) symmetric group of the same order as the complexes. If `W` is not provided, the function will use the symmetric group of the same order as the complexes. # Examples ``` -julia> Γ(n,k,l) = uniform_hypergraph.(subsets(subsets(n, k), l), n) -julia> Ks = Γ(4,2,5) -julia> G, D = construct_full_graph(Ks) +julia> gamma(n,k,l) = uniform_hypergraph.(subsets(subsets(n, k), l), n) + +julia> Ks = gamma(4,2,5) + +julia> G, D = partial_shift_graph(QQ, Ks) ``` """ -function partial_shift_graph(F::Field, complexes::Vector{T}, W::Union{Nothing, WeylGroup, Vector{WeylGroupElem}} = nothing; +function partial_shift_graph(F::Field, complexes::Vector{T}, W::Union{WeylGroup, Vector{WeylGroupElem}}; parallel::Bool = false) :: Tuple{Graph{Directed}, EdgeLabels} where T <: ComplexOrHypergraph; # Deal with trivial case if length(complexes) <= 1 @@ -103,15 +136,10 @@ function partial_shift_graph(F::Field, complexes::Vector{T}, W::Union{Nothing, W # inverse lookup K → index of K in complexes complex_labels = Dict(Set(facets(K)) => index for (index, K) in enumerate(complexes)) - - # set the weyl group to be used to construct the shifts - if isnothing(W) - W = weyl_group(:A, n - 1); - else - W2 = only(unique(parent.(W))) - rs_type = root_system_type(root_system(W2)) - @req rs_type[1][1] == :A && rs_type[1][2] == n - 1 "Only Weyl groups type A_$(n-1) are currently support and received type $(T[1])." - end + + W2 = only(unique(parent.(W))) + rs_type = root_system_type(root_system(W2)) + @req rs_type[1][1] == :A && rs_type[1][2] == n - 1 "Only Weyl groups type A_$(n-1) are currently support and received type $(T[1])." task_size = 1 map_function = map @@ -141,3 +169,13 @@ function partial_shift_graph(F::Field, complexes::Vector{T}, W::Union{Nothing, W return (graph, edge_labels) end +function partial_shift_graph(F::Field, complexes::Vector{T}; parallel=false) where T <: ComplexOrHypergraph + # Deal with trivial case + if length(complexes) <= 1 + return (graph_from_adjacency_matrix(Directed, zeros(length(complexes),length(complexes))), EdgeLabels()) + end + + n = n_vertices(complexes[1]) + W = weyl_group(:A, n - 1) + return partial_shift_graph(F, complexes, W;parallel=parallel) +end diff --git a/experimental/AlgebraicShifting/src/UniformHypergraph.jl b/experimental/AlgebraicShifting/src/UniformHypergraph.jl index e79e8a455b7d..8b77727fb676 100644 --- a/experimental/AlgebraicShifting/src/UniformHypergraph.jl +++ b/experimental/AlgebraicShifting/src/UniformHypergraph.jl @@ -5,38 +5,66 @@ function complex_faces(K :: SimplicialComplex, d :: Int) :: Vector{Vector{Int}} end struct UniformHypergraph - n_vertices :: Int - k :: Int - faces :: Vector{Vector{Int}} + n_vertices::Int + k::Int + faces::Vector{Vector{Int}} end -function uniform_hypergraph(faces :: Vector{Vector{Int}}, n :: Int, k :: Int) +function uniform_hypergraph(faces::Vector{Vector{Int}}, n::Int, k::Int) faces = sort(collect(Set(sort.(collect.(Set.(faces)))))) @req all(length(f) == k && 1 <= minimum(f) && maximum(f) <= n for f in faces) "Parameters don't define a uniform hypergraph." return UniformHypergraph(n, k, faces) end -function uniform_hypergraph(faces :: Vector{Vector{Int}}, n :: Int) +function uniform_hypergraph(faces::Vector{Vector{Int}}, n::Int) return uniform_hypergraph(faces, n, only(Set(length.(faces)))) end -function uniform_hypergraph(faces :: Vector{Vector{Int}}) +function uniform_hypergraph(faces::Vector{Vector{Int}}) return uniform_hypergraph(faces, maximum(maximum.(faces))) end -function uniform_hypergraph(K :: SimplicialComplex, k :: Int) +@doc raw""" + uniform_hypergraph(faces::Vector{Vector{Int}}, n::Int, k::Int) + uniform_hypergraph(faces::Vector{Vector{Int}}, n::Int) + uniform_hypergraph(faces::Vector{Vector{Int}}) + uniform_hypergraph(K::SimplicialComplex, k::Int) + +Create a uniform hypergraph using `faces`, the size of each face should be `k` and all faces should be subsets of $[n]$. +One can also create a `UniformHypergraph` for the `k` faces of a `SimplicialComplex` `K`. + +#Examples +```jldoctext +julia> U = uniform_hypergraph([[1, 2], [2, 3]], 4) +UniformHypergraph(4, 2, [[1, 2], [2, 3]]) + +julia> U = uniform_hypergraph([[1, 2], [2, 3]]) +UniformHypergraph(3, 2, [[1, 2], [2, 3]]) + +julia> U = uniform_hypergraph(simplicial_complex([[1 ,2, 3], [1, 3, 4]]), 2) +UniformHypergraph(4, 2, [[1, 2], [1, 3], [1, 4], [2, 3], [3, 4]]) + +julia> face_size(U) +2 + +julia> faces(U) +5-element Vector{Vector{Int64}}: + [1, 2] + [1, 3] + [1, 4] + [2, 3] + [3, 4] +``` +""" +function uniform_hypergraph(K::SimplicialComplex, k::Int) return uniform_hypergraph(complex_faces(K, k-1), n_vertices(K), k) end -import Oscar: n_vertices, simplicial_complex - -function simplicial_complex(K :: UniformHypergraph) +function simplicial_complex(K::UniformHypergraph) return simplicial_complex([[[i] for i in 1:n_vertices(K)]; faces(K)]) end -function n_vertices(K :: UniformHypergraph) - return K.n_vertices -end +n_vertices(K::UniformHypergraph) = K.n_vertices faces(K::UniformHypergraph) = K.faces # added for covenience when writting functions for Simplicial complex and Uniform Hypergraph From 043f979b83280a632582524b93e4b2e713324ae3 Mon Sep 17 00:00:00 2001 From: Antony Della Vecchia Date: Wed, 30 Oct 2024 17:46:36 +0100 Subject: [PATCH 080/128] added progress meter + finished docs --- Project.toml | 2 + .../docs/src/partial_shift_graph.md | 2 + .../src/AlgebraicShifting.jl | 3 +- .../src/PartialShiftGraph.jl | 160 ++++++++++++++---- .../src/UniformHypergraph.jl | 2 +- src/Combinatorics/Graphs/functions.jl | 5 +- src/imports.jl | 1 + 7 files changed, 142 insertions(+), 33 deletions(-) diff --git a/Project.toml b/Project.toml index 2af6c6f1974b..62eb20332c8e 100644 --- a/Project.toml +++ b/Project.toml @@ -16,6 +16,7 @@ Markdown = "d6f4376e-aef5-505a-96c1-9c027394607a" Nemo = "2edaba10-b0f1-5616-af89-8c11ac63239a" Pkg = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f" Polymake = "d720cf60-89b5-51f5-aff5-213f193123e7" +ProgressMeter = "92933f4c-e287-5a05-a399-4b506db050ca" Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c" RandomExtensions = "fb686558-2515-59ef-acaa-46db3789a887" Serialization = "9e88b42a-f829-5b0c-bbe9-9e923198166b" @@ -37,6 +38,7 @@ Markdown = "1.6" Nemo = "0.47.1" Pkg = "1.6" Polymake = "0.11.20" +ProgressMeter = "1.10.2" Random = "1.6" RandomExtensions = "0.4.3" Serialization = "1.6" diff --git a/experimental/AlgebraicShifting/docs/src/partial_shift_graph.md b/experimental/AlgebraicShifting/docs/src/partial_shift_graph.md index c1de71984bd0..876ea0af7d97 100644 --- a/experimental/AlgebraicShifting/docs/src/partial_shift_graph.md +++ b/experimental/AlgebraicShifting/docs/src/partial_shift_graph.md @@ -7,4 +7,6 @@ DocTestSetup = Oscar.doctestsetup() ```@docs partial_shift_graph_vertices +partial_shift_graph +contracted_partial_shift_graph ``` diff --git a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl index b1a0a4f7efb9..ceb1b21351aa 100644 --- a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl +++ b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl @@ -5,11 +5,12 @@ include("PartialShiftGraph.jl") export UniformHypergraph export compound_matrix +export contracted_partial_shift_graph export exterior_shift export face_size export generic_unipotent_matrix -export partial_shift_graph_vertices export partial_shift_graph +export partial_shift_graph_vertices export rothe_matrix export uniform_hypergraph diff --git a/experimental/AlgebraicShifting/src/PartialShiftGraph.jl b/experimental/AlgebraicShifting/src/PartialShiftGraph.jl index 543c0b5348c9..d1b6a3d862a2 100644 --- a/experimental/AlgebraicShifting/src/PartialShiftGraph.jl +++ b/experimental/AlgebraicShifting/src/PartialShiftGraph.jl @@ -12,7 +12,7 @@ end Given two simplicial complexes `K1`, `K2` return true if `K1` is lexicographically less than `K2` """ -isless_lex(K1::SimplicialComplex, K2::SimplicialComplex) = isless_lex(Set(facets(K1)), Set(facets(K2))) +isless_lex(K1::ComplexOrHypergraph, K2::ComplexOrHypergraph) = isless_lex(Set(facets(K1)), Set(facets(K2))) @doc raw""" partial_shift_graph_vertices(F::Field,::SimplicialComplex, W::Union{WeylGroup, Vector{WeylGroupElem}};) @@ -51,7 +51,8 @@ function partial_shift_graph_vertices(F::Field, current = K visited = [current] # by properties of algebraic shifting - # we know that K we be the last in this sorted list + # we know that K will be the last in this sorted list + # sorting here should also speed up unique according to julia docs unvisited = unique( x -> Set(facets(x)), sort([exterior_shift(F, K, w) for w in W]; lt=isless_lex))[1:end - 1] @@ -79,7 +80,7 @@ function multi_edges(F::Field, complexes::Vector{Tuple{Int,T}}, complex_labels::Dict{Set{Set{Int}}, Int} ) :: Dict{Tuple{Int, Int}, Vector{WeylGroupElem}} where T <: ComplexOrHypergraph; - # For each complex K with index i, compute the shifted complex delta of K by w for each w ∈ W. + # For each complex K with index i, compute the shifted complex delta of K by w for each w in W. # For nontrivial delta, place (i, delta) → w in a singleton dictionary, and eventually merge all dictionaries # to obtain a dictionary (i, delta) → [w that yield the shift K → delta] reduce( @@ -102,38 +103,82 @@ end Constructs the partial shift graph on `complexes`. -Returns a tuple `(G, D)`, where `G` is a directed graph whose vertices correspond to the `complexes`, -such that there is an edge `K → L` if there exists a shift matrix `w` such that `L` is the partial generic shift of `K` by `w`. -If `K` and `L` are the `i`th and `j`th entry of `complexes`, resp., -`D[i,j]` contains all `w ∈ W` such that `L` is the partial generic shift of `K` by `w`. +Returns a tuple `(G, EL, VL)`, where `G` is a `Graph{Directed}`, `EL` is a `Dict{Tuple{Int Int}, Vector{Weylgroupelem}` and +`VL` is a lexicographically sorted `complexes`, hence is either a `Vector{SimplicialComplex}` or `Vector{Uniformhypergraph}`. +`EL` are the edges labels and `VL` are the vertex labels. +There is an edge from the vertex labelled `K` to the vertex labelled `L` if `L` is the partial shift of `K` by some `w` in `W`. +If `K` and `L` are the `i`th and `j`th entry of `VL`, resp., +`EL[i,j]` contains all `w` in `W` such that `L` is the partial generic shift of `K` by `w`. # Arguments -- `complexes`: A vector of simplicial complexes of uniform hypergraphs (all belonging to the same ``Γ(n, k, l)``). +- `complexes`: A vector of simplicial complexes or uniform hypergraphs (all should have the same number of vertices). - `parallel :: Bool` (default: `false`) run the process in parrallel using the `Distributed` package; make sure to do `@everywhere using Oscar`. - `W`: The user may provide a list `W` of Weyl group elements to be used to construct the shifts. - `W` must be a subset the (same instance of the) symmetric group of the same order as the complexes. - If `W` is not provided, the function will use the symmetric group of the same order as the complexes. + All elements of `W` should have the same parent. + `W` must be a subset the (same instance of the) symmetric group of order equal to the number of vertices of a complex in complexes (they should all be equal). + If `W` is not provided, the function will use the symmetric group of the same order as vertices in each complex complexes. # Examples ``` julia> gamma(n,k,l) = uniform_hypergraph.(subsets(subsets(n, k), l), n) +gamma (generic function with 1 method) julia> Ks = gamma(4,2,5) +6-element Vector{UniformHypergraph}: + UniformHypergraph(4, 2, [[1, 2], [1, 3], [1, 4], [2, 3], [3, 4]]) + UniformHypergraph(4, 2, [[1, 2], [1, 3], [2, 3], [2, 4], [3, 4]]) + UniformHypergraph(4, 2, [[1, 2], [1, 3], [1, 4], [2, 3], [2, 4]]) + UniformHypergraph(4, 2, [[1, 2], [1, 4], [2, 3], [2, 4], [3, 4]]) + UniformHypergraph(4, 2, [[1, 2], [1, 3], [1, 4], [2, 4], [3, 4]]) + UniformHypergraph(4, 2, [[1, 3], [1, 4], [2, 3], [2, 4], [3, 4]]) -julia> G, D = partial_shift_graph(QQ, Ks) +julia> G, EL, VL = partial_shift_graph(QQ, Ks); +Progress: 100%|█████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| Time: 0:00:00 + +julia> collect(edges(G)) +14-element Vector{Edge}: + Edge(2, 1) + Edge(3, 1) + Edge(3, 2) + Edge(4, 1) + Edge(4, 2) + Edge(5, 1) + Edge(5, 2) + Edge(5, 3) + Edge(5, 4) + Edge(6, 1) + Edge(6, 2) + Edge(6, 3) + Edge(6, 4) + Edge(6, 5) + +julia> EL[6, 5] +4-element Vector{WeylGroupElem}: + s1 * s2 + s2 + s3 * s1 * s2 + s3 * s2 + +julia> facets.(VL[[6, 5]]) +2-element Vector{Vector{Set{Int64}}}: + [Set([3, 1]), Set([4, 1]), Set([2, 3]), Set([4, 2]), Set([4, 3])] + [Set([2, 1]), Set([4, 1]), Set([2, 3]), Set([4, 2]), Set([4, 3])] ``` """ function partial_shift_graph(F::Field, complexes::Vector{T}, W::Union{WeylGroup, Vector{WeylGroupElem}}; - parallel::Bool = false) :: Tuple{Graph{Directed}, EdgeLabels} where T <: ComplexOrHypergraph; + parallel::Bool = false) :: Tuple{Graph{Directed}, EdgeLabels, Vector{ComplexOrHypergraph}} where T <: ComplexOrHypergraph; # Deal with trivial case if length(complexes) <= 1 return (graph_from_adjacency_matrix(Directed, zeros(length(complexes),length(complexes))), EdgeLabels()) end + # maybe we provide a flag to skip if the complexes are already sorted? + complexes = sort(complexes;lt=Oscar.isless_lex) + ns_vertices = Set(n_vertices.(complexes)) @req length(ns_vertices) == 1 "All complexes are required to have the same number of vertices." n = collect(ns_vertices)[1] - + # inverse lookup K → index of K in complexes complex_labels = Dict(Set(facets(K)) => index for (index, K) in enumerate(complexes)) @@ -142,31 +187,22 @@ function partial_shift_graph(F::Field, complexes::Vector{T}, W::Union{WeylGroup, @req rs_type[1][1] == :A && rs_type[1][2] == n - 1 "Only Weyl groups type A_$(n-1) are currently support and received type $(T[1])." task_size = 1 - map_function = map if parallel # setup parallel parameters channels = Oscar.params_channels(Union{RootSystem, WeylGroup, Vector{SimplicialComplex}, Vector{UniformHypergraph}}) # setup parents needed to be sent to each process Oscar.put_params(channels, root_system(W)) Oscar.put_params(channels, W) - map_function = pmap end - - # Basically, the following does the same as the following, but with a progress indicator: - # edge_tuples = multi_edges(W, collect(enumerate(complexes)), complex_labels) - edge_labels = multi_edges(F, W, collect(enumerate(complexes)), complex_labels) - #edge_labels = reduce( - # (d1, d2) -> mergewith!(vcat, d1, d2), - # # a progress bar here would be nice for the users, but this requires adding a dependency to Oscar - # # @showprogress map_function( - # map_function( - # Ks -> multi_edges(F, W, Ks, complex_labels), - # Iterators.partition(enumerate(complexes), task_size) - # ) - #) + # edge_tuples = multi_edges(F, W, collect(enumerate(complexes)), complex_labels) + # Basically, the following does the same as the preceeding, but with a progress indicator: + edge_labels = reduce((d1, d2) -> mergewith!(vcat, d1, d2), + @showprogress pmap( + Ks -> multi_edges(F, W, Ks, complex_labels), + Iterators.partition(enumerate(complexes), task_size))) graph = graph_from_edges(Directed, [[i,j] for (i,j) in keys(edge_labels)]) - return (graph, edge_labels) + return (graph, edge_labels, complexes) end function partial_shift_graph(F::Field, complexes::Vector{T}; parallel=false) where T <: ComplexOrHypergraph @@ -179,3 +215,69 @@ function partial_shift_graph(F::Field, complexes::Vector{T}; parallel=false) whe W = weyl_group(:A, n - 1) return partial_shift_graph(F, complexes, W;parallel=parallel) end + +@doc raw""" + contracted_partial_shift_graph(G::Graph{Directed}, edge_labels::Dict{Tuple{Int, Int}, Vector{WeylGroupElem}}) + +Returns a triple `(CG, S, P)`, where `CG` is a graph that contains a vertex `v` for every vertex `S[v]` in `G`. +`S` is a list of indices for the sinks in the original graph `G`. +A vertex `i` is in `P[s]` if there exists an edge from `i` to `s` in `G` with `w0` in its edge label, +in this way `P` is a partition of the vertices of the orignal graph `G`. +There is an edge from `s` to `t` in `CG` whenever there is an edge from `i` to `j` in `G` and `i` in `P[s]` and `j` in `P[t]`. + +#Examples +```jldoctest +julia> gamma(n,k,l) = uniform_hypergraph.(subsets(subsets(n, k), l), n) +gamma (generic function with 1 method) + +julia> Ks = gamma(4,2,5) +6-element Vector{UniformHypergraph}: + UniformHypergraph(4, 2, [[1, 2], [1, 3], [1, 4], [2, 3], [3, 4]]) + UniformHypergraph(4, 2, [[1, 2], [1, 3], [2, 3], [2, 4], [3, 4]]) + UniformHypergraph(4, 2, [[1, 2], [1, 3], [1, 4], [2, 3], [2, 4]]) + UniformHypergraph(4, 2, [[1, 2], [1, 4], [2, 3], [2, 4], [3, 4]]) + UniformHypergraph(4, 2, [[1, 2], [1, 3], [1, 4], [2, 4], [3, 4]]) + UniformHypergraph(4, 2, [[1, 3], [1, 4], [2, 3], [2, 4], [3, 4]]) + +julia> G, EL, VL = partial_shift_graph(QQ, Ks); +Progress: 100%|█████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| Time: 0:00:00 + +julia> contracted_partial_shift_graph(G, EL) +(Directed graph with 1 nodes and 0 edges, [1], [[5, 4, 6, 2, 3, 1]]) +``` +""" +function contracted_partial_shift_graph(G::Graph{Directed}, edge_labels::Dict{Tuple{Int, Int}, Vector{WeylGroupElem}}) + n = n_vertices(G) + W = parent(first(first(values(edge_labels)))) + w0 = longest_element(W) + + # all arrows corresponding to edges that contain w0 in their edge labels + w0_action = Dict(i => j for ((i,j), ws) in edge_labels if w0 in ws) + + sinks = findall(iszero, degree(G)) + sinks_indices = Dict(s => i for (i,s) in enumerate(sinks)) + for i in 1:n + if !haskey(w0_action, i) + @req i in sinks "Vertex $i is not a sink, but has no outbound edge with w0 in its edge label." + w0_action[i] = i + end + end + + p = [Int[] for _ in sinks] + for (i, s) in w0_action + push!(p[sinks_indices[s]], i) + end + + return ( + graph_from_edges(Directed, [ + [sinks_indices[s],sinks_indices[t]] + for (s,t) in ( + (w0_action[i], (haskey(w0_action, j) ? w0_action[j] : j)) + for (i, j) in keys(edge_labels) + ) + if s != t + ], length(sinks)), + sinks, + p + ) +end diff --git a/experimental/AlgebraicShifting/src/UniformHypergraph.jl b/experimental/AlgebraicShifting/src/UniformHypergraph.jl index 8b77727fb676..52f67c541b91 100644 --- a/experimental/AlgebraicShifting/src/UniformHypergraph.jl +++ b/experimental/AlgebraicShifting/src/UniformHypergraph.jl @@ -68,7 +68,7 @@ n_vertices(K::UniformHypergraph) = K.n_vertices faces(K::UniformHypergraph) = K.faces # added for covenience when writting functions for Simplicial complex and Uniform Hypergraph -facets(K::UniformHypergraph) = K.faces +facets(K::UniformHypergraph) = Set.(K.faces) face_size(K::UniformHypergraph) = K.k function Base.hash(K :: UniformHypergraph, u :: UInt) diff --git a/src/Combinatorics/Graphs/functions.jl b/src/Combinatorics/Graphs/functions.jl index 747ddf20595f..fddf4156e179 100644 --- a/src/Combinatorics/Graphs/functions.jl +++ b/src/Combinatorics/Graphs/functions.jl @@ -1172,8 +1172,9 @@ end function graph_from_edges(::Type{T}, edges::Vector{Edge}, n_vertices::Int=-1) where {T <: Union{Directed, Undirected}} - - n_needed = maximum(reduce(append!,[[src(e),dst(e)] for e in edges])) + isempty(edges) && return Graph{T}(n_vertices) + + n_needed = maximum(reduce(append!,[[src(e),dst(e)] for e in edges];)) @req (n_vertices >= n_needed || n_vertices < 0) "n_vertices must be at least the maximum vertex in the edges" g = Graph{T}(max(n_needed, n_vertices)) diff --git a/src/imports.jl b/src/imports.jl index 41769e0ab4bf..ed98de755884 100644 --- a/src/imports.jl +++ b/src/imports.jl @@ -1,5 +1,6 @@ # standard packages using Pkg +using ProgressMeter using Random using RandomExtensions using UUIDs From 7675df25f732b13cfb490462ea6ef168df530649 Mon Sep 17 00:00:00 2001 From: Michael Joswig Date: Wed, 30 Oct 2024 20:09:44 +0100 Subject: [PATCH 081/128] algebraic shifting: doc additions/fixes --- experimental/AlgebraicShifting/README.md | 9 +++---- .../docs/src/exterior_shifting.md | 2 +- .../docs/src/introduction.md | 7 +++++- .../AlgebraicShifting/src/PartialShift.jl | 25 +++++++++---------- 4 files changed, 23 insertions(+), 20 deletions(-) diff --git a/experimental/AlgebraicShifting/README.md b/experimental/AlgebraicShifting/README.md index 91cd0ee3dba2..c4d4b15e8874 100644 --- a/experimental/AlgebraicShifting/README.md +++ b/experimental/AlgebraicShifting/README.md @@ -2,12 +2,11 @@ ## Aims -This is an example for a file structure to set up a new package -in the experimental section. All files you find here are part of the -minimum requirements. See also the official Oscar documentation. +This package grew out of a project of Antony della Vecchia, Michael Joswig and Fabian Lenzen on "Partial Algebraic Shifting". +Part of this project is the development of new methods for algebraic shifting; these are implemented here. ## Status -We plan to also provide a function to automatically copy this template -for you to start your own package. +Full and partial shifting in the exterior algebra fully functional. + diff --git a/experimental/AlgebraicShifting/docs/src/exterior_shifting.md b/experimental/AlgebraicShifting/docs/src/exterior_shifting.md index 95038fc36f52..f482d29c781c 100644 --- a/experimental/AlgebraicShifting/docs/src/exterior_shifting.md +++ b/experimental/AlgebraicShifting/docs/src/exterior_shifting.md @@ -10,7 +10,7 @@ DocTestSetup = Oscar.doctestsetup() uniform_hypergraph ``` -## Helpful Matrix constructions +## Matrix Constructions ```@docs generic_unipotent_matrix diff --git a/experimental/AlgebraicShifting/docs/src/introduction.md b/experimental/AlgebraicShifting/docs/src/introduction.md index bb2f4a6ff870..0cf47324085b 100644 --- a/experimental/AlgebraicShifting/docs/src/introduction.md +++ b/experimental/AlgebraicShifting/docs/src/introduction.md @@ -6,7 +6,11 @@ DocTestSetup = Oscar.doctestsetup() # Introduction -This project aims to provide functionality for Algebraic Shifting, for some background on the subject we refer to [KAL02](@cite). +Algebraic shifting is a widely applicable method for converting a uniform hypergraph $S$ into another hypergraph, $\Delta(S)$, which is somehow simpler but still retains key properties of $S$. +Often this is applied to simplicial complexes, where each layer of $(k-1)$-faces forms a $k$-uniform hypergraph. + +Here we focus on full and partial algebraic shifting in the exterior algebra. +For some background on the subject we refer to [KAL02](@cite). ## Status @@ -17,6 +21,7 @@ This part of OSCAR is in an experimental state; please see [Adding new projects Please direct questions about this part of OSCAR to the following people: * [Antony Della Vecchia](https://antonydellavecchia.github.io) +* [Michael Joswig](https://page.math.tu-berlin.de/~joswig/) You can ask questions in the [OSCAR Slack](https://www.oscar-system.org/community/#slack). diff --git a/experimental/AlgebraicShifting/src/PartialShift.jl b/experimental/AlgebraicShifting/src/PartialShift.jl index 8d8242ce5227..fe3070cc5edc 100644 --- a/experimental/AlgebraicShifting/src/PartialShift.jl +++ b/experimental/AlgebraicShifting/src/PartialShift.jl @@ -32,7 +32,7 @@ end Constructs a unipotent matrix with entries in a polynomial ring `R`. One can also provide a field `F` and an integer `n`, -then the entries of the unipotent matrix will lie in a multi variate +then the entries of the unipotent matrix will lie in a multivariate polynomial ring over `F` with `n^2` variables. # Examples @@ -58,17 +58,17 @@ end @doc raw""" rothe_matrix(F::Field, w::WeylGroupElem; K::Union{SimplicialComplex, Nothing} = nothing) -For a base field `F` and a weyl group element `w` return the matrix with entries in the +For a base field `F` and a Weyl group element `w` return the matrix with entries in the multivariate polynomial ring `R` with `n^2` many indeterminants where `n - 1` is the rank of the -root system of the weyl group. -We know that since `general_linear_group(n^2, R)` has a Bruhat decomposition, any element lies in some double coset $BwB$. +root system of the Weyl group. +As `general_linear_group(n^2, R)` has a Bruhat decomposition, any element lies in a unique double coset $BwB$, where $B$ is the Borel group of upper triangular matrices. The Rothe matrix is a normal form for the matrix on the left of a representative for the double coset corresponding to `w`. -(this might need to be explained further and reference the preprint) -We use the name Rothe matrix because of its resemblance with a Rothe diagram. (add ref?) +This will be explained further once the corresponding preprint is on the arXiv. +We use the name Rothe matrix because of its resemblance with a Rothe diagram. (add ref? Knuth?) # Examples ```jldoctest - julia> W = weyl_group(:A, 4) +julia> W = weyl_group(:A, 4) Weyl group for root system defined by Cartan matrix [2 -1 0 0; -1 2 -1 0; 0 -1 2 -1; 0 0 -1 2] julia> s = gens(W) @@ -105,12 +105,11 @@ end compound_matrix(w::WeylGroupElem, k::Int) compound_matrix(m::MatElem, K::Vector{Vector{Int}}) -Given a matrix `m` return the matrix where each entry is a `k` minor of `m`. +Given a matrix `m`, return the matrix where each entry is a `k`$\times$`k`-minor of `m`. The entries of the compound matrix are ordered with respect to the lexicographic order on sets. -When passed a `PermGroupElem` or `WeylGroupElem`, return the copound matrix for their -permutation matrix representation. +When passed a `PermGroupElem` or `WeylGroupElem`, return the compound matrix for their permutation matrix representation. -Alternatively, passing a `UniformHypergraph` `K` will return the compound matrix with entries the `face_size(K)` minors, and restrict the rows to the rows corresponding to `K` +Alternatively, passing a `UniformHypergraph` `K` will return the compound matrix with entries the `face_size(K)` minors, and restrict the rows to the rows corresponding to `K`. # Examples ```jldoctest @@ -219,7 +218,7 @@ end Computes the (partial) exterior shift of a simplical complex or uniform hypergraph `K` with respect to the Weyl group element `w` and the field `F`. If the field is not given then `QQ` is used during the computation. -If `w` is not given then `longest_element(weyl_group(:A, n_vertices(K) - 1))` is used +If `w` is not given then `longest_element(Weyl_group(:A, n_vertices(K) - 1))` is used # Examples ```jldoctest @@ -248,7 +247,7 @@ true julia> betti_numbers(L) == betti_numbers(K) true -julia> W = weyl_group(:A, n_vertices(K) - 1) +julia> W = Weyl_group(:A, n_vertices(K) - 1) Weyl group for root system defined by Cartan matrix [2 -1 0 0 0; -1 2 -1 0 0; 0 -1 2 -1 0; 0 0 -1 2 -1; 0 0 0 -1 2] julia> s = gens(W) From c63d5ea361e03717eba0d1b229d014a6b0f8517e Mon Sep 17 00:00:00 2001 From: antonydellavecchia Date: Thu, 31 Oct 2024 10:09:18 +0100 Subject: [PATCH 082/128] Update docs/oscar_references.bib Co-authored-by: Max Horn --- docs/oscar_references.bib | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/oscar_references.bib b/docs/oscar_references.bib index 8e32460fd559..55dd6cc552dc 100644 --- a/docs/oscar_references.bib +++ b/docs/oscar_references.bib @@ -1566,7 +1566,7 @@ @InProceedings{KAL02 shortpublisher = {Math. Soc. Japan}, location = {Tokyo}, year = {2002}, - dor = {10.2969/aspm/03310121}, + doi = {10.2969/aspm/03310121}, } @InProceedings{KLT20, From 405a1955df1904fde2737ae2a0415548e8339ce0 Mon Sep 17 00:00:00 2001 From: Antony Della Vecchia Date: Thu, 31 Oct 2024 10:12:07 +0100 Subject: [PATCH 083/128] bibtool formatting --- docs/oscar_references.bib | 37 ++++++++++++++++++------------------- 1 file changed, 18 insertions(+), 19 deletions(-) diff --git a/docs/oscar_references.bib b/docs/oscar_references.bib index 8e32460fd559..d66cf682c456 100644 --- a/docs/oscar_references.bib +++ b/docs/oscar_references.bib @@ -1550,25 +1550,6 @@ @InCollection{KL91 doi = {10.1007/3-540-54522-0_108} } - -@InProceedings{KAL02, - author = {Kalai, Gil}, - title = {Algebraic shifting}, - booktitle = {Computational commutative algebra and combinatorics}, - editor = {Hibi, Takayuki}, - venue = {Osaka}, - eventdate={1999}, - series = {Advanced Studies in Pure Mathematics}, - shortseries = {Adv. Stud. Pure Math.}, - number = {33}, - pages = {121--163}, - publisher = {Mathematical Society of Japan}, - shortpublisher = {Math. Soc. Japan}, - location = {Tokyo}, - year = {2002}, - dor = {10.2969/aspm/03310121}, -} - @InProceedings{KLT20, author = {Kaluba, Marek and Lorenz, Benjamin and Timme, Sascha}, title = {Polymake.jl: A New Interface to polymake}, @@ -1650,6 +1631,24 @@ @Article{Kah10 doi = {10.1007/s10463-010-0290-9} } +@InProceedings{Kal02, + author = {Kalai, Gil}, + title = {Algebraic shifting}, + editor = {Hibi, Takayuki}, + booktitle = {Computational commutative algebra and combinatorics}, + series = {Advanced Studies in Pure Mathematics}, + number = {33}, + publisher = {Mathematical Society of Japan}, + pages = {121--163}, + year = {2002}, + venue = {Osaka}, + eventdate = {1999}, + shortseries = {Adv. Stud. Pure Math.}, + shortpublisher= {Math. Soc. Japan}, + location = {Tokyo}, + dor = {10.2969/aspm/03310121} +} + @Article{Kem02, author = {Kemper, Gregor}, title = {The calculation of radical ideals in positive characteristic}, From b8e8a005a80d15fe77fa489c0ab33ee1031f6c91 Mon Sep 17 00:00:00 2001 From: Antony Della Vecchia Date: Thu, 31 Oct 2024 10:24:52 +0100 Subject: [PATCH 084/128] removed tabs --- experimental/LieAlgebras/src/WeylGroup.jl | 38 +++++++++++------------ 1 file changed, 19 insertions(+), 19 deletions(-) diff --git a/experimental/LieAlgebras/src/WeylGroup.jl b/experimental/LieAlgebras/src/WeylGroup.jl index e8558348e4b1..f0a4600edc66 100644 --- a/experimental/LieAlgebras/src/WeylGroup.jl +++ b/experimental/LieAlgebras/src/WeylGroup.jl @@ -686,14 +686,14 @@ end function perm(w::WeylGroupElem) coxeter_type, n = root_system_type(root_system(parent(w)))[1] - @req coxeter_type == :A "Weyl group is not the symmetric group" - G = symmetric_group(n + 1) - return reduce(*, [cperm(G, [i, i + 1]) for i in word(w)]; init = cperm(G)) + @req coxeter_type == :A "Weyl group is not the symmetric group" + G = symmetric_group(n + 1) + return reduce(*, [cperm(G, [i, i + 1]) for i in word(w)]; init = cperm(G)) end function (W::WeylGroup)(p::PermGroupElem) coxeter_type, n = root_system_type(root_system(W))[1] - @req coxeter_type == :A && degree(parent(p)) == n+1 "Weyl group is not Sym($(n+1))." + @req coxeter_type == :A && degree(parent(p)) == n+1 "Weyl group is not Sym($(n+1))." word = UInt8[] for cycle in cycles(p) transpositions = [ @@ -716,40 +716,40 @@ permutation_matrix(R::Ring, w::WeylGroupElem) = permutation_matrix(R, perm(w)) # BJORNER, Brenti, Theorem 2.1.5 function bruhat_leq(v::PermGroupElem, w::PermGroupElem) @req parent(v) == parent(w) "Can only compare elements of symmetric group of same size." - n = degree(parent(v)) + n = degree(parent(v)) - bracket = (u, i, j) -> count(true for a in 1:i if u(a) >= j) - return all(bracket(v, i, j) <= bracket(w, i, j) for i in 1:n for j in 1:n) + bracket = (u, i, j) -> count(true for a in 1:i if u(a) >= j) + return all(bracket(v, i, j) <= bracket(w, i, j) for i in 1:n for j in 1:n) end # not sure if we need to bring in these * functions function Base.:(*)(w::WeylGroupElem, m::MatElem) - return permutation_matrix(base_ring(m), w) * m + return permutation_matrix(base_ring(m), w) * m end function Base.:(*)(m::MatElem, w::WeylGroupElem) - return m * permutation_matrix(base_ring(m), w) + return m * permutation_matrix(base_ring(m), w) end # not sure if it's a good idea to make <= the strong order function Base.:(<=)(x::WeylGroupElem, y::WeylGroupElem) coxeter_type_x, _ = root_system_type(root_system(parent(x)))[1] coxeter_type_y, _ = root_system_type(root_system(parent(y)))[1] - if coxeter_type_x == coxeter_type_y == :A - return bruhat_leq(perm(x), perm(y)) - else - error("unimplemented") - end + if coxeter_type_x == coxeter_type_y == :A + return bruhat_leq(perm(x), perm(y)) + else + error("unimplemented") + end end function Base.:(<)(x::WeylGroupElem, y::WeylGroupElem) coxeter_type_x, _ = root_system_type(root_system(parent(x)))[1] coxeter_type_y, _ = root_system_type(root_system(parent(y)))[1] - if coxeter_type_x == coxeter_type_y == :A - return x != y && bruhat_leq(perm(x), perm(y)) - else - error("unimplemented") - end + if coxeter_type_x == coxeter_type_y == :A + return x != y && bruhat_leq(perm(x), perm(y)) + else + error("unimplemented") + end end function isless(w::WeylGroupElem, v::WeylGroupElem) From dc6cbcbf9432d97dc26679d13fea038c09a22490 Mon Sep 17 00:00:00 2001 From: Antony Della Vecchia Date: Thu, 31 Oct 2024 11:21:38 +0100 Subject: [PATCH 085/128] added some docs to simplicial complex functions --- experimental/LieAlgebras/src/WeylGroup.jl | 98 +++++-------------- experimental/LieAlgebras/src/serialization.jl | 7 +- src/Combinatorics/SimplicialComplexes.jl | 62 ++++++++++++ 3 files changed, 92 insertions(+), 75 deletions(-) diff --git a/experimental/LieAlgebras/src/WeylGroup.jl b/experimental/LieAlgebras/src/WeylGroup.jl index f0a4600edc66..97145b27c829 100644 --- a/experimental/LieAlgebras/src/WeylGroup.jl +++ b/experimental/LieAlgebras/src/WeylGroup.jl @@ -251,32 +251,32 @@ Returns whether `x` is smaller than `y` with respect to the Bruhat order, i.e., whether some (not necessarily connected) subexpression of a reduced decomposition of `y`, is a reduced decomposition of `x`. """ -#function Base.:(<)(x::WeylGroupElem, y::WeylGroupElem) -# @req parent(x) === parent(y) "$x, $y must belong to the same Weyl group" -# -# if length(x) >= length(y) -# return false -# elseif isone(x) -# return true -# end -# -# tx = deepcopy(x) -# for i in 1:length(y) -# b, j, _ = explain_lmul(tx, y[i]) -# if !b -# deleteat!(word(tx), j) -# if isone(tx) -# return true -# end -# end -# -# if length(tx) > length(y) - i -# return false -# end -# end -# -# return false -#end +function Base.:(<)(x::WeylGroupElem, y::WeylGroupElem) + @req parent(x) === parent(y) "$x, $y must belong to the same Weyl group" + + if length(x) >= length(y) + return false + elseif isone(x) + return true + end + + tx = deepcopy(x) + for i in 1:length(y) + b, j, _ = explain_lmul(tx, y[i]) + if !b + deleteat!(word(tx), j) + if isone(tx) + return true + end + end + + if length(tx) > length(y) - i + return false + end + end + + return false +end function Base.:(==)(x::WeylGroupElem, y::WeylGroupElem) return parent(x) === parent(y) && word(x) == word(y) @@ -709,49 +709,3 @@ function (W::WeylGroup)(p::PermGroupElem) end permutation_matrix(R::Ring, w::WeylGroupElem) = permutation_matrix(R, perm(w)) - -################################################################################ -# Bruhat Strong order - -# BJORNER, Brenti, Theorem 2.1.5 -function bruhat_leq(v::PermGroupElem, w::PermGroupElem) - @req parent(v) == parent(w) "Can only compare elements of symmetric group of same size." - n = degree(parent(v)) - - bracket = (u, i, j) -> count(true for a in 1:i if u(a) >= j) - return all(bracket(v, i, j) <= bracket(w, i, j) for i in 1:n for j in 1:n) -end - -# not sure if we need to bring in these * functions -function Base.:(*)(w::WeylGroupElem, m::MatElem) - return permutation_matrix(base_ring(m), w) * m -end - -function Base.:(*)(m::MatElem, w::WeylGroupElem) - return m * permutation_matrix(base_ring(m), w) -end - -# not sure if it's a good idea to make <= the strong order -function Base.:(<=)(x::WeylGroupElem, y::WeylGroupElem) - coxeter_type_x, _ = root_system_type(root_system(parent(x)))[1] - coxeter_type_y, _ = root_system_type(root_system(parent(y)))[1] - if coxeter_type_x == coxeter_type_y == :A - return bruhat_leq(perm(x), perm(y)) - else - error("unimplemented") - end -end - -function Base.:(<)(x::WeylGroupElem, y::WeylGroupElem) - coxeter_type_x, _ = root_system_type(root_system(parent(x)))[1] - coxeter_type_y, _ = root_system_type(root_system(parent(y)))[1] - if coxeter_type_x == coxeter_type_y == :A - return x != y && bruhat_leq(perm(x), perm(y)) - else - error("unimplemented") - end -end - -function isless(w::WeylGroupElem, v::WeylGroupElem) - return w < v -end diff --git a/experimental/LieAlgebras/src/serialization.jl b/experimental/LieAlgebras/src/serialization.jl index 1ce95aea069b..9c3071466fa3 100644 --- a/experimental/LieAlgebras/src/serialization.jl +++ b/experimental/LieAlgebras/src/serialization.jl @@ -314,12 +314,13 @@ end @register_serialization_type WeylGroup uses_id function save_object(s::SerializerState, W::WeylGroup) - RS_ref = save_as_ref(s, root_system(W)) - save_object(s, RS_ref) + save_data_dict(s) do + save_typed_object(s, root_system(W), :root_system) + end end function load_object(s::DeserializerState, ::Type{WeylGroup}) - R = load_ref(s) + R = load_typed_object(s, :rootsystem) return weyl_group(R) end diff --git a/src/Combinatorics/SimplicialComplexes.jl b/src/Combinatorics/SimplicialComplexes.jl index 6aa1ed554af7..55164f34b70b 100644 --- a/src/Combinatorics/SimplicialComplexes.jl +++ b/src/Combinatorics/SimplicialComplexes.jl @@ -698,15 +698,77 @@ function on_simplicial_complex(K::SimplicialComplex, g::PermGroupElem) simplicial_complex(collect(new_facets)) end +@doc raw""" + simplicial_product(K1::SimplicialComplex, K2::SimplicialComplex) + +Given simplicial complexes `K1` and `K2` return their simplicial product. + +# Examples +```jldoctest +julia> K1 = simplicial_complex([[1, 2], [2, 3]]) +Abstract simplicial complex of dimension 1 on 3 vertices + +julia> K2 = simplicial_complex([[1, 2], [1, 3]]) +Abstract simplicial complex of dimension 1 on 3 vertices + +julia> facets(simplicial_product(K1, K2)) +8-element Vector{Set{Int64}}: + Set([5, 2, 1]) + Set([5, 4, 1]) + Set([2, 8, 1]) + Set([7, 8, 1]) + Set([6, 2, 3]) + Set([5, 6, 2]) + Set([2, 9, 3]) + Set([2, 9, 8]) +``` +""" function simplicial_product(K1::SimplicialComplex, K2::SimplicialComplex) return SimplicialComplex(Polymake.topaz.simplicial_product(pm_object(K1), pm_object(K2))) end +@doc raw""" + link_subcomplex(K::SimplicialComplex, f::Union{<:AbstractSet{Int},<:AbstractVector{Int}})) + +Given simplicial complex `K` and a face of `face` of `K` return the link of `face`. +simplicial complex at the . + +# Examples +```jldoctest +julia> K = simplicial_complex([[1, 2], [2, 3], [3, 4]]) +Abstract simplicial complex of dimension 1 on 4 vertices + +julia> facets(link_subcomplex(K, [2])) +2-element Vector{Set{Int64}}: + Set([1]) + Set([2]) +``` +""" function link_subcomplex(K::SimplicialComplex, face::Union{<:AbstractSet{Int},<:AbstractVector{Int}}) zero_based_face = Polymake.to_zero_based_indexing(face) return SimplicialComplex(Polymake.link_subcomplex(pm_object(K), zero_based_face)) end +@doc raw""" + barycentric_subdivision(K::SimplicialComplex) + +Given simplicial complex `K` returns its barycentric subdivision. + +# Examples +```jldoctest +julia> K = simplicial_complex([[1, 2, 3]]) +Abstract simplicial complex of dimension 2 on 3 vertices + +julia> facets(barycentric_subdivision(K)) +6-element Vector{Set{Int64}}: + Set([5, 2, 1]) + Set([5, 3, 1]) + Set([6, 2, 1]) + Set([4, 6, 1]) + Set([7, 3, 1]) + Set([4, 7, 1]) +``` +""" function barycentric_subdivision(K::SimplicialComplex) return SimplicialComplex(Polymake.topaz.barycentric_subdivision(pm_object(K))) end From 496837651536553f931d4820c15e086f5b809c2d Mon Sep 17 00:00:00 2001 From: antonydellavecchia Date: Thu, 31 Oct 2024 11:29:06 +0100 Subject: [PATCH 086/128] Update experimental/LieAlgebras/src/serialization.jl MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Co-authored-by: Lars Göttgens --- experimental/LieAlgebras/src/serialization.jl | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/experimental/LieAlgebras/src/serialization.jl b/experimental/LieAlgebras/src/serialization.jl index 9c3071466fa3..52b76c7dc997 100644 --- a/experimental/LieAlgebras/src/serialization.jl +++ b/experimental/LieAlgebras/src/serialization.jl @@ -320,7 +320,7 @@ function save_object(s::SerializerState, W::WeylGroup) end function load_object(s::DeserializerState, ::Type{WeylGroup}) - R = load_typed_object(s, :rootsystem) + R = load_typed_object(s, :root_system) return weyl_group(R) end From 4ef8766bcf796b56e62df358ce6462e1c07c3b66 Mon Sep 17 00:00:00 2001 From: antonydellavecchia Date: Thu, 31 Oct 2024 11:29:45 +0100 Subject: [PATCH 087/128] Apply suggestions from code review MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Co-authored-by: Lars Göttgens --- docs/oscar_references.bib | 2 +- src/Combinatorics/Graphs/functions.jl | 4 +--- 2 files changed, 2 insertions(+), 4 deletions(-) diff --git a/docs/oscar_references.bib b/docs/oscar_references.bib index d66cf682c456..8b180aaf9e49 100644 --- a/docs/oscar_references.bib +++ b/docs/oscar_references.bib @@ -1646,7 +1646,7 @@ @InProceedings{Kal02 shortseries = {Adv. Stud. Pure Math.}, shortpublisher= {Math. Soc. Japan}, location = {Tokyo}, - dor = {10.2969/aspm/03310121} + doi = {10.2969/aspm/03310121} } @Article{Kem02, diff --git a/src/Combinatorics/Graphs/functions.jl b/src/Combinatorics/Graphs/functions.jl index fddf4156e179..67ea43033131 100644 --- a/src/Combinatorics/Graphs/functions.jl +++ b/src/Combinatorics/Graphs/functions.jl @@ -1172,9 +1172,7 @@ end function graph_from_edges(::Type{T}, edges::Vector{Edge}, n_vertices::Int=-1) where {T <: Union{Directed, Undirected}} - isempty(edges) && return Graph{T}(n_vertices) - - n_needed = maximum(reduce(append!,[[src(e),dst(e)] for e in edges];)) + n_needed = maximum(reduce(append!,[[src(e),dst(e)] for e in edges];); init=0) @req (n_vertices >= n_needed || n_vertices < 0) "n_vertices must be at least the maximum vertex in the edges" g = Graph{T}(max(n_needed, n_vertices)) From bf7f71c98ec4d7e97eda7952d4c004e9427b9ea6 Mon Sep 17 00:00:00 2001 From: Antony Della Vecchia Date: Thu, 31 Oct 2024 12:13:42 +0100 Subject: [PATCH 088/128] create isomorphisms between weyl group and perm group --- experimental/LieAlgebras/src/WeylGroup.jl | 44 +++++++++++++---------- 1 file changed, 26 insertions(+), 18 deletions(-) diff --git a/experimental/LieAlgebras/src/WeylGroup.jl b/experimental/LieAlgebras/src/WeylGroup.jl index 97145b27c829..34bd7c577bef 100644 --- a/experimental/LieAlgebras/src/WeylGroup.jl +++ b/experimental/LieAlgebras/src/WeylGroup.jl @@ -684,28 +684,36 @@ end ################################################################################ # converting to permutations -function perm(w::WeylGroupElem) - coxeter_type, n = root_system_type(root_system(parent(w)))[1] +function isomorphism(::Type{PermGroup}, W::WeylGroup) + coxeter_type, n = root_system_type(root_system(W))[1] @req coxeter_type == :A "Weyl group is not the symmetric group" G = symmetric_group(n + 1) - return reduce(*, [cperm(G, [i, i + 1]) for i in word(w)]; init = cperm(G)) -end -function (W::WeylGroup)(p::PermGroupElem) - coxeter_type, n = root_system_type(root_system(W))[1] - @req coxeter_type == :A && degree(parent(p)) == n+1 "Weyl group is not Sym($(n+1))." - word = UInt8[] - for cycle in cycles(p) - transpositions = [ - sort([c, cycle[i + 1]]) for (i, c) in enumerate(cycle) if i < length(cycle)] - for t in transpositions - word = reduce(vcat, [ - [i for i in t[1]:t[2] - 1], - [i for i in reverse(t[1]:t[2] - 2)], - word]) + iso = function (w::WeylGroupElem) + reduce(*, [cperm(G, [i, i + 1]) for i in word(w)]; init=cperm(G)) + end + + isoinv = function (g::PermGroupElem) + word = UInt8[] + for cycle in cycles(p) + transpositions = [ + sort([c, cycle[i + 1]]) for (i, c) in enumerate(cycle) if i < length(cycle)] + for t in transpositions + word = reduce( + vcat, + [ + [i for i in t[1]:(t[2] - 1)], + [i for i in reverse(t[1]:(t[2] - 2))], + word], + ) + end end + return W(word) end - return W(word) + + return MapFromFunc(W, G, iso, isoinv) end -permutation_matrix(R::Ring, w::WeylGroupElem) = permutation_matrix(R, perm(w)) +function permutation_matrix(R::Ring, w::WeylGroupElem) + permutation_matrix(R, isomorphism(PermGroup, parent(w))(w)) +end From a4f0127172e56e8b2c1aef254b7c2cf7b99bfc5e Mon Sep 17 00:00:00 2001 From: Antony Della Vecchia Date: Thu, 31 Oct 2024 12:14:18 +0100 Subject: [PATCH 089/128] missing line from docs --- experimental/AlgebraicShifting/src/PartialShift.jl | 3 +++ 1 file changed, 3 insertions(+) diff --git a/experimental/AlgebraicShifting/src/PartialShift.jl b/experimental/AlgebraicShifting/src/PartialShift.jl index fe3070cc5edc..afbc6f0f0fcc 100644 --- a/experimental/AlgebraicShifting/src/PartialShift.jl +++ b/experimental/AlgebraicShifting/src/PartialShift.jl @@ -222,6 +222,9 @@ If `w` is not given then `longest_element(Weyl_group(:A, n_vertices(K) - 1))` is # Examples ```jldoctest +julia> K = real_projective_plane() +Abstract simplicial complex of dimension 2 on 6 vertices + julia> is_shifted(K) false From e552dfb9dc26fa09f7cd2cc03cdaecb0d263de25 Mon Sep 17 00:00:00 2001 From: Antony Della Vecchia Date: Thu, 31 Oct 2024 12:15:27 +0100 Subject: [PATCH 090/128] fixes to bib refs --- docs/oscar_references.bib | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/docs/oscar_references.bib b/docs/oscar_references.bib index 8b180aaf9e49..c486f333ccec 100644 --- a/docs/oscar_references.bib +++ b/docs/oscar_references.bib @@ -1641,12 +1641,12 @@ @InProceedings{Kal02 publisher = {Mathematical Society of Japan}, pages = {121--163}, year = {2002}, + doi = {10.2969/aspm/03310121}, venue = {Osaka}, eventdate = {1999}, shortseries = {Adv. Stud. Pure Math.}, shortpublisher= {Math. Soc. Japan}, - location = {Tokyo}, - doi = {10.2969/aspm/03310121} + location = {Tokyo} } @Article{Kem02, From 00879482e883241590bee116cc9378405daf2da0 Mon Sep 17 00:00:00 2001 From: Antony Della Vecchia Date: Thu, 31 Oct 2024 12:31:16 +0100 Subject: [PATCH 091/128] removes the use of perm for weyl group elements --- experimental/AlgebraicShifting/src/PartialShift.jl | 10 ++++++---- 1 file changed, 6 insertions(+), 4 deletions(-) diff --git a/experimental/AlgebraicShifting/src/PartialShift.jl b/experimental/AlgebraicShifting/src/PartialShift.jl index afbc6f0f0fcc..9fea71ef68bf 100644 --- a/experimental/AlgebraicShifting/src/PartialShift.jl +++ b/experimental/AlgebraicShifting/src/PartialShift.jl @@ -90,13 +90,15 @@ julia> rothe_matrix(GF(2), w) ``` """ function rothe_matrix(F::Field, w::WeylGroupElem) - n = rank(root_system(parent(w)))+1 + W = parent(w) + n = rank(root_system(W)) + 1 Fx, x = polynomial_ring(F, :x => (1:n, 1:n)) u = identity_matrix(Fx, n) - for (i, j) in inversions(perm(w)) + phi = isomorphism(PermGroup, W) + for (i, j) in inversions(phi(w)) u[i, j] = x[i, j] end - return u * permutation_matrix(F, perm(w)) + return u * permutation_matrix(F, w) end @doc raw""" @@ -155,7 +157,7 @@ end compound_matrix(m::MatElem, k::Int) = compound_matrix(m, uniform_hypergraph(sort(subsets(size(m, 1), k)))) compound_matrix(p::PermGroupElem, k::Int) = compound_matrix(permutation_matrix(ZZ, p), k) -compound_matrix(w::WeylGroupElem, k::Int) = compound_matrix(perm(w), k) +compound_matrix(w::WeylGroupElem, k::Int) = compound_matrix(permutation_matrix(ZZ, w), k) # this might be removed (currently is not used) function _set_to_zero(K::SimplicialComplex, indices::Tuple{Int, Int}) From 4edfdeed3222d28649d0f1a92b01472a1b645764 Mon Sep 17 00:00:00 2001 From: Antony Della Vecchia Date: Thu, 31 Oct 2024 12:31:45 +0100 Subject: [PATCH 092/128] fixed to docs --- experimental/AlgebraicShifting/docs/src/introduction.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/experimental/AlgebraicShifting/docs/src/introduction.md b/experimental/AlgebraicShifting/docs/src/introduction.md index 0cf47324085b..517644268648 100644 --- a/experimental/AlgebraicShifting/docs/src/introduction.md +++ b/experimental/AlgebraicShifting/docs/src/introduction.md @@ -10,7 +10,7 @@ Algebraic shifting is a widely applicable method for converting a uniform hyperg Often this is applied to simplicial complexes, where each layer of $(k-1)$-faces forms a $k$-uniform hypergraph. Here we focus on full and partial algebraic shifting in the exterior algebra. -For some background on the subject we refer to [KAL02](@cite). +For some background on the subject we refer to [Kal02](@cite). ## Status From 37d40a24f4048f22340e3ff3a58ac001ca340458 Mon Sep 17 00:00:00 2001 From: Antony Della Vecchia Date: Thu, 31 Oct 2024 13:41:15 +0100 Subject: [PATCH 093/128] speed up from using transpose --- experimental/AlgebraicShifting/src/PartialShift.jl | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/experimental/AlgebraicShifting/src/PartialShift.jl b/experimental/AlgebraicShifting/src/PartialShift.jl index 9fea71ef68bf..448e5e8e9e6d 100644 --- a/experimental/AlgebraicShifting/src/PartialShift.jl +++ b/experimental/AlgebraicShifting/src/PartialShift.jl @@ -190,7 +190,7 @@ function exterior_shift(K::UniformHypergraph, g::MatElem) @req size(g, 1) == n_vertices(K) "Matrix size does not match K." matrix_base = base_ring(g) nCk = sort!(subsets(n_vertices(K), face_size(K))) - c = compound_matrix(g, K) + c = transpose(compound_matrix(g, K)) if matrix_base isa MPolyRing Oscar.ModStdQt.ref_ff_rc!(c) elseif matrix_base isa MPolyQuoRing @@ -200,7 +200,7 @@ function exterior_shift(K::UniformHypergraph, g::MatElem) else rref!(c) end - return uniform_hypergraph(nCk[independent_columns(c)], n_vertices(K), face_size(K)) + return uniform_hypergraph(nCk[independent_columns(transpose(c))], n_vertices(K), face_size(K)) end function exterior_shift(K::SimplicialComplex, g::MatElem) From 7553c5a3cf890a458504ee01129b213cfb69d0ce Mon Sep 17 00:00:00 2001 From: Antony Della Vecchia Date: Thu, 31 Oct 2024 15:54:26 +0100 Subject: [PATCH 094/128] using transpose isn't quite right --- experimental/AlgebraicShifting/src/PartialShift.jl | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/experimental/AlgebraicShifting/src/PartialShift.jl b/experimental/AlgebraicShifting/src/PartialShift.jl index 448e5e8e9e6d..fa93a11a1cf4 100644 --- a/experimental/AlgebraicShifting/src/PartialShift.jl +++ b/experimental/AlgebraicShifting/src/PartialShift.jl @@ -190,7 +190,7 @@ function exterior_shift(K::UniformHypergraph, g::MatElem) @req size(g, 1) == n_vertices(K) "Matrix size does not match K." matrix_base = base_ring(g) nCk = sort!(subsets(n_vertices(K), face_size(K))) - c = transpose(compound_matrix(g, K)) + c = compound_matrix(g, K) if matrix_base isa MPolyRing Oscar.ModStdQt.ref_ff_rc!(c) elseif matrix_base isa MPolyQuoRing From 70fc86a83d059a626116a3c1aec65e0170b2a45a Mon Sep 17 00:00:00 2001 From: Antony Della Vecchia Date: Thu, 31 Oct 2024 16:36:37 +0100 Subject: [PATCH 095/128] creates isomorphism only once when finding vertices + constructing graph --- .../AlgebraicShifting/src/PartialShift.jl | 35 ++++++++++++------- .../src/PartialShiftGraph.jl | 28 ++++++++------- 2 files changed, 37 insertions(+), 26 deletions(-) diff --git a/experimental/AlgebraicShifting/src/PartialShift.jl b/experimental/AlgebraicShifting/src/PartialShift.jl index fa93a11a1cf4..b90b75afde58 100644 --- a/experimental/AlgebraicShifting/src/PartialShift.jl +++ b/experimental/AlgebraicShifting/src/PartialShift.jl @@ -87,18 +87,27 @@ julia> rothe_matrix(GF(2), w) [0 1 0 0 0] [0 0 1 0 0] [0 0 0 1 0] + +julia> rothe_matrix(QQ, perm([2, 3, 1])) +[x[1, 3] 1 0] +[x[2, 3] 0 1] +[ 1 0 0] ``` """ function rothe_matrix(F::Field, w::WeylGroupElem) W = parent(w) - n = rank(root_system(W)) + 1 + phi = isomorphism(PermGroup, W) + return rothe_matrix(F, phi(w)) +end + +function rothe_matrix(F::Field, p::PermGroupElem) + n = degree(parent(p)) Fx, x = polynomial_ring(F, :x => (1:n, 1:n)) u = identity_matrix(Fx, n) - phi = isomorphism(PermGroup, W) - for (i, j) in inversions(phi(w)) + for (i, j) in inversions(p) u[i, j] = x[i, j] end - return u * permutation_matrix(F, w) + return u * permutation_matrix(F, p) end @doc raw""" @@ -270,17 +279,17 @@ julia> L = exterior_shift(GF(2), K, w) Abstract simplicial complex of dimension 2 on 6 vertices ``` """ -function exterior_shift(F::Field, K::ComplexOrHypergraph, w::WeylGroupElem) +function exterior_shift(F::Field, K::ComplexOrHypergraph, p::PermGroupElem) n = n_vertices(K) - @req n == rank(root_system(parent(w))) + 1 "number of vertices - 1 should equal the rank of the root system" - - # in some cases this provides a speed up, not extremely important, we can chose to omit - # these lines - # handle some pre computation row reduction of compound matrix - #bool_mat = matrix(F, [!_set_to_zero(K, (i, j)) for i in 1:n, j in 1:n]) - #M = (bool_mat * permutation_matrix(F, perm(w))) .* + @req n == degree(parent(p)) "number of vertices - 1 should equal the rank of the root system" - return exterior_shift(K, rothe_matrix(F, w)) + return exterior_shift(F, K, rothe_matrix(F, p)) +end + +function exterior_shift(F::Field, K::ComplexOrHypergraph, w::WeylGroupElem) + n = n_vertices(K) + phi = isomorphism(PermGroup, parent(w)) + return exterior_shift(F, K, phi(w)) end function exterior_shift(F::Field, K::ComplexOrHypergraph) diff --git a/experimental/AlgebraicShifting/src/PartialShiftGraph.jl b/experimental/AlgebraicShifting/src/PartialShiftGraph.jl index d1b6a3d862a2..7c4264f39304 100644 --- a/experimental/AlgebraicShifting/src/PartialShiftGraph.jl +++ b/experimental/AlgebraicShifting/src/PartialShiftGraph.jl @@ -50,19 +50,20 @@ function partial_shift_graph_vertices(F::Field, W::Union{WeylGroup, Vector{WeylGroupElem}};) current = K visited = [current] + phi = isomorphism(PermGroup, parent(first(W))) # by properties of algebraic shifting # we know that K will be the last in this sorted list # sorting here should also speed up unique according to julia docs unvisited = unique( x -> Set(facets(x)), - sort([exterior_shift(F, K, w) for w in W]; lt=isless_lex))[1:end - 1] + sort([exterior_shift(F, K, phi(w)) for w in W]; lt=isless_lex))[1:end - 1] while(!isempty(unvisited)) current = pop!(unvisited) push!(visited, current) shifts = unique( x -> Set(facets(x)), - sort([exterior_shift(F, current, w) for w in W]; lt=isless_lex))[1:end - 1] + sort([exterior_shift(F, current, phi(w)) for w in W]; lt=isless_lex))[1:end - 1] # dont visit things twice new_facets = filter(x -> !(x in Set.(facets.(visited))), Set.(facets.(shifts))) @@ -76,10 +77,10 @@ end other complexes can be reached by applying the partial shifts `deltas` to K, and store the shift matrices that give rise to each edge.""" function multi_edges(F::Field, - W::WeylGroup, + permutations::Vector{PermGroupElem}, complexes::Vector{Tuple{Int,T}}, complex_labels::Dict{Set{Set{Int}}, Int} -) :: Dict{Tuple{Int, Int}, Vector{WeylGroupElem}} where T <: ComplexOrHypergraph; +) :: Dict{Tuple{Int, Int}, Vector{PermGroupElem}} where T <: ComplexOrHypergraph; # For each complex K with index i, compute the shifted complex delta of K by w for each w in W. # For nontrivial delta, place (i, delta) → w in a singleton dictionary, and eventually merge all dictionaries # to obtain a dictionary (i, delta) → [w that yield the shift K → delta] @@ -88,9 +89,9 @@ function multi_edges(F::Field, ( Dict((i, complex_labels[Set(facets(delta))]) => [w]) for (i, K) in complexes - for (w, delta) in ((w, exterior_shift(F, K, w)) for w in W) + for (p, delta) in ((p, exterior_shift(F, K, p)) for p in permutations) if Set(facets(delta)) != Set(facets(K))); - init=Dict{Tuple{Int, Int}, Vector{WeylGroupElem}}() + init=Dict{Tuple{Int, Int}, Vector{PermGroupElem}}() ) end @@ -185,24 +186,25 @@ function partial_shift_graph(F::Field, complexes::Vector{T}, W::Union{WeylGroup, W2 = only(unique(parent.(W))) rs_type = root_system_type(root_system(W2)) @req rs_type[1][1] == :A && rs_type[1][2] == n - 1 "Only Weyl groups type A_$(n-1) are currently support and received type $(T[1])." - + + phi = isomorphism(PermGroup, parent(first(W))) + G = codomain(phi) task_size = 1 if parallel # setup parallel parameters - channels = Oscar.params_channels(Union{RootSystem, WeylGroup, Vector{SimplicialComplex}, Vector{UniformHypergraph}}) + channels = Oscar.params_channels(Union{PermGroup, Vector{SimplicialComplex}, Vector{UniformHypergraph}}) # setup parents needed to be sent to each process - Oscar.put_params(channels, root_system(W)) - Oscar.put_params(channels, W) + Oscar.put_params(channels, G) end - # edge_tuples = multi_edges(F, W, collect(enumerate(complexes)), complex_labels) + # edge_tuples = multi_edges(F, phi.(W), collect(enumerate(complexes)), complex_labels) # Basically, the following does the same as the preceeding, but with a progress indicator: edge_labels = reduce((d1, d2) -> mergewith!(vcat, d1, d2), @showprogress pmap( - Ks -> multi_edges(F, W, Ks, complex_labels), + Ks -> multi_edges(F, phi.(W), Ks, complex_labels), Iterators.partition(enumerate(complexes), task_size))) graph = graph_from_edges(Directed, [[i,j] for (i,j) in keys(edge_labels)]) - return (graph, edge_labels, complexes) + return (graph, Dict(k => inv(phi).(v) for (k, v) in edge_labels), complexes) end function partial_shift_graph(F::Field, complexes::Vector{T}; parallel=false) where T <: ComplexOrHypergraph From 6207e4b54bc50fbd422f4a47d938114a145fb800 Mon Sep 17 00:00:00 2001 From: Antony Della Vecchia Date: Thu, 31 Oct 2024 17:13:21 +0100 Subject: [PATCH 096/128] fixes some regressions --- experimental/AlgebraicShifting/src/PartialShift.jl | 4 ++-- experimental/AlgebraicShifting/src/PartialShiftGraph.jl | 5 ++--- experimental/LieAlgebras/src/WeylGroup.jl | 2 +- 3 files changed, 5 insertions(+), 6 deletions(-) diff --git a/experimental/AlgebraicShifting/src/PartialShift.jl b/experimental/AlgebraicShifting/src/PartialShift.jl index b90b75afde58..b15f739edd71 100644 --- a/experimental/AlgebraicShifting/src/PartialShift.jl +++ b/experimental/AlgebraicShifting/src/PartialShift.jl @@ -209,7 +209,7 @@ function exterior_shift(K::UniformHypergraph, g::MatElem) else rref!(c) end - return uniform_hypergraph(nCk[independent_columns(transpose(c))], n_vertices(K), face_size(K)) + return uniform_hypergraph(nCk[independent_columns(c)], n_vertices(K), face_size(K)) end function exterior_shift(K::SimplicialComplex, g::MatElem) @@ -283,7 +283,7 @@ function exterior_shift(F::Field, K::ComplexOrHypergraph, p::PermGroupElem) n = n_vertices(K) @req n == degree(parent(p)) "number of vertices - 1 should equal the rank of the root system" - return exterior_shift(F, K, rothe_matrix(F, p)) + return exterior_shift(K, rothe_matrix(F, p)) end function exterior_shift(F::Field, K::ComplexOrHypergraph, w::WeylGroupElem) diff --git a/experimental/AlgebraicShifting/src/PartialShiftGraph.jl b/experimental/AlgebraicShifting/src/PartialShiftGraph.jl index 7c4264f39304..020d5b60b6d3 100644 --- a/experimental/AlgebraicShifting/src/PartialShiftGraph.jl +++ b/experimental/AlgebraicShifting/src/PartialShiftGraph.jl @@ -87,7 +87,7 @@ function multi_edges(F::Field, reduce( (d1, d2) -> mergewith!(vcat, d1, d2), ( - Dict((i, complex_labels[Set(facets(delta))]) => [w]) + Dict((i, complex_labels[Set(facets(delta))]) => [p]) for (i, K) in complexes for (p, delta) in ((p, exterior_shift(F, K, p)) for p in permutations) if Set(facets(delta)) != Set(facets(K))); @@ -188,13 +188,12 @@ function partial_shift_graph(F::Field, complexes::Vector{T}, W::Union{WeylGroup, @req rs_type[1][1] == :A && rs_type[1][2] == n - 1 "Only Weyl groups type A_$(n-1) are currently support and received type $(T[1])." phi = isomorphism(PermGroup, parent(first(W))) - G = codomain(phi) task_size = 1 if parallel # setup parallel parameters channels = Oscar.params_channels(Union{PermGroup, Vector{SimplicialComplex}, Vector{UniformHypergraph}}) # setup parents needed to be sent to each process - Oscar.put_params(channels, G) + Oscar.put_params(channels, codomain(phi)) end # edge_tuples = multi_edges(F, phi.(W), collect(enumerate(complexes)), complex_labels) diff --git a/experimental/LieAlgebras/src/WeylGroup.jl b/experimental/LieAlgebras/src/WeylGroup.jl index 34bd7c577bef..554d62749291 100644 --- a/experimental/LieAlgebras/src/WeylGroup.jl +++ b/experimental/LieAlgebras/src/WeylGroup.jl @@ -695,7 +695,7 @@ function isomorphism(::Type{PermGroup}, W::WeylGroup) isoinv = function (g::PermGroupElem) word = UInt8[] - for cycle in cycles(p) + for cycle in cycles(g) transpositions = [ sort([c, cycle[i + 1]]) for (i, c) in enumerate(cycle) if i < length(cycle)] for t in transpositions From b3610b7e1ade616ba1f52d2708a173d231ed1e8e Mon Sep 17 00:00:00 2001 From: antonydellavecchia Date: Fri, 1 Nov 2024 11:15:20 +0100 Subject: [PATCH 097/128] fix for empty grpah --- src/Combinatorics/Graphs/functions.jl | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/Combinatorics/Graphs/functions.jl b/src/Combinatorics/Graphs/functions.jl index 67ea43033131..af7296239dac 100644 --- a/src/Combinatorics/Graphs/functions.jl +++ b/src/Combinatorics/Graphs/functions.jl @@ -1172,7 +1172,7 @@ end function graph_from_edges(::Type{T}, edges::Vector{Edge}, n_vertices::Int=-1) where {T <: Union{Directed, Undirected}} - n_needed = maximum(reduce(append!,[[src(e),dst(e)] for e in edges];); init=0) + n_needed = maximum(reduce(append!,[[src(e),dst(e)] for e in edges]; init=[0]);) @req (n_vertices >= n_needed || n_vertices < 0) "n_vertices must be at least the maximum vertex in the edges" g = Graph{T}(max(n_needed, n_vertices)) From 687c369ff00b0e4a6bf9d2854ee03ea7618a601b Mon Sep 17 00:00:00 2001 From: antonydellavecchia Date: Fri, 1 Nov 2024 14:11:40 +0100 Subject: [PATCH 098/128] suppres progress bar in doc strings --- .../AlgebraicShifting/src/PartialShift.jl | 4 +- .../src/PartialShiftGraph.jl | 37 +++++++++++-------- 2 files changed, 23 insertions(+), 18 deletions(-) diff --git a/experimental/AlgebraicShifting/src/PartialShift.jl b/experimental/AlgebraicShifting/src/PartialShift.jl index b15f739edd71..7d3266c010d7 100644 --- a/experimental/AlgebraicShifting/src/PartialShift.jl +++ b/experimental/AlgebraicShifting/src/PartialShift.jl @@ -229,7 +229,7 @@ end Computes the (partial) exterior shift of a simplical complex or uniform hypergraph `K` with respect to the Weyl group element `w` and the field `F`. If the field is not given then `QQ` is used during the computation. -If `w` is not given then `longest_element(Weyl_group(:A, n_vertices(K) - 1))` is used +If `w` is not given then `longest_element(weyl_group(:A, n_vertices(K) - 1))` is used # Examples ```jldoctest @@ -261,7 +261,7 @@ true julia> betti_numbers(L) == betti_numbers(K) true -julia> W = Weyl_group(:A, n_vertices(K) - 1) +julia> W = weyl_group(:A, n_vertices(K) - 1) Weyl group for root system defined by Cartan matrix [2 -1 0 0 0; -1 2 -1 0 0; 0 -1 2 -1 0; 0 0 -1 2 -1; 0 0 0 -1 2] julia> s = gens(W) diff --git a/experimental/AlgebraicShifting/src/PartialShiftGraph.jl b/experimental/AlgebraicShifting/src/PartialShiftGraph.jl index 020d5b60b6d3..3b11f64acdf6 100644 --- a/experimental/AlgebraicShifting/src/PartialShiftGraph.jl +++ b/experimental/AlgebraicShifting/src/PartialShiftGraph.jl @@ -96,10 +96,10 @@ function multi_edges(F::Field, end @doc raw""" - partial_shift_graph(F::Field, complexes::Vector{Simplicialcomplex}; parallel=false) - partial_shift_graph(F::Field, complexes::Vector{Uniformhypergraph}; parallel=false) - partial_shift_graph(F::Field, complexes::Vector{Simplicialcomplex}, W::Union{WeylGroup, Vector{WeylGroupElem}}; parallel=false) - partial_shift_graph(F::Field, complexes::Vector{Uniformhypergraph}, W::Union{WeylGroup, Vector{WeylGroupElem}}; parallel=false) + partial_shift_graph(F::Field, complexes::Vector{Simplicialcomplex}; parallel=false, show_progress=true) + partial_shift_graph(F::Field, complexes::Vector{Uniformhypergraph}; parallel=false, show_progress=true) + partial_shift_graph(F::Field, complexes::Vector{Simplicialcomplex}, W::Union{WeylGroup, Vector{WeylGroupElem}}; parallel=false, show_progress=true) + partial_shift_graph(F::Field, complexes::Vector{Uniformhypergraph}, W::Union{WeylGroup, Vector{WeylGroupElem}}; parallel=false, show_progress=true) Constructs the partial shift graph on `complexes`. @@ -133,8 +133,7 @@ julia> Ks = gamma(4,2,5) UniformHypergraph(4, 2, [[1, 2], [1, 3], [1, 4], [2, 4], [3, 4]]) UniformHypergraph(4, 2, [[1, 3], [1, 4], [2, 3], [2, 4], [3, 4]]) -julia> G, EL, VL = partial_shift_graph(QQ, Ks); -Progress: 100%|█████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| Time: 0:00:00 +julia> G, EL, VL = partial_shift_graph(QQ, Ks; show_progress=false); julia> collect(edges(G)) 14-element Vector{Edge}: @@ -167,7 +166,7 @@ julia> facets.(VL[[6, 5]]) ``` """ function partial_shift_graph(F::Field, complexes::Vector{T}, W::Union{WeylGroup, Vector{WeylGroupElem}}; - parallel::Bool = false) :: Tuple{Graph{Directed}, EdgeLabels, Vector{ComplexOrHypergraph}} where T <: ComplexOrHypergraph; + parallel::Bool = false, show_progress::Bool = true) :: Tuple{Graph{Directed}, EdgeLabels, Vector{ComplexOrHypergraph}} where T <: ComplexOrHypergraph; # Deal with trivial case if length(complexes) <= 1 return (graph_from_adjacency_matrix(Directed, zeros(length(complexes),length(complexes))), EdgeLabels()) @@ -196,17 +195,23 @@ function partial_shift_graph(F::Field, complexes::Vector{T}, W::Union{WeylGroup, Oscar.put_params(channels, codomain(phi)) end - # edge_tuples = multi_edges(F, phi.(W), collect(enumerate(complexes)), complex_labels) - # Basically, the following does the same as the preceeding, but with a progress indicator: - edge_labels = reduce((d1, d2) -> mergewith!(vcat, d1, d2), - @showprogress pmap( - Ks -> multi_edges(F, phi.(W), Ks, complex_labels), - Iterators.partition(enumerate(complexes), task_size))) + if show_progress + edge_labels = reduce((d1, d2) -> mergewith!(vcat, d1, d2), + @showprogress pmap( + Ks -> multi_edges(F, phi.(W), Ks, complex_labels), + Iterators.partition(enumerate(complexes), task_size))) + else + edge_labels = multi_edges(F, + phi.(W), + collect(enumerate(complexes)), + complex_labels) + end graph = graph_from_edges(Directed, [[i,j] for (i,j) in keys(edge_labels)]) return (graph, Dict(k => inv(phi).(v) for (k, v) in edge_labels), complexes) end -function partial_shift_graph(F::Field, complexes::Vector{T}; parallel=false) where T <: ComplexOrHypergraph +function partial_shift_graph(F::Field, complexes::Vector{T}; + kwargs...) where T <: ComplexOrHypergraph # Deal with trivial case if length(complexes) <= 1 return (graph_from_adjacency_matrix(Directed, zeros(length(complexes),length(complexes))), EdgeLabels()) @@ -214,7 +219,7 @@ function partial_shift_graph(F::Field, complexes::Vector{T}; parallel=false) whe n = n_vertices(complexes[1]) W = weyl_group(:A, n - 1) - return partial_shift_graph(F, complexes, W;parallel=parallel) + return partial_shift_graph(F, complexes, W; kwargs...) end @doc raw""" @@ -241,7 +246,7 @@ julia> Ks = gamma(4,2,5) UniformHypergraph(4, 2, [[1, 3], [1, 4], [2, 3], [2, 4], [3, 4]]) julia> G, EL, VL = partial_shift_graph(QQ, Ks); -Progress: 100%|█████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| Time: 0:00:00 + julia> contracted_partial_shift_graph(G, EL) (Directed graph with 1 nodes and 0 edges, [1], [[5, 4, 6, 2, 3, 1]]) From 6a0dc54de09d46d60312d560bdc16bc4c7b5b4b1 Mon Sep 17 00:00:00 2001 From: antonydellavecchia Date: Fri, 1 Nov 2024 16:02:56 +0100 Subject: [PATCH 099/128] fixes for merge --- experimental/LieAlgebras/src/WeylGroup.jl | 32 +---------------------- 1 file changed, 1 insertion(+), 31 deletions(-) diff --git a/experimental/LieAlgebras/src/WeylGroup.jl b/experimental/LieAlgebras/src/WeylGroup.jl index 51f364c82e56..a7b9923acb5c 100644 --- a/experimental/LieAlgebras/src/WeylGroup.jl +++ b/experimental/LieAlgebras/src/WeylGroup.jl @@ -735,37 +735,7 @@ function Base.iterate(iter::WeylOrbitIterator, state::WeylIteratorNoCopyState) end ################################################################################ -# converting to permutations - -function isomorphism(::Type{PermGroup}, W::WeylGroup) - coxeter_type, n = root_system_type(root_system(W))[1] - @req coxeter_type == :A "Weyl group is not the symmetric group" - G = symmetric_group(n + 1) - - iso = function (w::WeylGroupElem) - reduce(*, [cperm(G, [i, i + 1]) for i in word(w)]; init=cperm(G)) - end - - isoinv = function (g::PermGroupElem) - word = UInt8[] - for cycle in cycles(g) - transpositions = [ - sort([c, cycle[i + 1]]) for (i, c) in enumerate(cycle) if i < length(cycle)] - for t in transpositions - word = reduce( - vcat, - [ - [i for i in t[1]:(t[2] - 1)], - [i for i in reverse(t[1]:(t[2] - 2))], - word], - ) - end - end - return W(word) - end - - return MapFromFunc(W, G, iso, isoinv) -end +# converting to permutation matrices function permutation_matrix(R::Ring, w::WeylGroupElem) permutation_matrix(R, isomorphism(PermGroup, parent(w))(w)) From f8a4532ea219a474089b6478ea5b88f3adec64ea Mon Sep 17 00:00:00 2001 From: Antony Della Vecchia Date: Fri, 1 Nov 2024 16:29:10 +0100 Subject: [PATCH 100/128] remove permutation matrix function --- experimental/AlgebraicShifting/src/PartialShift.jl | 6 +++++- experimental/LieAlgebras/src/WeylGroup.jl | 7 ------- 2 files changed, 5 insertions(+), 8 deletions(-) diff --git a/experimental/AlgebraicShifting/src/PartialShift.jl b/experimental/AlgebraicShifting/src/PartialShift.jl index 7d3266c010d7..f88f7f817541 100644 --- a/experimental/AlgebraicShifting/src/PartialShift.jl +++ b/experimental/AlgebraicShifting/src/PartialShift.jl @@ -166,7 +166,11 @@ end compound_matrix(m::MatElem, k::Int) = compound_matrix(m, uniform_hypergraph(sort(subsets(size(m, 1), k)))) compound_matrix(p::PermGroupElem, k::Int) = compound_matrix(permutation_matrix(ZZ, p), k) -compound_matrix(w::WeylGroupElem, k::Int) = compound_matrix(permutation_matrix(ZZ, w), k) + +function compound_matrix(w::WeylGroupElem, k::Int) + iso = isomorphism(PermGroup, parent(w)) + return compound_matrix(permutation_matrix(ZZ, iso(w)), k) +end # this might be removed (currently is not used) function _set_to_zero(K::SimplicialComplex, indices::Tuple{Int, Int}) diff --git a/experimental/LieAlgebras/src/WeylGroup.jl b/experimental/LieAlgebras/src/WeylGroup.jl index a7b9923acb5c..e4d0fd98e021 100644 --- a/experimental/LieAlgebras/src/WeylGroup.jl +++ b/experimental/LieAlgebras/src/WeylGroup.jl @@ -733,10 +733,3 @@ function Base.iterate(iter::WeylOrbitIterator, state::WeylIteratorNoCopyState) (wt, _), state = it return deepcopy(wt), state end - -################################################################################ -# converting to permutation matrices - -function permutation_matrix(R::Ring, w::WeylGroupElem) - permutation_matrix(R, isomorphism(PermGroup, parent(w))(w)) -end From 39f66a331696f9f2d182f581680c1fa0c0eb393d Mon Sep 17 00:00:00 2001 From: Antony Della Vecchia Date: Mon, 4 Nov 2024 10:40:27 +0100 Subject: [PATCH 101/128] suppress progress bar in docs --- experimental/AlgebraicShifting/src/PartialShiftGraph.jl | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/experimental/AlgebraicShifting/src/PartialShiftGraph.jl b/experimental/AlgebraicShifting/src/PartialShiftGraph.jl index 3b11f64acdf6..91a7162b8493 100644 --- a/experimental/AlgebraicShifting/src/PartialShiftGraph.jl +++ b/experimental/AlgebraicShifting/src/PartialShiftGraph.jl @@ -245,7 +245,7 @@ julia> Ks = gamma(4,2,5) UniformHypergraph(4, 2, [[1, 2], [1, 3], [1, 4], [2, 4], [3, 4]]) UniformHypergraph(4, 2, [[1, 3], [1, 4], [2, 3], [2, 4], [3, 4]]) -julia> G, EL, VL = partial_shift_graph(QQ, Ks); +julia> G, EL, VL = partial_shift_graph(QQ, Ks; show_progess=false); julia> contracted_partial_shift_graph(G, EL) From c2f1c3eca2e942a756bb3aa5a09dc7c44f0c4b1d Mon Sep 17 00:00:00 2001 From: Antony Della Vecchia Date: Mon, 4 Nov 2024 11:17:28 +0100 Subject: [PATCH 102/128] fix _set_to_zero --- experimental/AlgebraicShifting/src/PartialShift.jl | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/experimental/AlgebraicShifting/src/PartialShift.jl b/experimental/AlgebraicShifting/src/PartialShift.jl index f88f7f817541..cbc5446a7655 100644 --- a/experimental/AlgebraicShifting/src/PartialShift.jl +++ b/experimental/AlgebraicShifting/src/PartialShift.jl @@ -178,10 +178,10 @@ function _set_to_zero(K::SimplicialComplex, indices::Tuple{Int, Int}) row == col && return false K_facets = facets(K) for facet in K_facets - # if column index is not in face there is nothing to do - !(col in facet) && continue + # if row index is not in face there is nothing to do + !(row in facet) && continue # replace index from row with index from col in facet - S = push!(delete!(copy(facet), col), row) + S = push!(delete!(copy(facet), row), col) !any(is_subset(S, check_facet) for check_facet in K_facets) && return false end return true From 79a12f1da015a226eb14c4f774caf65a6276efc7 Mon Sep 17 00:00:00 2001 From: Antony Della Vecchia Date: Mon, 4 Nov 2024 11:35:16 +0100 Subject: [PATCH 103/128] fixes white space --- .../src/AlgebraicShifting.jl | 4 +-- .../AlgebraicShifting/src/PartialShift.jl | 32 ++++++++----------- .../src/PartialShiftGraph.jl | 20 ++++++------ 3 files changed, 24 insertions(+), 32 deletions(-) diff --git a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl index ceb1b21351aa..4dc743c923a4 100644 --- a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl +++ b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl @@ -29,8 +29,8 @@ function independent_columns(A::MatElem) end -@doc raw""" - symmetric_shift(F::Field, K::SimplicialComplex) +""" + symmetric_shift(F::Field, K::SimplicialComplex) Returns the symmetric shift of `K` diff --git a/experimental/AlgebraicShifting/src/PartialShift.jl b/experimental/AlgebraicShifting/src/PartialShift.jl index cbc5446a7655..5c0916472305 100644 --- a/experimental/AlgebraicShifting/src/PartialShift.jl +++ b/experimental/AlgebraicShifting/src/PartialShift.jl @@ -27,8 +27,8 @@ function generic_unipotent_matrix(R::MPolyRing) end @doc raw""" - generic_unipotent_matrix(R::MPolyRing) - generic_unipotent_matrix(F::Field, n::Int) + generic_unipotent_matrix(R::MPolyRing) + generic_unipotent_matrix(F::Field, n::Int) Constructs a unipotent matrix with entries in a polynomial ring `R`. One can also provide a field `F` and an integer `n`, @@ -37,7 +37,6 @@ polynomial ring over `F` with `n^2` variables. # Examples ```jldoctest - julia> R, x = polynomial_ring(QQ, :x=> (1:2, 1:2)) (Multivariate polynomial ring in 4 variables over QQ, QQMPolyRingElem[x[1, 1] x[1, 2]; x[2, 1] x[2, 2]]) @@ -56,7 +55,7 @@ function generic_unipotent_matrix(F::Field, n::Int) end @doc raw""" - rothe_matrix(F::Field, w::WeylGroupElem; K::Union{SimplicialComplex, Nothing} = nothing) + rothe_matrix(F::Field, w::WeylGroupElem; K::Union{SimplicialComplex, Nothing} = nothing) For a base field `F` and a Weyl group element `w` return the matrix with entries in the multivariate polynomial ring `R` with `n^2` many indeterminants where `n - 1` is the rank of the @@ -111,10 +110,10 @@ function rothe_matrix(F::Field, p::PermGroupElem) end @doc raw""" - compound_matrix(m::MatElem, k::Int) - compound_matrix(p::PermGroupElem, k::Int) - compound_matrix(w::WeylGroupElem, k::Int) - compound_matrix(m::MatElem, K::Vector{Vector{Int}}) + compound_matrix(m::MatElem, k::Int) + compound_matrix(p::PermGroupElem, k::Int) + compound_matrix(w::WeylGroupElem, k::Int) + compound_matrix(m::MatElem, K::Vector{Vector{Int}}) Given a matrix `m`, return the matrix where each entry is a `k`$\times$`k`-minor of `m`. The entries of the compound matrix are ordered with respect to the lexicographic order on sets. @@ -124,7 +123,6 @@ Alternatively, passing a `UniformHypergraph` `K` will return the compound matrix # Examples ```jldoctest - julia> M = generic_unipotent_matrix(QQ, 3) [1 x[1, 2] x[1, 3]] [0 1 x[2, 3]] @@ -192,10 +190,6 @@ _set_to_zero(K::UniformHypergraph, indices::Tuple{Int, Int}) = _set_to_zero(simp ############################################################################### # Exterior shift ############################################################################### -raw""" exterior_shift(K::UniformHypergraph, g::MatElem) - -Computes the exterior shift ``\Delta_g(K)`` of ``K`` w.r.t. the invertible matrix ``g``. -""" function exterior_shift(K::UniformHypergraph, g::MatElem) # the exterior shifting works in a different algebra that lends # itself to an easier implementation @@ -224,12 +218,12 @@ function exterior_shift(K::SimplicialComplex, g::MatElem) end @doc raw""" - exterior_shift(F::Field, K::SimplicialComplex, w::WeylGroupElem) - exterior_shift(F::Field, K::UniformHypergraph, w::WeylGroupElem) - exterior_shift(K::SimplicialComplex, w::WeylGroupElem) - exterior_shift(K::UniformHypergraph, w::WeylGroupElem) - exterior_shift(K::SimplicialComplex) - exterior_shift(K::UniformHypergraph) + exterior_shift(F::Field, K::SimplicialComplex, w::WeylGroupElem) + exterior_shift(F::Field, K::UniformHypergraph, w::WeylGroupElem) + exterior_shift(K::SimplicialComplex, w::WeylGroupElem) + exterior_shift(K::UniformHypergraph, w::WeylGroupElem) + exterior_shift(K::SimplicialComplex) + exterior_shift(K::UniformHypergraph) Computes the (partial) exterior shift of a simplical complex or uniform hypergraph `K` with respect to the Weyl group element `w` and the field `F`. If the field is not given then `QQ` is used during the computation. diff --git a/experimental/AlgebraicShifting/src/PartialShiftGraph.jl b/experimental/AlgebraicShifting/src/PartialShiftGraph.jl index 91a7162b8493..7a1b3de9c5f4 100644 --- a/experimental/AlgebraicShifting/src/PartialShiftGraph.jl +++ b/experimental/AlgebraicShifting/src/PartialShiftGraph.jl @@ -15,7 +15,7 @@ end isless_lex(K1::ComplexOrHypergraph, K2::ComplexOrHypergraph) = isless_lex(Set(facets(K1)), Set(facets(K2))) @doc raw""" - partial_shift_graph_vertices(F::Field,::SimplicialComplex, W::Union{WeylGroup, Vector{WeylGroupElem}};) + partial_shift_graph_vertices(F::Field,::SimplicialComplex, W::Union{WeylGroup, Vector{WeylGroupElem}};) Given a field `F` discover the vertices of the partial shift graph starting from `K` using exterior partial shifts corresponding to elements in `W`. @@ -96,11 +96,10 @@ function multi_edges(F::Field, end @doc raw""" - partial_shift_graph(F::Field, complexes::Vector{Simplicialcomplex}; parallel=false, show_progress=true) - partial_shift_graph(F::Field, complexes::Vector{Uniformhypergraph}; parallel=false, show_progress=true) - partial_shift_graph(F::Field, complexes::Vector{Simplicialcomplex}, W::Union{WeylGroup, Vector{WeylGroupElem}}; parallel=false, show_progress=true) - partial_shift_graph(F::Field, complexes::Vector{Uniformhypergraph}, W::Union{WeylGroup, Vector{WeylGroupElem}}; parallel=false, show_progress=true) - + partial_shift_graph(F::Field, complexes::Vector{Simplicialcomplex}; parallel=false, show_progress=true) + partial_shift_graph(F::Field, complexes::Vector{Uniformhypergraph}; parallel=false, show_progress=true) + partial_shift_graph(F::Field, complexes::Vector{Simplicialcomplex}, W::Union{WeylGroup, Vector{WeylGroupElem}}; parallel=false, show_progress=true) + partial_shift_graph(F::Field, complexes::Vector{Uniformhypergraph}, W::Union{WeylGroup, Vector{WeylGroupElem}}; parallel=false, show_progress=true) Constructs the partial shift graph on `complexes`. @@ -120,7 +119,7 @@ If `K` and `L` are the `i`th and `j`th entry of `VL`, resp., If `W` is not provided, the function will use the symmetric group of the same order as vertices in each complex complexes. # Examples -``` +```jldoctest julia> gamma(n,k,l) = uniform_hypergraph.(subsets(subsets(n, k), l), n) gamma (generic function with 1 method) @@ -223,7 +222,7 @@ function partial_shift_graph(F::Field, complexes::Vector{T}; end @doc raw""" - contracted_partial_shift_graph(G::Graph{Directed}, edge_labels::Dict{Tuple{Int, Int}, Vector{WeylGroupElem}}) + contracted_partial_shift_graph(G::Graph{Directed}, edge_labels::Dict{Tuple{Int, Int}, Vector{WeylGroupElem}}) Returns a triple `(CG, S, P)`, where `CG` is a graph that contains a vertex `v` for every vertex `S[v]` in `G`. `S` is a list of indices for the sinks in the original graph `G`. @@ -231,7 +230,7 @@ A vertex `i` is in `P[s]` if there exists an edge from `i` to `s` in `G` with `w in this way `P` is a partition of the vertices of the orignal graph `G`. There is an edge from `s` to `t` in `CG` whenever there is an edge from `i` to `j` in `G` and `i` in `P[s]` and `j` in `P[t]`. -#Examples +# Examples ```jldoctest julia> gamma(n,k,l) = uniform_hypergraph.(subsets(subsets(n, k), l), n) gamma (generic function with 1 method) @@ -245,8 +244,7 @@ julia> Ks = gamma(4,2,5) UniformHypergraph(4, 2, [[1, 2], [1, 3], [1, 4], [2, 4], [3, 4]]) UniformHypergraph(4, 2, [[1, 3], [1, 4], [2, 3], [2, 4], [3, 4]]) -julia> G, EL, VL = partial_shift_graph(QQ, Ks; show_progess=false); - +julia> G, EL, VL = partial_shift_graph(QQ, Ks; show_progress=false); julia> contracted_partial_shift_graph(G, EL) (Directed graph with 1 nodes and 0 edges, [1], [[5, 4, 6, 2, 3, 1]]) From 7f5444a671c309816dbbc901e7a92084b5e143cf Mon Sep 17 00:00:00 2001 From: Antony Della Vecchia Date: Mon, 4 Nov 2024 12:58:14 +0100 Subject: [PATCH 104/128] fixes for parallel and oscar tests --- .../src/PartialShiftGraph.jl | 21 ++++++++++++------- 1 file changed, 13 insertions(+), 8 deletions(-) diff --git a/experimental/AlgebraicShifting/src/PartialShiftGraph.jl b/experimental/AlgebraicShifting/src/PartialShiftGraph.jl index 7a1b3de9c5f4..adc5c042b93d 100644 --- a/experimental/AlgebraicShifting/src/PartialShiftGraph.jl +++ b/experimental/AlgebraicShifting/src/PartialShiftGraph.jl @@ -165,7 +165,9 @@ julia> facets.(VL[[6, 5]]) ``` """ function partial_shift_graph(F::Field, complexes::Vector{T}, W::Union{WeylGroup, Vector{WeylGroupElem}}; - parallel::Bool = false, show_progress::Bool = true) :: Tuple{Graph{Directed}, EdgeLabels, Vector{ComplexOrHypergraph}} where T <: ComplexOrHypergraph; + parallel::Bool = false, + show_progress::Bool = true, + task_size::Int=1) :: Tuple{Graph{Directed}, EdgeLabels, Vector{ComplexOrHypergraph}} where T <: ComplexOrHypergraph; # Deal with trivial case if length(complexes) <= 1 return (graph_from_adjacency_matrix(Directed, zeros(length(complexes),length(complexes))), EdgeLabels()) @@ -186,24 +188,27 @@ function partial_shift_graph(F::Field, complexes::Vector{T}, W::Union{WeylGroup, @req rs_type[1][1] == :A && rs_type[1][2] == n - 1 "Only Weyl groups type A_$(n-1) are currently support and received type $(T[1])." phi = isomorphism(PermGroup, parent(first(W))) - task_size = 1 + # oscar runs tests in parallel, which can make pmap run in parallel even if parallel=false + # next line fixes this issue + map_function = map if parallel # setup parallel parameters channels = Oscar.params_channels(Union{PermGroup, Vector{SimplicialComplex}, Vector{UniformHypergraph}}) # setup parents needed to be sent to each process Oscar.put_params(channels, codomain(phi)) + map_function = pmap end if show_progress edge_labels = reduce((d1, d2) -> mergewith!(vcat, d1, d2), - @showprogress pmap( + @showprogress map_function( + Ks -> multi_edges(F, phi.(W), Ks, complex_labels), + Iterators.partition(enumerate(complexes), task_size))) + elseif + edge_labels = reduce((d1, d2) -> mergewith!(vcat, d1, d2), + map_function( Ks -> multi_edges(F, phi.(W), Ks, complex_labels), Iterators.partition(enumerate(complexes), task_size))) - else - edge_labels = multi_edges(F, - phi.(W), - collect(enumerate(complexes)), - complex_labels) end graph = graph_from_edges(Directed, [[i,j] for (i,j) in keys(edge_labels)]) return (graph, Dict(k => inv(phi).(v) for (k, v) in edge_labels), complexes) From d687d4ee4eee50a460ede5b0eeccd62c5300cab7 Mon Sep 17 00:00:00 2001 From: Antony Della Vecchia Date: Mon, 4 Nov 2024 13:04:57 +0100 Subject: [PATCH 105/128] docs for kwargs --- experimental/AlgebraicShifting/src/PartialShiftGraph.jl | 9 +++++++-- 1 file changed, 7 insertions(+), 2 deletions(-) diff --git a/experimental/AlgebraicShifting/src/PartialShiftGraph.jl b/experimental/AlgebraicShifting/src/PartialShiftGraph.jl index adc5c042b93d..759242ad8f70 100644 --- a/experimental/AlgebraicShifting/src/PartialShiftGraph.jl +++ b/experimental/AlgebraicShifting/src/PartialShiftGraph.jl @@ -112,11 +112,16 @@ If `K` and `L` are the `i`th and `j`th entry of `VL`, resp., # Arguments - `complexes`: A vector of simplicial complexes or uniform hypergraphs (all should have the same number of vertices). -- `parallel :: Bool` (default: `false`) run the process in parrallel using the `Distributed` package; make sure to do `@everywhere using Oscar`. - `W`: The user may provide a list `W` of Weyl group elements to be used to construct the shifts. All elements of `W` should have the same parent. `W` must be a subset the (same instance of the) symmetric group of order equal to the number of vertices of a complex in complexes (they should all be equal). If `W` is not provided, the function will use the symmetric group of the same order as vertices in each complex complexes. +- `parallel`: run the process in parrallel using the `Distributed` package; make sure to do `@everywhere using Oscar`. +- `show_progress`: Set to `true` by default, can be used to suppress progress meter. +- `task_size`: While running in parallel serialization might become a bottleneck, +setting a higher task_size should increase performance if the processes are not running at maximum capacity + + # Examples ```jldoctest @@ -167,7 +172,7 @@ julia> facets.(VL[[6, 5]]) function partial_shift_graph(F::Field, complexes::Vector{T}, W::Union{WeylGroup, Vector{WeylGroupElem}}; parallel::Bool = false, show_progress::Bool = true, - task_size::Int=1) :: Tuple{Graph{Directed}, EdgeLabels, Vector{ComplexOrHypergraph}} where T <: ComplexOrHypergraph; + task_size::Int=100) :: Tuple{Graph{Directed}, EdgeLabels, Vector{ComplexOrHypergraph}} where T <: ComplexOrHypergraph; # Deal with trivial case if length(complexes) <= 1 return (graph_from_adjacency_matrix(Directed, zeros(length(complexes),length(complexes))), EdgeLabels()) From 2005a79546719e99b9c13b0133756bf770a7221e Mon Sep 17 00:00:00 2001 From: Antony Della Vecchia Date: Mon, 4 Nov 2024 13:52:44 +0100 Subject: [PATCH 106/128] typo --- experimental/AlgebraicShifting/src/PartialShiftGraph.jl | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/experimental/AlgebraicShifting/src/PartialShiftGraph.jl b/experimental/AlgebraicShifting/src/PartialShiftGraph.jl index 759242ad8f70..b9122155e34c 100644 --- a/experimental/AlgebraicShifting/src/PartialShiftGraph.jl +++ b/experimental/AlgebraicShifting/src/PartialShiftGraph.jl @@ -209,7 +209,7 @@ function partial_shift_graph(F::Field, complexes::Vector{T}, W::Union{WeylGroup, @showprogress map_function( Ks -> multi_edges(F, phi.(W), Ks, complex_labels), Iterators.partition(enumerate(complexes), task_size))) - elseif + else edge_labels = reduce((d1, d2) -> mergewith!(vcat, d1, d2), map_function( Ks -> multi_edges(F, phi.(W), Ks, complex_labels), From 87bfbd73456e4b8c632e024795fdb9f9252d6398 Mon Sep 17 00:00:00 2001 From: Michael Joswig Date: Tue, 26 Nov 2024 12:42:46 +0100 Subject: [PATCH 107/128] shifting docs: ref to arXiv:2410.24044 added --- docs/oscar_references.bib | 8 ++++++++ experimental/AlgebraicShifting/README.md | 6 ++---- experimental/AlgebraicShifting/docs/src/introduction.md | 2 +- 3 files changed, 11 insertions(+), 5 deletions(-) diff --git a/docs/oscar_references.bib b/docs/oscar_references.bib index c486f333ccec..4510a4231c1f 100644 --- a/docs/oscar_references.bib +++ b/docs/oscar_references.bib @@ -625,6 +625,14 @@ @Article{Cor21 doi = {10.1007/s00029-021-00679-6} } +@Article{D-VJL24, + author = {Della Vecchia, Antony and Joswig, Michael and Lenzen, Fabian}, + title = {Partial Algebraic Shifting}, + year = {2024}, + eprint = {2410.24044}, + archiveprefix = {arXiv} +} + @InCollection{DE02, author = {Decker, Wolfram and Eisenbud, David}, title = {Sheaf algorithms using the exterior algebra}, diff --git a/experimental/AlgebraicShifting/README.md b/experimental/AlgebraicShifting/README.md index c4d4b15e8874..1f915326b3f6 100644 --- a/experimental/AlgebraicShifting/README.md +++ b/experimental/AlgebraicShifting/README.md @@ -1,12 +1,10 @@ -# An example template for the experimental section +# Algebraic Shifting ## Aims -This package grew out of a project of Antony della Vecchia, Michael Joswig and Fabian Lenzen on "Partial Algebraic Shifting". +This package grew out of an ongoing project of Antony Della Vecchia, Michael Joswig and Fabian Lenzen on [Partial Algebraic Shifting](https://arxiv.org/abs/2410.24044). Part of this project is the development of new methods for algebraic shifting; these are implemented here. ## Status Full and partial shifting in the exterior algebra fully functional. - - diff --git a/experimental/AlgebraicShifting/docs/src/introduction.md b/experimental/AlgebraicShifting/docs/src/introduction.md index 517644268648..8485fcadc81f 100644 --- a/experimental/AlgebraicShifting/docs/src/introduction.md +++ b/experimental/AlgebraicShifting/docs/src/introduction.md @@ -10,7 +10,7 @@ Algebraic shifting is a widely applicable method for converting a uniform hyperg Often this is applied to simplicial complexes, where each layer of $(k-1)$-faces forms a $k$-uniform hypergraph. Here we focus on full and partial algebraic shifting in the exterior algebra. -For some background on the subject we refer to [Kal02](@cite). +For general background on the subject we refer to [Kal02](@cite); for details concerning the implementation see [D-VJL24](@cite). ## Status From a0feef61de9c5646cc243f3be6dea937f5449c8d Mon Sep 17 00:00:00 2001 From: antonydellavecchia Date: Tue, 26 Nov 2024 15:31:49 +0100 Subject: [PATCH 108/128] bibtool on references --- docs/oscar_references.bib | 2 -- 1 file changed, 2 deletions(-) diff --git a/docs/oscar_references.bib b/docs/oscar_references.bib index 617fa211d2b9..3ec4547a0b9b 100644 --- a/docs/oscar_references.bib +++ b/docs/oscar_references.bib @@ -657,8 +657,6 @@ @Article{Cor21 doi = {10.1007/s00029-021-00679-6} } - - @Book{Cut04, author = {Cutkosky, Steven Dale}, title = {Resolution of singularities}, From 4d8144522e321ab3191bc461c2e5bde872529660 Mon Sep 17 00:00:00 2001 From: antonydellavecchia Date: Wed, 27 Nov 2024 15:20:48 +0100 Subject: [PATCH 109/128] Apply suggestions from code review MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Co-authored-by: Lars Göttgens --- experimental/LieAlgebras/src/LieAlgebras.jl | 1 - 1 file changed, 1 deletion(-) diff --git a/experimental/LieAlgebras/src/LieAlgebras.jl b/experimental/LieAlgebras/src/LieAlgebras.jl index c102519fbca6..e866dfbd8e64 100644 --- a/experimental/LieAlgebras/src/LieAlgebras.jl +++ b/experimental/LieAlgebras/src/LieAlgebras.jl @@ -74,7 +74,6 @@ import ..Oscar: ngens, order, parent_type, - permutation_matrix, permutation_group, rank, root, From 3dee71be1b532c67c9e95bcc179cb50014912a3c Mon Sep 17 00:00:00 2001 From: antonydellavecchia Date: Wed, 27 Nov 2024 17:13:56 +0100 Subject: [PATCH 110/128] fixes for doctests --- experimental/AlgebraicShifting/src/PartialShift.jl | 9 +++++++-- 1 file changed, 7 insertions(+), 2 deletions(-) diff --git a/experimental/AlgebraicShifting/src/PartialShift.jl b/experimental/AlgebraicShifting/src/PartialShift.jl index 5c0916472305..71dbcfdaa55d 100644 --- a/experimental/AlgebraicShifting/src/PartialShift.jl +++ b/experimental/AlgebraicShifting/src/PartialShift.jl @@ -68,7 +68,9 @@ We use the name Rothe matrix because of its resemblance with a Rothe diagram. (a # Examples ```jldoctest julia> W = weyl_group(:A, 4) -Weyl group for root system defined by Cartan matrix [2 -1 0 0; -1 2 -1 0; 0 -1 2 -1; 0 0 -1 2] +Weyl group + of root system of rank 4 + of type A4 julia> s = gens(W) 4-element Vector{WeylGroupElem}: @@ -139,7 +141,10 @@ julia> compound_matrix(perm([1, 3, 2]), 2) [0 0 -1] julia> W = weyl_group(:A, 2) -Weyl group for root system defined by Cartan matrix [2 -1; -1 2] +Weyl group + of root system of rank 2 + of type A2 + julia> compound_matrix(longest_element(W), 2) [ 0 0 -1] From 052b3053dbc1fd7d17c59a68327b0cdc8a7c591b Mon Sep 17 00:00:00 2001 From: antonydellavecchia Date: Wed, 27 Nov 2024 20:53:51 +0100 Subject: [PATCH 111/128] fix doctest --- experimental/AlgebraicShifting/src/PartialShift.jl | 4 +++- 1 file changed, 3 insertions(+), 1 deletion(-) diff --git a/experimental/AlgebraicShifting/src/PartialShift.jl b/experimental/AlgebraicShifting/src/PartialShift.jl index 71dbcfdaa55d..e2a2b7446c7b 100644 --- a/experimental/AlgebraicShifting/src/PartialShift.jl +++ b/experimental/AlgebraicShifting/src/PartialShift.jl @@ -265,7 +265,9 @@ julia> betti_numbers(L) == betti_numbers(K) true julia> W = weyl_group(:A, n_vertices(K) - 1) -Weyl group for root system defined by Cartan matrix [2 -1 0 0 0; -1 2 -1 0 0; 0 -1 2 -1 0; 0 0 -1 2 -1; 0 0 0 -1 2] +Weyl group + of root system of rank 5 + of type A5 julia> s = gens(W) 5-element Vector{WeylGroupElem}: From 95b2f7ccc95da06dee414d23e5a3fe0cb21b8b17 Mon Sep 17 00:00:00 2001 From: antonydellavecchia Date: Fri, 29 Nov 2024 10:42:10 +0100 Subject: [PATCH 112/128] untabify` --- experimental/AlgebraicShifting/src/AlgebraicShifting.jl | 1 - experimental/AlgebraicShifting/src/PartialShift.jl | 8 ++++---- 2 files changed, 4 insertions(+), 5 deletions(-) diff --git a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl index 4dc743c923a4..119876212da0 100644 --- a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl +++ b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl @@ -28,7 +28,6 @@ function independent_columns(A::MatElem) return col_indices end - """ symmetric_shift(F::Field, K::SimplicialComplex) diff --git a/experimental/AlgebraicShifting/src/PartialShift.jl b/experimental/AlgebraicShifting/src/PartialShift.jl index e2a2b7446c7b..525f845d6287 100644 --- a/experimental/AlgebraicShifting/src/PartialShift.jl +++ b/experimental/AlgebraicShifting/src/PartialShift.jl @@ -160,11 +160,11 @@ julia> compound_matrix(M, K) ``` """ function compound_matrix(m::MatElem, K::UniformHypergraph) - @req size(m,1) == size(m,2) "Only valid for square matrices" - n = size(m, 1) - k = face_size(K) + @req size(m,1) == size(m,2) "Only valid for square matrices" + n = size(m, 1) + k = face_size(K) nCk = sort(subsets(n, k)) - return matrix(base_ring(m), [det(m[row, col]) for row in faces(K), col in nCk]) + return matrix(base_ring(m), [det(m[row, col]) for row in faces(K), col in nCk]) end compound_matrix(m::MatElem, k::Int) = compound_matrix(m, uniform_hypergraph(sort(subsets(size(m, 1), k)))) From 5211ab0caa77a6e05fabe2f4c5c4d3b9a707c3a4 Mon Sep 17 00:00:00 2001 From: antonydellavecchia Date: Fri, 29 Nov 2024 12:06:43 +0100 Subject: [PATCH 113/128] moved symmetric shift --- .../src/AlgebraicShifting.jl | 89 ----------------- .../AlgebraicShifting/src/PartialShift.jl | 95 +++++++++++++++++++ 2 files changed, 95 insertions(+), 89 deletions(-) diff --git a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl index 119876212da0..9b652bd32358 100644 --- a/experimental/AlgebraicShifting/src/AlgebraicShifting.jl +++ b/experimental/AlgebraicShifting/src/AlgebraicShifting.jl @@ -27,92 +27,3 @@ function independent_columns(A::MatElem) end return col_indices end - -""" - symmetric_shift(F::Field, K::SimplicialComplex) - -Returns the symmetric shift of `K` - -see survey on algebraic shifting Gil Kalai (properly cite at some point) -""" -function symmetric_shift(F::Field, K::SimplicialComplex; - change_of_basis::T = nothing) where T <: Union{Nothing, MatElem} - - n = n_vertices(K) - is_generic = false - if isnothing(change_of_basis) - is_generic = true - # generic change of basis - Fy, y = polynomial_ring(F, :y => (1:n, 1:n)) - change_of_basis = matrix(Fy, hcat(y)) - matrix_base = Fy - else - matrix_base = base_ring(change_of_basis) - if matrix_base isa MPolyRing - is_generic = true - end - end - - Rx, x = polynomial_ring(matrix_base, n) - # the generators of the stanley reisner ideal are combinations of [x_1, ..., x_n] - R_K, _ = stanley_reisner_ring(Rx, K) - - # the computation is a over the field of fractions Fyx - # we use a different ring to generate monomial_basis, coefficients need to be a field, - # but we want to avoid using fraction field of Ry during row reduction - mb_ring, z = graded_polynomial_ring(F, n) - - - input_faces = apply_on_faces(K) do (dim_face, faces) - r = dim_face + 1 - - mb = reverse(monomial_basis(mb_ring, r)) - A = Vector{elem_type(matrix_base)}[] - mb_exponents = first.(collect.(exponents.(mb))) # gets monomial exponents - - for b in mb - # need to compare with some alternatives - transformed_monomial = evaluate(b, change_of_basis * gens(R_K)) - - # we need to iterate through exponents here since the functions terms, coefficients or exponents - # do not return 0 terms and we need to make sure the generic col aligns with the others - # this is needed for the case when the field has finite characteristic - # we use the lift because currently there is no function for get the coeff of - # a MPolyQuoRingElem, which means we also need to check if it's zero before adding the coefficient - col = [ - !is_zero(R_K(monomial(Rx, e))) ? coeff(lift(transformed_monomial), e) : matrix_base(0) - for e in mb_exponents] - - push!(A, col) - end - - C = matrix(matrix_base, reduce(hcat, A)) - - if is_generic - Oscar.ModStdQt.ref_ff_rc!(C) - else - rref!(C) - end - - smallest_basis_el = z[r]^r - smallest_index = findfirst(a -> a == smallest_basis_el, mb) - col_indices = filter(x -> x >= smallest_index, independent_columns(C)) - monomial_exponents = first.(exponents.(mb[col_indices])) - - shifted_sets = Vector{Int}[] - for me in monomial_exponents - shifted_set = Int[] - index_count = 1 - for (i, e) in enumerate(me) - for j in 1:e - push!(shifted_set, i - (r - index_count)) - index_count += 1 - end - end - push!(shifted_sets, shifted_set) - end - return shifted_sets - end - - return simplicial_complex(input_faces) -end diff --git a/experimental/AlgebraicShifting/src/PartialShift.jl b/experimental/AlgebraicShifting/src/PartialShift.jl index 525f845d6287..cf8907653c93 100644 --- a/experimental/AlgebraicShifting/src/PartialShift.jl +++ b/experimental/AlgebraicShifting/src/PartialShift.jl @@ -304,3 +304,98 @@ function exterior_shift(F::Field, K::ComplexOrHypergraph) end exterior_shift(K::ComplexOrHypergraph) = exterior_shift(QQ, K) + + +############################################################################### +# Symmetric shift +############################################################################### + +""" + symmetric_shift(F::Field, K::SimplicialComplex) + +Returns the symmetric shift of `K` + +TODO: Clean this up so that it is similar to exterior shift and add tests +""" + +function symmetric_shift(F::Field, K::SimplicialComplex; + change_of_basis::T = nothing) where T <: Union{Nothing, MatElem} + + n = n_vertices(K) + is_generic = false + if isnothing(change_of_basis) + is_generic = true + # generic change of basis + Fy, y = polynomial_ring(F, :y => (1:n, 1:n)) + change_of_basis = matrix(Fy, hcat(y)) + matrix_base = Fy + else + matrix_base = base_ring(change_of_basis) + if matrix_base isa MPolyRing + is_generic = true + end + end + + Rx, x = polynomial_ring(matrix_base, n) + # the generators of the stanley reisner ideal are combinations of [x_1, ..., x_n] + R_K, _ = stanley_reisner_ring(Rx, K) + + # the computation is a over the field of fractions Fyx + # we use a different ring to generate monomial_basis, coefficients need to be a field, + # but we want to avoid using fraction field of Ry during row reduction + mb_ring, z = graded_polynomial_ring(F, n) + + + input_faces = apply_on_faces(K) do (dim_face, faces) + r = dim_face + 1 + + mb = reverse(monomial_basis(mb_ring, r)) + A = Vector{elem_type(matrix_base)}[] + mb_exponents = first.(collect.(exponents.(mb))) # gets monomial exponents + + for b in mb + # need to compare with some alternatives + transformed_monomial = evaluate(b, change_of_basis * gens(R_K)) + + # we need to iterate through exponents here since the functions terms, coefficients or exponents + # do not return 0 terms and we need to make sure the generic col aligns with the others + # this is needed for the case when the field has finite characteristic + # we use the lift because currently there is no function for get the coeff of + # a MPolyQuoRingElem, which means we also need to check if it's zero before adding the coefficient + col = [ + !is_zero(R_K(monomial(Rx, e))) ? coeff(lift(transformed_monomial), e) : matrix_base(0) + for e in mb_exponents] + + push!(A, col) + end + + C = matrix(matrix_base, reduce(hcat, A)) + + if is_generic + Oscar.ModStdQt.ref_ff_rc!(C) + else + rref!(C) + end + + smallest_basis_el = z[r]^r + smallest_index = findfirst(a -> a == smallest_basis_el, mb) + col_indices = filter(x -> x >= smallest_index, independent_columns(C)) + monomial_exponents = first.(exponents.(mb[col_indices])) + + shifted_sets = Vector{Int}[] + for me in monomial_exponents + shifted_set = Int[] + index_count = 1 + for (i, e) in enumerate(me) + for j in 1:e + push!(shifted_set, i - (r - index_count)) + index_count += 1 + end + end + push!(shifted_sets, shifted_set) + end + return shifted_sets + end + + return simplicial_complex(input_faces) +end From ca0c3d2d7084fbcc9dc25052934cf1fd9fe50128 Mon Sep 17 00:00:00 2001 From: antonydellavecchia Date: Fri, 29 Nov 2024 12:08:42 +0100 Subject: [PATCH 114/128] avoid caching polynomial rings --- experimental/AlgebraicShifting/src/PartialShift.jl | 10 +++++----- 1 file changed, 5 insertions(+), 5 deletions(-) diff --git a/experimental/AlgebraicShifting/src/PartialShift.jl b/experimental/AlgebraicShifting/src/PartialShift.jl index cf8907653c93..502d2d0baa1d 100644 --- a/experimental/AlgebraicShifting/src/PartialShift.jl +++ b/experimental/AlgebraicShifting/src/PartialShift.jl @@ -50,7 +50,7 @@ julia> generic_unipotent_matrix(GF(2), 2) ``` """ function generic_unipotent_matrix(F::Field, n::Int) - Fx, x = polynomial_ring(F, :x => (1:n, 1:n)) + Fx, x = polynomial_ring(F, :x => (1:n, 1:n); cached=false) return generic_unipotent_matrix(Fx) end @@ -103,7 +103,7 @@ end function rothe_matrix(F::Field, p::PermGroupElem) n = degree(parent(p)) - Fx, x = polynomial_ring(F, :x => (1:n, 1:n)) + Fx, x = polynomial_ring(F, :x => (1:n, 1:n); cached=false) u = identity_matrix(Fx, n) for (i, j) in inversions(p) u[i, j] = x[i, j] @@ -326,7 +326,7 @@ function symmetric_shift(F::Field, K::SimplicialComplex; if isnothing(change_of_basis) is_generic = true # generic change of basis - Fy, y = polynomial_ring(F, :y => (1:n, 1:n)) + Fy, y = polynomial_ring(F, :y => (1:n, 1:n); cached=false) change_of_basis = matrix(Fy, hcat(y)) matrix_base = Fy else @@ -336,14 +336,14 @@ function symmetric_shift(F::Field, K::SimplicialComplex; end end - Rx, x = polynomial_ring(matrix_base, n) + Rx, x = polynomial_ring(matrix_base, n) ; cached=false # the generators of the stanley reisner ideal are combinations of [x_1, ..., x_n] R_K, _ = stanley_reisner_ring(Rx, K) # the computation is a over the field of fractions Fyx # we use a different ring to generate monomial_basis, coefficients need to be a field, # but we want to avoid using fraction field of Ry during row reduction - mb_ring, z = graded_polynomial_ring(F, n) + mb_ring, z = graded_polynomial_ring(F, n; cached=false) input_faces = apply_on_faces(K) do (dim_face, faces) From 145ca6808b03a2612a508449e12940d5d5b98fff Mon Sep 17 00:00:00 2001 From: antonydellavecchia Date: Fri, 29 Nov 2024 13:16:41 +0100 Subject: [PATCH 115/128] option to pass polynomial ring --- .../AlgebraicShifting/src/PartialShift.jl | 45 ++++++++++++++++--- 1 file changed, 39 insertions(+), 6 deletions(-) diff --git a/experimental/AlgebraicShifting/src/PartialShift.jl b/experimental/AlgebraicShifting/src/PartialShift.jl index 502d2d0baa1d..4293d44e7caa 100644 --- a/experimental/AlgebraicShifting/src/PartialShift.jl +++ b/experimental/AlgebraicShifting/src/PartialShift.jl @@ -55,15 +55,18 @@ function generic_unipotent_matrix(F::Field, n::Int) end @doc raw""" - rothe_matrix(F::Field, w::WeylGroupElem; K::Union{SimplicialComplex, Nothing} = nothing) - + rothe_matrix(F::Field, w::WeylGroupElem) + rothe_matrix(F::Field, p::PermGroupElem) + rothe_matrix(R::MPolyRing, w::WeylGroupElem) + rothe_matrix(R::MPolyRing, p::PermGroupElem) For a base field `F` and a Weyl group element `w` return the matrix with entries in the multivariate polynomial ring `R` with `n^2` many indeterminants where `n - 1` is the rank of the root system of the Weyl group. As `general_linear_group(n^2, R)` has a Bruhat decomposition, any element lies in a unique double coset $BwB$, where $B$ is the Borel group of upper triangular matrices. The Rothe matrix is a normal form for the matrix on the left of a representative for the double coset corresponding to `w`. +There is also the possibility to pass the underlying polynomial ring `R` instead. This will be explained further once the corresponding preprint is on the arXiv. -We use the name Rothe matrix because of its resemblance with a Rothe diagram. (add ref? Knuth?) +We use the name Rothe matrix because of its resemblance with a Rothe diagram. # Examples ```jldoctest @@ -93,6 +96,23 @@ julia> rothe_matrix(QQ, perm([2, 3, 1])) [x[1, 3] 1 0] [x[2, 3] 0 1] [ 1 0 0] + +julia> Fx, x = polynomial_ring(GF(2), :x => (1:5, 1:5)) +(Multivariate polynomial ring in 25 variables over F, FqMPolyRingElem[x[1, 1] x[1, 2] … x[1, 4] x[1, 5]; x[2, 1] x[2, 2] … x[2, 4] x[2, 5]; … ; x[4, 1] x[4, 2] … x[4, 4] x[4, 5]; x[5, 1] x[5, 2] … x[5, 4] x[5, 5]]) + +julia> rothe_matrix(Fx, w) +[1 0 0 0 0] +[0 x[2, 3] x[2, 4] x[2, 5] 1] +[0 1 0 0 0] +[0 0 1 0 0] +[0 0 0 1 0] + +julia> rothe_matrix(Fx, perm([1, 3, 2, 5, 4])) +[1 0 0 0 0] +[0 x[2, 3] 1 0 0] +[0 1 0 0 0] +[0 0 0 x[4, 5] 1] +[0 0 0 1 0] ``` """ function rothe_matrix(F::Field, w::WeylGroupElem) @@ -103,12 +123,25 @@ end function rothe_matrix(F::Field, p::PermGroupElem) n = degree(parent(p)) - Fx, x = polynomial_ring(F, :x => (1:n, 1:n); cached=false) - u = identity_matrix(Fx, n) + Fx, _ = polynomial_ring(F, :x => (1:n, 1:n); cached=false) + return rothe_matrix(Fx, p) +end + +function rothe_matrix(R::MPolyRing{T}, w::WeylGroupElem) where T + W = parent(w) + phi = isomorphism(PermGroup, W) + return rothe_matrix(R, phi(w)) +end + +function rothe_matrix(R::MPolyRing{T}, p::PermGroupElem) where T + n = degree(parent(p)) + @req ngens(R) == n^2 "The number of generators of the ring should match the square of the degree of the permutation group" + u = identity_matrix(R, n) + x = reshape(gens(R), n, n) for (i, j) in inversions(p) u[i, j] = x[i, j] end - return u * permutation_matrix(F, p) + return u * permutation_matrix(R, p) end @doc raw""" From 0de8c7231fd8b5564b6c5f884fe04b5136871430 Mon Sep 17 00:00:00 2001 From: antonydellavecchia Date: Fri, 29 Nov 2024 13:20:06 +0100 Subject: [PATCH 116/128] fix compound matrix signature --- experimental/AlgebraicShifting/src/PartialShift.jl | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/experimental/AlgebraicShifting/src/PartialShift.jl b/experimental/AlgebraicShifting/src/PartialShift.jl index 4293d44e7caa..14110c948d9a 100644 --- a/experimental/AlgebraicShifting/src/PartialShift.jl +++ b/experimental/AlgebraicShifting/src/PartialShift.jl @@ -148,7 +148,7 @@ end compound_matrix(m::MatElem, k::Int) compound_matrix(p::PermGroupElem, k::Int) compound_matrix(w::WeylGroupElem, k::Int) - compound_matrix(m::MatElem, K::Vector{Vector{Int}}) + compound_matrix(m::MatElem, K::UniformHypergraph) Given a matrix `m`, return the matrix where each entry is a `k`$\times$`k`-minor of `m`. The entries of the compound matrix are ordered with respect to the lexicographic order on sets. From 63daa9fd3cf33e2bd0b5aa64e3c62c326b06d7b5 Mon Sep 17 00:00:00 2001 From: antonydellavecchia Date: Fri, 29 Nov 2024 13:23:26 +0100 Subject: [PATCH 117/128] cleanup white space --- .../AlgebraicShifting/src/PartialShift.jl | 21 +++++++++--------- .../src/PartialShiftGraph.jl | 22 +++++++++---------- .../src/UniformHypergraph.jl | 2 +- 3 files changed, 22 insertions(+), 23 deletions(-) diff --git a/experimental/AlgebraicShifting/src/PartialShift.jl b/experimental/AlgebraicShifting/src/PartialShift.jl index 14110c948d9a..d67577609988 100644 --- a/experimental/AlgebraicShifting/src/PartialShift.jl +++ b/experimental/AlgebraicShifting/src/PartialShift.jl @@ -16,7 +16,7 @@ function generic_unipotent_matrix(R::MPolyRing) @req is_square(n_vars) "indeterminants should come from a square matrix" n = Int(sqrt(n_vars)) x = matrix(R, reshape(x, n, n)) - u = identity_matrix(R, n) + u = identity_matrix(R, n) # make unipotent matrix for i in 1:n for j in i + 1:n @@ -178,7 +178,6 @@ Weyl group of root system of rank 2 of type A2 - julia> compound_matrix(longest_element(W), 2) [ 0 0 -1] [ 0 -1 0] @@ -226,11 +225,11 @@ end _set_to_zero(K::UniformHypergraph, indices::Tuple{Int, Int}) = _set_to_zero(simplicial_complex(K), indices) ############################################################################### -# Exterior shift +# Exterior shift ############################################################################### function exterior_shift(K::UniformHypergraph, g::MatElem) # the exterior shifting works in a different algebra that lends - # itself to an easier implementation + # itself to an easier implementation @req size(g, 1) == size(g, 2) "Change of basis matrix must be square." @req size(g, 1) == n_vertices(K) "Matrix size does not match K." matrix_base = base_ring(g) @@ -254,7 +253,7 @@ function exterior_shift(K::SimplicialComplex, g::MatElem) [[i] for i in 1:n_vertices(K)] # Make sure result is a complex on n vertices ]) end - + @doc raw""" exterior_shift(F::Field, K::SimplicialComplex, w::WeylGroupElem) exterior_shift(F::Field, K::UniformHypergraph, w::WeylGroupElem) @@ -320,7 +319,7 @@ Abstract simplicial complex of dimension 2 on 6 vertices function exterior_shift(F::Field, K::ComplexOrHypergraph, p::PermGroupElem) n = n_vertices(K) @req n == degree(parent(p)) "number of vertices - 1 should equal the rank of the root system" - + return exterior_shift(K, rothe_matrix(F, p)) end @@ -340,7 +339,7 @@ exterior_shift(K::ComplexOrHypergraph) = exterior_shift(QQ, K) ############################################################################### -# Symmetric shift +# Symmetric shift ############################################################################### """ @@ -369,13 +368,13 @@ function symmetric_shift(F::Field, K::SimplicialComplex; end end - Rx, x = polynomial_ring(matrix_base, n) ; cached=false + Rx, x = polynomial_ring(matrix_base, n) ; cached=false # the generators of the stanley reisner ideal are combinations of [x_1, ..., x_n] R_K, _ = stanley_reisner_ring(Rx, K) # the computation is a over the field of fractions Fyx # we use a different ring to generate monomial_basis, coefficients need to be a field, - # but we want to avoid using fraction field of Ry during row reduction + # but we want to avoid using fraction field of Ry during row reduction mb_ring, z = graded_polynomial_ring(F, n; cached=false) @@ -401,7 +400,7 @@ function symmetric_shift(F::Field, K::SimplicialComplex; push!(A, col) end - + C = matrix(matrix_base, reduce(hcat, A)) if is_generic @@ -409,7 +408,7 @@ function symmetric_shift(F::Field, K::SimplicialComplex; else rref!(C) end - + smallest_basis_el = z[r]^r smallest_index = findfirst(a -> a == smallest_basis_el, mb) col_indices = filter(x -> x >= smallest_index, independent_columns(C)) diff --git a/experimental/AlgebraicShifting/src/PartialShiftGraph.jl b/experimental/AlgebraicShifting/src/PartialShiftGraph.jl index b9122155e34c..3a1d6fddabf8 100644 --- a/experimental/AlgebraicShifting/src/PartialShiftGraph.jl +++ b/experimental/AlgebraicShifting/src/PartialShiftGraph.jl @@ -21,7 +21,7 @@ Given a field `F` discover the vertices of the partial shift graph starting from using exterior partial shifts corresponding to elements in `W`. Returns a `Vector{SimplicialCompplex}` ordered lexicographically. -#Example +# Examples ```jldoctest julia> K = simplicial_complex([[1, 2], [2, 3], [3, 4]]) Abstract simplicial complex of dimension 1 on 4 vertices @@ -47,7 +47,7 @@ julia> facets.(shifts) """ function partial_shift_graph_vertices(F::Field, K::SimplicialComplex, - W::Union{WeylGroup, Vector{WeylGroupElem}};) + W::Union{WeylGroup, Vector{WeylGroupElem}}) current = K visited = [current] phi = isomorphism(PermGroup, parent(first(W))) @@ -85,7 +85,7 @@ function multi_edges(F::Field, # For nontrivial delta, place (i, delta) → w in a singleton dictionary, and eventually merge all dictionaries # to obtain a dictionary (i, delta) → [w that yield the shift K → delta] reduce( - (d1, d2) -> mergewith!(vcat, d1, d2), + (d1, d2) -> mergewith!(vcat, d1, d2), ( Dict((i, complex_labels[Set(facets(delta))]) => [p]) for (i, K) in complexes @@ -107,7 +107,7 @@ Returns a tuple `(G, EL, VL)`, where `G` is a `Graph{Directed}`, `EL` is a `Dict `VL` is a lexicographically sorted `complexes`, hence is either a `Vector{SimplicialComplex}` or `Vector{Uniformhypergraph}`. `EL` are the edges labels and `VL` are the vertex labels. There is an edge from the vertex labelled `K` to the vertex labelled `L` if `L` is the partial shift of `K` by some `w` in `W`. -If `K` and `L` are the `i`th and `j`th entry of `VL`, resp., +If `K` and `L` are the `i`th and `j`th entry of `VL`, resp., `EL[i,j]` contains all `w` in `W` such that `L` is the partial generic shift of `K` by `w`. # Arguments @@ -184,17 +184,17 @@ function partial_shift_graph(F::Field, complexes::Vector{T}, W::Union{WeylGroup, ns_vertices = Set(n_vertices.(complexes)) @req length(ns_vertices) == 1 "All complexes are required to have the same number of vertices." n = collect(ns_vertices)[1] - + # inverse lookup K → index of K in complexes complex_labels = Dict(Set(facets(K)) => index for (index, K) in enumerate(complexes)) - + W2 = only(unique(parent.(W))) rs_type = root_system_type(root_system(W2)) @req rs_type[1][1] == :A && rs_type[1][2] == n - 1 "Only Weyl groups type A_$(n-1) are currently support and received type $(T[1])." phi = isomorphism(PermGroup, parent(first(W))) # oscar runs tests in parallel, which can make pmap run in parallel even if parallel=false - # next line fixes this issue + # next line fixes this issue map_function = map if parallel # setup parallel parameters @@ -207,12 +207,12 @@ function partial_shift_graph(F::Field, complexes::Vector{T}, W::Union{WeylGroup, if show_progress edge_labels = reduce((d1, d2) -> mergewith!(vcat, d1, d2), @showprogress map_function( - Ks -> multi_edges(F, phi.(W), Ks, complex_labels), + Ks -> multi_edges(F, phi.(W), Ks, complex_labels), Iterators.partition(enumerate(complexes), task_size))) else edge_labels = reduce((d1, d2) -> mergewith!(vcat, d1, d2), map_function( - Ks -> multi_edges(F, phi.(W), Ks, complex_labels), + Ks -> multi_edges(F, phi.(W), Ks, complex_labels), Iterators.partition(enumerate(complexes), task_size))) end graph = graph_from_edges(Directed, [[i,j] for (i,j) in keys(edge_labels)]) @@ -270,7 +270,7 @@ function contracted_partial_shift_graph(G::Graph{Directed}, edge_labels::Dict{Tu sinks = findall(iszero, degree(G)) sinks_indices = Dict(s => i for (i,s) in enumerate(sinks)) - for i in 1:n + for i in 1:n if !haskey(w0_action, i) @req i in sinks "Vertex $i is not a sink, but has no outbound edge with w0 in its edge label." w0_action[i] = i @@ -283,7 +283,7 @@ function contracted_partial_shift_graph(G::Graph{Directed}, edge_labels::Dict{Tu end return ( - graph_from_edges(Directed, [ + graph_from_edges(Directed, [ [sinks_indices[s],sinks_indices[t]] for (s,t) in ( (w0_action[i], (haskey(w0_action, j) ? w0_action[j] : j)) diff --git a/experimental/AlgebraicShifting/src/UniformHypergraph.jl b/experimental/AlgebraicShifting/src/UniformHypergraph.jl index 52f67c541b91..8a79e23db66d 100644 --- a/experimental/AlgebraicShifting/src/UniformHypergraph.jl +++ b/experimental/AlgebraicShifting/src/UniformHypergraph.jl @@ -64,7 +64,7 @@ function simplicial_complex(K::UniformHypergraph) return simplicial_complex([[[i] for i in 1:n_vertices(K)]; faces(K)]) end -n_vertices(K::UniformHypergraph) = K.n_vertices +n_vertices(K::UniformHypergraph) = K.n_vertices faces(K::UniformHypergraph) = K.faces # added for covenience when writting functions for Simplicial complex and Uniform Hypergraph From 5b276a16b95ad04d35ff88ad0d837c384a5ea4dc Mon Sep 17 00:00:00 2001 From: antonydellavecchia Date: Fri, 29 Nov 2024 14:11:50 +0100 Subject: [PATCH 118/128] adds reference for rother diagram --- docs/oscar_references.bib | 12 ++++++++++ experimental/AlgebraicShifting/docs/doc.main | 11 ++++----- .../AlgebraicShifting/src/PartialShift.jl | 2 +- .../src/PartialShiftGraph.jl | 13 +++++------ .../src/UniformHypergraph.jl | 23 ++++++++++++++++--- 5 files changed, 44 insertions(+), 17 deletions(-) diff --git a/docs/oscar_references.bib b/docs/oscar_references.bib index 3ec4547a0b9b..fb50e24ebeb0 100644 --- a/docs/oscar_references.bib +++ b/docs/oscar_references.bib @@ -1801,6 +1801,18 @@ @Book{Knu11 year = {2011} } +@Book{Knu98, + author = {Knuth, Donald Ervin}, + title = {Sorting and searching}, + volume = {3}, + publisher = {Addison-Wesley}, + edition = {2}, + year = {1998}, + maintitle = {The Art of Computer Programming}, + location = {Boston}, + langid = {english} +} + @Book{Kol13, author = {Kollár, János}, title = {Singularities of the minimal model program}, diff --git a/experimental/AlgebraicShifting/docs/doc.main b/experimental/AlgebraicShifting/docs/doc.main index bd183bbd137a..246ffba0cebb 100644 --- a/experimental/AlgebraicShifting/docs/doc.main +++ b/experimental/AlgebraicShifting/docs/doc.main @@ -1,8 +1,7 @@ [ - "Algebraic Shifting" => [ - "introduction.md", - "exterior_shifting.md", - "partial_shift_graph.md" - ] + "Algebraic Shifting" => [ + "introduction.md", + "exterior_shifting.md", + "partial_shift_graph.md" + ] ] - diff --git a/experimental/AlgebraicShifting/src/PartialShift.jl b/experimental/AlgebraicShifting/src/PartialShift.jl index d67577609988..10af06068832 100644 --- a/experimental/AlgebraicShifting/src/PartialShift.jl +++ b/experimental/AlgebraicShifting/src/PartialShift.jl @@ -66,7 +66,7 @@ As `general_linear_group(n^2, R)` has a Bruhat decomposition, any element lies i The Rothe matrix is a normal form for the matrix on the left of a representative for the double coset corresponding to `w`. There is also the possibility to pass the underlying polynomial ring `R` instead. This will be explained further once the corresponding preprint is on the arXiv. -We use the name Rothe matrix because of its resemblance with a Rothe diagram. +We use the name Rothe matrix because of its resemblance with a Rothe diagram, see [Knu98](@cite). # Examples ```jldoctest diff --git a/experimental/AlgebraicShifting/src/PartialShiftGraph.jl b/experimental/AlgebraicShifting/src/PartialShiftGraph.jl index 3a1d6fddabf8..1bae2c1e34ab 100644 --- a/experimental/AlgebraicShifting/src/PartialShiftGraph.jl +++ b/experimental/AlgebraicShifting/src/PartialShiftGraph.jl @@ -58,7 +58,7 @@ function partial_shift_graph_vertices(F::Field, x -> Set(facets(x)), sort([exterior_shift(F, K, phi(w)) for w in W]; lt=isless_lex))[1:end - 1] - while(!isempty(unvisited)) + while !isempty(unvisited) current = pop!(unvisited) push!(visited, current) shifts = unique( @@ -80,19 +80,18 @@ function multi_edges(F::Field, permutations::Vector{PermGroupElem}, complexes::Vector{Tuple{Int,T}}, complex_labels::Dict{Set{Set{Int}}, Int} -) :: Dict{Tuple{Int, Int}, Vector{PermGroupElem}} where T <: ComplexOrHypergraph; +) where T <: ComplexOrHypergraph; # For each complex K with index i, compute the shifted complex delta of K by w for each w in W. # For nontrivial delta, place (i, delta) → w in a singleton dictionary, and eventually merge all dictionaries # to obtain a dictionary (i, delta) → [w that yield the shift K → delta] - reduce( - (d1, d2) -> mergewith!(vcat, d1, d2), - ( + return reduce( + (d1, d2) -> mergewith!(vcat, d1, d2), ( Dict((i, complex_labels[Set(facets(delta))]) => [p]) for (i, K) in complexes for (p, delta) in ((p, exterior_shift(F, K, p)) for p in permutations) - if Set(facets(delta)) != Set(facets(K))); + if !issetequal(Set(facets(delta)), Set(facets(K)))); init=Dict{Tuple{Int, Int}, Vector{PermGroupElem}}() - ) + ) :: Dict{Tuple{Int, Int}, Vector{PermGroupElem}} end @doc raw""" diff --git a/experimental/AlgebraicShifting/src/UniformHypergraph.jl b/experimental/AlgebraicShifting/src/UniformHypergraph.jl index 8a79e23db66d..1d10e776771c 100644 --- a/experimental/AlgebraicShifting/src/UniformHypergraph.jl +++ b/experimental/AlgebraicShifting/src/UniformHypergraph.jl @@ -8,11 +8,15 @@ struct UniformHypergraph n_vertices::Int k::Int faces::Vector{Vector{Int}} + + function UniformHypergraph(n_vertices::Int, k::Int, faces::Vector{Vector{Int}}) + @req all(length(f) == k && 1 <= minimum(f) && maximum(f) <= n_vertices for f in faces) "Parameters don't define a uniform hypergraph." + return new(n_vertices, k, faces) + end end function uniform_hypergraph(faces::Vector{Vector{Int}}, n::Int, k::Int) faces = sort(collect(Set(sort.(collect.(Set.(faces)))))) - @req all(length(f) == k && 1 <= minimum(f) && maximum(f) <= n for f in faces) "Parameters don't define a uniform hypergraph." return UniformHypergraph(n, k, faces) end @@ -34,7 +38,7 @@ Create a uniform hypergraph using `faces`, the size of each face should be `k` a One can also create a `UniformHypergraph` for the `k` faces of a `SimplicialComplex` `K`. #Examples -```jldoctext +```jldoctest julia> U = uniform_hypergraph([[1, 2], [2, 3]], 4) UniformHypergraph(4, 2, [[1, 2], [2, 3]]) @@ -79,7 +83,20 @@ function Base.:(==)(K :: UniformHypergraph, L :: UniformHypergraph) return K.n_vertices == L.n_vertices && K.k == L.k && K.faces == L.faces end -raw""" Alexander dual, seen as bijection ``\binom{[n]}{k} \to \binom{[n]}{n-k}`` """ +@doc raw""" + alexander_dual(K::UniformHypergraph) + +Given a `UniformHypergraph` return the Alexander dual, seen as bijection ``\binom{[n]}{k} \to \binom{[n]}{n-k}`` + +# Examples +```jldoctest +julia> K = uniform_hypergraph([[1, 2], [2, 3], [3, 4]]) +UniformHypergraph(4, 2, [[1, 2], [2, 3], [3, 4]]) + +julia> alexander_dual(K) +UniformHypergraph(4, 2, [[1, 3], [2, 3], [2, 4]]) +``` +""" function alexander_dual(K::UniformHypergraph) return uniform_hypergraph(alexander_dual(simplicial_complex([[[i] for i in 1:K.n_vertices]; K.faces])), K.n_vertices - K.k) end From e2fe83e96c63e065644febb6f57d398fbaeef628 Mon Sep 17 00:00:00 2001 From: antonydellavecchia Date: Fri, 29 Nov 2024 17:21:33 +0100 Subject: [PATCH 119/128] minor adjustments --- src/Combinatorics/Graphs/functions.jl | 2 +- src/Combinatorics/SimplicialComplexes.jl | 3 +-- 2 files changed, 2 insertions(+), 3 deletions(-) diff --git a/src/Combinatorics/Graphs/functions.jl b/src/Combinatorics/Graphs/functions.jl index af7296239dac..352f810dd721 100644 --- a/src/Combinatorics/Graphs/functions.jl +++ b/src/Combinatorics/Graphs/functions.jl @@ -1172,7 +1172,7 @@ end function graph_from_edges(::Type{T}, edges::Vector{Edge}, n_vertices::Int=-1) where {T <: Union{Directed, Undirected}} - n_needed = maximum(reduce(append!,[[src(e),dst(e)] for e in edges]; init=[0]);) + n_needed = maximum(reduce(append!,[[src(e),dst(e)] for e in edges]; init=[0])) @req (n_vertices >= n_needed || n_vertices < 0) "n_vertices must be at least the maximum vertex in the edges" g = Graph{T}(max(n_needed, n_vertices)) diff --git a/src/Combinatorics/SimplicialComplexes.jl b/src/Combinatorics/SimplicialComplexes.jl index 55164f34b70b..602d92846b44 100644 --- a/src/Combinatorics/SimplicialComplexes.jl +++ b/src/Combinatorics/SimplicialComplexes.jl @@ -730,8 +730,7 @@ end @doc raw""" link_subcomplex(K::SimplicialComplex, f::Union{<:AbstractSet{Int},<:AbstractVector{Int}})) -Given simplicial complex `K` and a face of `face` of `K` return the link of `face`. -simplicial complex at the . +Given simplicial complex `K` and a face `f` of `K` return the link of `f`. # Examples ```jldoctest From c20543e51eaad6659d357eeecabd5bdd8ec84dd8 Mon Sep 17 00:00:00 2001 From: antonydellavecchia Date: Fri, 29 Nov 2024 17:38:04 +0100 Subject: [PATCH 120/128] fixes regression in symmetric shifting and adds test --- .../AlgebraicShifting/src/PartialShift.jl | 56 +++++-------------- .../AlgebraicShifting/test/runtests.jl | 7 +++ 2 files changed, 22 insertions(+), 41 deletions(-) diff --git a/experimental/AlgebraicShifting/src/PartialShift.jl b/experimental/AlgebraicShifting/src/PartialShift.jl index 10af06068832..612ae947310a 100644 --- a/experimental/AlgebraicShifting/src/PartialShift.jl +++ b/experimental/AlgebraicShifting/src/PartialShift.jl @@ -347,28 +347,14 @@ exterior_shift(K::ComplexOrHypergraph) = exterior_shift(QQ, K) Returns the symmetric shift of `K` -TODO: Clean this up so that it is similar to exterior shift and add tests +TODO: add more docs and and expose for users """ - -function symmetric_shift(F::Field, K::SimplicialComplex; - change_of_basis::T = nothing) where T <: Union{Nothing, MatElem} - +function symmetric_shift(F::Field, K::SimplicialComplex, p::PermGroupElem) n = n_vertices(K) - is_generic = false - if isnothing(change_of_basis) - is_generic = true - # generic change of basis - Fy, y = polynomial_ring(F, :y => (1:n, 1:n); cached=false) - change_of_basis = matrix(Fy, hcat(y)) - matrix_base = Fy - else - matrix_base = base_ring(change_of_basis) - if matrix_base isa MPolyRing - is_generic = true - end - end - - Rx, x = polynomial_ring(matrix_base, n) ; cached=false + Fy, y = polynomial_ring(F, :y => (1:n, 1:n); cached=false) + change_of_basis = rothe_matrix(Fy, p) * permutation_matrix(ZZ, p) * generic_unipotent_matrix(Fy) + + Rx, x = polynomial_ring(Fy, n) # the generators of the stanley reisner ideal are combinations of [x_1, ..., x_n] R_K, _ = stanley_reisner_ring(Rx, K) @@ -376,13 +362,10 @@ function symmetric_shift(F::Field, K::SimplicialComplex; # we use a different ring to generate monomial_basis, coefficients need to be a field, # but we want to avoid using fraction field of Ry during row reduction mb_ring, z = graded_polynomial_ring(F, n; cached=false) - - - input_faces = apply_on_faces(K) do (dim_face, faces) - r = dim_face + 1 - + input_faces = Vector{Int}[] + for r in 2:dim(K) + 1 mb = reverse(monomial_basis(mb_ring, r)) - A = Vector{elem_type(matrix_base)}[] + A = Vector{elem_type(Fy)}[] mb_exponents = first.(collect.(exponents.(mb))) # gets monomial exponents for b in mb @@ -392,29 +375,21 @@ function symmetric_shift(F::Field, K::SimplicialComplex; # we need to iterate through exponents here since the functions terms, coefficients or exponents # do not return 0 terms and we need to make sure the generic col aligns with the others # this is needed for the case when the field has finite characteristic - # we use the lift because currently there is no function for get the coeff of + # we use the lift because currently there is no function to get the coeff of # a MPolyQuoRingElem, which means we also need to check if it's zero before adding the coefficient col = [ - !is_zero(R_K(monomial(Rx, e))) ? coeff(lift(transformed_monomial), e) : matrix_base(0) + !is_zero(R_K(monomial(Rx, e))) ? coeff(lift(transformed_monomial), e) : Fy(0) for e in mb_exponents] - push!(A, col) end - - C = matrix(matrix_base, reduce(hcat, A)) - - if is_generic - Oscar.ModStdQt.ref_ff_rc!(C) - else - rref!(C) - end - + C = matrix(Fy, reduce(hcat, A)) + Oscar.ModStdQt.ref_ff_rc!(C) smallest_basis_el = z[r]^r smallest_index = findfirst(a -> a == smallest_basis_el, mb) col_indices = filter(x -> x >= smallest_index, independent_columns(C)) monomial_exponents = first.(exponents.(mb[col_indices])) - shifted_sets = Vector{Int}[] + # adjustment to convert monomial to simplex for me in monomial_exponents shifted_set = Int[] index_count = 1 @@ -424,9 +399,8 @@ function symmetric_shift(F::Field, K::SimplicialComplex; index_count += 1 end end - push!(shifted_sets, shifted_set) + push!(input_faces, shifted_set) end - return shifted_sets end return simplicial_complex(input_faces) diff --git a/experimental/AlgebraicShifting/test/runtests.jl b/experimental/AlgebraicShifting/test/runtests.jl index 25e3adca9eb1..ab4532bd86d8 100644 --- a/experimental/AlgebraicShifting/test/runtests.jl +++ b/experimental/AlgebraicShifting/test/runtests.jl @@ -1,6 +1,13 @@ @testset "Algebraic Shifting" begin K = simplicial_complex([[1, 3] , [2, 3]]) + @testset "Symmetric Shifting" begin + K = simplicial_complex([[1, 2], [2, 3]]) + p = cperm([1, 3]) + shift = Oscar.symmetric_shift(GF(2), K, p) + @test facets(shift) == [Set([2, 1]), Set([3, 1])] + end + @testset "Partial Shift Graph" begin n = n_vertices(K) W = weyl_group(:A, n - 1) From aec70d1d933dcca4437725194d937889334c3884 Mon Sep 17 00:00:00 2001 From: antonydellavecchia Date: Fri, 29 Nov 2024 18:10:26 +0100 Subject: [PATCH 121/128] adds catch for partial shift graph --- .../src/PartialShiftGraph.jl | 49 ++++++++++++------- 1 file changed, 31 insertions(+), 18 deletions(-) diff --git a/experimental/AlgebraicShifting/src/PartialShiftGraph.jl b/experimental/AlgebraicShifting/src/PartialShiftGraph.jl index 1bae2c1e34ab..cc5732be929e 100644 --- a/experimental/AlgebraicShifting/src/PartialShiftGraph.jl +++ b/experimental/AlgebraicShifting/src/PartialShiftGraph.jl @@ -168,15 +168,20 @@ julia> facets.(VL[[6, 5]]) [Set([2, 1]), Set([4, 1]), Set([2, 3]), Set([4, 2]), Set([4, 3])] ``` """ -function partial_shift_graph(F::Field, complexes::Vector{T}, W::Union{WeylGroup, Vector{WeylGroupElem}}; +function partial_shift_graph(F::Field, complexes::Vector{T}, + W::Union{WeylGroup, Vector{WeylGroupElem}}; parallel::Bool = false, show_progress::Bool = true, - task_size::Int=100) :: Tuple{Graph{Directed}, EdgeLabels, Vector{ComplexOrHypergraph}} where T <: ComplexOrHypergraph; + task_size::Int=100) where T <: ComplexOrHypergraph # Deal with trivial case - if length(complexes) <= 1 - return (graph_from_adjacency_matrix(Directed, zeros(length(complexes),length(complexes))), EdgeLabels()) + if length(complexes) == 1 + @req is_shifted(complexes[1]) "The list of complexes should be closed under shifting by elements of W" + return ( + graph_from_adjacency_matrix(Directed, zeros(length(complexes),length(complexes))), + EdgeLabels(), + complexes) :: Tuple{Graph{Directed}, EdgeLabels, Vector{T}} end - + # maybe we provide a flag to skip if the complexes are already sorted? complexes = sort(complexes;lt=Oscar.isless_lex) @@ -202,20 +207,28 @@ function partial_shift_graph(F::Field, complexes::Vector{T}, W::Union{WeylGroup, Oscar.put_params(channels, codomain(phi)) map_function = pmap end - - if show_progress - edge_labels = reduce((d1, d2) -> mergewith!(vcat, d1, d2), - @showprogress map_function( - Ks -> multi_edges(F, phi.(W), Ks, complex_labels), - Iterators.partition(enumerate(complexes), task_size))) - else - edge_labels = reduce((d1, d2) -> mergewith!(vcat, d1, d2), - map_function( - Ks -> multi_edges(F, phi.(W), Ks, complex_labels), - Iterators.partition(enumerate(complexes), task_size))) + try + if show_progress + edge_labels = reduce((d1, d2) -> mergewith!(vcat, d1, d2), + @showprogress map_function( + Ks -> multi_edges(F, phi.(W), Ks, complex_labels), + Iterators.partition(enumerate(complexes), task_size))) + else + edge_labels = reduce((d1, d2) -> mergewith!(vcat, d1, d2), + map_function( + Ks -> multi_edges(F, phi.(W), Ks, complex_labels), + Iterators.partition(enumerate(complexes), task_size))) + end + graph = graph_from_edges(Directed, [[i,j] for (i,j) in keys(edge_labels)]) + return (graph, + Dict(k => inv(phi).(v) for (k, v) in edge_labels), + complexes) :: Tuple{Graph{Directed}, EdgeLabels, Vector{T}} + catch e + if e isa KeyError + error("The list of complexes should be closed under shifting by elements of W") + end + rethrow(e) end - graph = graph_from_edges(Directed, [[i,j] for (i,j) in keys(edge_labels)]) - return (graph, Dict(k => inv(phi).(v) for (k, v) in edge_labels), complexes) end function partial_shift_graph(F::Field, complexes::Vector{T}; From b973efd7e0ea94b7fd92b3d1edd470a418fbcba5 Mon Sep 17 00:00:00 2001 From: antonydellavecchia Date: Fri, 29 Nov 2024 18:14:07 +0100 Subject: [PATCH 122/128] added ref to preprint in function docs --- experimental/AlgebraicShifting/src/PartialShiftGraph.jl | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/experimental/AlgebraicShifting/src/PartialShiftGraph.jl b/experimental/AlgebraicShifting/src/PartialShiftGraph.jl index cc5732be929e..cb7bd7222709 100644 --- a/experimental/AlgebraicShifting/src/PartialShiftGraph.jl +++ b/experimental/AlgebraicShifting/src/PartialShiftGraph.jl @@ -119,7 +119,7 @@ If `K` and `L` are the `i`th and `j`th entry of `VL`, resp., - `show_progress`: Set to `true` by default, can be used to suppress progress meter. - `task_size`: While running in parallel serialization might become a bottleneck, setting a higher task_size should increase performance if the processes are not running at maximum capacity - +See [D-VJL24](@cite) for background. # Examples @@ -251,6 +251,7 @@ Returns a triple `(CG, S, P)`, where `CG` is a graph that contains a vertex `v` A vertex `i` is in `P[s]` if there exists an edge from `i` to `s` in `G` with `w0` in its edge label, in this way `P` is a partition of the vertices of the orignal graph `G`. There is an edge from `s` to `t` in `CG` whenever there is an edge from `i` to `j` in `G` and `i` in `P[s]` and `j` in `P[t]`. +See [D-VJL24](@cite) for background. # Examples ```jldoctest From 271b2641177168dc5a5838eadeafbd52e4cbc760 Mon Sep 17 00:00:00 2001 From: antonydellavecchia Date: Fri, 29 Nov 2024 18:27:07 +0100 Subject: [PATCH 123/128] Update experimental/AlgebraicShifting/src/PartialShiftGraph.jl MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Co-authored-by: Lars Göttgens --- experimental/AlgebraicShifting/src/PartialShiftGraph.jl | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/experimental/AlgebraicShifting/src/PartialShiftGraph.jl b/experimental/AlgebraicShifting/src/PartialShiftGraph.jl index cb7bd7222709..6d058a8aba0b 100644 --- a/experimental/AlgebraicShifting/src/PartialShiftGraph.jl +++ b/experimental/AlgebraicShifting/src/PartialShiftGraph.jl @@ -89,7 +89,7 @@ function multi_edges(F::Field, Dict((i, complex_labels[Set(facets(delta))]) => [p]) for (i, K) in complexes for (p, delta) in ((p, exterior_shift(F, K, p)) for p in permutations) - if !issetequal(Set(facets(delta)), Set(facets(K)))); + if !issetequal(facets(delta), facets(K))); init=Dict{Tuple{Int, Int}, Vector{PermGroupElem}}() ) :: Dict{Tuple{Int, Int}, Vector{PermGroupElem}} end From 63a39bc7276b5e3bfe0e3ea19ad953fc75409759 Mon Sep 17 00:00:00 2001 From: antonydellavecchia Date: Fri, 29 Nov 2024 19:17:51 +0100 Subject: [PATCH 124/128] fixes doctest + only uses @showprogress --- experimental/AlgebraicShifting/src/PartialShift.jl | 2 +- src/imports.jl | 2 +- 2 files changed, 2 insertions(+), 2 deletions(-) diff --git a/experimental/AlgebraicShifting/src/PartialShift.jl b/experimental/AlgebraicShifting/src/PartialShift.jl index 612ae947310a..3c186552bb72 100644 --- a/experimental/AlgebraicShifting/src/PartialShift.jl +++ b/experimental/AlgebraicShifting/src/PartialShift.jl @@ -98,7 +98,7 @@ julia> rothe_matrix(QQ, perm([2, 3, 1])) [ 1 0 0] julia> Fx, x = polynomial_ring(GF(2), :x => (1:5, 1:5)) -(Multivariate polynomial ring in 25 variables over F, FqMPolyRingElem[x[1, 1] x[1, 2] … x[1, 4] x[1, 5]; x[2, 1] x[2, 2] … x[2, 4] x[2, 5]; … ; x[4, 1] x[4, 2] … x[4, 4] x[4, 5]; x[5, 1] x[5, 2] … x[5, 4] x[5, 5]]) +(Multivariate polynomial ring in 25 variables over GF(2), FqMPolyRingElem[x[1, 1] x[1, 2] … x[1, 4] x[1, 5]; x[2, 1] x[2, 2] … x[2, 4] x[2, 5]; … ; x[4, 1] x[4, 2] … x[4, 4] x[4, 5]; x[5, 1] x[5, 2] … x[5, 4] x[5, 5]]) julia> rothe_matrix(Fx, w) [1 0 0 0 0] diff --git a/src/imports.jl b/src/imports.jl index ed98de755884..80fc1c3dfe67 100644 --- a/src/imports.jl +++ b/src/imports.jl @@ -1,6 +1,6 @@ # standard packages using Pkg -using ProgressMeter +using ProgressMeter: @showprogress using Random using RandomExtensions using UUIDs From 26920c9fba3c0cfe3fa092dbf82c65b49950bf9f Mon Sep 17 00:00:00 2001 From: antonydellavecchia Date: Sun, 1 Dec 2024 13:18:32 +0100 Subject: [PATCH 125/128] fix regression in test --- experimental/AlgebraicShifting/src/PartialShift.jl | 5 +++++ experimental/AlgebraicShifting/test/runtests.jl | 10 ++++------ 2 files changed, 9 insertions(+), 6 deletions(-) diff --git a/experimental/AlgebraicShifting/src/PartialShift.jl b/experimental/AlgebraicShifting/src/PartialShift.jl index 3c186552bb72..b8853fd82770 100644 --- a/experimental/AlgebraicShifting/src/PartialShift.jl +++ b/experimental/AlgebraicShifting/src/PartialShift.jl @@ -405,3 +405,8 @@ function symmetric_shift(F::Field, K::SimplicialComplex, p::PermGroupElem) return simplicial_complex(input_faces) end + +function symmetric_shift(F::Field, K::SimplicialComplex, w::WeylGroupElem) + iso = isomorphism(PermGroup, parent(w)) + return symmetric_shift(F, K, iso(w)) +end diff --git a/experimental/AlgebraicShifting/test/runtests.jl b/experimental/AlgebraicShifting/test/runtests.jl index ab4532bd86d8..d3df1fc5abed 100644 --- a/experimental/AlgebraicShifting/test/runtests.jl +++ b/experimental/AlgebraicShifting/test/runtests.jl @@ -1,16 +1,14 @@ @testset "Algebraic Shifting" begin K = simplicial_complex([[1, 3] , [2, 3]]) + n = n_vertices(K) + W = weyl_group(:A, n - 1) @testset "Symmetric Shifting" begin - K = simplicial_complex([[1, 2], [2, 3]]) - p = cperm([1, 3]) - shift = Oscar.symmetric_shift(GF(2), K, p) - @test facets(shift) == [Set([2, 1]), Set([3, 1])] + shift = Oscar.symmetric_shift(GF(2), K, longest_element(W)) + @test facets(shift) == [Set([2, 1]), Set([3, 2])] end @testset "Partial Shift Graph" begin - n = n_vertices(K) - W = weyl_group(:A, n - 1) s = gens(W) all_shifts = partial_shift_graph_vertices(QQ, K, W) directed_graph, edge_labels = partial_shift_graph(QQ, all_shifts) From 1cf2f552627de1f3fcc21fe55b22cab1423cbc03 Mon Sep 17 00:00:00 2001 From: Antony Della Vecchia Date: Mon, 2 Dec 2024 10:13:05 +0100 Subject: [PATCH 126/128] adds uniform hypergraphs as input to partial_shift_graph_vertices --- .../AlgebraicShifting/src/PartialShiftGraph.jl | 14 +++++++++++--- experimental/AlgebraicShifting/test/runtests.jl | 3 ++- 2 files changed, 13 insertions(+), 4 deletions(-) diff --git a/experimental/AlgebraicShifting/src/PartialShiftGraph.jl b/experimental/AlgebraicShifting/src/PartialShiftGraph.jl index 6d058a8aba0b..0110ea93f509 100644 --- a/experimental/AlgebraicShifting/src/PartialShiftGraph.jl +++ b/experimental/AlgebraicShifting/src/PartialShiftGraph.jl @@ -15,10 +15,12 @@ end isless_lex(K1::ComplexOrHypergraph, K2::ComplexOrHypergraph) = isless_lex(Set(facets(K1)), Set(facets(K2))) @doc raw""" - partial_shift_graph_vertices(F::Field,::SimplicialComplex, W::Union{WeylGroup, Vector{WeylGroupElem}};) + partial_shift_graph_vertices(F::Field,K::SimplicialComplex, W::Union{WeylGroup, Vector{WeylGroupElem}};) + partial_shift_graph_vertices(F::Field,K::UniformHypergraph, W::Union{WeylGroup, Vector{WeylGroupElem}};) -Given a field `F` discover the vertices of the partial shift graph starting from `K` -using exterior partial shifts corresponding to elements in `W`. + +Given a field `F` find the vertices of the partial shift graph starting from `K` +and discoverable from elements in `W`. Returns a `Vector{SimplicialCompplex}` ordered lexicographically. # Examples @@ -73,6 +75,12 @@ function partial_shift_graph_vertices(F::Field, return sort(collect(visited); lt=isless_lex) end +function partial_shift_graph_vertices(F::Field, + K::UniformHypergraph, + W::Union{WeylGroup, Vector{WeylGroupElem}}) + return partial_shift_graph_vertices(F, simplicial_complex(K), W) +end + """ Compute the multi edges, that is, for each complex `K` compute which other complexes can be reached by applying the partial shifts `deltas` to K, and store the shift matrices that give rise to each edge.""" diff --git a/experimental/AlgebraicShifting/test/runtests.jl b/experimental/AlgebraicShifting/test/runtests.jl index d3df1fc5abed..d474e99526ba 100644 --- a/experimental/AlgebraicShifting/test/runtests.jl +++ b/experimental/AlgebraicShifting/test/runtests.jl @@ -10,7 +10,8 @@ @testset "Partial Shift Graph" begin s = gens(W) - all_shifts = partial_shift_graph_vertices(QQ, K, W) + U = uniform_hypergraph(K) + all_shifts = partial_shift_graph_vertices(QQ, U, W) directed_graph, edge_labels = partial_shift_graph(QQ, all_shifts) @test collect(edges(directed_graph)) == [Edge(t...) for t in [[2, 1], [3, 1], [3, 2]]] @test word.(edge_labels[2, 1]) == word.([s[1], s[1] * s[2], s[1] * s[2] * s[1], s[2] * s[1]]) From cd86c2f4a91033ea09f77e89c1bf4fc32ce46bcd Mon Sep 17 00:00:00 2001 From: Antony Della Vecchia Date: Mon, 2 Dec 2024 10:17:00 +0100 Subject: [PATCH 127/128] fix test --- experimental/AlgebraicShifting/test/runtests.jl | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/experimental/AlgebraicShifting/test/runtests.jl b/experimental/AlgebraicShifting/test/runtests.jl index d474e99526ba..27c778e081f2 100644 --- a/experimental/AlgebraicShifting/test/runtests.jl +++ b/experimental/AlgebraicShifting/test/runtests.jl @@ -10,7 +10,7 @@ @testset "Partial Shift Graph" begin s = gens(W) - U = uniform_hypergraph(K) + U = uniform_hypergraph(K, 2) all_shifts = partial_shift_graph_vertices(QQ, U, W) directed_graph, edge_labels = partial_shift_graph(QQ, all_shifts) @test collect(edges(directed_graph)) == [Edge(t...) for t in [[2, 1], [3, 1], [3, 2]]] From 8892244dc80d2795c91c51449f92e915c58ca6bf Mon Sep 17 00:00:00 2001 From: antonydellavecchia Date: Tue, 3 Dec 2024 22:37:53 +0100 Subject: [PATCH 128/128] Update experimental/AlgebraicShifting/src/PartialShift.jl Co-authored-by: Max Horn --- experimental/AlgebraicShifting/src/PartialShift.jl | 1 + 1 file changed, 1 insertion(+) diff --git a/experimental/AlgebraicShifting/src/PartialShift.jl b/experimental/AlgebraicShifting/src/PartialShift.jl index b8853fd82770..3f912e1c8764 100644 --- a/experimental/AlgebraicShifting/src/PartialShift.jl +++ b/experimental/AlgebraicShifting/src/PartialShift.jl @@ -59,6 +59,7 @@ end rothe_matrix(F::Field, p::PermGroupElem) rothe_matrix(R::MPolyRing, w::WeylGroupElem) rothe_matrix(R::MPolyRing, p::PermGroupElem) + For a base field `F` and a Weyl group element `w` return the matrix with entries in the multivariate polynomial ring `R` with `n^2` many indeterminants where `n - 1` is the rank of the root system of the Weyl group.