deprecate SimplicialComplex for simplicial_complex (#3234)

* deprecate SimplicialComplex for simplicial_complex * adds a test for simplicial complex for graphs * Update src/Combinatorics/SimplicialComplexes.jl Co-authored-by: Max Horn <max@quendi.de> * readd SimplicalComplex to exports * fix doc * fixed internal use of simplicial complexes to align with deprecations * transpose incidence matrix of graph * tranpose incidence matrix for graph * fixes for test * fixes dep warning * fix docs for incidence matrix * fix typo in docs * adds function for convert graph to simplicial complex * adjust use of simplicial complex in Groups test * fix in docstring --------- Co-authored-by: Max Horn <max@quendi.de>
oscar-system · Jan 26, 2024 · 83f513a · 83f513a
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diff --git a/docs/src/Combinatorics/simplicialcomplexes.md b/docs/src/Combinatorics/simplicialcomplexes.md
@@ -18,7 +18,7 @@ General textbooks offering details on the theory include:
 ## Construction
 
 ```@docs
-SimplicialComplex(K::Vector{Vector{Int}})
+simplicial_complex(K::Vector{Vector{Int}})
 ```
 
 ### Subcomplexes

diff --git a/src/AlgebraicGeometry/ToricVarieties/NormalToricVarieties/attributes.jl b/src/AlgebraicGeometry/ToricVarieties/NormalToricVarieties/attributes.jl
@@ -268,7 +268,7 @@ end
 
 @attr Polymake.IncidenceMatrixAllocated{Polymake.NonSymmetric} function _minimal_nonfaces(v::NormalToricVarietyType)
     I = ray_indices(maximal_cones(v))
-    K = SimplicialComplex(I)
+    K = simplicial_complex(I)
     return minimal_nonfaces(IncidenceMatrix, K)
 end
 

diff --git a/src/Combinatorics/Graphs/functions.jl b/src/Combinatorics/Graphs/functions.jl
@@ -588,7 +588,9 @@ julia> incidence_matrix(g)
 []
 ```
 """
-incidence_matrix(g::Graph{T}) where {T <: Union{Directed, Undirected}} = IncidenceMatrix(Polymake.graph.incidence_matrix(pm_object(g)))
+function incidence_matrix(g::Graph{T}) where {T <: Union{Directed, Undirected}}
+  IncidenceMatrix(Polymake.graph.incidence_matrix(pm_object(g)))
+end
 
 @doc raw"""
     signed_incidence_matrix(g::Graph{Directed})

diff --git a/src/Combinatorics/SimplicialComplexes.jl b/src/Combinatorics/SimplicialComplexes.jl
@@ -13,26 +13,33 @@ 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
+
+julia> G = complete_bipartite_graph(2,3)
+Undirected graph with 5 nodes and the following edges:
+(3, 1)(3, 2)(4, 1)(4, 2)(5, 1)(5, 2)
+
+julia> K = simplicial_complex(G)
+Abstract simplicial complex of dimension 1 on 5 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 +54,27 @@ 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)
+  simplicial_complex(K)
+end
+
+function simplicial_complex(G::Graph)
+  IM = incidence_matrix(G)
+  edges_as_rows = IncidenceMatrix(transpose(IM))
+  simplicial_complex(edges_as_rows)
 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 +220,7 @@ 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 +235,7 @@ 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 +265,7 @@ 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
@@ -302,7 +315,7 @@ Return the Stanley-Reisner ring 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> stanley_reisner_ring(K)
 (Quotient of multivariate polynomial ring by ideal(x1*x4), Map: multivariate polynomial ring -> quotient of multivariate polynomial ring)
@@ -413,7 +426,7 @@ 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 +441,7 @@ 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 = simplicial_complex([[1,2,3],[2,3,4]]);
 
 julia> link_subcomplex(K,[2,3])
 Abstract simplicial complex of dimension 0 on 2 vertices
@@ -445,4 +458,3 @@ function Base.show(io::IO, K::SimplicialComplex)
     n = nvertices(K)
     print(io, "Abstract simplicial complex of dimension $(d) on $(n) vertices")
 end
-
diff --git a/src/PolyhedralGeometry/PolyhedralFan/properties.jl b/src/PolyhedralGeometry/PolyhedralFan/properties.jl
@@ -553,7 +553,7 @@ julia> primitive_collections(normal_fan(simplex(3)))
 function primitive_collections(PF::_FanLikeType)
     @req is_simplicial(PF) "PolyhedralFan must be simplicial."
     I = ray_indices(maximal_cones(PF))
-    K = SimplicialComplex(I)
+    K = simplicial_complex(I)
     return minimal_nonfaces(K)
 end
 

diff --git a/src/deprecations.jl b/src/deprecations.jl
@@ -509,6 +509,9 @@ end
 
 @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)
+
 Base.@deprecate_binding is_finitelygenerated is_finitely_generated
 Base.@deprecate_binding has_is_finitelygenerated has_is_finitely_generated
 Base.@deprecate_binding set_is_finitelygenerated set_is_finitely_generated

diff --git a/src/exports.jl b/src/exports.jl
@@ -1321,6 +1321,7 @@ export show_subquo
 export signed_incidence_matrix
 export signed_permutahedron
 export simplex
+export simplicial_complex
 export simplified_fp_group
 export simplify
 export simplify!

diff --git a/test/Combinatorics/SimplicialComplexes.jl b/test/Combinatorics/SimplicialComplexes.jl
@@ -1,58 +1,60 @@
 @testset "SimplicialComplex" begin
-
-    @testset "properties" begin
-
-        sphere = SimplicialComplex([[1, 2, 3], [1, 2, 4], [1, 3, 4], [2, 3, 4]])
-
-        sphere2 = SimplicialComplex(IncidenceMatrix([[1, 2, 3], [1, 2, 4], [1, 3, 4], [2, 3, 4]]))
-
-        @test sphere isa SimplicialComplex
-        @test sphere2 isa SimplicialComplex
-        @test vertexindices(sphere) == [1, 2, 3, 4]
-        @test nvertices(sphere) == 4
-        @test facets(sphere) == Set{Int}.([[1, 3, 2], [1, 4, 2], [1, 3, 4], [3, 4, 2]])
-        @test facets(sphere2) == facets(sphere)
-        @test dim(sphere) == 2
-        @test f_vector(sphere) == [4, 6, 4]
-        @test h_vector(sphere) == [1, 1, 1, 1]
-        @test betti_numbers(sphere) == [0, 0, 1]
-        @test euler_characteristic(sphere) == 1
-        @test minimal_nonfaces(sphere) == [Set{Int}([1, 2, 3, 4])]
-        R, _ = polynomial_ring(ZZ, ["a", "x", "i_7", "n"])
-        @test stanley_reisner_ideal(R, sphere) == ideal([R([1], [[1, 1, 1, 1]])])
-        @test is_isomorphic(fundamental_group(sphere), free_group())
-
-        # from #1440, make sure empty columns at the end are kept
-        sc = SimplicialComplex([[1, 2, 4], [2, 3, 4]])
-        @test size(minimal_nonfaces(IncidenceMatrix, sc)) == (1, 4)
-    end
-
-    @testset "standard examples" begin
-
-        for (SC, fv, bn) in ((torus(), [7, 21, 14], [0, 2, 1]),
-                            (klein_bottle(), [9, 27, 18], [0, 1, 0]),
-                            (real_projective_plane(), [6, 15, 10], [0, 0, 0]),
-                            (complex_projective_plane(), [9, 36, 84, 90, 36], [0, 0, 1, 0, 1]))
-
-            @test SC isa SimplicialComplex
-            @test f_vector(SC) == fv
-            @test betti_numbers(SC) == bn
-
-        end
-
-    end
 
-    @testset "torus homology" begin
-        T = torus()
-        H0 = homology(T, 0)
-        H1 = homology(T, 1)
-        H2 = homology(T, 2)
-        @test is_trivial(H0)
-        @test !is_trivial(H1)
-        @test !is_trivial(H2)
-        @test rank(H0) == 0
-        @test rank(H1) == 2
-        @test rank(H2) == 1
+  @testset "properties" begin
+
+    sphere = simplicial_complex([[1, 2, 3], [1, 2, 4], [1, 3, 4], [2, 3, 4]])
+
+    sphere2 = simplicial_complex(IncidenceMatrix([[1, 2, 3], [1, 2, 4], [1, 3, 4], [2, 3, 4]]))
+
+    @test sphere isa SimplicialComplex
+    @test sphere2 isa SimplicialComplex
+    @test vertexindices(sphere) == [1, 2, 3, 4]
+    @test nvertices(sphere) == 4
+    @test facets(sphere) == Set{Int}.([[1, 3, 2], [1, 4, 2], [1, 3, 4], [3, 4, 2]])
+    @test facets(sphere2) == facets(sphere)
+    @test dim(sphere) == 2
+    @test f_vector(sphere) == [4, 6, 4]
+    @test h_vector(sphere) == [1, 1, 1, 1]
+    @test betti_numbers(sphere) == [0, 0, 1]
+    @test euler_characteristic(sphere) == 1
+    @test minimal_nonfaces(sphere) == [Set{Int}([1, 2, 3, 4])]
+    R, _ = polynomial_ring(ZZ, ["a", "x", "i_7", "n"])
+    @test stanley_reisner_ideal(R, sphere) == ideal([R([1], [[1, 1, 1, 1]])])
+    @test is_isomorphic(fundamental_group(sphere), free_group())
+
+    # from #1440, make sure empty columns at the end are kept
+    sc = simplicial_complex([[1, 2, 4], [2, 3, 4]])
+    @test size(minimal_nonfaces(IncidenceMatrix, sc)) == (1, 4)
+  end
+
+  @testset "standard examples" begin
+    G = simplicial_complex(complete_bipartite_graph(2, 3))
+    for (SC, fv, bn) in ((torus(), [7, 21, 14], [0, 2, 1]),
+                         (klein_bottle(), [9, 27, 18], [0, 1, 0]),
+                         (real_projective_plane(), [6, 15, 10], [0, 0, 0]),
+                         (complex_projective_plane(), [9, 36, 84, 90, 36], [0, 0, 1, 0, 1]),
+                         (G, [5, 6], [0, 2]))
+
+
+      @test SC isa SimplicialComplex
+      @test f_vector(SC) == fv
+      @test betti_numbers(SC) == bn
+
     end
-
+
+  end
+
+  @testset "torus homology" begin
+    T = torus()
+    H0 = homology(T, 0)
+    H1 = homology(T, 1)
+    H2 = homology(T, 2)
+    @test is_trivial(H0)
+    @test !is_trivial(H1)
+    @test !is_trivial(H2)
+    @test rank(H0) == 0
+    @test rank(H1) == 2
+    @test rank(H2) == 1
+  end
+
 end
diff --git a/test/Groups/describe.jl b/test/Groups/describe.jl
@@ -79,7 +79,7 @@ end
 end
 
 @testset "describe() for some real world examples" begin
-   P = SimplicialComplex([[1,2,4,9],[1,2,4,15],[1,2,6,14],[1,2,6,15],[1,2,9,14],[1,3,4,12],[1,3,4,15],[1,3,7,10],[1,3,7,12],[1,3,10,15],[1,4,9,12],[1,5,6,13],[1,5,6,14],[1,5,8,11],[1,5,8,13],[1,5,11,14],[1,6,13,15],[1,7,8,10],[1,7,8,11],[1,7,11,12],[1,8,10,13],[1,9,11,12],[1,9,11,14],[1,10,13,15],[2,3,5,10],[2,3,5,11],[2,3,7,10],[2,3,7,13],[2,3,11,13],[2,4,9,13],[2,4,11,13],[2,4,11,15],[2,5,8,11],[2,5,8,12],[2,5,10,12],[2,6,10,12],[2,6,10,14],[2,6,12,15],[2,7,9,13],[2,7,9,14],[2,7,10,14],[2,8,11,15],[2,8,12,15],[3,4,5,14],[3,4,5,15],[3,4,12,14],[3,5,10,15],[3,5,11,14],[3,7,12,13],[3,11,13,14],[3,12,13,14],[4,5,6,7],[4,5,6,14],[4,5,7,15],[4,6,7,11],[4,6,10,11],[4,6,10,14],[4,7,11,15],[4,8,9,12],[4,8,9,13],[4,8,10,13],[4,8,10,14],[4,8,12,14],[4,10,11,13],[5,6,7,13],[5,7,9,13],[5,7,9,15],[5,8,9,12],[5,8,9,13],[5,9,10,12],[5,9,10,15],[6,7,11,12],[6,7,12,13],[6,10,11,12],[6,12,13,15],[7,8,10,14],[7,8,11,15],[7,8,14,15],[7,9,14,15],[8,12,14,15],[9,10,11,12],[9,10,11,16],[9,10,15,16],[9,11,14,16],[9,14,15,16],[10,11,13,16],[10,13,15,16],[11,13,14,16],[12,13,14,15],[13,14,15,16]])
+   P = simplicial_complex([[1,2,4,9],[1,2,4,15],[1,2,6,14],[1,2,6,15],[1,2,9,14],[1,3,4,12],[1,3,4,15],[1,3,7,10],[1,3,7,12],[1,3,10,15],[1,4,9,12],[1,5,6,13],[1,5,6,14],[1,5,8,11],[1,5,8,13],[1,5,11,14],[1,6,13,15],[1,7,8,10],[1,7,8,11],[1,7,11,12],[1,8,10,13],[1,9,11,12],[1,9,11,14],[1,10,13,15],[2,3,5,10],[2,3,5,11],[2,3,7,10],[2,3,7,13],[2,3,11,13],[2,4,9,13],[2,4,11,13],[2,4,11,15],[2,5,8,11],[2,5,8,12],[2,5,10,12],[2,6,10,12],[2,6,10,14],[2,6,12,15],[2,7,9,13],[2,7,9,14],[2,7,10,14],[2,8,11,15],[2,8,12,15],[3,4,5,14],[3,4,5,15],[3,4,12,14],[3,5,10,15],[3,5,11,14],[3,7,12,13],[3,11,13,14],[3,12,13,14],[4,5,6,7],[4,5,6,14],[4,5,7,15],[4,6,7,11],[4,6,10,11],[4,6,10,14],[4,7,11,15],[4,8,9,12],[4,8,9,13],[4,8,10,13],[4,8,10,14],[4,8,12,14],[4,10,11,13],[5,6,7,13],[5,7,9,13],[5,7,9,15],[5,8,9,12],[5,8,9,13],[5,9,10,12],[5,9,10,15],[6,7,11,12],[6,7,12,13],[6,10,11,12],[6,12,13,15],[7,8,10,14],[7,8,11,15],[7,8,14,15],[7,9,14,15],[8,12,14,15],[9,10,11,12],[9,10,11,16],[9,10,15,16],[9,11,14,16],[9,14,15,16],[10,11,13,16],[10,13,15,16],[11,13,14,16],[12,13,14,15],[13,14,15,16]])
    pi_1 = fundamental_group(P)
    @test describe(pi_1) == "SL(2,5)"