Issue/677

docs/doc.main

@@ -93,13 +93,14 @@
          "PolyhedralGeometry/Polyhedra/constructions.md",
          "PolyhedralGeometry/Polyhedra/polymake.md",
          "PolyhedralGeometry/Polyhedra/auxiliary.md",
-         "PolyhedralGeometry/Polyhedra/serialization.md"
+         "PolyhedralGeometry/Polyhedra/serialization.md",
+         "PolyhedralGeometry/Polyhedra/visualization.md",
        ],
         "PolyhedralGeometry/cones.md",
         "PolyhedralGeometry/fans.md",
         "PolyhedralGeometry/graphs.md",
         "PolyhedralGeometry/linear_programs.md",
-        "PolyhedralGeometry/subdivisions_of_points.md"
+        "PolyhedralGeometry/subdivisions_of_points.md",
     ],
 
   "Commutative Algebra" => [

docs/src/PolyhedralGeometry/Polyhedra/auxiliary.md

@@ -26,10 +26,12 @@ isfulldimensional(P::Polyhedron)
 isnormal(P::Polyhedron)
 issmooth(P::Polyhedron)
 lattice_points(P::Polyhedron)
+lineality_dim(P::Polyhedron)
 lineality_space(P::Polyhedron)
 nfacets(P::Polyhedron)
 normalized_volume(P::Polyhedron)
 nvertices(P::Polyhedron)
+polarize(P::Polyhedron)
 print_constraints(A::AnyVecOrMat, b::AbstractVector; trivial::Bool = false)
 print_constraints(P::Polyhedron; trivial::Bool = false)
 rays(P::Polyhedron)

docs/src/PolyhedralGeometry/Polyhedra/visualization.md

@@ -0,0 +1,18 @@
+```@meta
+CurrentModule = Oscar
+```
+
+```@setup oscar
+using Oscar
+```
+
+```@contents
+Pages = ["visualization.md"]
+```
+
+
+# Visualization
+
+```@docs
+visualize(P::Polyhedron)
+```

docs/src/PolyhedralGeometry/cones.md

@@ -59,12 +59,22 @@ load_cone(filename::String)
 ## Auxiliary functions
 ```@docs
 ambient_dim(C::Cone)
+f_vector(C::Cone)
 hilbert_basis(C::Cone)
 codim(C::Cone)
 dim(C::Cone)
+dual_cone(C::Cone)
+intersect(C0::Cone, C1::Cone)
 ispointed(C::Cone)
 isfulldimensional(C::Cone)
+lineality_dim(C::Cone)
 lineality_space(C::Cone)
+nfacets(C::Cone)
 nrays(C::Cone)
 rays(C::Cone)
 ```
+
+### Visualization
+```@docs
+visualize(C::Cone)
+```

docs/src/PolyhedralGeometry/fans.md

@@ -57,3 +57,26 @@ both polymake and Oscar.
 save_polyhedralfan(PF::PolyhedralFan, filename::String)
 load_polyhedralfan(filename::String)
 ```
+
+## Auxiliary functions
+```@docs
+ambient_dim(PF::PolyhedralFan)
+dim(PF::PolyhedralFan)
+f_vector(PF::PolyhedralFan)
+iscomplete(PF::PolyhedralFan)
+ispointed(PF::PolyhedralFan)
+isregular(PF::PolyhedralFan)
+issmooth(PF::PolyhedralFan)
+lineality_dim(PF::PolyhedralFan)
+lineality_space(PF::PolyhedralFan)
+maximal_cones(PF::PolyhedralFan)
+maximal_cones_as_incidence_matrix(PF::PolyhedralFan)
+nmaximal_cones(PF::PolyhedralFan)
+nrays(PF::PolyhedralFan)
+rays(PF::PolyhedralFan)
+```
+
+### Visualization
+```@docs
+visualize(PF::PolyhedralFan)
+```

src/Polytopes/Cone/constructors.jl

@@ -37,7 +37,7 @@ A polyhedral cone in ambient dimension 2
 """
 function Cone(R::Union{VectorIterator{RayVector}, Oscar.MatElem, AbstractMatrix}, L::Union{VectorIterator{RayVector}, Oscar.MatElem, AbstractMatrix, Nothing} = nothing; non_redundant::Bool = false)
     RM = matrix_for_polymake(R)
-    LM = isnothing(L) ? Polymake.Matrix{Polymake.Rational}(undef, 0, size(RM, 2)) : matrix_for_polymake(L)
+    LM = isnothing(L) || isempty(L) ? Polymake.Matrix{Polymake.Rational}(undef, 0, size(RM, 2)) : matrix_for_polymake(L)
 
     if non_redundant
         return Cone(Polymake.polytope.Cone{Polymake.Rational}(RAYS = RM, LINEALITY_SPACE = LM,))
@@ -96,11 +96,14 @@ julia> rays(C)
  [1, 1]
 ```
 """
-function cone_from_inequalities(I::Union{HalfspaceIterator, Oscar.MatElem,AbstractMatrix}; non_redundant::Bool = false)
+function cone_from_inequalities(I::Union{HalfspaceIterator, Oscar.MatElem, AbstractMatrix}, E::Union{Nothing, HalfspaceIterator, Oscar.MatElem, AbstractMatrix} = nothing; non_redundant::Bool = false)
+    IM = -matrix_for_polymake(I)
+    EM = isnothing(E) || isempty(E) ? Polymake.Matrix{Polymake.Rational}(undef, 0, size(IM, 2)) : matrix_for_polymake(E)
+
     if non_redundant
-        return Cone(Polymake.polytope.Cone{Polymake.Rational}(FACETS = -matrix_for_polymake(I)))
+        return Cone(Polymake.polytope.Cone{Polymake.Rational}(FACETS = IM, LINEAR_SPAN = EM))
     else
-        return Cone(Polymake.polytope.Cone{Polymake.Rational}(INEQUALITIES = -matrix_for_polymake(I)))
+        return Cone(Polymake.polytope.Cone{Polymake.Rational}(INEQUALITIES = -matrix_for_polymake(I), EQUATIONS = EM))
     end
 end
 

src/Polytopes/Cone/properties.jl

@@ -48,6 +48,23 @@ faces(C::Cone, face_dim::Int) = faces(Cone, C, face_dim)
 ###############################################################################
 ## Scalar properties
 ###############################################################################
+@doc Markdown.doc"""
+    nfacets(C::Cone)
+
+Return the number of facets of a cone `C`.
+
+# Examples
+The cone over a square at height one has four facets.
+```jldoctest
+julia> C = positive_hull([1 0 0; 1 1 0; 1 1 1; 1 0 1])
+A polyhedral cone in ambient dimension 3
+
+julia> nfacets(C)
+4
+```
+"""
+nfacets(C::Cone) = pm_cone(C).N_FACETS
+
 
 @doc Markdown.doc"""
     nrays(C::Cone)
@@ -115,6 +132,72 @@ julia> codim(C)
 """
 codim(C::Cone) = ambient_dim(C)-dim(C)
 
+
+@doc Markdown.doc"""
+    f_vector(C::Cone)
+
+Compute the vector $(f₁,f₂,...,f_{(dim(C)-1))$` where $f_i$ is the number of
+faces of $C$ of dimension $i$.
+
+# Examples
+Take the cone over a square, then the f-vector of the cone is the same as of the square.
+```jldoctest
+julia> C = positive_hull([1 0 0; 1 1 0; 1 1 1; 1 0 1])
+A polyhedral cone in ambient dimension 3
+
+julia> f_vector(C)
+2-element Vector{Polymake.Integer}:
+ 4
+ 4
+
+julia> square = cube(2)
+A polyhedron in ambient dimension 2
+
+julia> f_vector(square)
+2-element Vector{Int64}:
+ 4
+ 4
+```
+"""
+function f_vector(C::Cone)
+    pmc = pm_cone(C)
+    ldim = pmc.LINEALITY_DIM
+    return vcat(fill(0,ldim),pmc.F_VECTOR)
+end
+
+
+@doc Markdown.doc"""
+    lineality_dim(C::Cone)
+
+Compute the dimension of the lineality space of $C$, i.e. the largest linear
+subspace contained in $C$.
+
+# Examples
+A cone is pointed if and only if the dimension of its lineality space is zero.
+```jldoctest
+julia> C = positive_hull([1 0 0; 1 1 0; 1 1 1; 1 0 1])
+A polyhedral cone in ambient dimension 3
+
+julia> ispointed(C)
+true
+
+julia> lineality_dim(C)
+0
+
+julia> C1 = Cone([1 0],[0 1; 0 -1])
+A polyhedral cone in ambient dimension 2
+
+julia> ispointed(C1)
+false
+
+julia> lineality_dim(C1)
+1
+```
+"""
+lineality_dim(C::Cone) = pm_cone(C).LINEALITY_DIM
+
+
+
 ###############################################################################
 ## Boolean properties
 ###############################################################################
@@ -234,6 +317,26 @@ julia> lineality_space(UH)
 """
 lineality_space(C::Cone) = VectorIterator{RayVector{Polymake.Rational}}(pm_cone(C).LINEALITY_SPACE)
 
+@doc Markdown.doc"""
+    linear_span(C::Cone)
+
+Return the (linear) hyperplanes generating the linear span of `C`.
+
+# Examples
+This 2-dimensional cone in $\mathbb{R}^3$ lives in exactly one hyperplane $H$, with
+$H = \{ (x_1, x_2, x_3) | x_3 = 0 \}$.
+```jldoctest
+julia> c = Cone([1 0 0; 0 1 0]);
+
+julia> linear_span(c)
+1-element HalfspaceIterator{Hyperplane}:
+ The Hyperplane of R^3 described by
+1: x₃ = 0
+
+```
+"""
+linear_span(C::Cone) = HalfspaceIterator{Hyperplane}(C.pm_cone.LINEAR_SPAN)
+
 @doc Markdown.doc"""
     hilbert_basis(C::Cone)
 

src/Polytopes/Cone/standard_constructions.jl

@@ -0,0 +1,56 @@
+###############################################################################
+###############################################################################
+### Standard constructions
+###############################################################################
+###############################################################################
+@doc Markdown.doc"""
+    intersect(C0::Cone, C1::Cone)
+
+Return the intersection $C0 \cap C1$ of `C0` and `C1`.
+
+# Examples
+```jldoctest
+julia> C0 = positive_hull([1 0])
+A polyhedral cone in ambient dimension 2
+
+julia> C1 = positive_hull([0 1])
+A polyhedral cone in ambient dimension 2
+
+julia> C01 = intersect(C0, C1)
+A polyhedral cone in ambient dimension 2
+
+julia> rays(C01)
+0-element VectorIterator{RayVector{Polymake.Rational}}
+
+julia> dim(C01)
+0
+```
+"""
+function intersect(C0::Cone, C1::Cone)
+   return Cone(Polymake.polytope.intersection(pm_cone(C0), pm_cone(C1)))
+end
+
+
+@doc Markdown.doc"""
+    dual_cone(C::Cone)
+
+Return the dual cone of `C` consisting of all those linear functions that
+evaluate positively on all of `C`.
+
+# Examples
+```jldoctest
+julia> C = positive_hull([1 0; -1 2])
+A polyhedral cone in ambient dimension 2
+
+julia> Cv = dual_cone(C)
+A polyhedral cone in ambient dimension 2
+
+julia> rays(Cv)
+2-element VectorIterator{RayVector{Polymake.Rational}}:
+ [1, 1/2]
+ [0, 1]
+```
+"""
+function dual_cone(C::Cone)
+    return Cone(Polymake.polytope.polarize(pm_cone(C)))
+end