Enhance documentation and add further functions inherited from polymake

docs/oscar_references.bib

@@ -1842,7 +1842,7 @@ @Book{JT13
 @Article{JZ00,
   author        = {Joswig, Michael and Ziegler, Günter M.},
   title         = {Neighborly Cubical Polytopes},
-  journal       = {Discrete \& Computational Geometry },
+  journal       = {Discrete \& Computational Geometry},
   volume        = {24},
   pages         = {325--344},
   year          = {2000},

docs/src/PolyhedralGeometry/Polyhedra/auxiliary.md

@@ -6,7 +6,9 @@ DocTestSetup = Oscar.doctestsetup()
 
 # Auxiliary functions
 
-## Geometric data
+## Basic geometric data
+
+These are basic functions which depend on the vertex and facet coordinates.
 
 ```@docs
 facets(as::Type{T}, P::Polyhedron{S}) where {S<:scalar_types,T<:Union{AffineHalfspace{S},AffineHyperplane{S},Pair{R,S} where R,Polyhedron{S}}}
@@ -30,18 +32,39 @@ relative_interior_point(P::Polyhedron{T}) where T<:scalar_types
 
 ## Combinatorial data
 
+These are functions which only depend on the combinatorial type, i.e., the isomorphism type of the face poset.
+
 ```@docs
 n_facets(P::Polyhedron)
 n_vertices(P::Polyhedron)
+is_simple(P::Polyhedron)
+is_simplicial(P::Polyhedron)
+is_neighborly(P::Polyhedron)
+is_cubical(P::Polyhedron)
 f_vector(P::Polyhedron)
-facet_sizes(P::Polyhedron)
 g_vector(P::Polyhedron)
 h_vector(P::Polyhedron)
-is_simple(P::Polyhedron)
+facet_sizes(P::Polyhedron)
 vertex_sizes(P::Polyhedron)
 ```
 
+## Volume and triangulation related functions
+
+While these functions are geometric, too, they play a special role.  In particular, they can be costly.
+
+```@docs
+volume(P::Polyhedron{T}) where T<:scalar_types
+normalized_volume(P::Polyhedron)
+regular_triangulation
+regular_triangulations
+secondary_polytope
+all_triangulations
+```
+
 ## Groups
+
+There are several groups naturally associated to a polytope or polyhedron.
+
 ```@docs
 combinatorial_symmetries(P::Polyhedron)
 linear_symmetries(P::Polyhedron)
@@ -52,6 +75,9 @@ automorphism_group_generators(IM::IncidenceMatrix)
 ```
 
 ## Lattice polytopes
+
+Here a polytope is lattice if each vertex has integral coordinates.
+
 ```@docs
 boundary_lattice_points(P::Polyhedron{QQFieldElem})
 castelnuovo_excess(P::Polyhedron{QQFieldElem})
@@ -71,27 +97,21 @@ lattice_volume(P::Polyhedron{QQFieldElem})
 ## Other
 
 ```@docs
-all_triangulations
 Base.in(v::AbstractVector, P::Polyhedron)
 Base.issubset(P::Polyhedron{T}, Q::Polyhedron{T}) where T<:scalar_types
 demazure_character(lambda::AbstractVector, sigma::PermGroupElem)
 is_archimedean_solid(P::Polyhedron)
 is_johnson_solid(P::Polyhedron)
 is_platonic_solid(P::Polyhedron)
-normalized_volume(P::Polyhedron)
 polarize(P::Polyhedron{T}) where T<:scalar_types
 project_full(P::Polyhedron{T}) where T<:scalar_types
 print_constraints(io::IO, A::AnyVecOrMat, b::AbstractVector; trivial::Bool = false, numbered::Bool = false, cmp = :lte)
 print_constraints(io::IO, P::Polyhedron; trivial::Bool = false, numbered::Bool = false)
-regular_triangulations
-regular_triangulation
-secondary_polytope
 solve_ineq(as::Type{T}, A::ZZMatrix, b::ZZMatrix) where {T}
 solve_mixed(as::Type{T}, A::ZZMatrix, b::ZZMatrix, C::ZZMatrix, d::ZZMatrix) where {T}
 solve_mixed(as::Type{T}, A::ZZMatrix, b::ZZMatrix, C::ZZMatrix) where {T}
 solve_non_negative(as::Type{T}, A::ZZMatrix, b::ZZMatrix) where {T}
 support_function(P::Polyhedron{T}; convention::Symbol = :max) where T<:scalar_types
-volume(P::Polyhedron{T}) where T<:scalar_types
 ```
 
 

src/PolyhedralGeometry/Polyhedron/properties.jl

@@ -1330,7 +1330,7 @@ is_bounded(P::Polyhedron) = pm_object(P).BOUNDED::Bool
 @doc raw"""
     is_simple(P::Polyhedron)
 
-Check whether `P` is simple.
+Check whether `P` is simple, i.e., each vertex figure is a simplex.
 
 # Examples
 ```jldoctest
@@ -1346,10 +1346,46 @@ is_simple(P::Polyhedron) = pm_object(P).SIMPLE::Bool
 @doc raw"""
     is_simplicial(P::Polyhedron)
 
-Check whether `P` is simplicial.
+Check whether `P` is simplicial, i.e., each proper face is a simplex.
 """
 is_simplicial(P::Polyhedron) = pm_object(P).SIMPLICIAL::Bool
 
+@doc raw"""
+    is_neighborly(P::Polyhedron)
+
+Check whether `P` is neighborly, i.e., if the dimension is $d$, each $\lfloor d/2 \rfloor$-subset of the vertices forms a face.
+Neighborly polytopes in even dimension are necessarily simplicial.
+
+# Examples
+
+A 4-polytope is neighborly if and only if the vertex-edge graph is complete.
+
+```jldoctest
+julia> is_neighborly(cyclic_polytope(4,8))
+true
+```
+"""
+is_neighborly(P::Polyhedron) = pm_object(P).NEIGHBORLY::Bool
+
+@doc raw"""
+    is_cubical(P::Polyhedron)
+
+Check whether `P` is cubical, i.e., each proper face is combinatorially equivalent to a cube.
+
+# Examples
+
+For details concerning the following construction see [JZ00](@cite).
+
+```jldoctest
+julia> Q = cube(2,-1,1); Q2 = cube(2,-2,2); P = convex_hull(product(Q,Q2), product(Q2,Q))
+Polyhedron in ambient dimension 4
+
+julia> is_cubical(P)
+true
+```
+"""
+is_cubical(P::Polyhedron) = pm_object(P).CUBICAL::Bool
+
 @doc raw"""
     is_fulldimensional(P::Polyhedron)
 

src/exports.jl

@@ -905,6 +905,7 @@ export is_conjugate_with_data
 export is_connected
 export is_coroot
 export is_coroot_with_index
+export is_cubical
 export is_cyclic, has_is_cyclic, set_is_cyclic
 export is_degenerate
 export is_dense
@@ -983,6 +984,7 @@ export is_negative_coroot
 export is_negative_coroot_with_index
 export is_negative_root
 export is_negative_root_with_index
+export is_neighborly
 export is_nilpotent, has_is_nilpotent, set_is_nilpotent
 export is_noetherian
 export is_non_zero_divisor