`matrix(QQ,foo)` not working for `vertices_and_rays` output

[YueRen]

Apologies for the very crude report (busy with workshop), but the following errors were encountered with @yassineELMAAZOUZ

julia> VR = [0 0 0; 1 0 0; 0 1 0; -1 0 0];

julia> IM = IncidenceMatrix([[1,2,3],[1,3,4]]);

julia> far_vertices = [2,3,4];

julia> L = [0 0 1];

julia> PC = polyhedral_complex(IM, VR, far_vertices, L)
Polyhedral complex in ambient dimension 3

julia> matrix(QQ,vertices_and_rays(PC))
ERROR: ArgumentError: Matrix for Polymake not defined in this context.
Stacktrace:
 [1] matrix_for_polymake(iter::SubObjectIterator{Union{PointVector{QQFieldElem}, RayVector{QQFieldElem}}}; homogenized::Bool)
   @ Oscar ~/.julia/dev/Oscar/src/PolyhedralGeometry/iterators.jl:275
 [2] matrix_for_polymake
   @ ~/.julia/dev/Oscar/src/PolyhedralGeometry/iterators.jl:271 [inlined]
 [3] matrix(R::QQField, iter::SubObjectIterator{Union{PointVector{QQFieldElem}, RayVector{QQFieldElem}}})
   @ Oscar ~/.julia/dev/Oscar/src/PolyhedralGeometry/iterators.jl:292
 [4] top-level scope
   @ REPL[115]:1

[YueRen]

Thanks for fixing the issue title, @lgoettgens!

I've changed the labels, since this is more an issue in polyhedral geometry:

julia> VR = [0 0 0; 1 0 0; 0 1 0; -1 0 0];

julia> IM = IncidenceMatrix([[1,2,3],[1,3,4]]);

julia> far_vertices = [2,3,4];

julia> L = [0 0 1];

julia> PC = polyhedral_complex(IM, VR, far_vertices, L)
Polyhedral complex in ambient dimension 3

julia> matrix(QQ,vertices_and_rays(PC))
ERROR: ArgumentError: Matrix for Polymake not defined in this context.
Stacktrace:
 [1] matrix_for_polymake(iter::SubObjectIterator{Union{PointVector{QQFieldElem}, RayVector{QQFieldElem}}}; homogenized::Bool)
   @ Oscar ~/.julia/dev/Oscar/src/PolyhedralGeometry/iterators.jl:275
 [2] matrix_for_polymake
   @ ~/.julia/dev/Oscar/src/PolyhedralGeometry/iterators.jl:271 [inlined]
 [3] matrix(R::QQField, iter::SubObjectIterator{Union{PointVector{QQFieldElem}, RayVector{QQFieldElem}}})
   @ Oscar ~/.julia/dev/Oscar/src/PolyhedralGeometry/iterators.jl:292
 [4] top-level scope
   @ REPL[115]:1

[benlorenz]

The issue with directly converting this to an Oscar matrix is somewhat related to what you complained about in the other issue, i.e. vectors losing type information. Merging the rays and vertices into one matrix might produce something like [1 0 0; 1 0 0] where the first line was a vertex and the second was a ray.
The other issue I see is that matrix(QQ, ...) only accepts Vector{<:Vector} but not Vector{<:AbstractVector}, so one workaround would be this:

julia> matrix(QQ, Vector.(vertices_and_rays(PC)))
[0   0]
[1   0]
[1   1]
[0   1]

In general I would really recommend not using vertices_and_rays but use vertices and rays separately. But we might need to fix something about the other constructor as well.
We will have another look at these constructors.

This issue is basically the same as #2313

[YueRen]

@benlorenz Got it. When using vertices and rays (or minimal_faces and rays_modulo_lineality), is there a way to find out which ray or vertex the indices in the incidence matrix of the maximal polyhedra refer to?

julia> maximal_polyhedra(IncidenceMatrix,PC)
2×4 IncidenceMatrix
[1, 2, 3]
[1, 3, 4]

[benlorenz]

You can use these instead:

julia> vertex_indices(maximal_polyhedra(PC))
2×3 IncidenceMatrix
[1, 2, 3]
[1, 3]


julia> ray_indices(maximal_polyhedra(PC))
2×1 IncidenceMatrix
[]
[1]

[YueRen]

Oh wow, I didn't know these existed, thanks!

Is there by any chance also a constructor for PolyhedralComplex where you can enter vertices, rays, and their incidences separately? If yes, then I'm more than happy to forget about vertices_and_rays and from now on always work with vertices and rays seprately.

[benlorenz]

There is this one

function polyhedral_complex(f::scalar_type_or_field, 
                            v::AbstractCollection[PointVector],
                            vi::IncidenceMatrix, 
                            r::AbstractCollection[RayVector], 
                            ri::IncidenceMatrix,
                            L::Union{AbstractCollection[RayVector], Nothing} = nothing; 
                            non_redundant::Bool = false)

but it doesn't seem to work correctly with the SubobjectIterators right now, we will check it and add it to the docs.

Using matrices does work though:

julia> ppc = polyhedral_complex(QQ,
                                matrix(QQ,vertices(PC)),
                                vertex_indices(maximal_polyhedra(PC)),
                                matrix(QQ,rays(PC)),
                                ray_indices(maximal_polyhedra(PC)))
Polyhedral complex in ambient dimension 2

[fingolfin]

@benlorenz wrote:

The other issue I see is that matrix(QQ, ...) only accepts Vector{<:Vector} but not Vector{<:AbstractVector},

Agreed, so "someone"(TM) should work on this