Wrong f-vector for unbounded polyhedra

[kliem]

#28625 fixed the f_vector in the case of unpointed polyhedra/polyhedra with lines.

We add doctests showing that #28625 fixed a bug in f_vector.

Before:

sage: Polyhedron(ieqs=[[1,-1,0],[1,1,0]]).f_vector()
(1, 2, 1)

But this polyhedron does not have zero-dimensional faces, and #28625 has correctly changed that:

sage: Polyhedron(ieqs=[[1,-1,0],[1,1,0]]).f_vector()
(1, 0, 2, 1)

Also we add documentation, specifically warning users that the methods

• vertices,
• vertices_list,
• vertices_generator
• vertices_matrix,
• n_vertices,
  treat vertices of the Vrepresentation and not vertices of the polyhedron in the unpointed case.

Depends on #28625

CC: @jplab @mo271

Component: geometry

Author: Jonathan Kliem

Branch/Commit: 1c5378c

Reviewer: Jean-Philippe Labbé

Issue created by migration from https://trac.sagemath.org/ticket/26922

[kliem]

comment:1

This will be probably solved at some point by
#26887
The calculation is correct there.

Also it can be corrected quickly now by calculating the dimension of the first level in the face lattice.

[embray]

comment:2

Retarging tickets optimistically to the next milestone. If you are responsible for this ticket (either its reporter or owner) and don't believe you are likely to complete this ticket before the next release (8.7) please retarget this ticket's milestone to sage-pending or sage-wishlist.

[embray]

comment:4

As the Sage-8.8 release milestone is pending, we should delete the sage-8.8 milestone for tickets that are not actively being worked on or that still require significant work to move forward. If you feel that this ticket should be included in the next Sage release at the soonest please set its milestone to the next release milestone (sage-8.9).

[jplab]

comment:5

In principle, the problem is that the face lattice has four elements, but the elements on the second level are not 0-dimensional, but 1-dimensional.

So, depending on the definition of the f-vector:

• Counting the number of elements at each level of the face lattice
• Vector counting the number of faces by dimension

It should return different things.

One thing that should be done, is to make this explicit in the documentation of f_vector once this ticket is fixed and give an example of the difference with unbounded polyhedra.

[kliem]

comment:6

#27063 will change the calculation of the f-vector (hopefully soon) to make use of CombinatorialPolyhedron.

This will count the number of faces per dimension, as the docstring of f_vector states (there is a +2 or -2 two missing, as the first entry gives the -1-dimensional faces count.

We could make this ticket depend on #27063 and then just append the docstring accordingly.

One could also fix it for now (just append a few zeros according to n_lines).

Replying to @jplab:

In principle, the problem is that the face lattice has four elements, but the elements on the second level are not 0-dimensional, but 1-dimensional.

So, depending on the definition of the f-vector:

• Counting the number of elements at each level of the face lattice

I think f-vectors of fixed dimension polyhedra should be have sums/addition.
Also if one considers how adding or deleting inequalities can alter the f-vector this is strange.
Anyway, it's most important to be precise, which one we use. Adding a zero or deleting it, if one really depends one version is trivial.

• Vector counting the number of faces by dimension

It should return different things.

One thing that should be done, is to make this explicit in the documentation of f_vector once this ticket is fixed and give an example of the difference with unbounded polyhedra.

[jplab]

comment:7

ping!