#8656: face_lattice does not seem to work for unbounded polyhedra
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Reporter: novoselt | Owner: mhampton
Type: defect | Status: new
Priority: major | Milestone: sage-4.4
Component: geometry | Keywords:
Author: | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Recent ticket #8650 (required for the output below) fixed a bug in
face_lattice computation for polytopes. However, I think that both of the
following examples for unbounded polyhedra are incorrect.
{{{
sage: for lset in Polyhedron(rays=[(1,0)]).face_lattice().level_sets():
lset
[(None, (0, 1))]
[((0,), (0,)), ((1,), (0, 1))]
[((0, 1), (0,))]
[((0, 1), None)]
}}}
This ray has three faces: empty, vertex, and the whole ray (including the
vertex at which it originates). Five are shown, including a face
containing the ray, but not the vertex from which it originates.
{{{
sage: for lset in Polyhedron(rays=[(1,0),
(0,1)]).face_lattice().level_sets(): lset
[(None, (0, 1))]
[((1,), (0,)), ((0,), (1,)), ((2,), (0, 1))]
[((1, 2), (0,)), ((0, 2), (1,))]
[((0, 1, 2), None)]
}}}
For the quadrant we have five faces: empty, vertex, two rays, and the
whole quadrant. The above output has seven.
The easiest fix is probably to raise an exception if the polyhedron is
unbounded and state in the documentation that face_lattice works only for
polytopes, but of course it would be nice to be able to compute correct
faces in all cases.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8656>
Sage <http://www.sagemath.org>
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