#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-4.4.2
Component: geometry | Keywords:
Author: | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Comment(by vbraun):
I tend to think of non-compact polyhedra in `R^n` as compact polyhedra in
`RP^n`. This is also what TOPCOM and, I think, cdd do (though its never
spelled out in the cdd manual). The faces of the non-compact polyhedron
consist of all faces of the projective polyhedron that can be spanned by
affine points and rays.
I think the rationale is that you tend to do this if you naively apply an
algorithm for compact polyhedra in the non-compact case.
Though I agree that, from a user perspective, your definition of faces
(always including at least one vertex) would be nicer. However, I think
you can not derive it from the incidence matrix alone but you will have to
distinguish cases for the different H/V-representation objects. It would
be great if you could polish your implementation for inclusion. Let me
know if I can help with anything. I do need a working face lattice for
non-compact polyhedra for the toric varieties package I'm currently
working on...
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8656#comment:4>
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