#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):
The non-compactness is not the issue, the 1-d interval in a 2-d ambient
space fails as well:
{{{
sage: for lset in
Polyhedron(vertices=[(1,0),(0,1)]).face_lattice().level_sets(): print lset
....:
[(None, (0, 1, 2))]
[((1,), (0, 2)), ((0,), (0, 1))]
[((0, 1), (0,))]
[((0, 1), None)]
}}}
On the other hand, I would argue that the novoselt's Quadrant example is
correct: The rays stand for points at infinite distance and are properly
counted as points. A triangle would have 8 faces. The edge at infinity is
not counted as a face of the quadrant (=double infinite triangle), hence
the quadrant does have 7 faces.
The fundamental flaw of the face_lattice() function is that
1) its description does not explain in detail what is computed
2) The result should be returned by means of the H/Vrepresentation
objects, and not by their indices.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8656#comment:1>
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