#9954: f_vector outputs an extra top-dimensional cell
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Reporter: schilly | Owner: mhampton
Type: defect | Status: needs_review
Priority: major | Milestone: sage-4.6.1
Component: geometry | Keywords:
Author: Volker Braun | Upstream: N/A
Reviewer: Andrey Novoseltsev | Merged:
Work_issues: |
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Changes (by novoselt):
* reviewer: => Andrey Novoseltsev
Comment:
Shouldn't lines be added to all faces including the "empty one"? I am
thinking here by analogy with equations that are "saturated" for all faces
including the "full face". I agree that it is a bit weird, but I think
this is correct from the point of view of dual representations.
I guess I then also want this "empty face" to have the dimension less by
one then the dimension of the linear space generated by lines, by analogy
to vertex - dimension 0, empty set - dimension -1. This is really weird,
perhaps because in both cases "empty face" should have dimension
-infinity?.. But it seems to me that "perfect duality" justifies a strange
choice of dimension for a strange/empty face - if one works with such a
face, he better know what he is doing. In which case, e.g. -1 is a great
choice for the dimension of the empty face of a supporting polytope of a
cone.
In the documentation the sentence "In the case of a full-dimensional
polytope, the faces are pairs (vertices, inequalities) ..." needs some
rewording - it is a bit misleading since faces are now represented by a
special class (which is great, by the way!).
I didn't finish reading the patch yet, but hope to do so tomorrow.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9954#comment:4>
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