#13638: fix adjacency of rays
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Reporter: vbraun | Owner: mhampton
Type: defect | Status: needs_review
Priority: major | Milestone: sage-5.5
Component: geometry | Resolution:
Keywords: | Work issues:
Report Upstream: N/A | Reviewers:
Authors: Volker Braun | Merged in:
Dependencies: | Stopgaps:
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Comment (by dimpase):
Replying to [comment:10 vbraun]:
> A ray by itself does not define an edge, so you can't identify these two
concepts. I claim that it does make sense to treat V-representation
objects (vertices, rays, lines) on the same footing when talking about
vertex-adjacencies.
It might make sense for the purpose of drawing things, perhaps. I don't
mind this being implemented in a way you see fit, I'm just objecting to
the names used to describe the objects, as they are hugely misleading.
By they way, it would be great to know what exactly you (and Sage :-))
mean by the V-representation. Is it always reduced?
Does it always distinguish between vertices, rays, and lines? A reference?
> To span an edge you need two vertices, a vertex and a ray, or a vertex
and a line.
the classical definition of a face of a convex set B is that it is the
intersection of a supporting hyperplane with B.
And the dimension of the face is the topological dimension of the
intersection. This way it certainly does not make sense to talk about
adjacency beween vertices and rays, as they are objects of different
''type'' (i.e., dimension).
>
> Alternatively, you can understand this by going to projective space. Now
rays are just points at infinity...
No, you certainly do not want to squash your affine space. You want to add
the hyperplane at infinity. Then the rays have two vertices, one of which
at infinity. (And parallel rays intersect at infinity, which might make
sense for your purposes, or not...)
Regarding lines, there are two schools, one of which just forbids full
lines in convex sets in {{{RP^n}}} all together.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13638#comment:11>
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