#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 vbraun):
I'm basing the nomenclature on "Representations of Convex Polyhedra" in
the PPL docs
[http://bugseng.com/products/ppl/documentation#%2Fproducts%2Fppl%2Fdocumentation%2F%2Fdevref
%2Fppl-devref-1.0-html%2Findex.html], if you want a reference. The
representation is always reduced.
With regard to the projective space, I guess it would be best to
compactify by adding rays as extra "points". Instead of lines, which would
give you the usual real projective space. Note that you don't have to say
rays/lines modulo parallel transport since the rays/lines don't have a
base point in my notation.
So there is no such thing as parallel rays, only parallel edges. Two
parallel half-infinite edges intersect at infinity.
The `Polyhedron` class doesn't keep track of extra generators at infinity.
So two half-infinite edges that are not parallel can be thought of as
closed up by a edge that is at infinity, but that is not part of the data
we track.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13638#comment:12>
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