#9337: Add toric divisors
--------------------------------------------+-------------------------------
Reporter: vbraun | Owner: AlexGhitza
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-4.6
Component: algebraic geometry | Keywords:
Author: Volker Braun | Upstream: N/A
Reviewer: Andrey Novoseltsev | Merged:
Work_issues: non-reduced divisor handling |
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Comment(by novoselt):
1. I agree that `lattice_polytope` should return something canonical.
However enlarging is definitely not unique and therefore cannot be
canonical. For example, take a polytope consisting of a single point 1/2
in a 1-d space. Your method of enveloping will turn it into `[0,1]`,
bumping up the dimension. Now take a point (1/2, 1/2) in a 2-d space. Your
method will turn it into a square `[0,1]x[0,1]`. Why not a line segment
from (0,0) to (1,1)? I also think that the following two blocks should be
equivalent:
{{{
sage: if p.is_lattice_polytope():
... lp = p.lattice_polytope()
}}}
and
{{{
sage: try:
... lp = p.lattice_polytope()
... except ValueError:
... pass
}}}
And while for finding integral points inside a polyhedron constructing an
envelope is the most useful option, in general I think I would want to
convert a polyhedron to a lattice polytope only if I was getting the same
mathematical object. Therefore, if my code tries to perform the conversion
without any checks, it should mean that I know that the polytope in
question is a lattice one and if this is not the case I would like to see
and exception, so that I can fix the bug. Envelope can have different
dimension, different facet normals, and, ultimately, completely different
face structure. So I think that NOT constructing an envelope is actually
the most useful option, as well as the most transparent one. If you
disagree with these arguments we should bring it up on sage-devel and I
promise to conform with the majority ;-)
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9337#comment:45>
Sage <http://www.sagemath.org>
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