#5134: Polyhedron: conversion from V-form to H-form fails if no extreme point is
given
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Reporter: sbarthelemy | Owner: mhampton
Type: defect | Status: new
Priority: major | Milestone:
Component: geometry | Keywords:
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Let's consider the first diagonal in {{{R^2}}} as a polyhedron. It has one
extreme point (the origin) and one ray.
It can be defined in sage in V-form and converted to H-form as shown
{{{
sage: p1v1r = Polyhedron([[0,0]],[[1,1]])
sage: p1v1r
A Polyhedron with 1 vertex with 1 rays.
sage: p1v1r.ieqs()
[[1, 0, 0], [0, 1, 0]]
sage: p1v1r.linearities()
[[0, -1, 1]]
}}}
the H-form can be read as
{{{
p1v1r = { (x,y) such that
1 + 0*x + 0*y >= 0 and
1 + 1*x + 0*y >= 0 and
1 - 1*x + 1*y >= 0
}}}
Sage also allows us to define the polyhedron without the vertex
{{{
sage: p0v1r = Polyhedron([], [[1,1]])
sage: p0v1r
A Polyhedron with 1 vertex.
sage: p0v1r.ieqs()
[]
sage: p0v1r.linearities()
[]
}}}
However, then
1. the _repr_() text is different
2. the conversion to H-form failed
problem 2 comes from cdd which requires to be given the extreme point. We
could fix it by adding the point before calling cdd.
However, from a theorical point of view, I think that it would also make
sense to always require at least one vertex:
One can consider the polyhedron as a region of an euclidean space. In such
a case, vertices are *points* and rays are * free vectors*. Then one would
always require at least one point.
What do you think?
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5134>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
Reinventing the Wheel
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