#17215: Bounding hyperplanes for polyhedra
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Reporter: darij | Owner:
Type: task | Status: new
Priority: major | Milestone: sage-6.4
Component: combinatorics | Resolution:
Keywords: polytopes, linear | Merged in:
programming, linear optimization | Reviewers:
Authors: | Work issues:
Report Upstream: N/A | Commit:
Branch: | Stopgaps:
Dependencies: |
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Comment (by vbraun):
All backends right now compute both H/V-representation; the dual is of
course a much more complete certificate that a vertex is really a vertex.
Also, the bounding hyperplane is not canonical---which one to pick? If you
really need one you can construct one from the incident hyperplane
equations of the vertex (or, more generally, d-dimensional face).
{{{
sage: P = polytopes.n_cube(3)
sage: v = P.vertices()[0]
sage: v
A vertex at (-1, -1, -1)
sage: A = sum(h.A() for h in v.incident())
sage: b = sum(h.b() for h in v.incident())
sage: b, A
(3, (1, 1, 1))
sage: Polyhedron(eqns=[[b] + list(A)]) & P
A 0-dimensional polyhedron in QQ^3 defined as the convex hull of 1 vertex
}}}
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Ticket URL: <http://trac.sagemath.org/ticket/17215#comment:5>
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