Am 24.02.2011 19:29, schrieb Dmitri:
A chosen set of points is convex if it is equal to its convex hull.
as far as I see this is equivalent to, all points are on a facet of the
polytope.
I think my problem is actually doing the comparison. So I have this
chosen set of points which I don't
On Mar 1, 2:11 pm, Volker Braun vbraun.n...@gmail.com wrote:
I agree with your example, of course. But I interpreted Dmitri's question
somewhat differently, that he wants to start with some set of lattice points
and find out if they all lattice points of the convex hull. Though thinking
One solution would be to compute the volume of P, Q, and intersect(P,Q). All
three are convex, so its easy enough to compute the volumes. Then
Vol(union(P,Q)) = Vol(P) + Vol(Q) - Vol(intersect(P,Q)) = Vol(conv(P,Q))
with equality if and only if union(P,Q) is already convex.
I don't quite
On Feb 24, 10:57 am, Volker Braun vbraun.n...@gmail.com wrote:
On Thursday, February 24, 2011 6:29:11 PM UTC, Dmitri wrote:
I think my problem is actually doing the comparison. So I have this
chosen set of points which I don't know is convex. I compute its
convex hull. Now how do I compare
On Tuesday, March 1, 2011 9:55:01 PM UTC, Ursula Whitcher wrote:
This won't always work.
I agree with your example, of course. But I interpreted Dmitri's question
somewhat differently, that he wants to start with some set of lattice points
and find out if they all lattice points of the
A chosen set of points is convex if it is equal to its convex hull. So all
you have to do is compute the hull and compare with it.
I think my problem is actually doing the comparison. So I have this
chosen set of points which I don't know is convex. I compute its
convex hull. Now how do I
On Thursday, February 24, 2011 6:29:11 PM UTC, Dmitri wrote:
I think my problem is actually doing the comparison. So I have this
chosen set of points which I don't know is convex. I compute its
convex hull. Now how do I compare these two objects?
Assuming that we are still talking about
Thanks for the quick response. My question is somewhat different.
Specifically, I have a set of equations that define each facet of some
polytope. The intersection of all these equations forms a lattice
polytope (finite and bounded). I want to know if that polytope is
convex or not. If it helps to
On Thursday, February 24, 2011 12:12:12 AM UTC, Dmitri wrote:
[...] The intersection of all these equations forms a lattice
polytope (finite and bounded). I want to know if that polytope is
convex or not.
I'm confused. Intersections of convex sets are convex.
[...] One question that
Polyhedron and Polytope (=compact Polyhedron) implies convex. For example:
sage: lp = LatticePolytope(matrix([[-1,-1], [-1,0], [0,0], [1,0],
[1,-1]]).transpose())
sage: lp.points()
[-1 -1 1 1 0 0]
[-1 0 0 -1 -1 0]
sage: lp.vertices()
[-1 -1 1 1]
[-1 0 0 -1]
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