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force 0/1 in V-representation of a set of inequalities

asked 2017-02-21 18:07:12 -0500

moati gravatar image

updated 2017-08-01 05:24:36 -0500

FrédéricC gravatar image


If I have an array of inequalities (ieqs) that I define as a polyhedron through the command p = Polyhedron(ieqs = ieqs) and then I get the list of vertices of that polyhedron using [p.Vrepresentation( )], however the vertices are fractional so is there any way to force the vertices to be 0-1?

If not, is there a way so that I convert the vertices myself?

Thanks and sorry if my question is so basic

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Could you provide an explicit example of your construction ?

tmonteil gravatar imagetmonteil ( 2017-02-22 00:49:33 -0500 )edit

My problem does not start with a construction. It starts with a Boolean function which I convert to a set of linear inequalities and then input those inequalities as a H-representation of a convex hull to Sage, then convert it to its V-representation to make sure that the set of linear inequalities I generate is correct. Please let me know if this is clear enough. Thanks

moati gravatar imagemoati ( 2017-02-22 09:08:06 -0500 )edit

Could you please provide an explicit example of a boolean function converted into a polytope etc. With that, it is easier to understand the problem without having to spend hours to guess what your problem is, also we can experiment with it, dicuss the kind of output you would like to see, etc.

tmonteil gravatar imagetmonteil ( 2017-02-22 15:38:30 -0500 )edit

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answered 2017-10-09 09:14:57 -0500

jipilab gravatar image

From what I understand of your question, you could scale the polyhedron by the lcm of the denominators of the coordinates of the vertices. This will give you a polyhedron with integer vertices.

Nevertheless, in general, it is not true that every (combinatorial type of) polyhedron object has a 0/1 V-representation. So your example should have a special structure that allows this to be possible.

Unfortunately, we can not help further since we don't have an explicit example...

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Asked: 2017-02-21 18:07:12 -0500

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Last updated: Oct 09 '17