But what you write means that the returned number of facets print $p->N_FACETS; is only correct if $p is bounded. (Of course I can live with that.) polymake's polytope semantics describes a projectively equivalent (bounded) polytope for every possibly unbounded polyhedron. Not every unbounded polyh...
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First, a few general remarks: It is NP-complete to decide if a polyhedron contains one integer point or not. Checking if a polytope, given by its facets, is integral is also NP-hard [Papadimitriou and Yannakakis (1990)]. For variations and related results see the recent paper by Boros et al., Ann Op...
It seems that there is a custom made piece of software for your needs: azove by Behle. There is even a polymake interface, install azove, and then do "reconfigure 'azove.rules';" within polymake's polytope application. This could be useful for your more tricky input. Please try it and give...
Everything works like described in Bogart, Contois and Gubeladze: Hom-Polytopes, arXiv:1111.3880 . The coordinates of Hom(P,Q) are grouped into dim Q blocks of length (dim P + 1). Each of these blocks of length dim P + 1 gives a column of the transformation. Since we are working with homogeneous coo...
Can you give me a hint what I am supposed to do here ?
Nothing.
polymake transformed your files into a new format. On the way it trashed the properties DIM and AMBIENT_DIM which became user functions. That's why you got a warning (but no error). No information lost in your data.
You can force polymake to write out the labels: > $p=cube(2); > $q=new Polytope<Rational>(POINTS=>new Matrix<Rational>([[1, 0], [1, 1]]); > $hom=mapping_polytope($p, $q, relabel=>1); > print rows_labeled($hom->VERTICES,$hom->VERTEX_LABELS); v0*F1,v1*F1,v2*F0,v3*F0:1 1/2 0 1/2 v0*F1,v1*F1,v2*F1,v3*F1...
Please use the function regular_subdivision: polytope > help "regular_subdivision"; functions/Subdivisions/regular_subdivision: regular_subdivision(points, weights) -> Array<Set<Int>> Compute a regular subdivision of the polytope obtained by lifting points to weights and taking the lower c...
I grabbed the vertices from my polytopes and I'm gonna use a projection operator to plot them together in a 2d space. In general, this is one of the very few sensible options. A special situation occurs if the vertices of the two polytopes in 4-space are in convex position. Then one could introduce...
