Hom-, or Mapping-Polytopes

[jackeddielove]

I am brand new to Polymake. I'm working with Dr. Gubeladze at San Francisco State University on Hom-polytopes. I understand Polymake will tell me the number of vertices of the Hom-polytope between a specified source and target polytope of sufficiently small dimension. How do I ask Polymake to do this?

[joswig]

Here is one example:

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polytope > $m=mapping_polytope(simplex(2),cube(2)); polytope > print $m->N_VERTICES; 64

For more information on creating polytopes and such please look at the tutorials. Also useful is polymake's online help functionality.

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polytope > help "mapping_polytope"; functions/Producing a new polyhedron from others/mapping_polytope: mapping_polytope(P1, P2; Options) -> Polytope Construct a new polytope as the mapping polytope of two polytopes P1 and P2. The mapping polytope is the set of all affine maps from R<sup>p</sup> to R<sup>q</sup>, that map P1 into P2. The label of a new facet corresponding to v<sub>1</sub> and h<sub>1</sub> will have the form "v<sub>1</sub>*h<sub>1</sub>". Arguments: Polytope P1 Polytope P2 Options: relabel => Bool Returns Polytope

[jackeddielove]

Thank you!