Hom-, or Mapping-Polytopes
Posted: 20 Jan 2012, 23:15
by 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?
Re: Hom-, or Mapping-Polytopes
Posted: 23 Jan 2012, 10:33
by joswig
Here is one example:
Code: Select all
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.
Code: Select all
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
Re: Hom-, or Mapping-Polytopes
Posted: 23 Jan 2012, 23:03
by jackeddielove
Thank you!