Hello everyone.

So far I have been using Mathematica for simple operations on lattice polytopes (as matrices where each column represents a vertex). I have been mapping them around, and checking their widths in a given direction.

Now I need to use more complex operations, such as finding the h-description of polytopes, and finding the convex hull of the interior lattice points and express it as the convex hull of its extreme points. After searching around, I found polymake. One major problem is that I use windows, and is unable to fully use polymake besides the interactive version. I might be able to overcome this problem, but another problem is having to rewrite what I have in polymake.

My basic question is, is it possible to write functions in polymake, and use it in Mathematica. For example, say I have a matrix representing a polytope, and I want to evaluate the half spaces representation of it in polytope, how hard would this be?