I often find myself working with lattice polytopes whose vertices live in an affine hyperplane H of R^d defined by H={ x in R^d : <v,x>=1 } where v is some fixed integral vector. What is the best way to input these polytopes into polymake?
For example, suppose that the vertices of my polytope are the columns of
The vertices of this polytope live in the hyperplane defined by the integral vector v=<1,1,1>. To input my data into polymake I need to translate this hyperplane defined by e=<1,0,0>.
Banging my head against the wall, I find that A = R*B where
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R= B=
-4 2 -1 1 1 1 1
3 -1 0 0 1 0 1
2 -1 1 0 0 1 1
Since det R = -1 I find that my original polytope is the square and I can use the columns of B to define my polytope in polymake.
Can polymake automate this process?