## From V-representation to H-representation

Questions and problems about using polymake go here.
polymake_rulez44
Posts: 6
Joined: 30 Aug 2019, 10:42

### From V-representation to H-representation

I want to compute the inequality description from the V-representation of a polyhedron and then test if the matrix is TU.
From the examples i was able to arrive at this code. What is missing is the step ??? from computing the inequalities to populating the inequalities section of the polytop. So how is this step done correctly?

Code: Select all

$p = new Polytope(POINTS=>[[1,-1,-1],[1,1,-1],[1,-1,1],[1,1,1],[1,0,0]]); ???? (print$p->FACETS; - this does not populate the inequalities section) $A = new Matrix<Integer>($p->INEQUALITIES->minor(All, ~[0])); print totally_unimodular(\$A);

gawrilow
Main Author
Posts: 386
Joined: 25 Dec 2010, 17:40

### Re: From V-representation to H-representation

INEQUALITIES is a pure input property, it's what you can pass to the Polytope or Cone object constructor. It can have duplicate and redundant inequalities, and hidden equations. FACETS is what you get out of the convex hull solver - this is the "canonical" H-representation, free of redundancies and equations (the latter go into LINEAR_SPAN). Once you've got FACETS, just work with them.