forum.polymake.org

Hello,

I wanted to solve the following problem with polymake and could not find the solution in the tutorial.
I have a lp-file with about 20 (in-)equalities and 18 variables which I have read in with polymake with "lp2poly("myfile.lp");". now I can take a look at the inequalities as well as at the vertices and the facets (though there is a warning and I am not quite sure if that works correctly).

What I am a really looking for are the lattice points and the integer hull.

I hope somebody can help me with that little problem.

Stefan

lp2poly() returns a Polytope<Float>, which does not provide all the properties you need for your task. Therefore, you should convert it to a Polytope<Rational> via the user function convert_to<Rational>(), i.e., Now one way to compute the integer hull in polymake is to produce a new polytope from the lattice points of $p_rat: The facets of $p_lat describe the integer hull.
Warning: The computation of the lattice points is quite expensive, so it might take some time, even for small examples.

There is also a script "gc_closure" that takes a rational polytope and returns its Chvatal-Gomory closure. Iterating this could be faster than computing all lattice points in the polytope. Scripts have to be loaded first: If $p is your rational polytope, then computes the first elementary closure of $p.

Here is also a (somewhat incomplete) tutorial about solving ILP's with polymake. Computation of the integer hull is not yet included.

Hello,

is the script "gc_closure" available for download?

Thanks

is the script "gc_closure" available for download?

I am sorry, I was too quick with my answer.

The script is unfortunately not included in the current release 2.9.9 as it builds on things only available in the next release (computations with cones), so it won't help to make this available for download. If you want I can send you a workaround via mail. This would need an installed version of either 4ti2 or normaliz2 in addition to polymake.