Well, I have to admit that I don't know whether there is an algorithm for calculating mixed-integer polytopes in polymake. We will have to ask my colleagues. In the tutorial that you mentioned, the continuous variables are projected out. Do you want to keep them or do you want to project them out? B...

Hi, thanks for the LP file. Could you please elaborate a little on which information you need. Solving the LP and iterating the integer solutions seems rather easy. There are only 4 different feasible assignments for the integer variables. Are you looking for facets that belong to the convex hull of...

Please post the LP file. I don't know whether it helps, but it might be interesting to have a look at it.

Best regards,
Thomas

I guess the biggest problem is that you are on Windows. While it might be possible to use the callable library to somehow connect Mathematica and polymake, I doubt, you will get polymake up and running natively on Windows. Maybe the easiest way is to transfer data between Mathematica and polymake th...

it makes a minor difference in my codes whether something is an equality or an inequality, so I somehow lost some theoretical understanding. Hmm, at least you should deal with them differently when importing them as input, shouldn't you? Yes and no. The interface to polymake (which was not written ...

Thanks for elaborating. When implementing my solver code, these things were all just "constraints", as it makes a minor difference in my codes whether something is an equality or an inequality, so I somehow lost some theoretical understanding.

Best regards,
Thomas

Well, there are not that many ways to define a facet, I guess. The only source of confusion I could imagine might be the concrete matrix representation: if you have a linear system A*x <= B, you have to specify INEQUALITIES and FACETS as a block matrix (B | -A) because polymake's polyhedra are alwa...

There is absolutely no magic. You create a Polytope object with INEQUALITIES and EQUATIONS, then add an LP subobject with LINEAR_OBJECTIVE vector and ask for LP.MINIMAL_VALUE or LP.MAXIMAL_VALUE or LP.MINIMAL_VERTEX or LP.MAXIMAL_VERTEX. Depending on your current preferences, either your implementa...

Hi, if I add the output of "Affine hull:" (189 constraints) instead of "Facets:" (32 constraints) to the IP and make in an LP, then I obtain 178 as optimal value. (Adding the factes yields 163.429 .) I hope my colleagues can explain this. I am not an expert on how Polymake handle...

Hi!

Could you try to zip the file and attach it afterwards? If this still does not work, could you upload it somewhere?

Best regards,
Thomas