Lattice points at the intersection of 3 hyperplanes
Posted: 23 Jan 2018, 13:36
I'm wondering whether polymake can help me with the following problem.
I wish to enumerate all lattice points contained in the intersection of three hyperplanes in the non-negative half-space. That is to say, I have three linear equations of d variables and I would like to find all non-negative integer solutions.
I guess one should be able to consider the above as a polyhedron where the faces are the three hyperplanes and the ones arising from restricting to non-negative solutions only, but would the lattice points at the intersection be a subset of the vertices in that case? If so, would there be any way to find the subset directly, or is the only option to find all vertices and then filter?
I wish to enumerate all lattice points contained in the intersection of three hyperplanes in the non-negative half-space. That is to say, I have three linear equations of d variables and I would like to find all non-negative integer solutions.
I guess one should be able to consider the above as a polyhedron where the faces are the three hyperplanes and the ones arising from restricting to non-negative solutions only, but would the lattice points at the intersection be a subset of the vertices in that case? If so, would there be any way to find the subset directly, or is the only option to find all vertices and then filter?