I am using Python but I wouldn't mind changing language. All I have gotten from my research are tools to count the number of (lattice) points inside a region given the equations for the planes that enclose it. Other tools are made to optimize a given function inside the polytope (linear programming).
How about finding the lattice points alone? For example, a function of the kind
latticePoints( 'x < 5 & x > 0' ) = [ 1, 2, 3, 4]
Plus I am looking for something to work in the multivariate scenario (constrains on x, y, z, ...).
I am currently trying to solve this using ppl.