ehrhart can only be applied to polytopes, i.e. compact polyhedra. To calculate the Ehrhart polynomial, the number of lattice points in the first n dilations of the polytope are calculated, where n is the dimension of the polytope. A system of linear equations is then solved to find the polynomial.
i1 : P = convexHull transpose matrix {{0,0,0},{1,0,0},{0,1,0},{1,1,3}} o1 = {ambient dimension => 3 } dimension of lineality space => 0 dimension of polyhedron => 3 number of facets => 4 number of rays => 0 number of vertices => 4 o1 : Polyhedron |
i2 : ehrhart P 1 3 2 3 o2 = -x + x + -x + 1 2 2 o2 : QQ[x] |
The object ehrhart is a method function.