Counting lattice points via Hirzebruch–Riemann–Roch

Given a lattice polytope P, one can construct a toric variety X, together with an ample line bundle L on X. It turns out that its Euler characteristic is equal to the number of lattice points contained in P. Moreover, the Hirzebruch–Riemann–Roch theorem tells us how to calculate this Euler characteristic in terms of the Todd class of the toric variety X. This yields an efficient method for counting the lattice points in P, because there is a polynomial time algorithm that computes the Todd class of X given the polytope P.