Global residues for sparse polynomial systems

We consider families of sparse Laurent polynomials f1,…,fnf1,…,fn with a finite set of common zeros ZfZf in the torus Tn=(C−{0})nTn=(C−{0})n. The global residue assigns to every Laurent polynomial gg the sum of its Grothendieck residues over ZfZf. We present a new symbolic algorithm for computing the global residue as a rational function of the coefficients of the fifi when the Newton polytopes of the fifi are full-dimensional. Our results have consequences in sparse polynomial interpolation and lattice point enumeration in Minkowski sums of polytopes.