Global residues for sparse polynomial systems

We consider families of sparse Laurent polynomials f1, ..., fn with a finite set of common zeros Zf in the torus Tn = (C - {0})n. The global residue assigns to every Laurent polynomial g the sum of its Grothendieck residues over Zf. We present a new symbolic algorithm for computing the global residue as a rational function of the coefficients of the fi when the Newton polytopes of the fi are full-dimensional. Our results have consequences in sparse polynomial interpolation and lattice point enumeration in Minkowski sums of polytopes. © 2006 Elsevier Ltd. All rights reserved.