Global residues for sparse polynomial systems

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