  We consider families of sparse Laurent polynomials f_1,...,f_n with a finite
set of common zeroes Z_f in the complex algebraic n-torus. The global residue
assigns to every Laurent polynomial g the sum of its Grothendieck residues over
the set 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.
