Title: Global residues for sparse polynomial systems [PDF]

Author: Ivan Soprunov

Abstract: We consider families of sparse Laurent polynomials  f₁, . . . , f_n  with a finite set of common zeroes  Z_f  in the torus  (C-{0})ⁿ . The global residue assigns to every Laurent polynomial 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.