Global residues for sparse polynomial systems
arXiv:math/0511684 · doi:10.1016/j.jpaa.2006.06.012
Abstract
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.
Typos corrected, reference added, 13 pages, 5 figures. To appear in JPAA