On Combinatorial Coefficients and the Gelfond-khovanskii Residue Formula
Topics in Algebraic Geometry and Geometric Modeling
The Gelfond-Khovanskii residue formula computes the sum of the values of any Laurent polynomial over solutions of a system of Laurent polynomial equations whose Newton polytopes have sufficiently general relative position. We discuss two important consequences of this result: an explicit elimination algorithm for such systems and a new formula for the mixed volume. The integer coefficients that appear in the Gelfond-Khovanskii residue formula are geometric invariants that depend only on combinatorics of the polytopes. We explain how to compute them explicitly.
Soprunov, Ivan, "On Combinatorial Coefficients and the Gelfond-khovanskii Residue Formula" (2003). Mathematics Faculty Publications. 282.