On Combinatorial Coefficients and the Gelfond-khovanskii Residue Formula
Document Type
Conference Proceeding
Publication Date
10-11-2003
Publication Title
Topics in Algebraic Geometry and Geometric Modeling
Abstract
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.
Repository Citation
Soprunov, Ivan, "On Combinatorial Coefficients and the Gelfond-khovanskii Residue Formula" (2003). Mathematics and Statistics Faculty Publications. 282.
https://engagedscholarship.csuohio.edu/scimath_facpub/282
DOI
10.1090/conm/334
Volume
334
