On combinatorial coefficients and the Gelfond-Khovanskii residue formula
Algebraic Geometry
2007-05-23 v1
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.
Keywords
Cite
@article{arxiv.math/0310168,
title = {On combinatorial coefficients and the Gelfond-Khovanskii residue formula},
author = {Ivan Soprounov},
journal= {arXiv preprint arXiv:math/0310168},
year = {2007}
}
Comments
7 pages, 2 figures (.eps) To appear in the Procedings of the Workshop on Geometric Modeling and Algebraic Geometry, Vilnius, Lithuania, August 2002