On combinatorial coefficients and the Gelfond-Khovanskii residue formula

Details On combinatorial coefficients and the Gelfond-Khovanskii residue formula On combinatorial coefficients and the Gelfond-Khovanskii residue formula

2003-10-11

arxiv.org/abs/math/0310168v1

Topics in algebraic geometry and geometric modeling, 343--349, Contemp. Math., 334, AMS 2003

Mathematics

Algebraic Geometry

7 pages, 2 figures (.eps) To appear in the Procedings of the Workshop on Geometric Modeling and Algebraic Geometry, Vilnius, L

Scientific paper

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.

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