2003/10/11 by Ivan Soprounov
Mathematics · #math.AG #msc:14M25 #msc:52B11
published as Topics in algebraic geometry and geometric modeling, 343--349, Contemp. Math., 334, AMS 2003 · 7 pages, 2 figures (.eps) To appear in the Procedings of the Workshop on Geometric Modeling and Algebraic Geometry, Vilnius, Lithuania, August 2002
arxiv created 2003/10/11 · arxiv updated 2009/12/01
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.