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On combinatorial coefficients and the Gelfond-Khovanskii residue formula

Ivan Soprounov
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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.

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Ivan Soprounov. 2003-10-11. On combinatorial coefficients and the Gelfond-Khovanskii residue formula. https://arxiv.org/abs/math/0310168

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