Counting Solutions to Binomial Complete Intersections

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We study the problem of counting the total number of affine solutions of a system of n binomials in n variables over an algebraically closed field of characteristic zero. We show that we may decide in polynomial time if that number is finite. We give a combinatorial formula for computing the total number of affine solutions (with or without multiplicity) from which we deduce that this counting problem is #P-complete. We discuss special cases in which this formula may be computed in polynomial time; in particular, this is true for generic exponent vectors.
Several minor improvements. Final version to appear in the J. of Complexity

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Commutative Algebra, Computational Complexity, Combinatorics

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http://salesiana.dossiersoluciones.com/handle/123456789/103794

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0510520
 http://arxiv.org/abs/math/0510520

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arXiv