Counting Solutions to Binomial Complete Intersections

Details Counting Solutions to Binomial Complete Intersections Counting Solutions to Binomial Complete Intersections

2005-10-25

arxiv.org/abs/math/0510520v2

Mathematics

Commutative Algebra

Several minor improvements. Final version to appear in the J. of Complexity

Scientific paper

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.

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