Counting Solutions to Binomial Complete Intersections

E. CATTANI, A. DICKENSTEIN

JOURNAL OF COMPLEXITY

Elsevier

Lugar: Europa; Año: 2007 vol. 23 p. 82 - 107

0885-064X

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.