Counting Solutions to Binomial Complete Intersections
نویسندگان
چکیده
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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ورودعنوان ژورنال:
- J. Complexity
دوره 23 شماره
صفحات -
تاریخ انتشار 2007