On The Intractability Of Hilbert's Nullstellensatz And An Algebraic Version Of . .

Section 1. Introduction In this paper we relate an elementary problem in number theory to the intractability of deciding whether an algebraic set defined over the complex numbers (or any algebraically closed field of characteristic zero) is empty. More precisely, we first conjecture: The Hilbert Nullstellensatz is intractible. there is a z ∈ m such that f i (z) = 0 for all i. Brownawell has made the most decisive next step by finding a good bound on the degrees of these g i. With that one may decide if (*) has a solution by linear algebra,