Hilbert's Nullstellensatz

*To*: mathgroup at yoda.physics.unc.edu*Subject*: Hilbert's Nullstellensatz*From*: sutner at sparc1.stevens-tech.edu (Klaus Sutner)*Date*: Mon, 13 Apr 92 09:40:20 EDT

Hello. A colleague of mine asked me to post the following questions. Has anybody perhaps written a package that solves his problems? (1) The first is relatively simple and is the question of solutions to Hilbert's Nullstellensatz. Specifically, given a set of m polynomials a_1, a_2, a_3,... a_m in n variables x=(x_1, x_2, ...x_n), which do not have any common zeros, find polynomial(s) b_1, b_2,...b_m in x such that a_1.b_1 +...+a_m.b_m = 1. (2) The second is related to Serra conjecture (Quillen-Suslin theorem). Given the polynomials a_1,...a_m as above, find a (m x m) unimodular polynomial matrix M i.e., matrix whose entries are polynomials in x with the further property that its determinant is a nonzero constant such that the first row of M is (a_1, a_2,...a_m). The feasibility of this is the essential core of the proof of Quillen-Suslin theorem. Thanks. --------------------------------------------------------------------------- Klaus Sutner sutner at sparc1.stevens-tech.edu CS Department 201.216.5435 Stevens Institute of Technology 201.216.8246 fax Hoboken, NJ 07030 ---------------------------------------------------------------------------