       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
---------------------------------------------------------------------------

```

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