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Hilbert's Nullstellensatz


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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