Mathematica 9 is now available
Services & Resources / Wolfram Forums
-----
 /
MathGroup Archive
1992
*January
*February
*March
*April
*May
*June
*July
*August
*September
*October
*November
*December
*Archive Index
*Ask about this page
*Print this page
*Give us feedback
*Sign up for the Wolfram Insider

MathGroup Archive 1992

[Date Index] [Thread Index] [Author Index]

Search the Archive

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






  • Prev by Date: Re: Problem with evaluating Integral
  • Next by Date: Yet another Integrate bug.
  • Previous by thread: Re: Problem with evaluating Integral
  • Next by thread: Yet another Integrate bug.