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From giesl@kirmes.intellektik.informatik.th-darmstadt.de Mon Feb  1 14:39:51 JST 1993
Article: 23115 of sci.math
Path: kudpc!kuis!wnoc-kyo!icspub!oskgate0.mei!chorus.mei!adagio.panasonic.com!sgiblab!spool.mu.edu!yale.edu!ira.uka.de!math.fu-berlin.de!news.th-darmstadt.de!kirmes!giesl
From: giesl@kirmes.intellektik.informatik.th-darmstadt.de (Juergen Giesl)
Newsgroups: sci.math
Subject: Algorithm for Polynomial Inequalities?
Keywords: Polynomial Inequalities
Message-ID: <1k6b8mINNg4u@rs2.hrz.th-darmstadt.de>
Date: 27 Jan 93 15:55:02 GMT
Sender: giesl@kirmes (Juergen Giesl)
Organization: Technical University Darmstadt
Lines: 46
NNTP-Posting-Host: kirmes.inferenzsysteme.informatik.th-darmstadt.de


A POLYNOMIAL INEQUATION over the natural numbers
is a formula of the following type:

FOR ALL natural numbers n1,..,nk: p(n1,...,nk) > 0,

where p is a multivariate polynomial of any degree 
with variable coefficients p0,...,pj. 


A mapping from {po,...,pj} to the natural numbers is a 
SOLUTION to the above inequation, if substituting each pi 
by the number it is mapped to makes the inequation true. 


A polynomial equation and its solutions are defined analogously. 


A solution to a set of polynomial inequations and equations 
is a mapping from all occurring variable coefficients to the
natural numbers, which solves each inequation and each equation
in the set.

  _______________________________________________________
 | I am searching for an algorithm working as follows:   |
 | Given a set of polynomial inequations and equations   | 
 | over natural numbers,                                 |
 | it returns "solvable" or "don't know".                |
 | If it returns "solvable" then there exists a solution |
 | to the set of inequations and equations.              |
  -------------------------------------------------------
 

Due to Lankford the problem of deciding inequalities between
n polynomials over the natural numbers is undecidable. (Although
it is decidable over the real numbers).


So if anybody knows where to find an algorithm which is able to find
a solution for a reasonably big class of these problems, please
tell me.


Thank you,

Juergen Giesl.
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