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A Complete Discrimination System for Polynomials\footnote{
   This work is supported in part by the National Science Foundation of China.
   Participation in and presentation of the paper at the conference was
   made possible through a generous grant from UNU/IIST, the United Nations
   University. International Institute for Software Technology, Macau.}
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Lu Yang, Xiao-Rong Hou, Zhen-Bing Zeng

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Date:  July 19th (Friday)\\
Time: 09:30-10:00\\

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Abstract
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Given a polynomial with symbolic/literal coefficients, a complete discrimination system is a set of
explicit expressions in terms of the coefficients, which is sufficient for determining the numbers
and multiplicities of the real and imaginary roots. Though it is of great significance, such a
criterion for root-classification had never been given for polynomials with degrees greater than 4.
The lack of efficient tools in this aspect extremely prevents computer implementations for
Tarski's method and other ones in Automated Theorem Proving. To remedy this defect, the authors
propose a generic algorithm to produce a complete discrimination system for a polynomial with
any degree. This result has extensive applications in various fields, and its efficiency was
demonstrated by computer implementations. 

