A COMPLETE DISCRIMINATION SYSTEM FOR POLYNOMIALS

Citation
L. Yang et al., A COMPLETE DISCRIMINATION SYSTEM FOR POLYNOMIALS, SCI CHINA E, 39(6), 1996, pp. 628-646
Citations number
11
Categorie Soggetti
Engineering,"Material Science
Journal title
SCIENCE IN CHINA SERIES E-TECHNOLOGICAL SCIENCES
ISSN journal
20950624 → ACNP
Volume
39
Issue
6
Year of publication
1996
Pages
628 - 646
Database
ISI
SICI code
2095-0624(1996)39:6<628:ACDSFP>2.0.ZU;2-A
Abstract
Given a polynomial with symbolic/literal coefficients, a complete disc rimination system is a set of explicit expressions in terms of the coe fficients, which is sufficient for determining the numbers and multipl icities of the real and imaginary roots. Though it is of great signifi cance, such a criterion for root-classification has never been given f or polynomials with degrees greater than 4. The lack of efficient tool s in this aspect extremely prevents computer implementations for Tarsk i's and other methods in automated theorem proving. To remedy this def ect, a generic algorithm is proposed to produce a complete discriminat ion system for a polynomial with any degrees. This result has extensiv e applications in various fields, and its efficiency was demonstrated by computer implementations.