A COMPLETE DISCRIMINATION SYSTEM FOR POLYNOMIALS

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.