MEGA 2007 Effective Methods in Algebraic Geometry Strobl, Austria, June 25th - 29th http://www.ricam.oeaw.ac.at/mega2007

Abstract

Title	The Automatic Computation of the Complete Root Classification for a Parametric Polynomial
Keywords	Complete root classification, parametric polynomial, real quantifier elimination, root classification
Abstract	A new algorithm for the automatic computation of the complete root classification of a real parametric polynomial is described. The improvement lies in the fact that previous algorithms required `revised sign lists' derived from the discriminant sequence. This is replaced here by the direct use of `sign lists' derived from the discriminant sequence without the need for revision of the lists. As well as offering greater efficiency, the new algorithm offers a better filter for eliminating non-realizable conditions. The new algorithm is applied to the problem of determining the conditions for the positive definiteness of a polynomial. For a class of sparse polynomials, the number of conditions remains surprisingly small.

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