The complete root classification of a parametric polynomial on an interval

Authors:
Songxin Liang;David J. Jeffrey;Marc Moreno Maza
Affiliations:
University of Western Ontario, London, ON, Canada;University of Western Ontario, London, ON, Canada;University of Western Ontario, London, ON, Canada
Venue:
Proceedings of the twenty-first international symposium on Symbolic and algebraic computation
Year:
2008

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Abstract

Given a real parametric polynomial p(x) and an interval (a,b) ⊂ R, the Complete Root Classification (CRC) of p(x) on (a,b) is a collection of all possible cases of its root classification on (a,b), together with the conditions its coefficients must satisfy for each case. In this paper, a new algorithm is proposed for the automatic computation of the complete root classification of a parametric polynomial on an interval. As a direct application, the new algorithm is applied to some real quantifier elimination problems.