Automatic computation of the complete root classification for a parametric polynomial |
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Authors: | Songxin Liang David J Jeffrey |
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Affiliation: | Department of Applied Mathematics, University of Western Ontario, London, Ontario, Canada |
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Abstract: | An improved algorithm, together with its implementation, is presented for the automatic computation of the complete root classification of a real parametric polynomial. The algorithm offers improved efficiency and a new test for non-realizable conditions. The improvement lies in the direct use of ‘sign lists’, obtained from the discriminant sequence, rather than ‘revised sign lists’. It is shown that the discriminant sequences, upon which the sign lists are based, are closely related both to Sturm–Habicht sequences and to subresultant sequences. Thus calculations based on any of these quantities are essentially equivalent. |
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Keywords: | Complete root classification Parametric polynomial Real quantifier elimination Real root Subresultant polynomial |
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