Automatic computation of the complete root classification for a parametric polynomial (Q840716)

The authors present an improvement of their algorithm to compute complete root classifications (CRC) of univariate polynomials with real parametric coefficients [An algorithm for computing the complete root classification of a parametric polynomial. Artificial intelligence and symbolic computation. 8th international conference, AISC 2006, Beijing, China, September 20--22, 2006. Proceedings. Berlin: Springer. Lecture Notes in Artificial Intelligence, Lecture Notes Comput. Sci. 4120, 116--130 (2006; Zbl 1156.68632)]. This improvement consists mainly on working directly with 'sign lists' rather than 'revised sign lists'. A second improvement is to simplify the set of generated conditions, by means of a test for extraneous cases (empty conditions). The authors discuss the equivalence of discriminant sequences, principal Sturm-Habicht coefficient sequences, and principal and signed subresultant coefficient sequences for CRC computations. They also review some previous algorithms by different authors and present some sparse examples.