rootsur.lib. A Singular 3-1-6 library for counting the number of real roots of a univariate polynomial. Routines for bounding and counting the number of real roots of a univariate polynomial, by means of several different methods, namely Descartes’ rule of signs, the Budan-Fourier theorem, Sturm sequences and Sturm-Habicht sequences. The first two give bounds on the number of roots. The other two compute the actual number of roots of the polynomial. There are several wrapper functions, to simplify the application of the aforesaid theorems and some functions to determine whether a given polynomial is univariate. References: Basu, Pollack, Roy, ”Algorithms in Real Algebraic Geometry”, Springer, 2003.

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  1. Marais, Magdaleen S.; Steenpaß, Andreas: The classification of real singularities using Singular. I: Splitting lemma and simple singularities (2015)