Real algebraic numbers and polynomial systems of small degree

We present exact and complete algorithms based on precomputed Sturm-Habicht sequences, discriminants and invariants, that classify, isolate with rational points and compare the real roots of polynomials of degree up to 4. We have closed formulas for all isolating points. Moreover we combine these results with a simple version of rational univariate representation so as to isolate and compute the multiplicity of all common real roots of a bivariate system of integer polynomials of total degree 2. We present our implementation within synaps and we perform experimentation and comparison with all available software. Our package is 2

• Type: Journal
• Year: 2008
• Where: TCS
• Authors: Ioannis Z. Emiris, Elias P. Tsigaridas
• Keywords: Polynomial, Rational Univariate Representation, Real Roots, TCS 2008, Theoretical Computer Science