Sturm—Habicht Sequences, Determinants and Real Roots of Univariate Polynomials

Abstract

The real root counting problem is one of the main computational problems in Real Algebraic Geometry. It is the following: Let $\mathbb{D}$ be an ordered domain and $\mathbb{B}$ a real closed field containing $\mathbb{D}$. Find algorithms which for every P ∈ $\mathbb{D}$ [x] compute the number of roots of P in $\mathbb{B}$. More precisely we shall study the following problem.