Vincent's Theorem

Vincent's theorem, named after Alexandre Joseph Hidulphe Vincent, isolates the real roots of polynomials with rational coefficients and underlies the fastest known method for real-root isolation. Despite this practical importance, the theorem was largely forgotten during the twentieth century, overshadowed by Sturm's theorem and omitted from nearly every classical text on the theory of equations except one by Uspensky. Two variants of Vincent's theorem exist, each giving rise to its own family of root-isolation methods based on continued fractions or bisection.