An Exact Method for Finding the Roots of a Complex Polynomial

Abstract

Let G be a univariate polynomial with rational complex coefficients. A new SAC-1 module is described which uses algebraic algorithms based on the classical theorems of Sturm and Routh to isolate the unique roots of G into disjoint squares m the complex plane. These squares can then be refined to any prespecified rational width. Furthermore, the algorithms can associate with each square the multiplicity of the unique root of G contained in that square.