Polynomials: An Algorithmic Approach (Discrete Mathematics and Theoretical Computer Science)

A well-balanced presentation of the classic procedures of polynomial algebra that are computationally relevant. The first chapter discusses the construction and the representation of polynomials, while the second focuses on the computational aspects of their analytical theory. Polynomials with coefficients in a finite field are then described in chapter three, and the final chapter is devoted to factorisation with integral coefficients. Aimed primarily at graduates with a prerequisite knowledge of set theory, usual fields and basic algebra, the text contains fully worked out examples, hints and references, and details concerning the implementation of algorithms as well as indicators of their efficiency. XXXXXXX NEUER TEXT This is a well-balanced presentation of the classic procedures of polynomial algebra that are computationally relevant. Algorithms developed during the last decade are provided along with their implementation and indications of their efficiency. The construction, computational aspects, and factorization of polynomials are covered and will be useful to those working in computational mathematics, scientific computing, and the theory of computation. "This textbook gives a well-balanced presentation of the classic procedures of polynomial algebra which are computationally relevant and some algorithms developed during the last decade."--BOOK JACKET. "This book is primarily intended for graduate students taking courses in Polynomial Algebra, with prior knowledge of set theory, usual fields and basic algebra. Fully worked out examples, hints and references complement the main text, and details concerning the implementation of algorithms as well as indicators of their efficiency are provided. The book is also useful as a supplementary text for courses in scientific computing, analysis of algorithms, computational polynomial factorization, and computational geometry of polynomials."--BOOK JACKET A presentation of the classic procedures of polynomial algebra that are computationally relevant. The book covers such topics as the construction and representation of polynomials, the computational aspects of their analytical theory, and polynomials with coefficients in a finite field.