Algorithms for Computer Algebra

by Keith O. Geddes, Stephen R. Czapor, George Labahn

Overview

Algorithms for Computer Algebra is the first comprehensive textbook to be published on the topic of computational symbolic mathematics. The book first develops the foundational material from modern algebra that is required for subsequent topics. It then presents a thorough development of modern computational algorithms for such problems as multivariate polynomial arithmetic and greatest common divisor calculations, factorization of multivariate polynomials, symbolic solution of linear and polynomial systems of equations, and analytic integration of elementary functions. Numerous examples are integrated into the text as an aid to understanding the mathematical development. The algorithms developed for each topic are presented in a Pascal-like computer language. An extensive set of exercises is presented at the end of each chapter.
Algorithms for Computer Algebra is suitable for use as a textbook for a course on algebraic algorithms at the third-year, fourth-year, or graduate level. Although the mathematical development uses concepts from modern algebra, the book is self-contained in the sense that a one-term undergraduate course introducing students to rings and fields is the only prerequisite assumed. The book also serves well as a supplementary textbook for a traditional modern algebra course, by presenting concrete applications to motivate the understanding of the theory of rings and fields.

Product Details

ISBN-13:	9781475783230
Publisher:	Springer US
Publication date:	03/24/2013
Edition description:	Softcover reprint of the original 1st ed. 1992
Pages:	586
Product dimensions:	6.10(w) x 9.25(h) x 0.05(d)

Table of Contents

to Computer Algebra.- Algebra of Polynomials, Rational Functions, and Power Series.- Normal Forms and Algebraic Representations.- Arithmetic of Polynomials, Rational Functions, and Power Series.- Homomorphisms and Chinese Remainder Algorithms.- Newton’s Iteration and the Hensel Construction.- Polynomial GCD Computation.- Polynomial Factorization.- Solving Systems of Equations.- Gröbner Bases for Polynomial Ideals.- Integration of Rational Functions.- The Risch Integration Algorithm.

Editorial Reviews

Begins by developing the foundational material from modern algebra that is required for subsequent topics, then presents a thorough development of modern computational algorithms for such problems as multivariate polynomial arithmetic and greatest common divisor calculations, factorization of multivariate polynomials, symbolic solution of linear and polynomial systems of equations, and analytic integration of elementary functions. Algorithms are presented in a Pascal-like language. Examples and exercises are provided. Annotation c. Book News, Inc., Portland, OR (booknews.com)

Booknews

‘The Computer Algebra community has been waiting for years for this book to appear. ...the book is a masterpiece and can be recommended to everyone interested in the algorithms for computer algebra, either as a reference for further research or just to give the casual user an idea why things work as good (or as bad) as they do in computer algebra packages. ...the recommendation would be clear: Buy this book! As it stands now my only advice is to stay away from this book, because you might be tempted to buy it anyway (at least I was).'
Computer Algebra Nederland Newsletter, June 1993

From the Publisher