Effective Polynomial Computation is an introduction to the algorithms of computer algebra. It discusses the basic algorithms for manipulating polynomials including factoring polynomials. These algorithms are discussed from both a theoretical and practical perspective. Those cases where theoretically optimal algorithms are inappropriate are discussed and the practical alternatives are explained.
Effective Polynomial Computation provides much of the mathematical motivation of the algorithms discussed to help the reader appreciate the mathematical mechanisms underlying the algorithms, and so that the algorithms will not appear to be constructed out of whole cloth.
Preparatory to the discussion of algorithms for polynomials, the first third of this book discusses related issues in elementary number theory. These results are either used in later algorithms (e.g. the discussion of lattices and Diophantine approximation), or analogs of the number theoretic algorithms are used for polynomial problems (e.g. Euclidean algorithm and p-adic numbers).
Among the unique features of Effective Polynomial Computation is the detailed material on greatest common divisor and factoring algorithms for sparse multivariate polynomials. In addition, both deterministic and probabilistic algorithms for irreducibility testing of polynomials are discussed.

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Authors and Affiliations

Cornell University, USA

Richard Zippel

Bibliographic Information

Book Title: Effective Polynomial Computation
Authors: Richard Zippel
Series Title: The Springer International Series in Engineering and Computer Science
DOI: https://doi.org/10.1007/978-1-4615-3188-3
Publisher: Springer New York, NY
eBook Packages: Springer Book Archive
Copyright Information: Springer Science+Business Media New York 1993
Hardcover ISBN: 978-0-7923-9375-7Published: 31 July 1993
Softcover ISBN: 978-1-4613-6398-9Published: 08 October 2012
eBook ISBN: 978-1-4615-3188-3Published: 06 December 2012
Series ISSN: 0893-3405
Edition Number: 1
Number of Pages: XI, 363
Topics: Symbolic and Algebraic Manipulation, Numeric Computing, Algebra, Number Theory

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Table of contents (21 chapters)

Front Matter

About this book