Effective Polynomial Computation
By: by Richard Zippel
Series: The Springer International Series in Engineering and Computer Science -- 241; International series in engineering and computer science -- 241.
Publisher: Springer US
Published: 1993
Place of publication: Boston, MA
Language: eng
Format: [electronic resource] /
Number of pages: 363
ISBN-13: 9781461363989; 9781461531883
Subjects: Electronic data processing; Algebra; Computer science; Data processing; Number theory
Description: 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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