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Effective Polynomial Computation : Evaluation in Education and Human Services - Richard Zippel

Effective Polynomial Computation

Evaluation in Education and Human Services

Hardcover Published: 31st July 1993
ISBN: 9780792393757
Number Of Pages: 363

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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.

Euclid's Algorithmp. 1
Continued Fractionsp. 11
Diophantine Equationsp. 41
Lattice Techniquesp. 57
Arithmetic Functionsp. 73
Residue Ringsp. 85
Polynomial Arithmeticp. 107
Polynomial GCD's: Classical Algorithmsp. 125
Polynomial Eliminationp. 137
Formal Power Seriesp. 157
Bounds on Polynomialsp. 173
Zero Equivalence Testingp. 189
Univariate Interpolationp. 207
Multivariate Interpolationp. 231
Polynomial GCD's: Interpolation Algorithmsp. 247
Hensel Algorithmsp. 261
Sparse Hensel Algorithmsp. 285
Factoring over Finite Fieldsp. 293
Irreducibility of Polynomialsp. 303
Univariate Factorizationp. 321
Multivariate Factorizationp. 329
List of symbolsp. 341
Bibliographyp. 343
Indexp. 357
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780792393757
ISBN-10: 0792393759
Series: Evaluation in Education and Human Services
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 363
Published: 31st July 1993
Country of Publication: NL
Dimensions (cm): 24.28 x 16.56  x 2.64
Weight (kg): 0.71

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