Effective Polynomial Computation

By: Richard Zippel

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Hardcover | 31 July 1993

At a Glance

Hardcover
376 Pages

Dimensions(cm)
24.77 x 17.15 x 1.91

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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.

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You Can Find This Book In

Non-Fiction Mathematics Algebra Number Theory Computing & I.T.Computer Science Image Processing Mathematical Theory of Computation Maths for Computer Scientists Computer Programming & Software Development Algorithms & Data Structures Databases

Data Capture & Analysis

Euclid's Algorithm	p. 1
Continued Fractions	p. 11
Diophantine Equations	p. 41
Lattice Techniques	p. 57
Arithmetic Functions	p. 73
Residue Rings	p. 85
Polynomial Arithmetic	p. 107
Polynomial GCD's: Classical Algorithms	p. 125
Polynomial Elimination	p. 137
Formal Power Series	p. 157
Bounds on Polynomials	p. 173
Zero Equivalence Testing	p. 189
Univariate Interpolation	p. 207
Multivariate Interpolation	p. 231
Polynomial GCD's: Interpolation Algorithms	p. 247
Hensel Algorithms	p. 261
Sparse Hensel Algorithms	p. 285
Factoring over Finite Fields	p. 293
Irreducibility of Polynomials	p. 303
Univariate Factorization	p. 321
Multivariate Factorization	p. 329
List of symbols	p. 341
Bibliography	p. 343
Index	p. 357
Table of Contents provided by Blackwell. All Rights Reserved.

Effective Polynomial Computation

At a Glance

Hardcover

Shipping

How to return your order

Defective items

You Can Find This Book In

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