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Author Geddes, K. O. (Keith O.), 1947-
Title Algorithms for computer algebra / K.O. Geddes, S.R. Czapor, G. Labahn.
Imprint Boston : Kluwer Academic, [1992]

Author Geddes, K. O. (Keith O.), 1947-
Subject Algebra -- Data processing.
Alt Name Czapor, S. R. (Stephen R.), 1957-
Labahn, G. (George), 1951-
Description xviii, 585 pages : illustrations ; 25 cm
Bibliography Note Includes bibliographical references and index.
ISBN 0792392590 (alk. paper)
OCLC # 26212117
Table of Contents
Ch. 1Introduction to Computer Algebra 
 1.2Symbolic versus Numeric Computation2
 1.3A Brief Historical Sketch4
 1.4An Example of a Computer Algebra System: MAPLE11
Ch. 2Algebra of Polynomials, Rational Functions, and Power Series 
 2.2Rings and Fields23
 2.3Divisibility and Factorization in Integral Domains26
 2.4The Euclidean Algorithm32
 2.5Univariate Polynomial Domains38
 2.6Multivariate Polynomial Domains46
 2.7The Primitive Euclidean Algorithm52
 2.8Quotient Fields and Rational Functions60
 2.9Power Series and Extended Power Series63
 2.10Relationships among Domains70
Ch. 3Normal Forms and Algebraic Representations 
 3.2Levels of Abstraction79
 3.3Normal Form and Canonical Form80
 3.4Normal Forms for Polynomials84
 3.5Normal Forms for Rational Functions and Power Series88
 3.6Data Structures for Multiprecision Integers and Rational Numbers93
 3.7Data Structures for Polynomials, Rational Functions, and Power Series96
Ch. 4Arithmetic of Polynomials, Rational Functions, and Power Series 
 4.2Basic Arithmetic Algorithms112
 4.3Fast Arithmetic Algorithms: Karatsuba's Algorithm118
 4.4Modular Representations120
 4.5The Fast Fourier Transform123
 4.6The Inverse Fourier Transform128
 4.7Fast Polynomial Multiplication132
 4.8Computing Primitive N-th Roots of Unity133
 4.9Newton's Iteration for Power Series Division136
Ch. 5Homomorphisms and Chinese Remainder Algorithms 
 5.2Intermediate Expression Swell: An Example151
 5.3Ring Morphisms153
 5.4Characterization of Morphisms160
 5.5Homomorphic Images167
 5.6The Integer Chinese Remainder Algorithm174
 5.7The Polynomial Interpolation Algorithm183
 5.8Further Discussion of the Two Algorithms189
Ch. 6Newton's Iteration and the Hensel Construction 
 6.2P-adic and Ideal-adic Representations205
 6.3Newton's Iteration for F(u)=0214
 6.4Hensel's Lemma226
 6.5The Univariate Hensel Lifting Algorithm232
 6.6Special Techniques for the Non-monic Case240
 6.7The Multivariate Generalization of Hensel's Lemma250
 6.8The Multivariate Hensel Lifting Algorithm260
Ch. 7Polynomial GCD Computation 
 7.2Polynomial Remainder Sequences280
 7.3The Sylvester Matrix and Subresultants285
 7.4The Modular GCD Algorithm300
 7.5The Sparse Modular GCD Algorithm311
 7.6GCD's using Hensel Lifting: The EZ-GCD Algorithm314
 7.7A Heuristic Polynomial GCD Algorithm320
Ch. 8Polynomial Factorization 
 8.2Square-Free Factorization337
 8.3Square-Free Factorization Over Finite Fields343
 8.4Berlekamp's Factorization Algorithm347
 8.5The Big Prime Berlekamp Algorithm359
 8.6Distinct Degree Factorization368
 8.7Factoring Polynomials over the Rationals374
 8.8Factoring Polynomials over Algebraic Number Fields378
Ch. 9Solving Systems of Equations 
 9.2Linear Equations and Gaussian Elimination390
 9.3Fraction-Free Gaussian Elimination393
 9.4Alternative Methods for Solving Linear Equations399
 9.5Nonlinear Equations and Resultants405
Ch. 10Grobner Bases for Polynomial Ideals 
 10.2Term Orderings and Reduction431
 10.3Grobner Bases and Buchberger's Algorithm439
 10.4Improving Buchberger's Algorithm447
 10.5Applications of Grobner Bases451
 10.6Additional Applications462
Ch. 11Integration of Rational Functions 
 11.2Basic Concepts of Differential Algebra474
 11.3Rational Part of the Integral: Hermite's Method482
 11.4Rational Part of the Integral: Horowitz' Method488
 11.5Logarithmic Part of the Integral492
Ch. 12The Risch Integration Algorithm 
 12.2Elementary Functions512
 12.3Differentiation of Elementary Functions519
 12.4Liouville's Principle523
 12.5The Risch Algorithm for Transcendental Elementary Functions529
 12.6The Risch Algorithm for Logarithmic Extensions530
 12.7The Risch Algorithm for Exponential Extensions547
 12.8Integration of Algebraic Functions561

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