From: kogeddes@daisy.uwaterloo.ca (Keith O. Geddes)
Subject: Re: Computer Algebra book?
Organization: University of Waterloo
Date: Sat, 3 Oct 1992 17:41:19 GMT

In article <JAFFER.92Oct1220940@camelot.ai.mit.edu> jaffer@zurich.ai.mit.edu (Aubrey Jaffer) writes:
>In article <Bv336K.8L6@news.cso.uiuc.edu> gaylord@ux1.cso.uiuc.edu (Richard J. Gaylord) writes:
>
>   i just called kluwer (617-871-6600) and  the book "Algorithms for
>   Computer Algebra"  ...
	. . .
	. . .
>
> ... Can someone post the table of contents?



            ALGORITHMS FOR COMPUTER ALGEBRA

            K.O. Geddes, S.R. Czapor, and G. Labahn

            Kluwer Academic Publishers, Boston, 1992, 585 pages
            ISBN 0-7923-9259-0

CONTENTS

Chapter 1  Introduction to Computer Algebra
      1.1  Introduction
      1.2  Symbolic versus Numeric Computation
      1.3  A Brief Historical Sketch
      1.4  An Example of a Computer Algebra System: MAPLE
             Exercises

Chapter 2  Algebra of Polynomials, Rational Functions, and Power Series
      2.1  Introduction
      2.2  Rings and Fields
      2.3  Divisibility and Factorization in Integral Domains
      2.4  The Euclidean Algorithm
      2.5  Univariate Polynomial Domains
      2.6  Multivariate Polynomial Domains
      2.7  The Primitive Euclidean Algorithm
      2.8  Quotient Fields and Rational Functions
      2.9  Power Series and Extended Power Series
      2.10 Relationships among Domains
             Exercises

Chapter 3  Normal Forms and Algebraic Representations
      3.1  Introduction
      3.2  Levels of Abstraction
      3.3  Normal Form and Canonical Form
      3.4  Normal Forms for Polynomials
      3.5  Normal Forms for Rational Functions and Power Series
      3.6  Data Structures for Multiprecision Integers and Rational Numbers
      3.7  Data Structures for Polynomials, Rational Functions,
             and Power Series
             Exercises

Chapter 4  Arithmetic of Polynomials, Rational Functions, and Power Series
      4.1  Introduction
      4.2  Basic Arithmetic Algorithms
      4.3  Fast Arithmetic Algorithms:  Karatsuba's Algorithm
      4.4  Modular Representations
      4.5  The Fast Fourier Transform
      4.6  The Inverse Fourier Transform
      4.7  Fast Polynomial Multiplication
      4.8  Computing Primitive N-th Roots of Unity
      4.9  Newton's Iteration for Power Series Division
             Exercises

Chapter 5  Homomorphisms and Chinese Remainder Algorithms
      5.1  Introduction
      5.2  Intermediate Expression Swell:  An Example
      5.3  Ring Morphisms
      5.4  Characterization of Morphisms
      5.5  Homomorphic Images
      5.6  The Integer Chinese Remainder Algorithm
      5.7  The Polynomial Interpolation Algorithm
      5.8  Further Discussion of the Two Algorithms
             Exercises

Chapter 6  Newton's Iteration and the Hensel Construction
      6.1  Introduction
      6.2  P-adic and Ideal-adic Representations
      6.3  Newton's Iteration for F(u)=0
      6.4  Hensel's Lemma
      6.5  The Univariate Hensel Lifting Algorithm
      6.6  Special Techniques for the Non-monic Case
      6.7  The Multivariate Generalization of Hensel's Lemma
      6.8  The Multivariate Hensel Lifting Algorithm
             Exercises

Chapter 7  Polynomial GCD Computation
      7.1  Introduction
      7.2  Polynomial Remainder Sequences
      7.3  The Sylvester Matrix and Subresultants
      7.4  The Modular GCD Algorithm
      7.5  The Sparse Modular GCD Algorithm
      7.6  GCD's using Hensel Lifting:  The EZ-GCD Algorithm
      7.7  A Heuristic Polynomial GCD Algorithm
             Exercises

Chapter 8  Polynomial Factorization
      8.1  Introduction
      8.2  Square-Free Factorization
      8.3  Square-Free Factorization Over Finite Fields
      8.4  Berlekamp's Factorization Algorithm
      8.5  The Big-Prime Berlekamp Algorithm
      8.6  Distinct Degree Factorization
      8.7  Factoring Polynomials over the Rationals
      8.8  Factoring Polynomials over Algebraic Number Fields
             Exercises

Chapter 9   Solving Systems of Equations
      9.1  Introduction
      9.2  Linear Equations and Gaussian Elimination
      9.3  Fraction-Free Gaussian Elimination
      9.4  Alternative Methods for Solving Linear Equations
      9.5  Nonlinear Equations and Resultants
             Exercises

Chapter 10  Groebner Bases for Polynomial Ideals
      10.1  Introduction
      10.2  Term Orderings and Reduction
      10.3  Groebner Bases and Buchberger's Algorithm
      10.4  Improving Buchberger's Algorithm
      10.5  Applications of Groebner Bases
      10.6  Additional Applications
              Exercises

Chapter 11  Integration of Rational Functions
      11.1  Introduction
      11.2  Basic Concepts of Differential Algebra
      11.3  Rational Part of the Integral:  Hermite's Method
      11.4  Rational Part of the Integral:  Horowitz' Method
      11.5  Logarithmic Part of the  Integral
              Exercises

Chapter 12  The Risch Integration Algorithm
      12.1  Introduction
      12.2  Elementary Functions
      12.3  Differentiation of Elementary Functions
      12.4  Liouville's Principle
      12.5  The Risch Algorithm for Transcendental Elementary Functions
      12.6  The Risch Algorithm for Logarithmic Extensions
      12.7  The Risch Algorithm for Exponential Extensions
      12.8  Integration of Algebraic Functions
              Exercises