Polynomial Algorithms in Computer Algebra
For several years now I have been teaching courses in computer algebra at the Universitat Linz, the University of Delaware, and the Universidad de Alcala de Henares. In the summers of 1990 and 1992 I have organized and taught summer schools in computer algebra at the Universitat Linz. Gradually a se...
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Format:  eBook 
Language:  English 
Published: 
Vienna
Springer Vienna
1996, 1996

Edition:  1st ed. 1996 
Series:  Texts & Monographs in Symbolic Computation, A Series of the Research Institute for Symbolic Computation, Johannes Kepler University, Linz, Austria

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Collection:  Springer Book Archives 2004  Collection details see MPG.ReNa 
Table of Contents:
 10.1 Gosper’s algorithm
 10.2 Bibliographic notes
 11 Parametrization of algebraic curves
 11.1 Plane algebraic curves
 11.2 A parametrization algorithm
 11.3 Bibliographic notes
 Solutions of selected exercises
 References
 1 Introduction
 1.1 What is computer algebra?
 1.2 Program systems in computer algebra
 1.3 Algebraic preliminaries
 1.4 Representation of algebraic structures
 1.5 Measuring the complexity of algorithms
 1.6 Bibliographic notes
 2 Arithmetic in basic domains
 2.1 Integers
 2.2 Polynomials
 2.3 Quotient fields
 2.4 Algebraic extension fields
 2.5 Finite fields
 2.6 Bibliographic notes
 3 Computing by homomorphic images
 3.1 The Chinese remainder problem and the modular method
 3.2 padic approximation
 3.3 The fast Fourier transform
 3.4 Bibliographic notes
 4 Greatest common divisors of polynomials
 4.1 Polynomial remainder sequences
 4.2 A modular gcd algorithm
 4.3 Computation of resultants
 4.4 Squarefree factorization
 4.5 Squarefree partial fraction decomposition
 4.6 Integration of rational functions
 4.7 Bibliographic notes
 5 Factorization of polynomials
 5.1 Factorization over finite fields
 5.2 Factorization over the integers
 5.3 A polynomialtime factorization algorithm over the integers
 5.4 Factorization over algebraic extension fields
 5.5 Factorization over an algebraically closed field
 5.6 Bibliographic notes
 6 Decomposition of polynomials
 6.1 A polynomialtime algorithm for decomposition
 6.2 Bibliographic notes
 7 Linear algebra—solving linear systems
 7.1 Bareiss’s algorithm
 7.2 Hankel matrices
 7.3 Application of Hankel matrices to polynomial problems
 7.4 Bibliographic notes
 8 The method of Gröbner bases
 8.1 Reduction relations
 8.2 Polynomial reduction and Gröbner bases
 8.3 Computation of Gröbner bases
 8.4 Applications of Gröbner bases
 8.5 Speedups and complexity considerations
 8.6 Bibliographic notes
 9 Quantifier elimination in real closed fields
 9.1 The problem of quantifier elimination
 9.2 Cylindrical algebraic decomposition
 9.3 Bibliographic notes
 10 Indefinite summation