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Algorithms for Computer Algebra

  • Book
  • © 1992

Overview

Authors:
  1. K. O. Geddes

    1. University of Waterloo, Canada

  2. S. R. Czapor

    1. Laurentian University, Canada

  3. G. Labahn

    1. University of Waterloo, Canada

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About this book

Algorithms for Computer Algebra is the first comprehensive textbook to be published on the topic of computational symbolic mathematics. The book first develops the foundational material from modern algebra that is required for subsequent topics. It then presents a thorough development of modern computational algorithms for such problems as multivariate polynomial arithmetic and greatest common divisor calculations, factorization of multivariate polynomials, symbolic solution of linear and polynomial systems of equations, and analytic integration of elementary functions. Numerous examples are integrated into the text as an aid to understanding the mathematical development. The algorithms developed for each topic are presented in a Pascal-like computer language. An extensive set of exercises is presented at the end of each chapter.
Algorithms for Computer Algebra is suitable for use as a textbook for a course on algebraic algorithms at the third-year, fourth-year, or graduate level. Although the mathematical development uses concepts from modern algebra, the book is self-contained in the sense that a one-term undergraduate course introducing students to rings and fields is the only prerequisite assumed. The book also serves well as a supplementary textbook for a traditional modern algebra course, by presenting concrete applications to motivate the understanding of the theory of rings and fields.

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Table of contents (12 chapters)

  1. Front Matter

    Pages I-XVIII
    Download chapter PDF

  2. Introduction to Computer Algebra

    • K. O. Geddes, S. R. Czapor, G. Labahn
    Pages 1-22

  3. Algebra of Polynomials, Rational Functions, and Power Series

    • K. O. Geddes, S. R. Czapor, G. Labahn
    Pages 23-77

  4. Normal Forms and Algebraic Representations

    • K. O. Geddes, S. R. Czapor, G. Labahn
    Pages 79-109

  5. Arithmetic of Polynomials, Rational Functions, and Power Series

    • K. O. Geddes, S. R. Czapor, G. Labahn
    Pages 111-149

  6. Homomorphisms and Chinese Remainder Algorithms

    • K. O. Geddes, S. R. Czapor, G. Labahn
    Pages 151-203

  7. Newton’s Iteration and the Hensel Construction

    • K. O. Geddes, S. R. Czapor, G. Labahn
    Pages 205-277

  8. Polynomial GCD Computation

    • K. O. Geddes, S. R. Czapor, G. Labahn
    Pages 279-335

  9. Polynomial Factorization

    • K. O. Geddes, S. R. Czapor, G. Labahn
    Pages 337-388

  10. Solving Systems of Equations

    • K. O. Geddes, S. R. Czapor, G. Labahn
    Pages 389-428

  11. Gröbner Bases for Polynomial Ideals

    • K. O. Geddes, S. R. Czapor, G. Labahn
    Pages 429-471

  12. Integration of Rational Functions

    • K. O. Geddes, S. R. Czapor, G. Labahn
    Pages 473-510

  13. The Risch Integration Algorithm

    • K. O. Geddes, S. R. Czapor, G. Labahn
    Pages 511-573
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Reviews

`The Computer Algebra community has been waiting for years for this book to appear. ...the book is a masterpiece and can be recommended to everyone interested in the algorithms for computer algebra, either as a reference for further research or just to give the casual user an idea why things work as good (or as bad) as they do in computer algebra packages. ...the recommendation would be clear: Buy this book! As it stands now my only advice is to stay away from this book, because you might be tempted to buy it anyway (at least I was).'
Computer Algebra Nederland Newsletter, June 1993

Authors and Affiliations

  • University of Waterloo, Canada

    K. O. Geddes, G. Labahn

  • Laurentian University, Canada

    S. R. Czapor

Bibliographic Information

  • Book Title: Algorithms for Computer Algebra

  • Authors: K. O. Geddes, S. R. Czapor, G. Labahn

  • DOI: https://doi.org/10.1007/b102438

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1992

  • Hardcover ISBN: 978-0-7923-9259-0Published: 30 September 1992

  • Softcover ISBN: 978-1-4757-8323-0Published: 24 March 2013

  • eBook ISBN: 978-0-585-33247-5Published: 30 June 2007

  • Edition Number: 1

  • Number of Pages: XXII, 586

  • Topics: Mathematical Software, Image Processing and Computer Vision, Algebra, Symbolic and Algebraic Manipulation, Numeric Computing, Computer Science, general

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