Computer Algebra

Symbolic and Algebraic Computation

  • Bruno Buchberger
  • George Edwin Collins
  • Rüdiger Loos

Part of the Computing Supplementum book series (COMPUTING, volume 4)

Table of contents

  1. Front Matter
    Pages I-VII
  2. R. Loos
    Pages 1-10
  3. B. Buchberger, R. Loos
    Pages 11-43
  4. A. C. Norman
    Pages 57-69
  5. J. C. Lafon
    Pages 71-77
  6. G. E. Collins, R. Loos
    Pages 83-94
  7. E. Kaltofen
    Pages 95-113
  8. M. Lauer
    Pages 139-168
  9. A. C. Norman
    Pages 169-172
  10. R. Loos
    Pages 173-187
  11. G. E. Collins, M. Mignotte, F. Winkler
    Pages 189-220
  12. J. A. van Hulzen, J. Calmet
    Pages 221-243
  13. J. Calmet, J. A. van Hulzen
    Pages 245-258
  14. M. Mignotte
    Pages 259-263
  15. Back Matter
    Pages 265-285

About this book

Introduction

The journal Computing has established a series of supplement volumes the fourth of which appears this year. Its purpose is to provide a coherent presentation of a new topic in a single volume. The previous subjects were Computer Arithmetic 1977, Fundamentals of Numerical Computation 1980, and Parallel Processes and Related Automata 1981; the topic of this 1982 Supplementum to Computing is Computer Algebra. This subject, which emerged in the early nineteen sixties, has also been referred to as "symbolic and algebraic computation" or "formula manipulation". Algebraic algorithms have been receiving increasing interest as a result of the recognition of the central role of algorithms in computer science. They can be easily specified in a formal and rigorous way and provide solutions to problems known and studied for a long time. Whereas traditional algebra is concerned with constructive methods, computer algebra is furthermore interested in efficiency, in implementation, and in hardware and software aspects of the algorithms. It develops that in deciding effectiveness and determining efficiency of algebraic methods many other tools - recursion theory, logic, analysis and combinatorics, for example - are necessary. In the beginning of the use of computers for symbolic algebra it soon became apparent that the straightforward textbook methods were often very inefficient. Instead of turning to numerical approximation methods, computer algebra studies systematically the sources of the inefficiency and searches for alternative algebraic methods to improve or even replace the algorithms.

Keywords

algebra computer algebra computeralgebra

Editors and affiliations

  • Bruno Buchberger
    • 1
  • George Edwin Collins
    • 2
  • Rüdiger Loos
    • 3
  1. 1.Institut für MathematikJohannes Kepler Universität LinzAustria
  2. 2.Computer Science DepartmentUniversity of Wisconsin-MadisonMadisonUSA
  3. 3.Institut für Informatik IUniversität KarlsruheFederal Republic of Germany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-7091-3406-1
  • Copyright Information Springer-Verlag Vienna 1982
  • Publisher Name Springer, Vienna
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-211-81684-4
  • Online ISBN 978-3-7091-3406-1
  • Series Print ISSN 0344-8029
  • About this book