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Some Tapas of Computer Algebra

  • Textbook
  • © 1999

Overview

Editors:
  1. Arjeh M. Cohen

    1. Department of Mathematics and Computing Science, Eindhoven University of Technology, Eindhoven, The Netherlands

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  2. Hans Cuypers

    1. Department of Mathematics and Computing Science, Eindhoven University of Technology, Eindhoven, The Netherlands

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  3. Hans Sterk

    1. Department of Mathematics and Computing Science, Eindhoven University of Technology, Eindhoven, The Netherlands

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  • This is a unique, multi-topic introductory textbook on symbolic integration written for students

Part of the book series: Algorithms and Computation in Mathematics (AACIM, volume 4)

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Table of contents (18 chapters)

  1. Front Matter

    Pages I-XIV
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  2. Gröbner Bases, an Introduction

    • Arjeh M. Cohen
    Pages 1-33

  3. Symbolic Recipes for Polynomial System Solving

    • Laureano Gonzalez-Vega, Fabrice Rouillier, Marie-Françoise Roy
    Pages 34-65

  4. Lattice Reduction

    • Frits Beukers
    Pages 66-77

  5. Factorisation of Polynomials

    • Frits Beukers
    Pages 78-90

  6. Computations in Associative and Lie Algebras

    • Gábor Ivanyos, Lajos Rónyai
    Pages 91-120

  7. Symbolic Recipes for Real Solutions

    • Laureano Gonzalez-Vega, Fabrice Rouillier, Marie-Françoise Roy, Guadalupe Trujillo
    Pages 121-167

  8. Gröbner Bases and Integer Programming

    • Günter M. Ziegler
    Pages 168-183

  9. Working with Finite Groups

    • Hans Cuypers, Leonard H. Soicher, Hans Sterk
    Pages 184-207

  10. Symbolic Analysis of Differential Equations

    • Marius van der Put
    Pages 208-236

  11. Gröbner Bases for Codes

    • Mario de Boer, Ruud Pellikaan
    Pages 237-259

  12. Gröbner Bases for Decoding

    • Mario de Boer, Ruud Pellikaan
    Pages 260-275

  13. Automatic Geometry Theorem Proving

    • Tomas Recio, Hans Sterk, M. Pilar Vélez
    Pages 276-296

  14. The Birkhoff Interpolation Problem

    • Maria-Jose Gonzalez-Lopez, Laureano Gonzalez-Vega
    Pages 297-304

  15. The Inverse Kinematics Problem in Robotics

    • Maria-Jose Gonzalez-Lopez, Laureano Gonzalez-Vega
    Pages 305-310

  16. Quaternion Algebras

    • Gábor Ivanyos, Lajos Rónyai
    Pages 311-314

  17. Explorations with the Icosahedral Group

    • Arjeh M. Cohen, Hans Cuypers, Remko Riebeek
    Pages 315-322

  18. The Small Mathieu Groups

    • Hans Cuypers, Leonard H. Soicher, Hans Sterk
    Pages 323-337

  19. The Golay Codes

    • Mario de Boer, Ruud Pellikaan
    Pages 338-347

  20. Back Matter

    Pages 349-352
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Keywords

About this book

In the years 1994, 1995, two EIDMA mini courses on Computer Algebra were given at the Eindhoven University of Technology by, apart from ourselves, various invited lecturers. (EIDMA is the Research School 'Euler Institute for Discrete Mathematics and its Applications'.) The idea of the courses was to acquaint young mathematicians with algorithms and software for mathemat­ ical research and to enable them to incorporate algorithms in their research. A collection of lecture notes was used at these courses. When discussing these courses in comparison with other kinds of courses one might give in a week's time, Joachim Neubüser referred to our courses as 'tapas'. This denomination underlined that the courses consisted of appe­ tizers for various parts of algorithmic algebra; indeed, we covered such spicy topics as the link between Gröbner bases and integer programming, and the detection of algebraic solutions to differential equations. As a collection, the not es turned out to have some appeal of their own, which is the main reason why the idea came up of transforming them into book form. We feIt however, that the book should be distinguishable from a standard text book on computer algebra in that it retains its appetizing flavour by presenting a variety of topics at an accessible level with a view to recent developments.

Reviews

"Tapas are hors d'oeuvres or snacks in the Spanish cuisine. And really, the topics treated by various authors can be considered a great variety of appetizers, which reach from mild to hot ones. ... All in all a very recommendable book which by the way has the advantage that one can get in it easily at many places and may pick out for oneself the most interesting themes."

Reviewed by G.Kowol, Monatshefte der Mathematik 2003, Vol. 138, Issue 1

Editors and Affiliations

  • Department of Mathematics and Computing Science, Eindhoven University of Technology, Eindhoven, The Netherlands

    Arjeh M. Cohen, Hans Cuypers, Hans Sterk

Bibliographic Information

  • Book Title: Some Tapas of Computer Algebra

  • Editors: Arjeh M. Cohen, Hans Cuypers, Hans Sterk

  • Series Title: Algorithms and Computation in Mathematics

  • DOI: https://doi.org/10.1007/978-3-662-03891-8

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1999

  • Hardcover ISBN: 978-3-540-63480-5Published: 15 December 1998

  • Softcover ISBN: 978-3-642-08335-8Published: 09 October 2011

  • eBook ISBN: 978-3-662-03891-8Published: 09 March 2013

  • Series ISSN: 1431-1550

  • Edition Number: 1

  • Number of Pages: XIV, 352

  • Number of Illustrations: 2 b/w illustrations

  • Topics: Algorithms, Symbolic and Algebraic Manipulation, Algebra, Combinatorics

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