Some Tapas of Computer Algebra

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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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.

• Interpolation
• Lattice
• Permutation
• algebra
• algorithms
• calculus
• computer algebra
• geometry
• combinatorics

"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

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

  Arjeh M. Cohen, Hans Cuypers, Hans Sterk

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