Some tapas of computer algebra

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Table of contents:

1. Gröbner Bases, an Introduction
2. Symbolic Recipes for Polynomial System Solving
3. Lattice Reduction
4. Factorisation of Polynomials
5. Computations in Associative and Lie Algebras
6. Symbolic Recipes for Real Solutions
7. Gröbner Bases and Integer Programming
8. Working with Finite Groups
9. Symbolic Analysis of Differential Equations
10. Gröbner Bases for Codes
11. Gröbner Bases for Decoding
12. Automatic Geometry Theorem Proving
13. The Birkhoff Interpolation Problem
14. The Inverse Kinematics Problem in Robotics
15. Quaternion Algebras
16. Explorations with the Icosahedral Group
17. The Small Mathieu Groups
18. The Golay Codes

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.