Some Tapas of Computer Algebra

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.

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

Résumé

"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

Contenu

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.- Project 1. Automatic Geometry Theorem Proving.- Project 2. The Birkhoff Interpolation Problem.- Project 3. The Inverse Kinematics Problem in Robotics.- Project 4. Quaternion Algebras.- Project 5. Explorations with the Icosahedral Group.- Project 6. The Small Mathieu Groups.- Project 7: The Golay Codes.