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.

Preface.- Chapt. 1. Gröbner Bases, an Introduction by A.M.Cohen.- Chapt. 2. Symbolic Recipes for Polynomial System Solving by L.Gonzalez-Vega, F.Rouillier, M.-F.Roy.- Chapt. 3. Lattice Reduction by F.Beukers.- Chapt. 4. Factorization of Polynomials by F.Beukers.- Chapt. 5. Computation in Associative and Lie Algebras by G.Ivanyos and L.Rónyai.- Chapt. 6. Symbolic Recipes for Real Solutions by L.Gonzalez-Vega, F.Rouillier, M.-F.Roy, G.Trujillo.- Chapt. 7. Gröbner Bases and Integer Programming by G.M.Ziegler.- Chapt. 8. Working With Finite Groups by H.Cuypers, L.H.Soicher, H.Sterk.- Chapt.9. Symbolic Analysis of Differential Equations by M.van der Put.- Chapt. 10. Gröbner Bases for Codes by M. de Boer, R.Pellikaan.- Chapt. 11. Gröbner Bases for Decoding by M. de Boer, R.Pellikaan.- Project 1. Automatic Geometry Theorem Proving by T.Recio, H.Sterk, M.P.Vélez.- Project 2. The Birkhoff Interpolation Problem by M.-J. Gonzalez-Lopez, L.Gonzalez-Vega.- Project 3. The Inverse Kinematics Problem in Robotics by M.-J.Gonzalez-Lopez, L.Gonzalez-Vega.- Project 4. Quaternion Algebras by G.Ivanyos, L. Rónyai.- Project 5. Explorations with the Icosahedral Group by A.M.Cohen, H.Cuypers, R.Riebeek.- Project 6. The Small Mathieu Groups by H.Cuypers, L.H.Soicher, H.Sterk.- Project 7. The Golay Codes by M. de Boer, R.Pellikaan