Some Tapas of Computer Algebra

This book arose from a series of courses on computer algebra which were given at Eindhoven Technical University. Its chapters present a variety of topics in computer algebra at an accessible (upper undergraduate/graduate) level with a view towards recent developments. For those wanting to acquaint themselves somewhat further with the material, the book also contains seven 'projects', which could serve as practical sessions related to one or more chapters.
The contributions focus on topics like Gröbner bases, real algebraic geometry, Lie algebras, factorisation of polynomials, integer programming, permutation groups, differential equations, coding theory, automatic theorem proving, and polyhedral geometry.
This book is a must-read for everybody interested in computer algebra.

Texte du rabat

This book presents the basic concepts and algorithms of computer algebra using practical examples that illustrate their actual use in symbolic computation. A wide range of topics are presented, including: Groebner bases, real algebraic geometry, lie algebras, factorization of polynomials, integer programming, permutation groups, differential equations, coding theory, automatic theorem proving, and polyhedral geometry. This book is a must read for anyone working in the area of computer algebra, symbolic computation, and computer science.

Contenu

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