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.
Author(s): Arjeh M. Cohen (auth.), Arjeh M. Cohen, Hans Cuypers, Hans Sterk (eds.)
Series: Algorithms and Computation in Mathematics 4
Edition: 1
Publisher: Springer-Verlag Berlin Heidelberg
Year: 1999
Language: English
Pages: 352
City: Berlin; New York
Tags: Algorithms; Symbolic and Algebraic Manipulation; Algebra; Combinatorics
Front Matter....Pages I-XIV
Gröbner Bases, an Introduction....Pages 1-33
Symbolic Recipes for Polynomial System Solving....Pages 34-65
Lattice Reduction....Pages 66-77
Factorisation of Polynomials....Pages 78-90
Computations in Associative and Lie Algebras....Pages 91-120
Symbolic Recipes for Real Solutions....Pages 121-167
Gröbner Bases and Integer Programming....Pages 168-183
Working with Finite Groups....Pages 184-207
Symbolic Analysis of Differential Equations....Pages 208-236
Gröbner Bases for Codes....Pages 237-259
Gröbner Bases for Decoding....Pages 260-275
Automatic Geometry Theorem Proving....Pages 276-296
The Birkhoff Interpolation Problem....Pages 297-304
The Inverse Kinematics Problem in Robotics....Pages 305-310
Quaternion Algebras....Pages 311-314
Explorations with the Icosahedral Group....Pages 315-322
The Small Mathieu Groups....Pages 323-337
The Golay Codes....Pages 338-347
Back Matter....Pages 349-352
