Computational Invariant Theory: v. 130 (Encyclopaedia of Mathematical Sciences) - Hardcover

Derksen, Harm; Kemper, Gregor

Hardcover

ISBN 10: 3540434763 ISBN 13: 9783540434764

Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K, 2002

Synopsis

This book, the first volume of a subseries on "Invariant Theory and Algebraic Transformation Groups", provides a comprehensive and up-to-date overview of the algorithmic aspects of invariant theory. Numerous illustrative examples and a careful selection of proofs make the book accessible to non-specialists.

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This book is about the computational aspects of invariant theory. Of central interest is the question how the invariant ring of a given group action can be calculated. Algorithms for this purpose form the main pillars around which the book is built. There are two introductory chapters, one on Gröbner basis methods and one on the basic concepts of invariant theory, which prepare the ground for the algorithms. Then algorithms for computing invariants of finite and reductive groups are discussed. Particular emphasis lies on interrelations between structural properties of invariant rings and computational methods. Finally, the book contains a chapter on applications of invariant theory, covering fields as disparate as graph theory, coding theory, dynamical systems, and computer vision. The book is intended for postgraduate students as well as researchers in geometry, computer algebra, and, of course, invariant theory. The text is enriched with numerous explicit examples which illustrate the theory and should be of more than passing interest.

Edition details

• Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
• Publication date: 2002
• Language: English
• ISBN 10: 3540434763
• ISBN 13: 9783540434764
• Binding: Hardcover
• Number of pages: 268