Computational Invariant Theory

  • Harm Derksen
  • Gregor Kemper
Part of the Encyclopaedia of Mathematical Sciences book series (EMS, volume 130)

Table of contents

  1. Front Matter
    Pages i-x
  2. Harm Derksen, Gregor Kemper
    Pages 1-5
  3. Harm Derksen, Gregor Kemper
    Pages 7-37
  4. Harm Derksen, Gregor Kemper
    Pages 39-72
  5. Harm Derksen, Gregor Kemper
    Pages 73-137
  6. Harm Derksen, Gregor Kemper
    Pages 139-207
  7. Harm Derksen, Gregor Kemper
    Pages 209-235
  8. Harm Derksen, Gregor Kemper
    Pages 237-246
  9. Back Matter
    Pages 247-268

About this book

Introduction

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.

Keywords

Gröbner basis Invariant theory algorithms coding theory computational commutative algebra geometry

Authors and affiliations

  • Harm Derksen
    • 1
  • Gregor Kemper
    • 2
  1. 1.Department of MathematicsUniversity of MichiganAnn ArborUSA
  2. 2.Institute for Scientific ComputingUniversity of HeidelbergHeidelbergGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-04958-7
  • Copyright Information Springer-Verlag Berlin Heidelberg 2002
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-07796-8
  • Online ISBN 978-3-662-04958-7
  • Series Print ISSN 0938-0396
  • About this book