Computational Invariant Theory

Derksen, Harm

ISBN 10: 3662049597 / ISBN 13: 9783662049594

Editore: Springer My Copy UK 2014-03, 2014

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Codice articolo 6666-IUK-9783662049594

Dati bibliografici

• Titolo: Computational Invariant Theory
• Editore: Springer My Copy UK 2014-03
• Data di pubblicazione: 2014
• Lingua: Inglese
• ISBN 10: 3662049597
• ISBN 13: 9783662049594
• Rilegatura: PF
• Condizione: New

Descrizione articolo

Riassunto

Invariant theory is a subject with a long tradition and an astounding abil­ ity to rejuvenate itself whenever it reappears on the mathematical stage. Throughout the history of invariant theory, two features of it have always been at the center of attention: computation and applications. This book is about the computational aspects of invariant theory. We present algorithms for calculating the invariant ring of a group that is linearly reductive or fi­ nite, including the modular case. These algorithms form the central pillars around which the book is built. To prepare the ground for the algorithms, we present Grabner basis methods and some general theory of invariants. Moreover, the algorithms and their behavior depend heavily on structural properties of the invariant ring to be computed. Large parts of the book are devoted to studying such properties. Finally, most of the applications of in­ variant theory depend on the ability to calculate invariant rings. The last chapter of this book provides a sample of applications inside and outside of mathematics.