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Computational Invariant Theory
Buch von Gregor Kemper (u. a.)
Sprache: Englisch

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Beschreibung
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.
More than ten years after the first publication of the book, the second edition now provides a major update and covers many recent developments in the field. Among the roughly 100 added pages there are two appendices, authored by Vladimir Popov, and an addendum by Norbert A'Campo and Vladimir Popov.
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.
More than ten years after the first publication of the book, the second edition now provides a major update and covers many recent developments in the field. Among the roughly 100 added pages there are two appendices, authored by Vladimir Popov, and an addendum by Norbert A'Campo and Vladimir Popov.
Inhaltsverzeichnis

Preface.- 1 Constructive Ideal Theory.- 2 Invariant Theory.- 3 Invariant Theory of Finite Groups.- 4 Invariant Theory of Reductive Groups.- 5 Applications of Invariant Theory.- A. Linear Algebraic Groups.- B. Is one of the two Orbits in the Closure of the Other? by V.L.Popov.- C. Stratification of the Nullcone by V.L.Popov.- Addendum to C. The Source Code of HNC by N.A'Campo and V.L.Popov.- Notation.- Index.

Details
Erscheinungsjahr: 2016
Fachbereich: Arithmetik & Algebra
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Seiten: 388
Reihe: Encyclopaedia of Mathematical Sciences
Inhalt: xxii
366 S.
13 farbige Illustr.
366 p. 13 illus. in color.
ISBN-13: 9783662484203
ISBN-10: 366248420X
Sprache: Englisch
Herstellernummer: 978-3-662-48420-3
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Kemper, Gregor
Derksen, Harm
Auflage: 2nd ed. 2015
Hersteller: Springer Berlin
Springer Berlin Heidelberg
Encyclopaedia of Mathematical Sciences
Maße: 241 x 160 x 27 mm
Von/Mit: Gregor Kemper (u. a.)
Erscheinungsdatum: 06.01.2016
Gewicht: 0,746 kg
preigu-id: 104292471
Inhaltsverzeichnis

Preface.- 1 Constructive Ideal Theory.- 2 Invariant Theory.- 3 Invariant Theory of Finite Groups.- 4 Invariant Theory of Reductive Groups.- 5 Applications of Invariant Theory.- A. Linear Algebraic Groups.- B. Is one of the two Orbits in the Closure of the Other? by V.L.Popov.- C. Stratification of the Nullcone by V.L.Popov.- Addendum to C. The Source Code of HNC by N.A'Campo and V.L.Popov.- Notation.- Index.

Details
Erscheinungsjahr: 2016
Fachbereich: Arithmetik & Algebra
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Seiten: 388
Reihe: Encyclopaedia of Mathematical Sciences
Inhalt: xxii
366 S.
13 farbige Illustr.
366 p. 13 illus. in color.
ISBN-13: 9783662484203
ISBN-10: 366248420X
Sprache: Englisch
Herstellernummer: 978-3-662-48420-3
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Kemper, Gregor
Derksen, Harm
Auflage: 2nd ed. 2015
Hersteller: Springer Berlin
Springer Berlin Heidelberg
Encyclopaedia of Mathematical Sciences
Maße: 241 x 160 x 27 mm
Von/Mit: Gregor Kemper (u. a.)
Erscheinungsdatum: 06.01.2016
Gewicht: 0,746 kg
preigu-id: 104292471
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