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Theory of Algebraic Invariants

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ISBN-10: 0521449030

ISBN-13: 9780521449038

Edition: 1993

Authors: David Hilbert, Bernd Sturmfels, Reinhard C. Laubenbacher

List price: $43.95
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Description:

In the summer semester of 1897 David Hilbert (1862-1943) gave an introductory course in Invariant Theory at the University of Gottingen. This book is an English translation of the handwritten notes taken from this course by Hilberts student Sophus Marxen. The year 1897 was the perfect time for Hilbert to present an introduction to invariant theory as his research in the subject had been completed. His famous finiteness theorem had been proved and published in two papers that changed the course of invariant theory dramatically and that laid the foundation for modern commutative algebra. Thus these lectures take into account both the old approach of his predecessors and his newer ideas. This…    
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Book details

List price: $43.95
Copyright year: 1993
Publisher: Cambridge University Press
Publication date: 11/26/1993
Binding: Paperback
Pages: 208
Size: 6.25" wide x 9.25" long x 0.50" tall
Weight: 0.638
Language: English

Preface
Introduction
The Elements of Invariant Theory
The forms
The linear transformation
The concept of an invariant
Properties of invariants and covariants
The operation symbols D and D
The smallest system of conditions for the determination of the invariants and covariants
The number of invariants of degree g
The invariants and covariants of degree two and three
Simultaneous invariants and covariants
Covariants of covariants
The invariants and covariants as functions of the roots
The invariants and covariants as functions of the one-sided derivatives
The symbolic representation of invariants and covariants
The Theory of Invariant Fields
Proof of the finitenesss of the full invariant system via representation by root differences
A generalizable proof for the finiteness of the full invariant system
The system of invariants I; I1, I2, ..., Ik
The vanishing of the invariants
The ternary nullform
The finiteness of the number of irreducible syzygies and of the syzygy chain
The inflection point problem for plane curves of order three
The generalization of invariant theory
Observations about new types of coordinates