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Theory of algebraic invariants

Author: David Hilbert; Bernd Sturmfels
Publisher: Cambridge [England] ; New York, NY, USA : Cambridge University Press, 1993.
Series: Cambridge mathematical library.
Edition/Format:   Print book : EnglishView all editions and formats
Database:WorldCat
Summary:

An English translation of the notes from David Hilbert's course in 1897 on Invariant Theory at the University of Gottingen taken by his student Sophus Marxen.

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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: David Hilbert; Bernd Sturmfels
ISBN: 0521449030 9780521449038 0521444578 9780521444576
OCLC Number: 27935089
Language Note: Translated from the German R. C. Laubenbacher.
Description: xiv, 191 pages : illustrations ; 23 cm.
Contents: I. The elements of invariant theory. I.1. The forms. I.2. The linear transformation. I.3. The concept of an invariant. I.4. Properties of invariants and covariants. I.5. The operation symbols D and [Delta]. I.6. The smallest system of conditions for the determination of the invariants and covariants. I.7. The number of invariants of degree g. I.8. The invariants and covariants of degrees two and three. I.9. Simultaneous invariants and covariants. I.10. Covariants of covariants. I.11. The invariants and covariants as functions of the roots. I.12. The invariants and covariants as functions of the one-sided derivatives. I.13. The symbolic representation of invariants and covariants --
II. The theory of invariant fields. II. 1. Proof of the finiteness of the full invariant system via representation by root differences. II. 2. A generalizable proof for the finiteness of the full invariant system. II. 3. The system of invariants I; I[subscript 1], I[subscript 2] ..., I[subscript k]. II. 4. The vanishing of the invariants. II. 5. The ternary nullform. II. 6. The finiteness of the number of irreducible syzygies and of the syzygy chain. II. 7. The inflection point problem for plane curves of order three. II. 8. The generalization of invariant theory. II. 9. Observations about new types of coordinates.
Series Title: Cambridge mathematical library.
Responsibility: David Hilbert ; translated by Reinhard C. Laubenbacher ; [edited by Reinhard C. Laubenbacher ; with an introduction by Bernd Sturmfels].
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