Algorithms in invariant theory /
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| Author / Creator: | Sturmfels, Bernd, 1962- |
|---|---|
| Imprint: | Wien ; New York : Springer-Verlag, c1993. |
| Description: | 197 p. : ill. ; 25 cm. |
| Language: | English |
| Series: | Texts and monographs in symbolic computation |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/1515364 |
Table of Contents:
- 1. Introduction. 1.1. Symmetric polynomials. 1.2. Grobner bases. 1.3. What is invariant theory? 1.4. Torus invanants and integer programming
- 2. Invariant theory of finite groups. 2.1. Finiteness and degree bounds. 2.2. Counting the number of invariants. 2.3. The Cohen-Macaulay property. 2.4. Reflection groups. 2.5. Algorithms for computing fundamental invariants. 2.6. Grobner bases under finite group action. 2.7. Abelian groups and permutation groups
- 3. Bracket algebra and projective geometry. 3.1. The straightening algorithm. 3.2. The first fundamental theorem. 3.3. The Grassmann-Cayley algebra. 3.4. Applications to projective geometry. 3.5. Cayley factorization. 3.6. Invariants and covariants of binary forms. 3.7. Gordan's finiteness theorem
- 4. Invariants of the general linear group. 4.1. Representation theory of the general linear group. 4.2. Binary forms revisited. 4.3. Cayley's [Omega]-process and Hilbert finiteness theorem. 4.4. Invariants and covariants of forms. 4.5. Lie algebra action and the symbolic method. 4.6. Hilbert's algorithm. 4.7. Degree bounds.