TY  - GEN
AU  - Derksen, Harm 
AU  - Kemper, Gregor
TI  - Computational invariant theory
SN  - 9783642077968
U1  - 512.5 DER 
PY  - 2002///
CY  - Berlin
PB  - Springer-Verlag
KW  - Gröbner basis
KW  - Invariant theory
KW  - algorithms
KW  - coding theory
KW  - computational commutative algebra
KW  - geometry
N1  - Includes References, Notations and Index
N2  - 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.   

https://link.springer.com/book/10.1007/978-3-662-04958-7
ER  -