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Algorithms in invariant theory. (English) Zbl 0802.13002
This monograph introduces to classical invariant theory from the perspective of computer algebra. The author presents algorithms for the computation of generators and relations of invariant rings of finite, special and general linear groups. Some of them are due to him. The main tool for these algorithms are Gröbner bases.
There are four chapters: 1. Introduction, 2. Invariant theory of finite groups, 3. Bracket algebra and projective geometry, 4. Invariants of the general linear group.
The book is well written, almost self-contained, and discusses several applications (e.g. to integer programming, projective geometry, Galois theory).

13A50 Actions of groups on commutative rings; invariant theory
68W30 Symbolic computation and algebraic computation
13P10 Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)
15A72 Vector and tensor algebra, theory of invariants