A database of invariant rings. (English) Zbl 1009.13002

Kemper, Gregor; Körding, Elmar; Malle, Gunter; Matzat, B. Heinrich; Vogel, Denis

Exp. Math. 10, No. 4, 537-542 (2001).

The paper describes a database of invariant rings created by the authors. Because of a permanent interest in computational aspects of invariant theory of finite groups they have decided to assemble a collection of examples in form of a database available to the public under ftp://ftp.iwr.uni-heidelberg.de/pub/kemper/DataBase. The computations for the data were done in the computer algebra system Magma. The structure of the database is oriented by Noether’s degree bound, the bound of generators of the Hilbert ideal, respectively the search for particular examples. In fact a user has several powerful retrieval functions and should be able to manipulate the retrieved data and not just to look at them.
In the database the authors provide access functions that take boolean-valued functions in the computer algebra systems Magma or Maple as argument. Users can define search criteria with such functions. The tools are illustrated by an example session documented in the paper.
Finally the authors use the database in order to review several conjectures in invariant theory, in particular in the modular case. Whence, the database provides a tool for researchers in invariant theory. For a theoretical background see also H. Derksen and G. Kemper, “Computational invariant theory” [Encyclopedia of Math. Sciences (Berlin 2002; Zbl 1011.13003)].

Reviewer: Peter Schenzel (Halle)

MSC:

13A50	Actions of groups on commutative rings; invariant theory
13P99	Computational aspects and applications of commutative rings

Keywords:

database of invariant rings; Magma; rings of invariants; finite groups; database

Citations:

Zbl 1011.13003

Software:

Magma; Maple

References:

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