Using extended Derksen ideals in computational invariant theory. (January 2016)

• Record Type: Journal Article
• Authors: Kemper, Gregor
• Is Part Of: Journal of symbolic computation. Volume 72(2016)
• Page Start: 161
• Page End: 181
• Publication Date: 2016-01
• Subjects: Algorithmic invariant theory -- Multiplicative invariant theory -- Arithmetic invariant theory -- Invariantization; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2015.02.004
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: This paper contains three new algorithms for computing invariant rings. The first two apply to invariants of a finite group acting on a finitely generated algebra over a Euclidean ring. This may be viewed as a first step in "computational arithmetic invariant theory." As a special case, the algorithms can compute multiplicative invariant rings. The third algorithm computes the invariant ring of a reductive group acting on a vector space, and often performs better than the algorithms known to date. The main tool upon which two of the algorithms are built is a generalized version of an ideal that was already used by Derksen in his algorithm for computing invariants of linearly reductive groups. As a further application, these so-called extended Derksen ideals give rise to invariantization maps, which turn an arbitrary ring element into an invariant. For the most part, the algorithms of this paper have been implemented.