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Using extended Derksen ideals in computational invariant theory.
- Source :
-
Journal of Symbolic Computation . Jan2016, Vol. 72, p161-181. 21p. - Publication Year :
- 2016
-
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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 07477171
- Volume :
- 72
- Database :
- Academic Search Index
- Journal :
- Journal of Symbolic Computation
- Publication Type :
- Academic Journal
- Accession number :
- 108342990
- Full Text :
- https://doi.org/10.1016/j.jsc.2015.02.004