Skip to Main content Skip to Navigation
Journal articles

Computing the Invariants of Finite Abelian Groups

Evelyne Hubert 1 George Labahn 2 
1 AROMATH - AlgebRe, geOmetrie, Modelisation et AlgoriTHmes
CRISAM - Inria Sophia Antipolis - Méditerranée , NKUA - National and Kapodistrian University of Athens
2 Symbolic Computation Group
SCG - Symbolic Computation Group
Abstract : We investigate the computation and applications of rational invariants of the linear action of a finite abelian group in the non-modular case. By diagonalization, the group action is accurately described by an integer matrix of exponents. We make use of linear algebra to compute a minimal generating set of invariants and the substitution to rewrite any invariant in terms of this generating set. We show how to compute a minimal generating set that consists of polynomial invariants. As an application, we provide a symmetry reduction scheme for polynomial systems whose solution set is invariant by a finite abelian group action. Finally, we also provide an algorithm to find such symmetries given a polynomial system.
Document type :
Journal articles
Complete list of metadata

Cited literature [36 references]  Display  Hide  Download
Contributor : Evelyne Hubert Connect in order to contact the contributor
Submitted on : Tuesday, October 21, 2014 - 5:18:47 PM
Last modification on : Friday, July 8, 2022 - 10:08:41 AM
Long-term archiving on: : Thursday, January 22, 2015 - 10:55:34 AM


Files produced by the author(s)




Evelyne Hubert, George Labahn. Computing the Invariants of Finite Abelian Groups. Mathematics of Computation, American Mathematical Society, 2016, 85 (302), pp.3029-3050. ⟨10.1090/mcom/3076⟩. ⟨hal-00921905v4⟩



Record views


Files downloads