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Journal Articles Mathematics of Computation Year : 2016

Computing the Invariants of Finite Abelian Groups

George Labahn
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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.
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Dates and versions

hal-00921905 , version 1 (22-12-2013)
hal-00921905 , version 2 (18-01-2014)
hal-00921905 , version 3 (20-01-2014)
hal-00921905 , version 4 (21-10-2014)

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