Computation of invariants of finite abelian groups
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- by Evelyne Hubert and George Labahn PDF
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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 nonmodular case. By diagonalization, such a group action can be described by integer matrices of orders and exponents. We make use of integer linear algebra to compute a minimal generating set of invariants along with the substitution needed to rewrite any invariant in terms of this generating set. In addition, we show how to construct a minimal generating set that consists only 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.References
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Additional Information
- Evelyne Hubert
- Affiliation: INRIA Méditerranée, 06902 Sophia Antipolis, France
- MR Author ID: 626362
- Email: evelyne.hubert@inria.fr
- George Labahn
- Affiliation: Cheriton School of Computer Science, University of Waterloo, Waterloo, ON, Canada N2L 3G1
- MR Author ID: 108900
- Email: glabahn@uwaterloo.ca
- Received by editor(s): January 24, 2014
- Received by editor(s) in revised form: September 4, 2014, and April 27, 2015
- Published electronically: January 14, 2016
- © Copyright 2016 American Mathematical Society
- Journal: Math. Comp. 85 (2016), 3029-3050
- MSC (2010): Primary 13A50, 15A72; Secondary 12Y05, 13P25, 13P15, 14L30
- DOI: https://doi.org/10.1090/mcom/3076
- MathSciNet review: 3522980