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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Computation of invariants of finite abelian groups
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by Evelyne Hubert and George Labahn PDF
Math. Comp. 85 (2016), 3029-3050 Request permission

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.
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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