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Rational invariants of scalings from Hermite normal forms

Evelyne Hubert 1, * George Labahn 2 
* Corresponding author
1 GALAAD - Geometry, algebra, algorithms
CRISAM - Inria Sophia Antipolis - Méditerranée , UNS - Université Nice Sophia Antipolis (1965 - 2019), CNRS - Centre National de la Recherche Scientifique : UMR6621
Abstract : Scalings form a class of group actions on affine spaces that have both theoretical and practical importance. A scaling is accurately described by an integer matrix. Tools from linear algebra are exploited to compute a minimal generating set of rational invariants, trivial rewriting and rational sections for such a group action. The primary tools used are Hermite normal forms and their unimodular multipliers. With the same line of ideas, a complete solution to the scaling symmetry reduction of a polynomial system is also presented.
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Submitted on : Monday, January 9, 2012 - 4:10:08 PM
Last modification on : Thursday, August 4, 2022 - 4:52:37 PM
Long-term archiving on: : Monday, November 19, 2012 - 1:01:17 PM


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Evelyne Hubert, George Labahn. Rational invariants of scalings from Hermite normal forms. International Conference on Symbolic and Algebraic Computation (ISSAC), Jul 2012, Grenoble, France. pp.219-226, ⟨10.1145/2442829.2442862⟩. ⟨hal-00657991⟩



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