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, 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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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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