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Rational Invariants of a Group Action. Construction and Rewriting

Abstract : Geometric constructions applied to a rational action of an algebraic group lead to a new algorithm for computing rational invariants. A finite generating set of invariants appears as the coefficients of a reduced Gröbner basis. The algorithm comes in two variants. In the first construction the ideal of the graph of the action is considered. In the second one the ideal of a cross-section is added to the ideal of the graph. Zero-dimensionality of the resulting ideal brings a computational advantage. In both cases, reduction with respect to the computed Gröbner basis allows us to express any rational invariant in terms of the generators.
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Contributor : Evelyne Hubert <>
Submitted on : Tuesday, December 18, 2007 - 9:20:12 AM
Last modification on : Thursday, August 22, 2019 - 1:13:24 AM

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Evelyne Hubert, Irina Kogan. Rational Invariants of a Group Action. Construction and Rewriting. Journal of Symbolic Computation, Elsevier, 2007, Effective Methods in Algebraic Geometry (MEGA 2005), 42 (1-2), pp.203-217. ⟨10.1016/j.jsc.2006.03.005⟩. ⟨inria-00198847⟩



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