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Invariant Algebraic Sets and Symmetrization of Polynomial Systems

Evelyne Hubert 1
1 AROMATH - AlgebRe, geOmetrie, Modelisation et AlgoriTHmes
CRISAM - Inria Sophia Antipolis - Méditerranée , NKUA - National and Kapodistrian University of Athens
Abstract : Assuming the variety of a polynomial set is invariant under a group action, we construct a set of invariants that define the same variety. Our construction can be seen as a generalization of the previously known construction for finite groups. The result though has to be understood outside an invariant variety which is independent of the polynomial set considered. We introduce the symmetrizations of a polynomial that are polynomials in a generating set of rational invariants. The generating set of rational invariants and the symmetrizations are constructed w.r.t. a section to the orbits of the group action.
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Submitted on : Tuesday, September 25, 2018 - 11:07:06 AM
Last modification on : Thursday, November 26, 2020 - 3:50:03 PM
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Evelyne Hubert. Invariant Algebraic Sets and Symmetrization of Polynomial Systems. Journal of Symbolic Computation, Elsevier, 2019, 95, pp.53-67. ⟨10.1016/j.jsc.2018.09.002⟩. ⟨hal-01254954v4⟩



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