Invariant Algebraic Sets and Symmetrization of Polynomial Systems

Evelyne Hubert (1)

1 AROMATH - AlgebRe, geOmetrie, Modelisation et AlgoriTHmes

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 once we introduce the symmetrizations of a polynomial w.r.t. a section to the orbits of the group action. The symmetrisations are polynomials in a generating set of rational invariants as constructed in [9]. The results have thus to be understood outside of a proper closed invariant variety, independent of the polynomial set considered.

Mots clés: Rational invariants; Polynomial systems with symmetry; Section

Domaines: Calcul formel [cs.SC]; Théorie des groupes [math.GR]; Algèbre commutative [math.AC]; Géométrie algébrique [math.AG]

Evelyne Hubert. Invariant Algebraic Sets and Symmetrization of Polynomial Systems. 2017. ⟨hal-01254954v3⟩