Invariantization and Polynomial Systems with Symmetry

Evelyne Hubert (1)

1 GALAAD2 - Géométrie , Algèbre, Algorithmes

Assuming the variety of a polynomial set is invariant under a group action, we provide a set of invariants that define the same variety. The contribution is about infinite algebraic groups, the case of finite group being previously known. We introduce for those a new definition of the concept of algebraic invariantization. It is based on the construction of rational invariants by Hubert and Kogan (2007), a construction for which we provide here new simplified proofs.

Mots clés: Rational invariants; Symmetric polynomial system; Section; Group actions

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

Evelyne Hubert. Invariantization and Polynomial Systems with Symmetry. 2016. ⟨hal-01254954v1⟩