Invariant algebraic sets and symmetrization of polynomial systems. (November 2019)

• Record Type: Journal Article
• Authors: Hubert, Evelyne
• Is Part Of: Journal of symbolic computation. Volume 95(2019)
• Page Start: 53
• Page End: 67
• Publication Date: 2019-11
• Subjects: Polynomial systems -- Symmetry -- Invariant theory -- Section; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2018.09.002
• Languages: English
• ISSNs: 0747-7171

Abstract

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.