Invariant Algebraic Sets and Symmetrization of Polynomial Systems

Evelyne Hubert 1
1 AROMATH - AlgebRe, geOmetrie, Modelisation et AlgoriTHmes
CRISAM - Inria Sophia Antipolis - Méditerranée , 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.
Complete list of metadatas

Cited literature [30 references]  Display  Hide  Download

https://hal.inria.fr/hal-01254954
Contributor : Evelyne Hubert <>
Submitted on : Tuesday, September 25, 2018 - 11:07:06 AM
Last modification on : Friday, November 9, 2018 - 2:42:02 AM
Long-term archiving on : Wednesday, December 26, 2018 - 4:22:42 PM

File

Hal01254954v4.pdf
Files produced by the author(s)

Identifiers

Collections

Citation

Evelyne Hubert. Invariant Algebraic Sets and Symmetrization of Polynomial Systems. Journal of Symbolic Computation, Elsevier, In press, ⟨10.1016/j.jsc.2018.09.002⟩. ⟨hal-01254954v4⟩

Share

Metrics

Record views

369

Files downloads

121