Invariant algebraic sets and symmetrization of polynomial systems
type: Item
instance of: scholarly article
title: Invariant algebraic sets and symmetrization of polynomial systems
zbMATH Open document ID: 1433.13004
author: Evelyne Hubert
published in: Journal of Symbolic Computation
publication date: 2019-06-28T00:00:00Z
full work available at URL: Hal01254954v4.pdf
review text: Consider the variety \(V \subset \mathbb{C}^n\) of a finite set of polynomials \(F \subset \mathbb{C}[z_1,\ldots ,z_n]\). Then one observes that \(V\) may be invariant under the action of a group \(G\) independent of the polynomial set \(F\). The aim of this paper is to construct a set of invariants that define the same variety \(V\), but outside of some proper subvariety of \(V\). For this, the considered group actions as well as the notion of section of degree \(e\) to the orbits are defined. It has been shown that the coefficients of a reduced Gröbner basis of the orbit-section ideal is a finite set of generating rational invariants. Then, one is able to give a constructive definition of symmetrization w.r.t. a given section to the orbits. Now a set of invariant functions \(\tilde{F}\) (polynomials in the constructed set of generating rational invariants) can be constructed such that the zero set of \(F\) is the same as that of \(\tilde{F}\), except outside of some proper subvariety of \(V\).
reviewed by: Amir Hashemi
Mathematics Subject Classification ID: 13A50
Mathematics Subject Classification ID: 68W30
Mathematics Subject Classification ID: 13P10
zbMATH DE Number: 7074701
zbMATH Keywords: polynomial systems
zbMATH Keywords: symmetry
zbMATH Keywords: invariant theory
zbMATH Keywords: section
describes a project that uses: grobcov.lib
describes a project that uses: SINGULAR
MaRDI profile type: Publication
OpenAlex ID: W2732096052
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Wikidata QID: Q129143790
DOI: 10.1016/J.JSC.2018.09.002
description: scientific article; zbMATH DE number 7074701