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MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
45/2017

Rational invariants of ternary forms under the orthogonal group

Paul Görlach, Evelyne Hubert and Théo Papadopoulo

Abstract

We study the action of the orthogonal group on the vector space $\mathbb{R}[x,y,z]_{2d}$ of ternary forms of fixed even degree from the perspective of Computational Rational Invariant Theory. Employing a technique known as the Slice Method, we determine a minimal generating set of rational invariants by specifying their restriction to a characterizing subspace. For these invariants, we give efficient solutions to the basic algorithmic problems of evaluation, rewriting and reconstruction. The constructiveness of the approach is based on the explicit construction of symmetric bases for the spaces of harmonic polynomials of fixed degree.

Received:
Aug 1, 2017
Published:
Aug 10, 2017
Keywords:
rational invariants, Orthogonal group

Related publications

inJournal
2019 Repository Open Access
Paul Görlach, Evelyne Hubert and Théo Papadopoulo

Rational invariants of even ternary forms under the orthogonal group

In: Foundations of computational mathematics, 19 (2019) 6, pp. 1315-1361