Rational invariants of ternary forms under the orthogonal group

Paul Görlach, Evelyne Hubert, and Théo Papadopoulo

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Submission date: 01. Aug. 2017
published in: Foundations of computational mathematics, 19 (2019) 6, p. 1315-1361 
DOI number (of the published article): 10.1007/s10208-018-9404-1
Bibtex
with the following different title: Rational invariants of even ternary forms under the orthogonal group
Keywords and phrases: rational invariants, Orthogonal group
Link to arXiv: See the arXiv entry of this preprint.

Abstract:
We study the action of the orthogonal group on the vector space 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.