MiS Preprint Repository

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.