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Rational invariants of even degree polynomials under the orthogonal group

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arxiv 2501.17504 v2 pith:PGRTZBT3 submitted 2025-01-29 math.AC

Henri Breloer This is my paper · ORCID
classification math.AC
keywords degreeevengroupinvariantsorthogonalpolynomialsproblemrational
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abstract

In this article, we construct a generating set of rational invariants for the action of the orthogonal group $\text{O}(n)$ on the space $\mathbb{R}[x_1,\dots,x_n]_{2d}$ of real homogeneous polynomials of even degree $2d$. This generalizes a paper which addressed the case $n=3$. The main difficult with the generalization lies in a surprising connection to the graph isomorphism problem, a classical problem of computer science.

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  1. Simple generators of rational function fields

    cs.SC 2026-02 conditional novelty 7.0 of 10

    A new randomized algorithm computes simpler generators of rational function fields by interpolating only low-degree Gröbner coefficients and searching for low-degree polynomial elements.

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