On computing joint invariants of vector fields

TL;DR

This paper presents a constructive, programmable version of the Frobenius integrability theorem, enabling effective computation of invariants of low-rank vector field groups and reproducing recent examples.

Contribution

It introduces a constructive approach to Frobenius integrability, facilitating the computation of joint invariants in a programmable manner.

Findings

Effective method for computing invariants of low-rank vector fields

Reproduction of examples from recent literature

Provides a constructive version of Frobenius integrability theorem

Abstract

A constructive version of the Frobenius integrability theorem -- that can be programmed effectively -- is given. This is used in computing invariants of groups of low ranks and recover examples from a recent paper of Boyko, Patera and Popoyvich \cite{BPP}.