# Minimal System of Generators and Syzygies of Centro-Affine Invariants and Covariants for Homogeneous Planar Cubic Differential Systems with Free Terms and Linear Part

## TL;DR

This paper describes a minimal generating set for the algebra of centro-affine covariants of homogeneous planar cubic differential systems with linear parts and free terms, using Gurevich's theorem to avoid complex determinant calculations.

## Contribution

It extends the known minimal generators to systems with free terms by applying Gurevich's theorem, simplifying the algebraic description.

## Key findings

- Explicit minimal generators for the algebra of covariants.
- Avoidance of Aronhold's identities through Gurevich's theorem.
- Enhanced understanding of invariants for cubic differential systems.

## Abstract

A minimal system of generators of the algebra of the centro-affine covariants for homogeneous planar cubic differential systems with linear part is known. With the help of the Gurevich theorem avoiding the Aronhold's identities based on the calculation of determinants, we describe the algebra of the centro-affne covariants for homogeneous planar cubic differential systems with free terms.