Computing necessary integrability conditions for planar parametrized homogeneous potentials

Alin Bostan, Thierry Combot, Safey El Din Mohab

Let $V\in\mathbb{Q}(i)(\a_1,\dots,\a_n)(\q_1,\q_2)$ be a rationally parametrized planar homogeneous potential of homogeneity degree $k\ne -2,0,2$. We design an algorithm that co…