Genericity of Assumption (J2)

Let $F(\mathbf{z})=G(\mathbf{z})/H(\mathbf{z})$ be a rational function, and let Assumption (J2) denote the Jacobian nondegeneracy condition used in the paper's critical-point system. Genericity conjecture. Assumption (J2) holds generically. This is used to ensure that the relevant polynomial system has finitely many solutions and hence that the algorithm can determine the critical points; the source gives no resolution, so the genericity assertion remains open.