  It was established before that fusion rings in a rational conformal field
theory (RCFT) can be described as rings of polynomials, with integer
coefficients, modulo some relations. We use the Galois group of these relations
to obtain a local set of equation for the points of the fusion variety. These
equations are sufficient to classify all the RCFT, Galois group by Galois
group. It is shown that the Galois group is equivalent to the pseudo RCFT
group. We prove that the Galois groups encountered in RCFT are all abelian,
implying solvability by radicals of the modular matrix.
