An improved method for obtaining the Ising partition function of n x n square grids with periodic boundary is presented. Our method applies results from Galois theory in order to split the computation into smaller parts and at the same time avoid the use of numerics. Using this method we have computed the exact partition function for the (320 x 320) grid, the ( 256 x 256 ) grid, and the ( 160 x 160 ) grid, as well as for a number of smaller grids. We obtain scaling parameters and compare with what theory prescribes.