Symmetries of large systems of differential equations

Hereman, Marchildon and Grundland have earlier reported on an investigation of Lie point symmetries of two systems of nonlinear partial differential equations, both representing classical field theories. Determining equations (more than 200 of them) associated with the first system (coupled electromagnetic and complex scalar fields) were solved completely. Here I develop the general solution of determining equations associated with the second system (coupled electromagnetic and Weyl spinor fields). The method used to solve these determining equations can likely be adapted to other related problems. (orig.)