REDUCE-Procedures for the Study of Adjoint Symmetries of Second-Order Differential Equations

Two REDUCE programs are presented which should be of assistance in computing and studying so-called adjoint symmetries of second-order ordinary differential equations. The first program essentially serves to construct the determining equations for adjoint symmetries, whose leading coefficients are allowed to be polynomial functions of the velocities. The second program runs various tests concerning the possible construction of a first integral or a Lagrangian for the given system.