The MAPLE package TDDS for computing Thomas decompositions of systems of nonlinear PDEs

Solution method: The solution method consists, in principle, of pseudo-division of differential polynomials, as in Euclid's algorithm, with case distinctions according to vanishing or non-vanishing leading coefficients and discriminants, combined with completion to involution for partial differential equations. Since an enormous growth of expressions can be expected in general, efficient versions of these techniques need to be used, e.g., subresultants, Janet division, and need to be applied in an appropriate order. Factorization of polynomials, while not strictly necessary for the method, should be utilized to reduce the size of expressions whenever possible.