  In this article we present first an algorithm for calculating the determining
equations associated with so-called ``nonclassical method'' of symmetry
reductions (a la Bluman and Cole) for systems of partial differentail
equations. This algorithm requires significantly less computation time than
that standardly used, and avoids many of the difficulties commonly encountered.
The proof of correctness of the algorithm is a simple application of the theory
of Grobner bases. In the second part we demonstrate some algorithms which may
be used to analyse, and often to solve, the resulting systems of overdetermined
nonlinear PDEs. We take as our principal example a generalised Boussinesq
equation, which arises in shallow water theory. Although the equation appears
to be non-integrable, we obtain an exact ``two-soliton'' solution from a
nonclassical reduction.
