  We consider the problem of constructing spatial finite difference
approximations on a fixed, arbitrary grid, which have analogues of any number
of integrals of the partial differential equation and of some of its
symmetries. A basis for the space of of such difference operators is
constructed; most cases of interest involve a single such basis element. (The
``Arakawa'' Jacobian is such an element.) We show how the topology of the grid
affects the complexity of the operators.
