  In order to perform numerical studies of long-term stability in nonlinear
Hamiltonian systems, one needs a numerical integration algorithm which is
symplectic. Further, this algorithm should be fast and accurate. In this paper,
we propose such a symplectic integration algorithm using polynomial map
refactorization of the symplectic map representing the Hamiltonian system. This
method should be particularly useful in long-term stability studies of particle
storage rings in accelerators.
