  We develop a numerical method for solving the spin-1 Gross-Pitaevskii
equation. The basis of our work is a two-way splitting of the spin-1 evolution
equation that leads to two exactly solvable flows. We use this to implement a
second-order and a fourth-order symplectic integration method. These are the
first fully symplectic methods for evolving spin-1 condensates. We develop two
non-trivial numerical tests to compare our methods against two other
approaches.
