  We propose a family of reliable symplectic integrators adapted to the
Discrete Non-Linear Schr\"odinger equation; based on an idea of Yoshida (H.
Yoshida, Construction of higher order symplectic integrators, Physics Letters
A, 150, 5,6,7, (1990), pp. 262.) we can construct high order numerical schemes,
that result to be explicit methods and thus very fast. The performances of the
integrators are discussed, studied as functions of the integration time step
and compared with some non symplectic methods.
