  Retraction maps have been generalized to discretization maps in (Barbero
Li\~n\'an and and Mart\'{\i}n de Diego, 2022). Discretization maps are used to
systematically derive numerical integrators that preserve the symplectic
structure, as well as the discrete momemtum map under the assumption of
symmetric preservation for the discretization map. The procedure described here
gives a geometrical construction that can be easily adapted to discretize
dynamics on more general structures and open the door to reduction processes.
