  This paper is devoted to study gauge embedding of either commutative and
noncommutative theories in the framework of the symplectic formalism. We
illustrate our ideas in the Proca model, the irrotational fluid model and the
noncommutative self-dual model. In the process of this new path of embedding,
the infinitesimal gauge generators of the gauge embedded theory are easily and
directly chosen. Among other advantages, this enables a greater control over
the final Lagrangian and puts some light on the so called ''arbitrariness
problem".
