  A hierarchy of multimode uncertainty relations on the second moments of n
pairs of canonical operators is derived in terms of quantities invariant under
linear canonical (i.e. symplectic) transformations. Conditions for the
separability of multimode continuous variable states are derived from the
uncertainty relations, generalizing the inequalities obtained in [Phys. Rev.
Lett. 96, 110402 (2006)] to states with some transposed symplectic eigenvalues
equal to 1. Finally, to illustrate the methodology proposed for the detection
of continuous variable entanglement, the separability of multimode noisy
GHZ-like states is analysed in detail with the presented techniques, deriving a
necessary and sufficient condition for the separability of such states under an
`even' bipartition of the modes.
