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Let  M  be a smooth manifold of dimension 2 n , and let  OM  be the dense open subbundle in ∧ 2T * M  of 2-covectors of maximal rank. The algebra of Di  M  -invariant smooth functions of first order on  OM  is proved to be isomorphic to the algebra of smooth  Sp (Ω x )-invariant functions on   ,  x  being a fixed point in  M  , and Ω x  a fixed element in ( OM  )x. The maximum number of functionally independent invariants is computed.

First-order invariants of differential 2-forms