In this paper, we define the curvature A-tensor of a symplectic A-connection and the curvature operator associated with a symplectic Yang-Mills field. We show that the symplectic curvature A-tensor, the Ricci curvature A-tensor and the symplectic Ricci A-tensor are invariant under the group sheaf of A-symplectomorphisms. Finally we introduce on a symplectic vector sheaf the Euler-Langrage equation for the symplectic Yang-Mills functional.