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Graded Lagrangian formalism in terms of a Grassmann-graded variationalbicomplex on graded manifolds is developed in a very general setting. Thisformalism provides the comprehensive description of reducible degenerateLagrangian systems, characterized by hierarchies of non-trivial higher-orderNoether identities and gauge symmetries. This is a general case of classicalfield theory and Lagrangian non-relativistic mechanics.

Grassmann-graded Lagrangian theory of even and odd variables