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In this article we introduce algorithms which compute iterations of Gauss-Manin connections, Picard-Fuchs equations of Abelian integrals and mixed Hodge structure of affine varieties of dimensionnin terms of differential forms. In the casen= 1 such computations have many applications in differential equations and counting their limit cycles. Forn> 3, these computations give us an explicit definition of Hodge cycles.

Calculation of Mixed Hodge Structures, Gauss-Manin Connections and Picard-Fuchs Equations