2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/73564In 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 dimension $n$ in terms of differential forms. In the case $n=1$ such computations have many applications in differential equations and counting their limit cycles. For $n>3$, these computations give us an explicit definition of Hodge cycles.14 pagesAlgebraic GeometryDifferential Geometry14C30text