the Taylor series of at the point p. Most importantly, the closure properties of I imply that E(∞) is tangent to the infinite-order contact structure on J∞(π), so that by restricting to E(∞) one gets the diffiety , and can study the associated Vinogradov (C-spectral) sequence. Remark This article has defined jets of local sections of a bundle, but it is possible to define jets of functions f: M → N, where M and N are manifolds; the jet of f then just corresponds to the jet of the sectiongrf: M → M × Ngrf(p) = (p, f(p))(grf is known as the graph of the function f) of the trivial bundle (M × N, π1, M). However, this restriction does not simplify the theory, as the global triviality of π does not imply the global triviality of π1. See also Jet group Jet (mathematics) Lagrangian system Variational bicomplex References Further reading Ehresmann, C., "Introduction à la théorie des structures infinitésimales et des pseudo-groupes de Lie." Geometrie Differentielle, Colloq. Inter. du Centre Nat. de la Recherche Scientifique, Strasbourg, 1953, 97-127. Kolář, I., Michor, P., Slovák, J., Natural operations in differential geometry.'' Springer-Verlag: Berlin Heidelberg, 1993. , . Saunders, D. J., "The Geometry of Jet Bundles", Cambridge University Press, 1989, Krasil'shchik, I. S., Vinogradov, A. M., [et al.], "Symmetries and conservation laws for differential equations of mathematical physics", Amer. Math. Soc., Providence, RI, 1999, . Olver, P. J., "Equivalence, Invariants and Symmetry", Cambridge University Press, 1995, Differential topology Differential equations Fiber bundles