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...Tensor calculus with lorene eric gourgoulhon laboratoire de l univers et ses th eories luth cnrs observatoire paris f meudon france obspm fr based on a collaboration philippe grandcl ement j er ome novak school spectral methods application to general relativity and field theory november http www features of in dimensional manifold only formalism main class stores components respect given triad not abstract tensors dierent metrics can be used at the same time metric their associated covariant derivatives dened irrespectively any connection dynamical gestion dependencies guaranties that all quantities are up date being recomputed if necessary...