xTensor

xTensor: Fast abstract tensor computer algebra xTensor extends Mathematica capabilities in abstract tensor calculus, specially in General Relativity. It works with tensors with arbitrary symmetries under permutations of indices, defined on several different manifolds and products of them. It computes covariant derivatives, Lie derivatives and parametric derivatives. It allows the presence of a metric in each manifold and defines all the associated tensors (Riemann, Ricci, Einstein, Weyl, etc.) xTensor does not perform component calculations. Use the companion package xCoba. xTensor needs the package xPerm in order to compute the canonical form of a list of indices under permutation symmetry groups.