MG11 
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Abstract

xTensor: a fast abstract tensor manipulator

The package xTensor is introduced, now the fastest and most general manipulator of tensor expressions for Mathematica. Manifolds can be defined containing tensor fields with arbitrary symmetry, connections of any type, metrics and other objects. Based on the Penrose abstract-index notation, xTensor has a single canonicalizer which fully simplifies all expressions, using highly efficient techniques of computational group theory. General tensor substitution rules, aware of symmetries, metrics, dummy indices and other details, can be defined. Specially designed for General Relativity, there are algorithms for ADM-type decomposition, perturbation theory, warped metrics and other topics. xTensor is GPL-free software: http://metric.iem.csic.es/Martin-Garcia/xAct/.

Computer algebra for tensors

The large complexity of the Einstein equations very often requires the use of computer algebra tools in General Relativity, both in analytical studies (e.g. perturbation theory) or in the numerical implementation of different versions of those equations. This talk briefly summarizes which Computer Algebra tools are available, describing the types of problems that can be addressed with them, the algorithms internally used, and comparing their efficiency.