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Does anyone know of any free tensor manipulation software for use in General relativity? e.g GR tensor (this includes software that needs programs such as mathematica or matlab to use)

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SageManifolds is a package included in the free computer algebra system SageMath 7.5. It is rather powerful and is developed by Eric Gourgoulhon and others.

There are various examples available and quiet a few are common GR problems.

I myself never worked with it but I know that it is quite popular in the numerical relativity community. With the examples it should be rather easy to get started and the whole package is well documented.

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