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I am looking for a Mathematica package that can manipulate tensors for supergravity, string theory or M-theory. I am particularly looking for a package that can do spinor and Clifford algebra computations. Also, I would like this package to be able to do wedge and hodge dual, and other computation relating to forms. Can anyone suggest a specific one? I looked for atlas2, but it seems I have to pay to use it without a trial version.

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    $\begingroup$ Tensor software on Wikipedia $\endgroup$ – Constandinos Damalas Jul 17 '14 at 5:48
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    $\begingroup$ This question appears to be off-topic because it is about scientific computing software and is better suited on scicomp.stackexchange.com. $\endgroup$ – Brandon Enright Jul 17 '14 at 6:47
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    $\begingroup$ @BrandonEnright nope we decided on meta that questions asking for software specifically used by / useful for physicists are on topic: Leave open. Therefore there is also no need for downvotes here ... $\endgroup$ – Dilaton Jul 17 '14 at 7:17
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    $\begingroup$ @Dilaton shrug. That's why I don't get a unilateral vote. In my opinion this is off topic. $\endgroup$ – Brandon Enright Jul 17 '14 at 7:21
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    $\begingroup$ @BrandonEnright All right, my fault. I ask here because when I ask the question in Mathematica, people suggested me also to ask the question in MathOverFlow and Physics Stack Exchange. If this question is not appropriate, then it is OK to close it. Sorry I am not aware that there is such controversy. $\endgroup$ – Kevin Ye Jul 17 '14 at 9:09
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For Mathematica the best I know is RGTC. I Used it a long time ago (briefly) for a calculation in IIA SUGRA in 10 dimensions. It calculate gravitational tensors, manages differential forms (also Lie algebra valued ones), calculates Hodge dualities, etc.


Personal comment: If you are more intrepid (and FLOSS lover), there is a software called SAGE, which now has a (still developing) package (sagemanifold) for differential geometry calculations... it allows the use of differential form, etc.

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As part of the sympy computer algebra system there are geometric (clifford) algebra modules. The latest can be found in my fork of sympy at

https://github.com/brombo/sympy

Their is a latex doc in the repository at sympy/doc/src/modules/galgebra/pdf/GA.pdf Various examples are in sympy/examples/galgebra (especially look at the latex examples).

In the geometric algebra module the user defines the metric orthogonal of non-orthognal. Differential operators of multivectors are implemented. I am will to help anyone who wishes to use the package.

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