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.
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.
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
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.