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| * [[http://grtensor.phy.queensu.ca/|GRTensor]] is a package for Maple (with a port to Mathematica) for geometry computations in general relativity. From the web page: ''GRTensor II is a computer algebra package for performing calculations in the general area of differential geometry. Its purpose is the calculation of tensor components on curved spacetimes specified in terms of a metric or set of basis vectors.'' * The [[http://www.math.washington.edu/~lee/Ricci/|Ricci]] package in Mathematica looks terrific, but I don't have Mathematica so I can't experiment with it. * [[http://cadabra.phi-sci.com/index.html|Cadabra]] is a tensor package designed for computations in field theory (HEP, GR). It looks very powerful and versatile, but the syntax is very terse. |
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| * [[http://grtensor.phy.queensu.ca/|GRTensor]] is a package for Maple (with a port to Mathematica) for geometry computations in general relativity. From the web page: ''GRTensor II is a computer algebra package for performing calculations in the general area of differential geometry. Its purpose is the calculation of tensor components on curved spacetimes specified in terms of a metric or set of basis vectors.'' | |
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| * [[http://sympy.blogspot.com/2007/04/relativitypy-is-working.html|sympy]] has a small relativity example. See also [[http://www.mail-archive.com/axiom-mail@nongnu.org/msg00314.html|this announcement]]. | |
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| * [[http://osdir.com/ml/sage-devel/2010-02/msg00294.html|GR calculations]]: adding support for GR calculations to Sage. |
Tensor Calculus in Sage
This page arose out of a thread at sage-devel on the use of differential forms in Sage. Differential forms have been mentioned on the mailing list a few times before, and in the current discussion a number of interesting packages for tensor calculus were mentioned, which are listed here.
This list is by no means complete, so please feel free to edit.
As tensor calculus is a vast subject, at some stage we will want to have a roadmap of which tasks to handle first, benchmarks, and useful applications.
Packages
Forms/Tensor packages
GRTensor is a package for Maple (with a port to Mathematica) for geometry computations in general relativity. From the web page: GRTensor II is a computer algebra package for performing calculations in the general area of differential geometry. Its purpose is the calculation of tensor components on curved spacetimes specified in terms of a metric or set of basis vectors.
The Ricci package in Mathematica looks terrific, but I don't have Mathematica so I can't experiment with it.
Cadabra is a tensor package designed for computations in field theory (HEP, GR). It looks very powerful and versatile, but the syntax is very terse.
Maxima seems to have a differential forms package.
FriCAS has support for a De Rham complex, which (among others) apparently allows you to represent differential forms.
Scmutils has lots of code to deal with forms, Riemannian geometry, etc. plus lots of cool applications.
Related code
sympy has a small relativity example. See also this announcement.
JET: Axiom code to deal with jet bundles, geometric ODEs/PDEs, Cartan-Kuranishi prolongations, etc. See the abstract here.
GluCat: GluCat is a library of template classes which model the universal Clifford algebras over the field of real numbers, with arbitrary dimension and arbitrary signature. GluCat implements a model of each Clifford algebra corresponding to each non-degenerate quadratic form up to a maximum number of dimensions.
Related Sage discussions
There are a few Sage projects in the works that might be interesting in the context of differential forms and tensor calculus. A quick search brings up the following.
GR calculations: adding support for GR calculations to Sage.
Topology: Sage support for topology.