Differences between revisions 1 and 2
Revision 1 as of 2010-05-14 09:50:44
Size: 2648
Comment:
Revision 2 as of 2010-05-30 10:22:42
Size: 3332
Comment:
Deletions are marked like this. Additions are marked like this.
Line 14: Line 14:
 * [[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.
Line 15: Line 18:
 * [[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.''
Line 22: Line 24:
 * [[http://sympy.blogspot.com/2007/04/relativitypy-is-working.html|sympy]] has a small relativity example. See also [[http://www.mail-archive.com/[email protected]/msg00314.html|this announcement]].
Line 29: Line 32:
 * [[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.

  • 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.

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.

tensorcalc (last edited 2017-12-29 17:41:26 by egourgoulhon)