# Tensorial Packages

Tensorial 4.0 - Version 6.0 Ready

Tensorial is a general purpose tensor calculus package for Mathematica 5.0 or later. Easy to learn and convenient for students and researchers. The authors are Renan Cabrera, University of Windsor, Canada, David Park, and Jean-François Gouyet, Ecole Polytechnique, Palaiseau France. Some of the features of Tensorial 4.0 are:

• Complete freedom in choosing tensor labels, indices and base indices.
• Flavored (colored or annotated) indices for various coordinate systems.
• Differently flavor indices may have different dimensions and base index sets.
• Minimum keystroke tensor input and formatted output that can be copied and pasted.
• Detailed set of index manipulation routines.
• Easy routines for setting tensor values or rules and expanding tensor sums and arrays.
• Zero tensors balance free indices, behave like zero and expand to zero arrays.
• CircleTimes and dot product routines.
• Routines to declare and apply tensor and tensor expression symmetries.
• Kronecker, generalized Kronecker and Levi-Civita routines.
• Partial, covariant, total, absolute and Lie derivative routines.
• Christoffel, Riemann, Ricci, Einstein, Weyl and scalar curvature routines.
• Conversions from coordinate basis to orthonormal basis.
• Dot mode routines to convert from index notation to Mathematica array form calculations.
• Blends naturally with the normal Mathematica notebook interface and kernel routines.
• Customizable
• Complete documented Help with individual pages and examples for each command. Additional tutorial notebooks.

The following pdf file illustrates a calculation performed with Tensorial. The example corresponds to exercise [22.32] in Penrose's Road to Reality , generation of the Laplacian operator on the surface of a sphere. Penrose classifies the exercise as 'not to be undertaken lightly'. Tensorial Example

Tensorial 4.0 has now been converted to Mathematica Version 6.0. The only deficiencies are that the special palette based copy and paste does not completely work and several of the Example notebooks use DrawGraphics and this has not yet been converted to Version 6.0. However, all the basic functionality works along with normal copy and paste.

If you purchase Tensorial you can download either the pre 6.0 Version or the 6.0 version, or both.

You may wish to check the site occasionally for updates. A section in the Help Introduction gives a history of the major additions and changes in usage. A copy of the installation instructions is included in the downloaded zip file.

Tensorial Installation Instructions 2KB, 3 Oct 2006.
Purchase Tensorial 4.0 Package \$100, 517KB The package, documentation, style sheet and palette, 18 Sep 2007.

The following is a documentation package for Tensorial 4.0 for those who wish to examine the package before purchasing. It contains all of the documentation and examples in evaluated form but lacks the actual package. There is also a Mathematica Slide Show that illustrates some of the main features. The evaluated documentation occupies about 29 MB. The downloaded zip file is about 3 MB. To install it just unzip into your personal Mathematica\Applications folder and rebuild the Help Index. This is for Mathematica 5.2.
Download TensorCalculus4Docs.zip 3.1 MB Tensorial 4.0 documentation without package, 1 May 2007.

TensorialForms is a subpackage for Tensorial 4.0 that adds differential forms that are built from 1-forms. It contains routines for wedge products, Hodge star, AngleBracket, increasing index sets, storing form values, simplexes, affine maps, exterior derivatives, form integrals, curvature and vector calculus. The package is developmental but generally useful. It is free and may be immediately downloaded. It installs in the same manner as Tensorial, creating a separate Help entry in the Help Browser. The package is now available for either Mathematica Version 6 or pre-Version 6.

TensorForms1.zip 194KB The pre-Version 6 package and documentation, 15 Aug 2006.