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
Ecole Polytechnique, Palaiseau France. Some of the features of
Tensorial 4.0 are:
• Complete freedom in choosing tensor labels, indices and base
• Flavored (colored or annotated) indices for various
• Differently flavor indices may have different dimensions and
base index sets.
• Minimum keystroke tensor input and formatted output that can
• Detailed set of index manipulation routines.
• Easy routines for setting tensor values or rules and
tensor sums and arrays.
• Zero tensors balance free indices, behave like zero and
to zero arrays.
• CircleTimes and dot product routines.
• Routines to declare and apply tensor and tensor expression
• Kronecker, generalized Kronecker and Levi-Civita routines.
• Partial, covariant, total, absolute and Lie derivative
• Christoffel, Riemann, Ricci, Einstein, Weyl and scalar
• Conversions from coordinate basis to orthonormal basis.
• Dot mode routines to convert from index notation to
• Blends naturally with the normal Mathematica notebook
• Complete documented Help with individual pages and examples
Additional tutorial notebooks.
The following pdf
file illustrates a calculation performed with
example corresponds to exercise [22.32] in Penrose's
generation of the Laplacian operator on the surface of a sphere.
classifies the exercise as 'not to be undertaken lightly'.
Tensorial 4.0 has now
been converted to Mathematica Version 6.0.
deficiencies are that the special palette based copy and paste does not
completely work and several of the Example notebooks use DrawGraphics
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
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
copy of the installation instructions is included in the downloaded zip
2KB, 3 Oct 2006.
$100, 517KB The package, documentation, style sheet and palette, 18 Sep
The following is a
documentation package for Tensorial 4.0 for
who wish to
examine the package before purchasing. It contains all of the
examples in evaluated form but lacks the actual package. There is also
Slide Show that illustrates some of the main features. The evaluated
occupies about 29 MB. The downloaded zip file is about 3 MB. To install
unzip into your personal Mathematica\Applications folder and rebuild
the Help Index.
This is for Mathematica 5.2.
3.1 MB Tensorial 4.0 documentation without package, 1 May 2007.
TensorialForms is a
subpackage for Tensorial 4.0 that adds
are built from 1-forms. It contains routines for wedge products, Hodge
increasing index sets, storing form values, simplexes, affine maps,
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.
194KB The pre-Version 6 package and documentation, 15 Aug 2006.
179KB The Version 6 package and documentation, 6 Jul 2007.
A number of Tensorial
4.0 Mathematica notebooks on various
available at Renan's web site
Tensorial 4.0 Examples.
There are also pdf files of the notebooks so that you can view examples
deciding on purchasing Tensorial. Some of the notebooks would also
is a package by Jean-François Gouyet
adds additional commands
to Tensorial 4.0 for working in continuum mechanics. It works through
in the well known Flugge text on continuum mechanics as way of
package is for Version 5.2 (and 4.2 version as well) of Mathematica and
the 5.2 version of Tensorial 4.0. It also uses the 5.2 version of
generate the graphics in the Flügge notebooks examples.
$50, 577KB The package, documentation, and text material, 7 Sep 2007.