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.
Download
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.
Download
TensorForms1.zip
194KB The pre-Version 6 package and documentation, 15 Aug 2006.
Download
TensorForms1V6.zip
179KB The Version 6 package and documentation, 6 Jul 2007.
A number of Tensorial
4.0 Mathematica notebooks on various
topics in
physics are
available at Renan's web site
Tensorial 4.0 Examples.
There are also pdf files of the notebooks so that you can view examples
before
deciding on purchasing Tensorial. Some of the notebooks would also
require
DrawGraphics.
TContinuumMechanics2
is a package by Jean-François Gouyet
that
adds additional commands
to Tensorial 4.0 for working in continuum mechanics. It works through
the material
in the well known Flugge text on continuum mechanics as way of
illustration. The
package is for Version 5.2 (and 4.2 version as well) of Mathematica and
requires
the 5.2 version of Tensorial 4.0. It also uses the 5.2 version of
DrawGraphics to
generate the graphics in the Flügge notebooks examples.
Purchase
TContinuumMechanics2 Package
$50, 577KB The package, documentation, and text material, 7 Sep 2007.