A Mathematica package for doing tensor calculations in differential geometry

Version 1.53

Last Updated July 12, 2015

Ricci is a Mathematica package for doing symbolic tensor computations that arise in differential geometry. It has the following features and capabilities:
Limitations: Ricci currently does not support computation of explicit values for tensor components in coordinates, or derivatives of tensors depending on parameters (as in geometric evolution equations or calculus of variations), although support for these is planned for a future release. Ricci also has no explicit support for general relativity, or for other mathematical physics or engineering applications, and none is planned. If you are interested in such support, I recommend that you consider the commercial package MathTensor, which is far more extensive than Ricci, and provides all these capabilities and more. MathTensor is available from MathTensor, Inc. <mathtensor@wolfram.com>.

Disclaimer: Be warned that I make no claims that this is a professional-quality software package. I have tried to make it as general and error-free as possible, and I think it is reasonably robust. However, I do most of the work on this package in my "spare time", with only very limited programming assistance, so I don't have time to check everything. I will try to fix any bugs that you encounter.

If you use this package at all, I would appreciate it if you would send me a message at lee@math.washington.edu describing your experience, and telling me whether you found the package useful or not. I'd especially like to hear about any bugs, anomalous behavior, things that look like they should simplify but don't, suggestions for improvement, things that seem to take longer than they should, etc. If I get e-mail from you, I'll put you on my mailing list to be informed whenever I release a new production version.

How to get Ricci

Before you obtain or use Ricci, please read the copyright notice. Then download the following files:

Once you have downloaded the files, put the source file Ricci.m in the directory in which you place Mathematica input files. If you plan to use TeXForm output from Ricci, put Ricci.tex in the directory in which TeX looks for its input files.

Using Ricci

Ricci requires Mathematica version 2.0 or greater. The source takes approximately 283K bytes of disk storage, including about 49K bytes of on-line documentation. I have tested the current version of the package with Mathematica 5.0 under Windows. Although I haven't tested it in other situations, I know of no reason why it should not run on any platform using Mathematica 2.0 or later.

To use Ricci, put the Ricci.m source file into a directory of your own that is accessible to Mathematica. (You may need to change the value of Mathematica's $Path variable in your initialization file--see the documentation for the version of Mathematica that you're using.) Then load the Ricci package by typing the following Mathematica command:


Once you've loaded Ricci into Mathematica, you can type ?name for information about any Ricci function or command.

Changes in Version 1.53

Here's a log of changes in prior versions of Ricci.

Plans for future releases

What follows is an (incomplete) list of capabilities that Ricci does not currently have, but that I plan to add to some future version. I have no idea how soon these will be ready, but they're listed in approximately the order in which I plan to add them.
John M. Lee

University of Washington
Department of Mathematics
Box 354350
Seattle, WA 98195-4350

Phone: (206) 543-1735
Fax: (206) 543-0397
E-mail: lee@math.washington.edu