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Ricci: a differential geometry package for Mathematica

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  • Subject: Ricci: a differential geometry package for Mathematica
  • From: John Lee <lee at>
  • Date: Fri, 28 Aug 92 12:48:56 -0700

                         Announcing the release of


            A Mathematica package for doing tensor calculations
                         in differential geometry

                                Version 1.0

The first public release of Ricci, my Mathematica package for doing tensor
computations in differential geometry, is now available.

Ricci is designed to assist with some of the tensor calculations needed by
pure mathematics researchers in differential geometry.  It has the
following features and capabilities:

* Manipulation of tensor expressions with and without indices
* Implicit use of the Einstein summation convention
* Correct manipulation of dummy indices
* Display of results in mathematical notation, with upper and lower indices
* Automatic calculation of covariant derivatives
* Automatic application of tensor symmetries
* Riemannian metrics and curvatures
* Differential forms
* Any number of vector bundles with user-defined characteristics
* Names of indices indicate which bundles they refer to
* Complex bundles and tensors
* Conjugation indicated by barred indices
* Connections with and without torsion

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
MathSolutions, Inc. (mathtensor at

Ricci requires Mathematica version 2.0 or greater.  The source takes
approximately 270K bytes of disk storage, including about 49K bytes of
on-line documentation.  The package was developed and tested on a
DECStation 5000 running Unix, but there are no known system-dependent
features, so it should run on any system that can run Mathematica with 7
megabytes or more of available memory.

The source files for Ricci are available to the public by anonymous ftp
from the Stanford Mathematica Users Forum library (  To
obtain them, you can log into any system that has an Internet connection
and supports the ftp (file transfer program) command.  Make yourself a
directory to hold the Ricci files.  Then, if you're using unix, you can cd
to your new directory and follow the script below.

  % ftp
  Connected to
  220 otter FTP server (Version 5.20 (NeXT 1.0) Sun Nov 11, 1990) ready.
  Name ( anonymous
  331 Guest login ok, send ident as password.
  Password:  <---------------------------------Type your e-mail address here.
  230 Guest login ok, access restrictions apply.
  ftp> cd mma/Geometry/Ricci
  250 CWD command successful.
  ftp> prompt  <---------------This turns off prompting for individual files.
  Interactive mode off.  
  ftp> mget *
  200 PORT command successful.
  150 Opening ASCII mode data connection for Bundle.m (14905 bytes).
  226 Transfer complete.
  local: Bundle.m remote: Bundle.m
  15268 bytes received in 0.53 seconds (28 Kbytes/s)
  ...  <-----------------------------------------------Lots more of the same.
  226 Transfer complete.
  local: Usage.m remote: Usage.m
  52928 bytes received in 1.2 seconds (43 Kbytes/s)
  ftp> bye
  221 Goodbye.

Once you've successfully transferred the Ricci files, look at the file
named README for more information about what's in the files and how to get
started using Ricci.

This is the first public release of Ricci.  If you use this package at all,
I would appreciate it if you would send me a message at the e-mail address
below 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.  And please feel free to get in touch with me if you have
questions about the software.  If I get e-mail from you, I'll inform you
whenever I release a new production version.

John M. Lee
Department of Mathematics, GN-50
University of Washington
Seattle, WA 98195

Internet: lee at
Fax:      206-543-0397

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