Cartan package for differential forms and Cartan-Kahler
analysis in Maple
Updated 7/30/2025
Please send comments,
questions, and ideas to me here.
This is a Maple package that I wrote for doing computations for
the Cartan-Kahler analysis of linear Pfaffian systems. It
can compute structure equations, absorb the torsion whenever
possible (and compute unabsorbable torsion when it is not
possible), compute Cartan characters and test for involutivity,
and compute prolongations. Cartan is based on (and includes)
the Forms package for doing computations involving differential
forms, which was written by Yunliang Yu of Duke University and
maintained by him through Maple V, Release 4. It was revised
for Maple V, Release 5 by myself, and for Maple 6 and higher by
myself and Tom Ivey.
This version is current as of July 2025 and should be compatible
with Maple versions up to Maple 2025. (Admittedly, testing
on recent versions of Maple has been limited; please feel free to
submit bug reports to the email above!)
Changes and improvements as of 7/30/25 include:
- The "L" command has been renamed to "LLL" to avoid a conflict
with a Maple variable.
- The package has been updated to avoid errors that began
appearing in Maple 2022 - BIG thanks to Tom Ivey for this
update!
- The Maple help interface has been deprecated, so the help
pages are no longer available within Maple. Instead, the
text of the help pages is included in the download folder in the
file "Cartan_Manual".
There are two versions of the package, depending on whether you
prefer to work in Maple's Document mode or the older Worksheet
mode. The only difference is the default wedge product
command:
- In Worksheet mode (the original Maple interface for
old-dogs-who-don't-like-new-tricks like me!), the default wedge
product command is "&^".
- In Document mode, the default wedge product command is
"&w"; the original version had to be changed because the "^"
character creates an exponent in Document mode.
The Forms package is used in Cartan with Yunliang Yu's permission;
installation instructions are included with each version.
The development of the Cartan package was partially supported by the
National Science Foundation under Grant No. DMS-0908456. Any
opinions, findings and conclusions or recommendations expressed in
this material are those of the author and do not necessarily reflect
the views of the National Science Foundation (NSF).