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:


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:

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).