Exterior differential systems

In my research I use the the theory of exterior differential systems quite often. Unfortunately, there is little software available to deal with exterior differential systems or ideals of differential forms. I wrote some software for special cases, but most of it is not usefull in general.

I wrote my own Maple package to calculate the prolongation of a given tableau. I use the code to calculate the dimension of the first prolongation of the tableau. Together with the Cartan characters one can then check using Cartan's test whether the tableau is in invulution or not. The code was tested with Maple 8, but later versions should work as well.

The package can be downloaded here. You need to download the MiscPTE package as well.

Some other software packages I know of:

• The standard difforms package for Maple
• Vessiot for Maple
• The jets package written by Mohamed Barakat. Very usefull to work with jet bundles and prolongations, but cannot handle differential forms yet.
• EDS for Reduce, I have not tried this package myself