Vessiot Tutorials
Individual Mfiles

It is perhaps fitting, then, that a Maple package designed to assist researchers in geometric methods in differential equations be named in his honor.

The software package Vessiot contains commands for all the basic operations of calculus on jet spaces.

Commands are included for computing flows of vector fields, for finding the structure constants of Lie algebras of vector fields, and for applying the standard radial homotopy operator for the local de Rham complex.

Euler-Lagrange expressions for Lagrangians, the prolongation of vector fields and transformations are readily computed in Vessiot.

In addition most of the operations used in the variational bicomplex are available. These include the vertical and horizontal exterior derivatives and homotopy operators; the integration by parts operator; decomposition of forms by bi-degree; total and evolutionary decomposition of vector fields.

Extensive applications packages are also available. These include a tensor package, a package for Lie algebra computations, software for computing Spencer cohomology, a Gelfand-Dickey transform package and a package for studying isometry groups of metrics.

The software and all accompanying documentation is free.

Please acknowledge the use of Vessiot in your publications and send copies of such papers to us.

1. Unzip the Vessiot mfiles. There are 20 files.
2. Save these files in a directory. eg. c:mystuff\Maplestuff\Vessiot
3. Under Windows find the directory MapleV/bin.wnt and open or createthe file maple.ini. Maple reads this file on startup.
4. Add the following line to this file: libname:=libname, "c:\\mystuff\\Maplestuff/Vessiot"
5. Start Maple and enter with(Vessiot).
6. If the undefined package error occurs, type libname at the Maple prompt to check that the maple.ini file was read.
7. For Macs, it may be neccessary to recreate the maple.ind and maple.lib files. Remove these two files and recreate them using the program march.
8. Enter ?Vessiot to check that the helpfiles are available.

1. In Release 1.1 (August 15 2001) the frame handling procedures are completely new and now allow for moving frames to be introduced. For details see the helpfile titled Programmers Guide. However, the bicomplex commands have yet to be extended to the moving frame.
2. Many of the global variables associated to a frame have been eliminiated and replaced by commands.
3. The Vessiot libraries have been expanded.
4. Extensive work on the Lie algebra package Koszul and Chevalley have been completed and new packages Spencer, isometries, invariant_metrics, de_appls, added.
5. Helpfiles are available for all packages except the tensor and Gelfand-Dickey packages.

1. Release 1.04 contains a corrected and enhanced version of the package Lie algebra package Koszul. Online helpfiles for all the Koszul commands are available.
2. This release also contains new frame handling procedures and global variable protocols in anticipation of developing moving frame cabablitites. At this time all procedures and global variables described in the Vessiot Handbook remain valid.
3. The command startup is not required to begin a Vessiot session. The startup procedure is automatically called the first time a coordinate system is initialized.

1. Release 1.03 (August 8, 2000) represents the first complete version of the basic Vessiot software package -- including helpfiles for all commands.
2. Subsequent releases will focus on completion of the tensor and Lie algebra applications and some standard computational tools for symmetry group calculations of differential equations.