LTP - Lie Tools Package

LTP - LIE TOOLS PACKAGE
HOME PAGE

The Lie Tools Package for the symbolic manipulation of Lie algebraic expressions.
The current version 1.03 - 17.MAR.2002 was implemented in Maple 6/7 in the form
of a library that can be loaded from the Maple environment. See documentation below
for further details. Source files and documentation include application examples.

Among other functionallity the package provides procedures for the:

Simplification of expressions containing Lie brackets.

Construction of Philip Hall bases.

Composition of exponential mappings using the Campbell-Baker-Hausdorff formula.

Derivation of the Wei-Norman equations for linear differential system with finite-dimensional Lie algebras.

Source Files (ltp.tar.gz, 187kBytes)

User's Guide and Reference Manual Ver. 1.03 in Postscript (ltp.ps.gz, 464kBytes)

User's Guide and Reference Manual Ver. 1.03 in PDF (ltp.pdf, 660kBytes)

On Line User's Guide and Reference Manual Ver. 1.03

Please send your questions or comments to migueltt@cim.mcgill.ca

Announcements

17 May 2003: Version 1.03 of the User's Guide and Reference Manual was posted. This new version includes improved examples and an extended section with mathematical background about basic notions in Lie algebras and groups.
10 June 2002: The Campbell-Baker-Hausdorff formula in Dynkin's form (CBHD) has been successfully tested. It will be included within the LTP module files in the coming days. The cbhd procedure is found in the file cbhd1.mws within the directory "ltp/dev" (the construction and development area of the package).
16 July 2002: The series expansion up to Lie brackets of order 10 for the exponent Z(X,Y) corresponding to the composition of exponentials exp(X)*exp(Y)=exp(Z) has been obtained using the Campbell-Baker-Hausdorff-Dynkin formula and is available as a Maple worksheet cbhd_z3_10.mws. The series has 202 terms, in terms of Lie monomials of a Hall basis, and its calculation took 25 hours with maximum memory usage of 17.5 Mbytes on a Pentium III with a 550 MHz CPU, 256 Mbytes RAM, running Maple 7 on Linux.

To Do

Send your suggestions for improvements to: migueltt@cim.mcgill.ca.

Releases

1.03 - 17.MAR.2003	- Corrected function wnde that computes the Wei-Norman formula. The equations were computed correctly, but the matrix was not always constructed adequately.
1.02 - 03.SEP.2002	- The Campbell-Baker-Hausdorff formula in Dynkin's form (CBHD) , cbhd, was added to the main library.
1.01 - 20.JUN.2002	- Corrected phbize by introducing steps to handle the simplification of an addition of products. Improved the procedure by eliminating redundancies.
1.00 - 22.APR.2002	- First release.