Where can I find the most up-to-date or whatever you consider to be the most useful symmetry-finding package for differential equations? I do not intend to restrict to, but would like to include those, that are designed to work within Mathematica.
Hi all please send me an mail at firstname.lastname@example.org or visit my web site www.math.upatras.gr/~spawn, although the version on the site is not updated you can find an online version of the help files of the package. Many things have been added since my thesis. Among them, I have added command for the algebraic manipulation of the symmetries (Levi decomposition, ideals, quotient algebras, etc.), contracting conservation laws using the self adjoint property of a Differential equation and the Noether operator and constructing the equivalent algebra and finding the discrete symmetries (following an idea of Hydon in his book). Many things are still in development/testing so i need your feedback!
See: Hereman's "24 [symmetry-finding] software packages mainly for Mathematica (commercial software), some for Macsyma* (commercial software)."
Gerd Baumann's Symmetry Analysis of Differential Equations with Mathematica® comes with some extra materials that include a Mathematica package called MathLie, freely downloadable here (20.5 MB).
The SYM package was developed by Stylianos Dimas and may be found in Appendix A of his thesis at http://nemertes.lis.upatras.gr/jspui/bitstream/10889/1697/1/thesis.pdf