Mathematica 11 Symmetry Packages

Question

Are there any symmetry finding packages (for differential equations) that work with Mathematica 11.1? I've tried MathLie but from looking at the documentation it had instructions for Windows 95... I attempted installation of the MathLie package on Windows 10 by placing it in the AddOns/Packages folder and the import (Needs[*]) worked but none of the commands did. After inspecting the files further it said it had support for v3-4 of Mathematica.

Then, I looked at SYM but had a similar problem. Looking at the site where it's download is listed it only seems to go up to Mathematica 8.x.

Answer 1

SYM is compatible with any version of Mathematica. My site writes up to 8 because that was the latest version at the time. I should update my site ... =)

Please send me an email at [email protected] and I will provide you with the up to date version of SYM.

P.S. Mathematica v10+ have a bug related to the UnProtect command, thats why you might have problems loading the version I have on my site (I should update that too! :$ )

Answer 2

I attempted installation of the MathLie package on Windows 10 by placing it in the AddOns/Packages folder…

You've placed the files in wrong place. As mentioned in SetupMathLie.nb, the MathLie folder should be copied to

FileNameJoin[{$TopDirectory, "AddOns", "Applications"}] // SystemOpen

Then just execute

$MathLiePath = FileNameJoin[{$TopDirectory, "AddOns", "Applications", "MathLie"}]; 

$Path = DeleteDuplicates @ Append[$Path, $MathLiePath];

<< MathLie`

The package will be successfully loaded. Some warnings are generated because MathLie has called several obsolete packages, but according to my quick test, the core functionality is not influenced. An example:

inf = Infinitesimals[D[u[x, t], t] + u[x, t] D[u[x, t], x] 
                     - 1/2 δ D[u[x, t], x, x] + 1/2 u[x, t] D[Log[A[t]], t] == 0, 
                     u, {x, t}, {a}];
inf // LTF