rt.representation theory - Software for Planar Algebras or Group Rings

Sage can do some things with group algebras, in particular, with group algebras for symmetric groups, but it doesn't seem to have anything about planar algebras. For example:

S = SymmetricGroupAlgebra(ZZ, 3) 
# ZZ, the integers, is the coefficient ring
# "3" means the symmetric group on 3 letters
a = S([2,1,3])  # turn the permutation [2,1,3] into an element of S
b = S([3,1,2])
(2*a + b)^2

prints out

4*[1, 2, 3] + 2*[1, 3, 2] + [2, 3, 1] + 2*[3, 2, 1]

If you'd started with a different coefficient ring:

S = SymmetricGroupAlgebra(GF(3), 3) 

then the output from the above would be

[1, 2, 3] + 2*[1, 3, 2] + [2, 3, 1] + 2*[3, 2, 1]

You can also do computations with other group algebras for other groups, but symmetric group algebras seem to be a bit better developed.