Software for Planar Algebras or Group Rings Does software exists for calculating with planar algebras or group rings?  It could be part of Mathematica or be an extension of Python or Java or C.  What would go into designing such a data-type anyway?  One would have to define a special class describing elements of your algebra and overload "+" and "x" so it felt natural.   
This request comes about because I am too lazy to write out all 16 terms in the young symmetrizer for the partition (2,2) and show that representation is two-dimensional space.  This will be even more unwieldy for larger partitions.
It would also be difficult to do computations with the Templerley-Lieb algebras without software.
An alternative question is: are there efficient ways to compute with Specht modules or the Temperley-Lieb algebras by hand?
 A: 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.
A: Both Magma and GAP contain interfaces for doing computations with group algebras.
A: If there is software for planar algebras I would interested in hearing about it.
For working in the Hecke algebra see my answer to
Do Jones-Wenzl idempotents lift to anything interesting in the Hecke algebra?
and for the one specific question you ask see my answer to Sammy's previous question
Does the super Temperley-Lieb algebra have a Z-form?
You should be able to do what you want by hand. If you can't then can you say what the problem is.
Also I don't see the connection between the two problems. How would planar algebra software help you with these algebras?
