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?