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?

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?