Computer algebra system designed for calculations in field theory. This is extremely powerful in dealing with abstract tensors, i.e. objects with certain number of indices, both vector and spinorial, with arbitrary components. For me, the most useful feature of Cadabra is complete control which one has over a calculation: the program will not even set derivatives of constants to zero unless it is explicitly told to do so.

Cadabra is available for various Linux distributions as well as for MacOS. Recently a version fo Windows became available. I am using Cadabra 1.x, however Cadabra 2.x is already there. The latter has slightly different syntax.

Lie Algebras Representation Theory is a Wolfram Mathematica package providing tools for manipulations with Lie algebras, root vectors, representations etc. In particular, this is really useful in finding branching rules, explicit expressions for simple roots and projection matrices.

The project has wonderful tutorial that contains not only the manual, but also some background theoretical material, and hence is worth studying on its own.

Another tool for manipulations with Lie algebras and their representations. In comparison to the LieART package, that uses well developed frontend of Mathematica, this program has a standalone interface, which has to be launched via gradle in Linux or MacOS terminal. This might seem inconvenient, however the loaded GUI is pretty nice and convenient.

This small package is able to construct branchings of irreps of Lie algebras entered by specification of their Dynkin diagram. On is able to work with infinite dimensional algebras such as E11, decompose their representations, identidy multiplicities, levels and particular weight vectors. The program is available via Github.