As it stated in the title I'm looking for specific software for doing computation with Lie algebras. It could be some add-on for wolfram mathematica or for else computing systems.
The precise thing I am expecting of this is the opportunity to write in a set of generators of a Lie algebra at hand and the commutation relation between them as an input and to get Cartan/Chevalley basis for chosen Cartan subalgebra (as a linear combinations of given generators), root system structure and so on as an output.
I know that it is mostly nothing but linear algebra computation, but it is annoying to do this manipulations by hand again and again everytime.
I'll be greatly pleased if there is something. Thanks in advance for any help in this direction.
Magma is very nice and also has an online calculator you can use interactively subject to some memory and time constraints.
magma.maths.usyd.edu.au/calc/
GAP also has some Lie Algebras functionality and is free.
https://www.gap-system.org/Manuals/doc/ref/chap64.html