On the root systems of the classical & exceptional Lie algebras Mathematica programs

Numerical procedures for obtaining the root systems of both classical and exceptional Lie algebras are slow and tedious when done by hand. This is a contribution in the field that uses a modern computer language Mathematica. This gives the benefits of high portability, efficiency and makes it easier to use either classical or exceptional Lie algebras in user programs. Root systems, positive roots and their sum, simple roots, Cartan's matrices, highest and fundamental weights are all calculated in the programs. The programs written with Mathematica 3.0 and can be run under any other version of it.