Weight diagrams for Lie group representations: A computer implementation of Freudenthal’s algorithm in ALGOL and FORTRAN. Implementations in FORTRAN and ALGOL of the Dynkin and Freudenthal algorithms for computing weight systems and for determining the multiplicities of the weights for irreducible representations of simple Lie algebras are described. Reasonable computing times are found for algebras of rank less than or equal to 8 and for representations of dimension less than 1000.