Programs for symmetry adaption coefficients for semisimple symmetry chains: The completely symmetric representations. Solution method: Starting from the state vector corresponding to the highest weight of an irreducible representation of SU(l+1), repeated application of shift operators generates all states within this irreducible representation. The initial states of all other irreducible representations of the given symmetry chain, which are contained in a representation [[N]] of SU(l+1), are automatically generated using a precomputed list of all dominant subalgebra weights.