… We give an algorithm to compute the set of primitive elements for an embedding
dimension three numerical semigroups. We show how we use this procedure in the study of
the construction of L-shapes and the tame degree of the semigroup. … In this work, we
particularize this method to the very particular case when S is a numerical semigroup with
embedding dimension three (n = 3). Prior to this, we present two examples where an
improvement of this procedure is welcomed. …