  Pisot numbers are real algebraic integers bigger than 1, whose other
conjugates have all modulus smaller than 1. In this paper we deal with the
algorithmic problem of finding the smallest Pisot unit generating a given
number field. We first solve this problem in all real fields, then we consider
the analogous problem involving the so called complex Pisot numbers and we
solve it in all number fields that admit such a generator, in particular all
fields without CM, but not only those.
