  In this article, we study the quotients of numerical semigroups, generated by
two coprime positive numbers, named (a,b) over d. We give formulae for the
usual invariants of these semigroups, expressed in terms of continued fraction
expansions and Ostrowski-like numeration of some rationals, simply related to
entries a, b, d. So, we obtain quadratic complexity algorithms to compute these
invariants. As a consequence, we will prove that, for these numerical
semigroups, the type is always lower than the embedding dimension and deduce
Wilf's property. We also consider the '' reverse problem'' : given J, a finite
set of integers, we obtain an expression of all possible triplets (a, b, d),
such that J is the set of minimal generators of (a,b) over d.
