  We can associate with any irreducible curve singularity (ics) a numerical
semigroup. Two ics are said to be equisingular if they have the same semigroup.
Two equisingular ics have the same Milnor number. Conversely, The set of ics
with a given Milnor number is a union of equisingular classes. Here we study
ics from an algorithmic viewpoint, by using the notion of approximate roots. We
give two algorithms: the first one constructs the canonical equation of a curve
with a given semigroup. The second one gives the set of semigroups with a fixed
Milnor number. The paper is backed by Maple and Mathematica programs which are
available upon request.
