  We present an algorithm which, given a deformation with trivial section of a
reduced plane curve singularity, computes equations for the equisingularity
stratum (that is, the mu-constant stratum in characteristic 0) in the parameter
space of the deformation. The algorithm works for any, not necessarily reduced,
parameter space and for algebroid curve singularities C defined over an
algebraically closed field of characteristic 0 (or of characteristic p>ord(C)).
It provides at the same time an algorithm for computing the equisingularity
ideal of J. Wahl. The algorithms have been implemented in the computer algebra
system Singular. We show them at work by considering two non-trivial examples.
As the article is also meant for non-specialists in singularity theory, we
include a short survey on new methods and results about equisingularity in
characteristic 0.
