Abstract:
The aim of the thesis is to study, develop and implement algorithms to compute in-
variants in singularity theory. A very important part is a parallel and very efficient
implementation in computer algebra system SINGULAR. Three different and inde-
pendent problems have been considered:
• The computation of the signature of a surface singularity defined by z N +
g(x, y) = 0.
• The computation of resolution graph and related invariants for plane curve
singularities.
• The classification of simple function germs with respect to right equivalence in
characteristic p > 0 and the implementation of a classifyer.
