COMPUTING IN SINGULARITY THEORY

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.