MAPLE subroutines for computing Milnor and Tyurina numbers of hypersurface singularities with application to Arnol'd adjacencies

In the present paper MAPLE subroutines computing Milnor and Tyurina numbers of an isolated algebraic hypersurface singularity are presented and described in detail. They represents examples, and perhaps the first ones, of a MAPLE implementation of local monomial ordering. As an application, the last section is devoted to writing down equations of algebraic stratifications of Kuranishi spaces of simple Arnol’d singularities: they geometrically represents, by means of inclusions of algebraic subsets, the partial ordering on classes of simple singularities induced by the adjacency relation.