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

TL;DR

This paper introduces MAPLE subroutines for calculating Milnor and Tyurina numbers of hypersurface singularities, demonstrating their application in algebraic stratifications of Kuranishi spaces related to Arnol'd singularities.

Contribution

It presents the first MAPLE implementation of local monomial ordering for singularity invariants and applies it to algebraic stratifications of singularity spaces.

Findings

Successful computation of Milnor and Tyurina numbers using MAPLE

Explicit equations for stratifications of Kuranishi spaces

Illustration of adjacency relations among simple singularities

Abstract

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.