The Classification of Real Singularities Using SINGULAR. Part I: Splitting Lemma and Simple Singularities

TL;DR

This paper introduces algorithms implemented in SINGULAR for classifying real hypersurface singularities, focusing on simple singularities and the splitting lemma, as part of a series on Arnold's classification.

Contribution

It provides the first algorithms for classifying simple real hypersurface singularities based on Arnold's classification, implemented in the SINGULAR library.

Findings

Algorithms successfully classify simple singularities

Implementation in SINGULAR facilitates practical applications

Framework sets the stage for future classification of more complex singularities

Abstract

We present algorithms to classify isolated hypersurface singularities over the real numbers according to the classification by V.I. Arnold (Arnold et al., 1985). This first part covers the splitting lemma and the simple singularities; a second and a third part will be devoted to the unimodal singularities up to corank 2. All algorithms are implemented in the SINGULAR library realclassify.lib (Marais and Steenpass, 2012).