The classification of real singularities using Singular Part I: Splitting Lemma and simple singularities

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).