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).