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

12 pages, 1 table

Cited by in corpus (5)

• The Classification of Real Singularities Using SINGULAR. Part II: The Structure of the Equivalence Classes of the Unimodal Singularities
• The Classification of Real Singularities Using Singular. Part III: Unimodal Singularities of Corank 2
• Classification of Complex Singularities with Non-Degenerate Newton Boundary
• A Classification Algorithm for Complex Singularities of Corank and Modality up to Two
• Free Cosmic Density Bispectrum on Small Scales