The classification of real singularities using Singular Part III: Unimodal singularities of corank 2. (July 2020)

• Record Type: Journal Article
• Authors: Böhm, Janko; Marais, Magdaleen S.; Steenpaß, Andreas
• Is Part Of: Journal of symbolic computation. Volume 99(2020)
• Page Start: 250
• Page End: 282
• Publication Date: 2020-07
• Subjects: Hypersurface singularities -- Algorithmic classification -- Real algebraic geometry; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2019.06.003
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: We present a classification algorithm for isolated hypersurface singularities of corank 2 and modality 1 over the real numbers. For a singularity given by a polynomial over the rationals, the algorithm determines its stable equivalence class by specifying all representatives in Arnold's list of normal forms (Arnold et al., 1985 ) belonging to this class, and the corresponding values of the moduli parameter. By specifying, in addition, the inertia index, the right equivalence class of the singularity is determined. We discuss how to computationally realize the individual steps of the algorithm for all singularities under consideration, and give explicit examples. The algorithm is implemented in the Singular library realclassify.lib .