The Classification of Real Singularities Using Singular. Part III: Unimodal Singularities of Corank 2
arXiv:1512.09028 · doi:10.1016/j.jsc.2019.06.003
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 right 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. We discuss how to computationally realize the individual steps of the algorithm for all singularities in consideration, and give explicit examples. The algorithm is implemented in the Singular library realclassify.lib.
31 pages, 5 figures, 1 table, improvements in the algorithms
References in corpus (3)
- The Classification of Real Singularities Using SINGULAR. Part I: Splitting Lemma and Simple Singularities
- The Classification of Real Singularities Using SINGULAR. Part II: The Structure of the Equivalence Classes of the Unimodal Singularities
- A Classification Algorithm for Complex Singularities of Corank and Modality up to Two