D.6.19 realclassify_lib

Library:

realclassify.lib

Purpose:

Classification of real singularities

Author:

Janko Boehm, [email protected]
Magdaleen Marais, [email protected]
Andreas Steenpass, [email protected]

Overview:

A library for classifying isolated hypersurface singularities over the reals w.r.t. right equivalence, based on the determinator of singularities by V.I. Arnold. This library is based on classify2.lib by the first and second author and G. Pfister, but handles the real case, while classify2.lib does the complex classification.

References:

Arnold, Varchenko, Gusein-Zade: Singularities of Differentiable Maps. Vol. 1: The classification of critical points caustics and wave fronts. Birkh"auser, Boston 1985

J. Boehm, M.S. Marais, A. Steenpass: The Classification of Real Singularities Using Singular. Part III: Unimodal Singularities of Corank 2, https://arxiv.org/abs/1512.09028

Greuel, Lossen, Shustin: Introduction to singularities and deformations. Springer, Berlin 2007

M.S. Marais, A. Steenpass: The Classification of Real Singularities Using SINGULAR. Part I: Splitting Lemma and Simple Singularities, J. Symb. Comput. 68 (2015), 61-71

M.S. Marais, A. Steenpass: The Classification of Real Singularities Using SINGULAR. Part II: The Structure of the Equivalence Classes of the Unimodal Singularities, J. Symb. Comput. 74 (2016), 346-366

Acknowledgements: This research was supported by
the Staff Exchange Bursary Programme of the University of Pretoria, DFG SPP 1489, and DFG TRR 195. The financial assistance of the National Research Foundation (NRF), South Africa, towards this research is hereby acknowledged. Opinions expressed and conclusions arrived at are those of the author and are not necessarily to be attributed to the National Research Foundation, South Africa.

Procedures:

D.6.19.1 realclassify		real classification of singularities of modality 0 and 1 up to stable equivalence
D.6.19.2 realmorsesplit		splitting lemma in the real case
D.6.19.3 milnornumber		Milnor number
D.6.19.4 determinacy		an upper bound for the determinacy
D.6.19.5 addnondegeneratevariables		find a right equivalent normal form by adding the non-degenerate variables
D.6.19.6 HilbertClassPoly		computes the Hilbert Class Polynomial