Singular

D.6.3 arnoldclassify_lib

Library:

arnoldClassify.lib

Purpose:

Arnol'd Classifier of Singularities

Author:

Eva Maria Hemmerling, [email protected]

Overview:

A library for classifying isolated hypersurface singularities from the list of V.I. Arnol'd w.r.t. right equivalence up to corank 2. The method relies on Baciu's list of Milnor codes and Newton's rotating ruler method to distinguish the Y- and Z- singularities.

References:

[AVG85] Arnold, Varchenko, Gusein-Zade: Singularities of Differentiable Maps. Vol. 1: The classification of critical points caustics and wave fronts. Birkh"auser, Boston 1985

[Bac01] Corina Baciu: The classification of Hypersurface Singularities using the Milnor Code, Diplomarbeit, Universit"at Kaiserslautern, 2001.

[GP12] Greuel, Pfister: A SINGULAR Introduction to Commutative Algebra, Springer Science and Business Media, 2012

[Hem17] Eva Maria Hemmerling: Algorithmic Arnol'd Classification in SINGULAR, Master Thesis, TU Kaiserslautern, 2017.

Procedures:

D.6.3.1 arnoldListAllSeries		list of all singularity series up to corank 2
D.6.3.2 arnoldShowSeries		data defining a singularity series S
D.6.3.3 arnoldNormalForm		normalform for a singularity series S
D.6.3.4 arnoldClassify		singularity class of a power series f
D.6.3.5 arnoldCorank		corank of singularity defined by f
D.6.3.6 arnoldDeterminacy		upper bound for the determinacy of f
D.6.3.7 arnoldMilnorCode		Milnor Code of a singularity f
D.6.3.8 arnoldMorseSplit		result of Splitting Lemma applied to f