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D.15.1 arnoldclassify_lib

Arnol'd Classifier of Singularities
Eva Maria Hemmerling, ehemmerl@rhrk.uni-kl.de

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.

[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.


D.15.1.1 arnoldListAllSeries  list of all singularity series up to corank 2
D.15.1.2 arnoldShowSeries  data defining a singularity series S
D.15.1.3 arnoldNormalForm  normalform for a singularity series S
D.15.1.4 arnoldClassify  singularity class of a power series f
D.15.1.5 arnoldCorank  corank of singularity defined by f
D.15.1.6 arnoldDeterminacy  upper bound for the determinacy of f
D.15.1.7 arnoldMilnorCode  Milnor Code of a singularity f
D.15.1.8 arnoldMorseSplit  result of Splitting Lemma applied to f
See also: classify_lib; realclassify_lib.