### D.6.3 arnoldclassify_lib

Library:
  arnoldClassify.lib
Purpose:
  Arnol'd Classifier of Singularities
Author:
  Eva Maria Hemmerling, ehemmerl@rhrk.uni-kl.de

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 arnoldClassify_to_string |  | singularity class of a power series f
> D.6.3.6 arnoldCorank |  | corank of singularity defined by f
> D.6.3.7 arnoldDeterminacy |  | upper bound for the determinacy of f
> D.6.3.8 arnoldMilnorCode |  | Milnor Code of a singularity f
> D.6.3.9 arnoldMorseSplit |  | result of Splitting Lemma applied to f

See also: arnold_lib; classify_lib; realclassify_lib.

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