### D.6.19 realclassify_lib

Library:
  realclassify.lib
Purpose:
  Classification of real singularities
Author:
  Janko Boehm, boehm@mathematik.uni-kl.de
  Magdaleen Marais, magdaleen@aims.ac.za
  Andreas Steenpass, steenpass@mathematik.uni-kl.de

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

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