D.6.5 classify2_lib

Library:

classify2.lib

Purpose:

Classification of isolated singularities

Authors:

Janko Boehm, email: boehm@mathematik.uni-kl.de
Magdaleen Marais, email: magdaleen.marais@up.ac.za
Gerhard Pfister, email: pfister@mathematik.uni-kl.de

Overview:

We classify isolated singularities of corank <=2 and modality <=2 with respect to right-equivalence over the complex numbers according to Arnold's list. We determine the type and, for positive modality, the parameter.

V.I. Arnold has described normal forms and has developed a classifier for, in particular, all isolated hypersurface singularities over the complex numbers up to modality 2. Building on a series of 105 theorems, this classifier determines the type of the given singularity. However, for positive modality, this does not fix the right equivalence class of the singularity, since the values of the moduli parameters are not specified.

This library implements an alternative classification algorithm for isolated hypersurface singularities of corank and modality up to two. For a singularity given by a polynomial over the rationals, the algorithm determines its right equivalence class by specifying a polynomial representative in Arnold's list of normal forms. In particular, the algorithm also determines values for the moduli parameters.

The implementation is based on the paper

Janko Boehm, Magdaleen Marais, Gerhard Pfister: A Classification Algorithm for Complex Singularities of Corank and Modality up to Two, Singularities and Computer Algebra - Festschrift for Gert-Martin Greuel on the Occasion of his 70th Birthday, Springer 2017, http://arxiv.org/abs/1604.04774, https://doi.org/10.1007/978-3-319-28829-1_2

There are functions for determining a normal form equation and for determining the complex type of the singularity.

Acknowledgements: This research was supported by
the Staff Exchange Bursary Programme of the University of Pretoria, DFG SPP 1489, 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.6.5.1 complexClassify		classifier returning a normal form equation
D.6.5.2 complexType		classifier returning the type and modality