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.
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