6 citations · 16 across the 11 of their papers we have counts for
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Moduli Parameters of Complex Singularities with Non-Degenerate Newton Boundary
Janko Boehm, Magdaleen S. Marais, Gerhard Pfister
Our recent extension of Arnold's classification includes all singularities of corank up to two equivalent to a germ with a non-degenerate Newton boundary, thus broadening the class…
Massively Parallel Modular Methods in Commutative Algebra and Algebraic Geometry
Dirk Basson, Janko Boehm, Magdaleen S. Marais +2
Computations over the rational numbers often encounter the problem of intermediate coefficient growth. A solution to this is provided by modular methods, which apply the algorithm…
Classification of Complex Singularities with Non-Degenerate Newton Boundary
Janko Boehm, Magdaleen S. Marais, Gerhard Pfister
In his groundbreaking work on classification of singularities with regard to right and stable equivalence of germs, Arnold has listed normal forms for all isolated hypersurface sin…
A Classification Algorithm for Complex Singularities of Corank and Modality up to Two
Janko Boehm, Magdaleen S. Marais, Gerhard Pfister
In (Arnold, 1985), V.I. Arnold has obtained normal forms and has developed a classifier for, in particular, all isolated hypersurface singularities over the complex numbers up to m…
3D printing dimensional calibration shape: Clebsch Cubic
Andre F. van der Merwe, Janko Boehm, Magdaleen S. Marais
3D printing and other layer manufacturing processes are challenged by dimensional accuracy. Several techniques are used to validate and calibrate dimensional accuracy through the c…
The Classification of Real Singularities Using Singular. Part III: Unimodal Singularities of Corank 2
Janko Boehm, Magdaleen S. Marais, Andreas Steenpass
We present a classification algorithm for isolated hypersurface singularities of corank 2 and modality 1 over the real numbers. For a singularity given by a polynomial over the rat…
The Classification of Real Singularities Using SINGULAR. Part II: The Structure of the Equivalence Classes of the Unimodal Singularities
Magdaleen S. Marais, Andreas Steenpass
In the classification of real singularities by Arnold et al. (1985), normal forms, as representatives of equivalence classes under right equivalence, are not always uniquely determ…
The Classification of Real Singularities Using SINGULAR. Part I: Splitting Lemma and Simple Singularities
Magdaleen S. Marais, Andreas Steenpass
We present algorithms to classify isolated hypersurface singularities over the real numbers according to the classification by V.I. Arnold (Arnold et al., 1985). This first part co…