Zobrazeno 1 - 10
of 33
pro vyhledávání: '"Marais, Magdaleen S."'
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 classification's scope significantly by a class which is unbounded with res
Externí odkaz:
http://arxiv.org/abs/2402.05093
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 under consideration modulo a number of primes and then lift the result
Externí odkaz:
http://arxiv.org/abs/2401.11606
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 singularities over the complex numbers with either modality less than or
Externí odkaz:
http://arxiv.org/abs/2010.10185
Publikováno v:
Singularities and Computer Algebra - Festschrift for Gert-Martin Greuel on the Occasion of his 70th Birthday, Springer 2017, 21-46
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 modality 2. Building on a series of 105 theorems, this classifier deter
Externí odkaz:
http://arxiv.org/abs/1604.04774
Publikováno v:
Journal of Symbolic Computation 99, 250-282 (2020)
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 rationals, the algorithm determines its right equivalence class by specif
Externí odkaz:
http://arxiv.org/abs/1512.09028
Publikováno v:
LNCS 9725 (2016), 117-126
3D printing and other layer manufacturing processes are challenged by dimensional accuracy. Several techniques are used to validate and calibrate dimensional accuracy through the complete building envelope. The validation process involves the growing
Externí odkaz:
http://arxiv.org/abs/1512.09036
Autor:
Marais, Magdaleen S., Ren, Yue
Publikováno v:
Internat. J. Algebra Comput. 25(7) (2015), 1125-1143
This article discusses a computational treatment of the localization A_L of an affine coordinate ring A at a prime ideal L and its associated graded ring Gr_a(A_L) with the means of standard basis techniques. Building on Mora's work, we present alter
Externí odkaz:
http://arxiv.org/abs/1504.01648
The classification of real singularities using Singular Part III: Unimodal singularities of corank 2
Publikováno v:
In Journal of Symbolic Computation July-August 2020 99:250-282
Publikováno v:
J. Symb. Comput. 74 (2016), 346-366
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 determined. We describe the complete structure of the equivalence classes of
Externí odkaz:
http://arxiv.org/abs/1310.0048
Publikováno v:
J. Symb. Comput. 68 (2015), 61-71
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 covers the splitting lemma and the simple singularities; a second and a
Externí odkaz:
http://arxiv.org/abs/1303.7114