A classifier for simple space curve singularities

2014 ◽  
Vol 51 (1) ◽  
pp. 92-104
Author(s):  
Faira Janjua ◽  
Gerhard Pfister
Keyword(s):  
Computer Algebra ◽  
Computer Algebra System ◽  
Plane Curve ◽  
Space Curve ◽  
Plane Curve Singularities ◽  
Curve Singularities

The classification of Bruce and Gaffney respectively Gibson and Hobbs for simple plane curve singularities respectively simple space curve singularities is characterized in terms of invariants. This is the basis for the implementation of a classifier in the computer algebra system singular.

Characterization of uni-modal parametric plane curve singularities

2017 ◽  
Vol 16 (02) ◽  
pp. 1750039
Author(s):  
Muhammad Ahsan Binyamin ◽  
Rabia ◽  
Hasan Mahmood ◽  
Junaid Alam Khan ◽  
Khawar Mehmood
Keyword(s):  
Computer Algebra ◽  
Computer Algebra System ◽  
Plane Curve ◽  
Plane Curve Singularities ◽  
Parametric Plane ◽  
Curve Singularities

In this article we characterize the classification of uni-modal parametric plane curve singularities given by Ishikawa and Janeczko, in terms of invariants. On the basis of this characterization we present an algorithm to classify the uni-modal parametric plane curve singularities and also give its implementation in computer algebra system SINGULAR.

Characterization of stably simple curve singularities

2016 ◽  
Vol 53 (3) ◽  
pp. 314-321
Author(s):  
Muhammad Ahsan Binyamin ◽  
Junaid Alam Khan ◽  
Faira Kanwal Janjua ◽  
Naveed Hussain
Keyword(s):  
Computer Algebra ◽  
Computer Algebra System ◽  
Curve Singularities

In this article we characterize the classification of stably simple curve singularities given by V. I. Arnold, in terms of invariants. On the basis of this characterization we describe an implementation of a classifier for stably simple curve singularities in the computer algebra system SINGULAR.

scholarly journals Analytic equivalence of plane curve singularities yn +xαy +xβa(x) = 0

2007 ◽  
pp. 69-78 ◽  
Author(s):  
V. Stepanovic ◽  
A. Lipkovski
Keyword(s):  
Algebraic Curves ◽  
Plane Curve ◽  
Difficult Case ◽  
Plane Curve Singularities ◽  
Curve Singularities

There are not many examples of complete analytical classification of specific families of singularities, even in the case of plane algebraic curves. In 1989, Kang and Kim published a paper on analytical classification of plane curve singularities yn+a(x)y+b(x) = 0, or, equivalently, yn+x?y+x?A(x) = 0 where A(x) is a unit in Ct{x}, ? and ? are integers, ? _ n ? 1 and ? _ n. The classification was not complete in the most difficult case ? n?1 = ? n. In the present paper, the classification is extended also in this case, the proofs are improved and some gaps are removed.

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