Primitive Genus Two Groups of Meta Type

2018 ◽  
Vol 7 (1-2) ◽  
pp. 1
Author(s):  
Haval Mohammed Salih
Keyword(s):  
Computer Algebra ◽  
Computer Algebra System ◽  
Complete Classification ◽  
Permutation Groups ◽  
Affine Groups ◽  
Two Systems ◽  
Genus Two

This paper is a contribution to the classification of the finite primitive permutation groups of genus two. We consider the case of affine groups. Our main result, Lemma 3.10 gives a complete classification of genus two systems when . We achieve this classification with the aid of the computer algebra system GAP.

scholarly journals An Implementation of Lipschitz Simple Functions in Computer Algebra System Singular

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-5
Author(s):  
Yanan Liu ◽  
Muhammad Ahsan Binyamin ◽  
Adnan Aslam ◽  
Minahal Arshad ◽  
Chengmei Fan ◽  
...  
Keyword(s):  
Normal Form ◽  
Computer Algebra ◽  
Computer Algebra System ◽  
Complete Classification ◽  
Simple Function ◽  
Complex Numbers ◽  
Lipschitz Equivalence

A complete classification of simple function germs with respect to Lipschitz equivalence over the field of complex numbers ℂ was given by Nguyen et al. The aim of this article is to implement a classifier in terms of easy computable invariants to compute the type of the Lipschitz simple function germs without computing the normal form in the computer algebra system Singular.

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.

On the classification of simple maps from the plane to the plane

2017 ◽  
Vol 16 (10) ◽  
pp. 1750199 ◽  
Author(s):  
Muhammad Ahsan Binyamin ◽  
Hasan Mahmood ◽  
Shamsa Kanwal
Keyword(s):  
Computer Algebra ◽  
Computer Algebra System

In this paper, we characterize the classification of simple maps from the plane to the plane given by J. H. Rieger, in terms of invariants. On the basis of this characterization we present an algorithm to classify the simple maps from the plane to the plane and also give its implementation in 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.

The complete classification of fibres in pencils of curves of genus two

1973 ◽  
Vol 9 (2) ◽  
pp. 143-186 ◽  
Author(s):  
Yukihiko Namikawa ◽  
Kenji Ueno
Keyword(s):  
Complete Classification ◽  
Genus Two

My Equations Are the Same as Yours!

2012 ◽  
pp. 259-273
Author(s):  
M Badger ◽  
C J Sangwin
Keyword(s):  
Computer Algebra ◽  
Computer Algebra System ◽  
System Of Equations ◽  
Systems Of Equations ◽  
Computer Aided ◽  
Two Systems

In this chapter we explain how computer aided assessment (CAA) can automatically assess an answer that consists of a system of equations. In particular, we will use a computer algebra system (CAS) and Buchberger’s Algorithm to establish when two systems of equations are the “same.”

Recognition of unimodal map germs from the plane to the plane by invariants

2018 ◽  
Vol 28 (07) ◽  
pp. 1199-1208
Author(s):  
Saima Aslam ◽  
Muhammad Ahsan Binyamin ◽  
Gerhard Pfister
Keyword(s):  
Normal Form ◽  
Computer Algebra ◽  
Computer Algebra System ◽  
Closed Field ◽  
Unimodal Maps ◽  
Unimodal Map ◽  
Algebraically Closed Field

In this paper, we characterize the classification of unimodal maps from the plane to the plane with respect to [Formula: see text]-equivalence given by Rieger in terms of invariants. We recall the classification over an algebraically closed field of characteristic [Formula: see text]. On the basis of this characterization, we present an algorithm to compute the type of the unimodal maps from the plane to the plane without computing the normal form and also give its implementation in the computer algebra system Singular.

scholarly journals Polarized Rigid Del Pezzo Surfaces in Low Codimension

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1567
Author(s):  
Muhammad Imran Qureshi
Keyword(s):  
Computer Algebra System ◽  
Symmetric Matrix ◽  
Single Equation ◽  
Complete Classification ◽  
Computer Assisted ◽  
Del Pezzo Surfaces ◽  
Linearly Independent ◽  
Del Pezzo ◽  
Detailed Computer

We provide explicit graded constructions of orbifold del Pezzo surfaces with rigid orbifold points of type ki×1ri(1,ai):3≤ri≤10,ki∈Z≥0 as well-formed and quasismooth varieties embedded in some weighted projective space. In particular, we present a collection of 147 such surfaces such that their image under their anti-canonical embeddings can be described by using one of the following sets of equations: a single equation, two linearly independent equations, five maximal Pfaffians of 5×5 skew symmetric matrix, and nine 2×2 minors of size 3 square matrix. This is a complete classification of such surfaces under certain carefully chosen bounds on the weights of ambient weighted projective spaces and it is largely based on detailed computer-assisted searches by using the computer algebra system MAGMA.

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.

A classifier for simple isolated complete intersection singularities

2015 ◽  
Vol 52 (1) ◽  
pp. 1-11
Author(s):  
Deeba Afzal ◽  
Gerhard Pfister
Keyword(s):  
Complete Intersection ◽  
Computer Algebra ◽  
Computer Algebra System

M. Giusti’s classification of the simple complete intersection singularities is characterized in terms of invariants. This is a basis for the implementation of a classifier in the computer algebra system Singular.

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