Recognition of Contact Map Germs from the Plane to the Plane by Invariants

Binyamin, Muhammad Ahsan; Aslam, Saima; Mahmood, Khawar; Mahmood, Hasan; Ishaq, Muhammad

doi:10.7546/crabs.2020.06.02

Cited by 2 publications

(2 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…3: Define the expected normal form (h 1 , h 2 ) depending on parameters. 4: Define J := ϕ(I ) − T h 1 h 2 . 5: Let K be the ideal generated by all the coefficients of J with respect to x, y.…”

Section: Characterization Of Unimodal Map Germs By Invariantsmentioning

confidence: 99%

“…In [9], Dimca and Gibson gave the classification of all map germs from the plane to the plane of Boardman symbol (2,1) and (2,2) with respect to K -equivalence. A classifier for the classification of Dimca and Gibson, in the case of Boardman symbol (2, 1) is given in [4]. This is equivalent to consider A (2,2) as the set of map germs (C 2 , 0) → (C 2 , 0) under the action of the group K = Aut C (C 2 , 0) × Gl 2 (C 2 , 0).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Contact unimodal map germs from the plane to the plane

Binyamin¹,

Aslam²,

Mehmood³

2020

Comptes Rendus. Mathématique

Self Cite

View full text Add to dashboard Cite

In this article, we correct the classification of unimodal map germs from the plane to the plane of Boardman symbol (2, 2) given by Dimca and Gibson. Also, we characterize this classification of unimodal map germs in terms of certain invariants. Moreover, on the basis of this characterization we present an algorithm to compute the type of unimodal map germs of the Boardman symbol (2, 2) without computing the normal form and give its implementation in the computer algebra system Singular [8].

show abstract

Section: Characterization Of Unimodal Map Germs By Invariantsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Contact unimodal map germs from the plane to the plane

Binyamin¹,

Aslam²,

Mehmood³

2020

Comptes Rendus. Mathématique

Self Cite

View full text Add to dashboard Cite

show abstract

A characterization and implementation of corank one map germs from $ 2 $-space to $ 3 $-space in the computer algebra system SINGULAR

Wang

Binyamin²,

Iqbal³

et al. 2023

MATH

View full text Add to dashboard Cite

<abstract>The classification and the geometry of corank one map germs from $ ({\mathbb{C}}^2, 0) \rightarrow ({\mathbb{C}}^3, 0) $ have been studied by Mond [<xref ref-type="bibr" rid="b1">1</xref>,<xref ref-type="bibr" rid="b2">2</xref>]. In this paper we characterize the classification of map germs of corank at most $ 1 $, in terms of certain invariants. Moreover, by using this characterization, we develop an algorithm to compute the type of map germs with out computing the normal form. Also, we give its implementation in the computer algebra system SINGULAR [<xref ref-type="bibr" rid="b15">15</xref>].</abstract>

show abstract

Recognition of Contact Map Germs from the Plane to the Plane by Invariants

Cited by 2 publications

References 0 publications

Contact unimodal map germs from the plane to the plane

Contact unimodal map germs from the plane to the plane

A characterization and implementation of corank one map germs from $ 2 $-space to $ 3 $-space in the computer algebra system SINGULAR

Contact Info

Product

Resources

About