Recognition and Implementation of Contact Simple Map Germs from (ℂ 2, 0) → (ℂ 2, 0)

Peng Xu, Muhammad Ahsan Binyamin (), Adnan Aslam, Muhammad Shahbaz, Saima Aslam and Salma Kanwal ()
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Peng Xu: Institute of Computational Science and Technology, Guangzhou University, Guangzhou 510006, China
Muhammad Ahsan Binyamin: Department of Mathematics, GC University, Faisalabad 38000, Pakistan
Adnan Aslam: Department of Natural Sciences and Humanities, University of Engineering and Technology, Lahore 54000, Pakistan
Muhammad Shahbaz: Department of Mathematics, GC University, Faisalabad 38000, Pakistan
Saima Aslam: Department of Mathematics, GC University, Faisalabad 38000, Pakistan
Salma Kanwal: Department of Mathematics, Lahore College for Women University, Lahore 54000, Pakistan

Mathematics, 2023, vol. 11, issue 7, 1-11

Abstract: The classification of contact simple map germs from ( C 2 , 0 ) → ( C 2 , 0 ) was given by Dimca and Gibson. In this article, we give a useful criteria to recognize this classification of contact simple map germs of holomorphic mappings with finite codimension. The recognition is based on the computation of explicit numerical invariants. By using this characterization, we implement an algorithm to compute the type of the contact simple map germs without computing the normal form and also give its implementation in the computer algebra system Singular .

Keywords: simple map germ; ?-equivalence; codimension (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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