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

Author

Listed:
  • Peng Xu

    (Institute of Computational Science and Technology, Guangzhou University, Guangzhou 510006, China
    School of Computer Science of Information Technology, Qiannan Normal University for Nationalities, Duyun 558000, 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)

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 .

Suggested Citation

  • Peng Xu & Muhammad Ahsan Binyamin & Adnan Aslam & Muhammad Shahbaz & Saima Aslam & Salma Kanwal, 2023. "Recognition and Implementation of Contact Simple Map Germs from (ℂ 2 , 0) → (ℂ 2 , 0)," Mathematics, MDPI, vol. 11(7), pages 1-11, March.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:7:p:1575-:d:1105879
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