Research article

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

  • Received: 03 September 2022 Revised: 04 November 2022 Accepted: 20 November 2022 Published: 28 November 2022
  • MSC : 58Q05, 14H20

  • 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 [1,2]. 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 [15].

    Citation: Ying Wang, Muhammad Ahsan Binyamin, Tauqeer Iqbal, Saima Aslam, Adnan Aslam. A characterization and implementation of corank one map germs from $ 2 $-space to $ 3 $-space in the computer algebra system SINGULAR[J]. AIMS Mathematics, 2023, 8(2): 3747-3762. doi: 10.3934/math.2023187

    Related Papers:

  • 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 [1,2]. 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 [15].



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    [9] M. A. Binyamin, S. Aslam, K. Mehmood, Contact unimodal map germs from the plane to the plane, Comptes Rendus Math., 358 (2020), 923–930. https://doi.org/10.5802/crmath.114 doi: 10.5802/crmath.114
    [10] S. Aslam, M. A. Binyamin, G. Pfister, Recognition of unimodal map germs from the plane to the plane by invariants, Int. J. Algebra Comput., 28 (2018), 1199–1208. https://doi.org/10.1142/S0218196718500534 doi: 10.1142/S0218196718500534
    [11] M. A. Binyamin, S. Aslam, K. Mehmood, H. Mahmood, M. Ishaq, Recognition of contact map germs from the plane to the plane by invariants, C. R. Acad. Bulg. Sci., 73 (2020), 758–766. https://doi.org/10.7546/CRABS.2020.06.02 doi: 10.7546/CRABS.2020.06.02
    [12] S. Aslam, M. A. Binyamin, H. Mahmood, A classifier for equidimensional contact unimodal map germs, Bull. Math. Soc. Sci. Math. Roumanie, 64 (2021), 287–302.
    [13] M. A. Binyamin, H. Mahmood, S. Kanwal, On the classification of simple maps from the plane to the plane, J. Algebra Appl., 16 (2017), 1750199. https://doi.org/10.1142/S0219498817501997 doi: 10.1142/S0219498817501997
    [14] M. A. Binyamin, K. Mehmood, G. Pfister, On Mond's classification of simle map germs from $\mathbb{C}^2$ to $\mathbb{C}^3$, C. R. Acad. Bulg. Sci., 74 (2021), 1109–1119. https://doi.org/10.7546/CRABS.2021.08.01 doi: 10.7546/CRABS.2021.08.01
    [15] W. Decker, G. M. Greuel, G. Pfister, H. Schönemann, SINGULAR. Available from: http://www.singular.uni-kl.de.
    [16] D. Ratcliffe, On the classification and geometry of finite map-germs, Ph.D. Thesis, University of Warwick, 1990.
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