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Asymptotic Behavior of a Surface Implicitly Defined

Author

Listed:
  • Elena Campo-Montalvo

    (Departamento de Automática, Universidad de Alcalá, E-28871 Madrid, Spain
    These authors contributed equally to this work.)

  • Marián Fernández de Sevilla

    (Departamento de Automática, Universidad de Alcalá, E-28871 Madrid, Spain
    These authors contributed equally to this work.)

  • Sonia Pérez-Díaz

    (Departamento de Automática, Universidad de Alcalá, E-28871 Madrid, Spain
    These authors contributed equally to this work.)

Abstract

In this paper, we introduce the notion of infinity branches and approaching surfaces. We obtain an algorithm that compares the behavior at the infinity of two given algebraic surfaces that are defined by an irreducible polynomial. Furthermore, we show that if two surfaces have the same asymptotic behavior, the Hausdorff distance between them is finite. All these concepts are new and represent a great advance for the study of surfaces and their applications.

Suggested Citation

  • Elena Campo-Montalvo & Marián Fernández de Sevilla & Sonia Pérez-Díaz, 2022. "Asymptotic Behavior of a Surface Implicitly Defined," Mathematics, MDPI, vol. 10(9), pages 1-19, April.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:9:p:1445-:d:801905
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    References listed on IDEAS

    as
    1. Hong, Hoon, 1996. "An efficient method for analyzing the topology of plane real algebraic curves," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 42(4), pages 571-582.
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    Cited by:

    1. Rafael Magdalena-Benedicto & Sonia Pérez-Díaz & Adrià Costa-Roig, 2023. "Challenges and Opportunities in Machine Learning for Geometry," Mathematics, MDPI, vol. 11(11), pages 1-24, June.

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