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The Newton–Puiseux Algorithm and Triple Points for Plane Curves

Author

Listed:
  • Stefano Canino

    (Dipartimento di Scienze Matematiche, Politecnico di Torino, 10129 Torino, Italy)

  • Alessandro Gimigliano

    (Dipartimento di Matematica, Università di Bologna, 40126 Bologna, Italy)

  • Monica Idà

    (Dipartimento di Matematica, Università di Bologna, 40126 Bologna, Italy)

Abstract

The paper is an introduction to the use of the classical Newton–Puiseux procedure, oriented towards an algorithmic description of it. This procedure allows to obtain polynomial approximations for parameterizations of branches of an algebraic plane curve at a singular point. We look for an approach that can be easily grasped and is almost self-contained. We illustrate the use of the algorithm first in a completely worked out example of a curve with a point of multiplicity 6, and secondly, in the study of triple points on reduced plane curves.

Suggested Citation

  • Stefano Canino & Alessandro Gimigliano & Monica Idà, 2023. "The Newton–Puiseux Algorithm and Triple Points for Plane Curves," Mathematics, MDPI, vol. 11(10), pages 1-31, May.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:10:p:2324-:d:1148397
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