The Newton–Puiseux Algorithm and Triple Points for Plane Curves

Stefano Canino, Alessandro Gimigliano () and Monica Idà
Additional contact information
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

Mathematics, 2023, vol. 11, issue 10, 1-31

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.

Keywords: plane curves singularities; Newton–Puiseux algorithm; triple points (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/10/2324/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/10/2324/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:11:y:2023:i:10:p:2324-:d:1148397

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().