The Newton–Puiseux Algorithm and Triple Points for Plane Curves
نویسندگان
چکیده
The paper is an introduction to the use of classical Newton–Puiseux procedure, oriented towards algorithmic description it. This procedure allows obtain polynomial approximations for parameterizations branches algebraic plane curve at a singular point. We look approach that can be easily grasped and almost self-contained. illustrate algorithm first in completely worked out example with point multiplicity 6, secondly, study triple points on reduced curves.
منابع مشابه
Singular Points of Plane Curves
ly isomorphic to (C×)r−1 × (C), and hence also to (S1)r−1 × (R), where r = |J | is the number of branches and k = δ(C)− r+1 = 1 2 (μ(C) + 1 − r). The construction of the Jacobian variety J(C̃) of the non-singular curve C̃ in the large is standard in algebraic geometry. There is also a notion of Jacobian of a singular curve C , defined e.g. in [85], which, like the other, is an abelian group. Ther...
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ژورنال
عنوان ژورنال: Mathematics
سال: 2023
ISSN: ['2227-7390']
DOI: https://doi.org/10.3390/math11102324