# Computing the equisingularity type of a pseudo-irreducible polynomial

@article{Poteaux2020ComputingTE, title={Computing the equisingularity type of a pseudo-irreducible polynomial}, author={Adrien Poteaux and Martin Weimann}, journal={Applicable Algebra in Engineering, Communication and Computing}, year={2020}, pages={1 - 26} }

Germs of plane curve singularities can be classified accordingly to their equisingularity type. For singularities over C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {C}$$\end{document}, this important data coincides with the topological class. In this paper, we characterise a family of singularities… Expand

#### References

SHOWING 1-10 OF 56 REFERENCES

A quasi-linear irreducibility test in $\mathbb{K}[[x]][y]$

- Mathematics
- 2019

We provide an irreducibility test in the ring $\mathbb{K}[[x]][y]$ whose complexity is quasi-linear with respect to the valuation of the discriminant, assuming the input polynomial $F$ square-free… Expand

Using approximate roots for irreducibility and equi-singularity issues in K[[x]][y]

- Mathematics
- 2019

We provide an irreducibility test in the ring K[[x]][y] whose complexity is quasi-linear with respect to the valuation of the discriminant, assuming the input polynomial F square-free and K a perfect… Expand

A quasi-linear irreducibility test in K

- 2019

We provide an irreducibility test in the ring K[[x]][y] whose complexity is quasi-linear with respect to the discriminant valuation, assuming the input polynomial F square-free and K a perfect field… Expand

Computing Puiseux series: a fast divide and conquer algorithm

- Mathematics
- Annales Henri Lebesgue
- 2021

Let $F ∈ K[X, Y ]$ be a polynomial of total degree D defined over a field K of characteristic zero or greater than D. Assuming F separable with respect to Y , we provide an algorithm that computes… Expand

Improving Complexity Bounds for the Computation of Puiseux Series over Finite Fields

- Computer Science, Mathematics
- ISSAC
- 2015

This paper reduces this bound to O~(d4+d2log q) using Hensel lifting and changes of variables in the Newton-Puiseux algorithm that give a better control of the number of steps. Expand

Irreducibility criterion for germs of analytic functions of two complex variables

- Mathematics
- 1989

Let S(X, Y) be the germ of an analytic function of two complex variables near the origin. To decide whether f is irreducible or not, we can apply a succession of blowing-ups to desingularize f and… Expand

Plane Curve Singularities

- Physics
- 2000

This chapter is devoted to the study of plane curve singularities. First of all, from the existence of the normalization, and the fact that one-dimensional normal singularities are smooth, which are… Expand

Complexity bounds for the rational Newton-Puiseux algorithm over finite fields

- Mathematics, Computer Science
- Applicable Algebra in Engineering, Communication and Computing
- 2011

It is proved that coefficients of F may be significantly truncated and that certain complexity upper bounds may be expressed in terms of the output size. Expand

A regularization method for computing approximate invariants of plane curves singularities

- Computer Science, Mathematics
- SNC '11
- 2012

The convergence for inexact data of the symbolic-numeric algorithms is proved by using concepts from algebraic geometry and topology to prove the validity for the convergence statement. Expand

An Adapted Version of the Bentley-Ottmann Algorithm for Invariants of Plane Curves Singularities

- Mathematics, Computer Science
- ICCSA
- 2011

An adapted version of the Bentley-Ottmann algorithm for computing all the intersection points among the edges of the projection of a three-dimensional graph, which represents the approximation of a closed and smooth implicitly defined space algebraic curve. Expand