English

Dynamic Newton-Puiseux Theorem

Commutative Algebra 2013-06-11 v2

Abstract

A constructive version of Newton-Puiseux theorem for computing the Puiseux expansions of algebraic curves is presented. The proof is based on a classical proof by Abhyankar. Algebraic numbers are evaluated dynamically; hence the base field need not be algebraically closed and a factorization algorithm of polynomials over the base field is not needed. The extensions obtained are a type of regular algebras over the base field and the expansions are given as formal power series over these algebras.

Keywords

Cite

@article{arxiv.1304.6770,
  title  = {Dynamic Newton-Puiseux Theorem},
  author = {Bassel Mannaa and Thierry Coquand},
  journal= {arXiv preprint arXiv:1304.6770},
  year   = {2013}
}

Comments

22 page

R2 v1 2026-06-22T00:05:59.444Z