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