Dynamic Newton–Puiseux theorem

Bassel Mannaa, Thierry Coquand
2013 Journal of Logic and Analysis  
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.
doi:10.4115/jla.2013.5.5 fatcat:rhy2cztplff37h2jtzgmn7bgxy