### Dynamic Newton-Puiseux theorem

#### 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.

#### Full Text:

5. [PDF]DOI: https://doi.org/10.4115/jla.2013.5.5

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Journal of Logic and Analysis ISSN: 1759-9008