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arXiv · 1304.6770

Dynamic Newton-Puiseux Theorem

Bassel Mannaa·Thierry Coquand
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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.

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Bassel Mannaa, Thierry Coquand. 2013-06-08. Dynamic Newton-Puiseux Theorem. https://doi.org/10.4115/jla.2013.5.5

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