##  [Newton Polygon Method](/newton-polygon-method) 

  ##  [Newton Polygon Method](https://algebra.quantumdictionary.io/newton-polygon-method-0) 

  

 [![Algebra](/sites/default/files/styles/large/public/2026-01/Algebra.png.webp?itok=3pHxBnUF)](/topic-specific-dictionaries/pure-mathematics/algebra)

- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A valuation-based graphical technique that builds the Newton polygon of a polynomial (or series) to read off slopes which correspond to valuations of roots and to guide factorization and ramification analysis in discretely valued (local) fields.