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

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

  

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- Natural & Formal Sciences -

**Mathematics & Logic Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A geometric construction that associates a convex polygon (or, in higher dimensions, a polyhedron) to a polynomial or formal power series by plotting points whose coordinates are the exponents and the valuations (or orders) of the corresponding coefficients, then taking a convex hull; used to analyze valuations of roots, factorization over valued fields, and ramification behaviour.