roots, in an algebraic closure. This has aspects both of ramification theory and singularity theory. The valid inferences possible are to the valuations of power sums, by means of Newton's identities. History Newton polygons are named after Isaac Newton, who first described them and some of their uses in correspondence from the year 1676 addressed to Henry Oldenburg. See also F-crystal Eisenstein's criterion Newton–Okounkov body Newton polytope References Gouvêa, Fernando: p-adic numbers: An introduction. Springer Verlag 1993. p. 199. External links Applet drawing a Newton Polygon Algebraic number theory Symmetric functions Isaac Newton