Algebraic Number Theory
《Algebraic Number Theory》 · 第 144 页 · Chapter II，Section 6「Henselian Fields」，定义段
Let $v$ be an arbitrary exponential valuation of the field $K$ and let $f(x)=a_0+a_1x+\cdots+a_nx^n\in K[x]$ be a polynomial satisfying $a_0a_n\ne0$. To each term $a_ix^i$ we associate a point $(i,v(a_i))\in\mathbb R^2$, ignoring however the point $(i,\infty)$ if $a_i=0$. We now take the lower convex envelope of the set of points $\{(0,v(a_0)),(1,v(a_1)),\ldots,(n,v(a_n))\}$. This produces a polygonal chain which is called the Newton polygon of $f(x)$.