Slopes of the Newton polygon of a polynomial (reviewed)

Given a polynomial $f$ defined over a local field $K$, the slopes of its Newton polygon are a list of increasing numbers $[s_1,s_2,s_3, \ldots]$ such that the Newton polygon of $f$ is given by a line segment of width 1 with slope $s_1$, followed by a line segment of width 1 with slope $s_2$, etc. Note that it is possible for a slope to appear multiple times if the Newton polygon has the same slope for a width of more than 1.