Reflected Newton polygon convention
= Reflected Newton polygon convention
{title2=$(d-j,v(a_j))$}
For a degree-$d$ <polynomial>, reflecting the usual coefficient-index axis replaces $(j,v(a_j))$ by $(d-j,v(a_j))$. The reflected lower polygon has slopes equal to root <valuations>, rather than their negatives. Horizontal lengths, and therefore multiplicities, are unchanged. This convention makes positive lower <ramification groups> breaks appear as positive slopes of a reduced ramification polygon.