fact: Definition sgr (x : R) : R := if x == 0 then 0 else if x < 0 then -1 else 1.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(ssrAC div fintype path bigop order finset fingroup) mathcomp(ssralg poly)