∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] (P : Polynomial R)
  {x : S}, P.newtonMap x = x - Ring.inverse ((Polynomial.aeval x) (Polynomial.derivative P)) * (Polynomial.aeval x) P