Section ZpolyScale.
Definition zcontents p :=
sgz (lead_coef p) * \big[gcdn/0%N]_(i < size p) `|(p`_i)%R|%N.
Definition zprimitive p := map_poly (divz^~ (zcontents p)) p.
Local Notation pZtoQ := (map_poly (intr : int -> rat)).

Lemma dvdp_rat_int p q : (pZtoQ p %| pZtoQ q) = (p %| q).