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 size_rat_int_poly p : size (pZtoQ p) = size p.