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.

Lemma zprimitive_monic p : p \in monic -> zprimitive p = p.