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 zcontentsM p q : zcontents (p * q) = zcontents p * zcontents q.