Section ZpolyScale.
Definition zcontents p :=
sgz (lead_coef p) * \big[gcdn/0%N]_(i < size p) `|(p`_i)%R|%N.

Lemma map_poly_divzK {a} p :
p \is a polyOver (dvdz a) -> a *: map_poly (divz^~ a) p = p.