End IntegralOverRing.
Section IntegralOverComRing.
Variables (R K : comRingType) (RtoK : {rmorphism R -> K}).

(* Specifications: *)
Lemma integral_horner_root w (p q : {poly K}) :
p \is monic -> root p w ->
{in p : seq K, integralRange RtoK} -> {in q : seq K, integralRange RtoK} ->
integralOver RtoK q.[w].
Lemma integral_root_monic u p :
p \is monic -> root p u -> {in p : seq K, integralRange RtoK} ->
integralOver RtoK u.