Definition horner_morph u of commr_rmorph u := fun p => (map_poly p).[u].
End Definitions.
Variables aR rR : ringType.
Section Combinatorial.
Variables (iR : ringType) (f : aR -> rR).
Local Notation "p ^f" := (map_poly f p) : ring_scope.

Lemma map_Poly_id0 s : f 0 = 0 -> (Poly s)^f = Poly (map f s).