End FieldRingMap.
Section FieldMap.
Variable rR : idomainType.
Variable f : {rmorphism F -> rR}.
Local Notation "p ^f" := (map_poly f p) : ring_scope.
Implicit Type a b : {poly F}.

Lemma gdcop_map p q : (gdcop p q)^f = (gdcop p^f q^f).