Section MoreAlgCaut.
Implicit Type rR : unitRingType.
End NumFieldProj.
(* Integral spans. *)
Definition Cint_span (s : seq algC) : pred algC :=
fun x => dec_Cint_span (in_tuple [seq \row_(i < 1) y | y <- s]) (\row_i x).
Fact Cint_span_key s : pred_key (Cint_span s). Proof. by []. Qed.
Canonical Cint_span_keyed s := KeyedPred (Cint_span_key s).
Canonical Cint_span_opprPred s := OpprPred (Cint_span_zmod_closed s).
Canonical Cint_span_addrPred s := AddrPred (Cint_span_zmod_closed s).
Canonical Cint_span_zmodPred s := ZmodPred (Cint_span_zmod_closed s).

(* Extended automorphisms of Q_n. *)
Lemma Qn_aut_exists k n :
coprime k n ->
{u : {rmorphism algC -> algC} | forall z, z ^+ n = 1 -> u z = z ^+ k}.