(* Roots of unity. *)

(* Specifications: *)
Lemma size_Xn_sub_1 n : n > 0 -> size ('X^n - 1 : {poly R}) = n.+1.
Lemma monic_Xn_sub_1 n : n > 0 -> 'X^n - 1 \is monic.
Definition root_of_unity n : pred R := root ('X^n - 1).