(* (Integral) Cyclotomic polynomials. *)
Notation "''Phi_' n" := (Cyclotomic n)
(at level 8, n at level 2, format "''Phi_' n").

(* Specifications: *)
Lemma Cyclotomic_monic n : 'Phi_n \is monic.
Lemma Cintr_Cyclotomic n z :
n.-primitive_root z -> pZtoC 'Phi_n = cyclotomic z n.
Lemma prod_Cyclotomic n :
(n > 0)%N -> \prod_(d <- divisors n) 'Phi_d = 'X^n - 1.
Lemma Cyclotomic0 : 'Phi_0 = 1.
Lemma size_Cyclotomic n : size 'Phi_n = (totient n).+1.
Lemma minCpoly_cyclotomic n z :
n.-primitive_root z -> minCpoly z = cyclotomic z n.