∀ {p : ℕ} {K : Type u} {L : Type v} {ζ : L} [inst : Field K] [inst_1 : Field L] [inst_2 : Algebra K L]
  [inst_3 : IsCyclotomicExtension {p} K L] [hp : Fact (Nat.Prime p)] (hζ : IsPrimitiveRoot ζ p),
  Irreducible (Polynomial.cyclotomic p K) →
    p ≠ 2 → Algebra.discr K ⇑(IsPrimitiveRoot.powerBasis K hζ).basis = (-1) ^ ((p - 1) / 2) * ↑p ^ (p - 2)