Theorems · Theorem · number theory
Polynomial.cyclotomic_eq_minpoly_rat
∀ {n : ℕ} {K : Type u_2} [inst : Field K] {μ : K},
IsPrimitiveRoot μ n → 0 < n → ∀ [inst_1 : CharZero K], Polynomial.cyclotomic n ℚ = minpoly ℚ μcyclotomic n ℚ is the minimal polynomial of a primitive n-th root of unity μ.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 209 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement and proof · cited by 5,681
- CharZerostatement and proof · cited by 932
- Polynomial.mapproof · cited by 806
- minpolystatement and proof · cited by 439
- IsPrimitiveRootstatement and proof · cited by 356
- Int.castRingHomproof · cited by 254
- Polynomial.cyclotomicstatement · cited by 130
- Polynomial.map_cyclotomic_intproof · cited by 21
- IsPrimitiveRoot.isIntegralproof · cited by 15
- minpoly.isIntegrallyClosed_eq_field_fractions'proof · cited by 11
- Polynomial.cyclotomic_eq_minpolyproof · cited by 7
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.cyclotomic_expand_eq_cyclotomic_mulproof · cited by 2
- IsPrimitiveRoot.sum_eq_zero_iff_forall_eqproof · cited by 1