Theorems · Theorem · number theory
Polynomial.natDegree_cyclotomic
∀ (n : ℕ) (R : Type u_1) [inst : Ring R] [Nontrivial R], (Polynomial.cyclotomic n R).natDegree = n.totient
The natural degree of cyclotomic n is totient n.
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 203 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RingNontrivial
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Ringstatement and proof · cited by 7,463
- Nontrivialstatement and proof · cited by 2,416
- WithBotproof · cited by 1,498
- Polynomial.natDegreestatement · cited by 1,105
- Polynomial.cyclotomicstatement and proof · cited by 130
- Nat.totientstatement and proof · cited by 111
- WithBot.unbotDproof · cited by 49
- Polynomial.degree_cyclotomicproof · cited by 3
Cited by12
Results whose statement or proof uses this declaration.
- IsCyclotomicExtension.finrankproof · cited by 12
- Polynomial.cyclotomic_eq_minpolyproof · cited by 7
- IsPrimitiveRoot.norm_eq_oneproof · cited by 3
- Polynomial.cyclotomic_expand_eq_cyclotomicproof · cited by 2
- Polynomial.cyclotomic_expand_eq_cyclotomic_mulproof · cited by 2
- IsPrimitiveRoot.integralPowerBasisOfPrimePow_dimproof · cited by 1
- cyclotomic_comp_X_add_one_isEisensteinAtproof · cited by 1
- cyclotomic_prime_pow_comp_X_add_one_isEisensteinAtproof · cited by 1
- Polynomial.cyclotomic_injectiveproof · cited by 1
- Polynomial.natDegree_cyclotomic_leproof · cited by 0
- IsPrimitiveRoot.integralPowerBasis_dimproof · cited by 0
- Polynomial.normalizedFactors_cyclotomic_cardproof · cited by 0