Theorems · Theorem · number theory
Polynomial.degree_cyclotomic
∀ (n : ℕ) (R : Type u_1) [inst : Ring R] [Nontrivial R], (Polynomial.cyclotomic n R).degree = ↑n.totient
The degree of cyclotomic n is totient n.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 202 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.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Ringstatement and proof · cited by 7,463
- Polynomialproof · cited by 5,681
- Nontrivialstatement and proof · cited by 2,416
- WithBotstatement and proof · cited by 1,498
- Polynomial.mapproof · cited by 806
- Polynomial.degreestatement and proof · cited by 643
- Int.cast_oneproof · cited by 371
- CharP.cast_eq_zeroproof · cited by 357
- Int.castRingHomproof · cited by 254
- Polynomial.cyclotomicstatement and proof · cited by 130
- eq_intCastproof · cited by 127
Cited by3
Results whose statement or proof uses this declaration.
- Polynomial.natDegree_cyclotomicproof · cited by 12
- Polynomial.degree_cyclotomic_posproof · cited by 2
- IsPrimitiveRoot.sum_eq_zero_iff_forall_eqproof · cited by 1