Theorems · Theorem · number theory
Polynomial.isRoot_cyclotomic_iff
∀ {R : Type u_1} [inst : CommRing R] {n : ℕ} [IsDomain R] [NeZero ↑n] {μ : R},
(Polynomial.cyclotomic n R).IsRoot μ ↔ IsPrimitiveRoot μ n- Cited by
- 12 results in Mathlib
- Foundations
- Depth 208 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Polynomialproof · cited by 5,681
- Algebra.algebraMapproof · cited by 4,706
- IsDomainstatement and proof · cited by 2,196
- Polynomial.mapproof · cited by 806
- IsPrimitiveRootstatement and proof · cited by 356
- FractionRingproof · cited by 200
- Polynomial.IsRootstatement and proof · cited by 152
- Polynomial.cyclotomicstatement and proof · cited by 130
- IsFractionRing.injectiveproof · cited by 70
- Polynomial.map_cyclotomicproof · cited by 15
Cited by12
Results whose statement or proof uses this declaration.
- IsPrimitiveRoot.minpoly_eq_cyclotomic_of_irreducibleproof · cited by 4
- IsPrimitiveRoot.sub_one_norm_eq_eval_cyclotomicproof · cited by 3
- Polynomial.cyclotomic_expand_eq_cyclotomicproof · cited by 2
- Polynomial.cyclotomic_expand_eq_cyclotomic_mulproof · cited by 2
- IsCyclotomicExtension.aeval_zetaproof · cited by 1
- Polynomial.roots_cyclotomic_nodupproof · cited by 1
- Nat.exists_prime_gt_modEq_oneproof · cited by 1
- IsPrimitiveRoot.exists_neg_pow_of_isOfFinOrderproof · cited by 1
- Polynomial.cyclotomic_injectiveproof · cited by 1
- Polynomial.isRoot_cyclotomic_iff_charZeroproof · cited by 0
- Polynomial.isRoot_cyclotomic_prime_pow_mul_iff_of_charPproof · cited by 0
- IsSepClosed.isCyclotomicExtensionproof · cited by 0