Theorems · Definition · number theory
IsPrimitiveRoot.toRootsOfUnity
{M : Type u_1} → [inst : CommMonoid M] → {μ : M} → {n : ℕ} → [NeZero n] → IsPrimitiveRoot μ n → ↥(rootsOfUnity n M)Turn a primitive root μ into a member of the rootsOfUnity subgroup.
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext
- Assumes
- CommMonoidNeZero
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Subgroupstatement · cited by 3,593
- Unitsstatement · cited by 2,804
- CommMonoidstatement and proof · cited by 2,264
- IsPrimitiveRootstatement and proof · cited by 356
- rootsOfUnitystatement · cited by 118
- IsPrimitiveRoot.pow_eq_oneproof · cited by 48
- rootsOfUnity.mkOfPowEqproof · cited by 7
Cited by10
Results whose statement or proof uses this declaration.
- IsPrimitiveRoot.autToPowproof · cited by 11
- IsPrimitiveRoot.autToPow_specproof · cited by 5
- IsPrimitiveRoot.idealQuotient_mkproof · cited by 1
- ZMod.exists_monoidHom_apply_ne_oneproof · cited by 1
- IsPrimitiveRoot.coe_autToPow_applystatement · cited by 1
- modularCyclotomicCharacter.toFun_spec''proof · cited by 1
- IsPrimitiveRoot.toRootsOfUnity.congr_simpstatement and proof · cited by 0
- MulEquiv.hasEnoughRootsOfUnityproof · cited by 0
- IsPrimitiveRoot.val_inv_toRootsOfUnity_coestatement · cited by 0
- IsPrimitiveRoot.val_toRootsOfUnity_coestatement and proof · cited by 0