Theorems · Theorem · number theory
IsCyclotomicExtension.autEquivPow_symm_apply
∀ {n : ℕ} [inst : NeZero n] {K : Type u_1} [inst_1 : Field K] (L : Type u_2) [inst_2 : CommRing L] [inst_3 : IsDomain L]
[inst_4 : Algebra K L] [inst_5 : IsCyclotomicExtension {n} K L] (h : Irreducible (Polynomial.cyclotomic n K))
(t : (ZMod n)ˣ),
(IsCyclotomicExtension.autEquivPow L h).symm t =
(IsPrimitiveRoot.powerBasis K ⋯).equivOfMinpoly (IsPrimitiveRoot.powerBasis K ⋯) ⋯- Defined in
- Mathlib.NumberTheory.Cyclotomic.Gal
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 215 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement · cited by 5,681
- Unitsstatement and proof · cited by 2,804
- IsDomainstatement and proof · cited by 2,196
- Units.valstatement · cited by 1,966
- AlgEquivstatement · cited by 1,681
- MulEquivstatement · cited by 1,142
- ZModstatement and proof · cited by 1,024
Cited by1
Results whose statement or proof uses this declaration.
- IsCyclotomicExtension.fromZetaAut_specproof · cited by 0