Theorems · Theorem · number theory
Polynomial.natDegree_of_mem_normalizedFactors_cyclotomic
∀ {K : Type u_1} [inst : Field K] [inst_1 : Fintype K] {p f n : ℕ} {P : Polynomial K},
Fintype.card K = p ^ f →
∀ (hn : p.Coprime n) [hp : Fact (Nat.Prime p)] [inst_2 : DecidableEq K],
P ∈ UniqueFactorizationMonoid.normalizedFactors (Polynomial.cyclotomic n K) →
P.natDegree = orderOf (ZMod.unitOfCoprime (p ^ f) ⋯)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 212 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FieldFintypeFactDecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fintypestatement and proof · cited by 7,736
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement and proof · cited by 5,681
- Unitsstatement · cited by 2,804
- Factstatement and proof · cited by 2,726
- Multisetstatement · cited by 2,627
- Nat.Primestatement and proof · cited by 2,059
- Fintype.cardstatement and proof · cited by 1,386
- Polynomial.natDegreestatement · cited by 1,105
- ZModstatement · cited by 1,024
- orderOfstatement · cited by 324
- UniqueFactorizationMonoid.normalizedFactorsstatement and proof · cited by 151
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.normalizedFactors_cyclotomic_cardproof · cited by 0