Theorems · Definition · number theory
RingOfIntegers.monicFactorsMod
{K : Type u_1} →
[inst : Field K] → NumberField.RingOfIntegers K → (p : ℕ) → [inst : Fact (Nat.Prime p)] → Finset (Polynomial (ZMod p))The finite set of monic irreducible factors of minpoly ℤ θ modulo p.
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 145 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement · cited by 13,712
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement · cited by 5,681
- Factstatement and proof · cited by 2,726
- Nat.Primestatement and proof · cited by 2,059
- ZModstatement and proof · cited by 1,024
- Polynomial.mapproof · cited by 806
- minpolyproof · cited by 439
- NumberField.RingOfIntegersstatement and proof · cited by 413
- Int.castRingHomproof · cited by 254
- Multiset.toFinsetproof · cited by 230
- UniqueFactorizationMonoid.normalizedFactorsproof · cited by 151
Cited by12
Results whose statement or proof uses this declaration.
- NumberField.Ideal.primesOverSpanEquivMonicFactorsModstatement · cited by 10
- NumberField.Ideal.primesOverSpanEquivMonicFactorsMod_symm_apply_eq_spanstatement and proof · cited by 2
- NumberField.Ideal.inertiaDeg_primesOverSpanEquivMonicFactorsMod_symm_applystatement and proof · cited by 1
- NumberField.Ideal.inertiaDeg_primesOverSpanEquivMonicFactorsMod_symm_apply'statement and proof · cited by 1
- NumberField.Ideal.liesOver_primesOverSpanEquivMonicFactorsMod_symmstatement and proof · cited by 1
- NumberField.Ideal.ramificationIdx_primesOverSpanEquivMonicFactorsMod_symm_applystatement and proof · cited by 1
- NumberField.Ideal.ramificationIdx_primesOverSpanEquivMonicFactorsMod_symm_apply'statement and proof · cited by 1
- RingOfIntegers.ZModXQuotSpanEquivQuotSpanPairstatement and proof · cited by 1
- IsCyclotomicExtension.Rat.inertiaDeg_eq_of_not_dvdproof · cited by 1
- IsCyclotomicExtension.Rat.ramificationIdx_eq_of_not_dvdproof · cited by 1
- NumberField.Ideal.primesOverSpanEquivMonicFactorsMod_symm_applystatement and proof · cited by 0
- NumberField.Ideal.primesOverSpanEquivMonicFactorsMod.congr_simpstatement · cited by 0