Theorems · Theorem · field theory
Polynomial.Gal.restrictDvd_def
∀ {F : Type u_1} [inst : Field F] {p q : Polynomial F} [inst_1 : Decidable (q = 0)] (hpq : p ∣ q),
Polynomial.Gal.restrictDvd hpq = if hq : q = 0 then 1 else Polynomial.Gal.restrict p q.SplittingField- Cited by
- 2 results in Mathlib
- Foundations
- Depth 161 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement and proof · cited by 5,681
- Algebra.algebraMapstatement · cited by 4,706
- MonoidHomstatement and proof · cited by 3,629
- AlgEquivstatement · cited by 1,681
- Polynomial.mapstatement · cited by 806
- Polynomial.Splitsstatement · cited by 290
- Polynomial.SplittingFieldstatement and proof · cited by 42
- Polynomial.Galstatement and proof · cited by 37
- Polynomial.map_ne_zerostatement · cited by 22
- Polynomial.SplittingField.splitsstatement · cited by 21
- Polynomial.Splits.of_dvdstatement · cited by 21
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.Gal.restrictProd_injectiveproof · cited by 1
- Polynomial.Gal.restrictDvd_surjectiveproof · cited by 1