Theorems · Definition · field theory
Polynomial.Separable
{R : Type u} → [inst : CommSemiring R] → Polynomial R → PropA polynomial is separable iff it is coprime with its derivative.
- Defined in
- Mathlib.FieldTheory.Separable
- Cited by
- 117 results in Mathlib
- Foundations
- Depth 106 from the axioms, rests on 2,256 definitions · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommSemiringstatement and proof · cited by 10,911
- Polynomialstatement and proof · cited by 5,681
- Polynomial.derivativeproof · cited by 331
- IsCoprimeproof · cited by 321
Cited by123
Results whose statement or proof uses this declaration.
- IsSeparableproof · cited by 68
- Polynomial.Separable.mapstatement and proof · cited by 14
- Polynomial.Separable.of_dvdstatement and proof · cited by 14
- Polynomial.nodup_rootsstatement and proof · cited by 10
- isPurelyInseparable_iff_pow_memproof · cited by 10
- Polynomial.separable_defstatement · cited by 7
- Polynomial.IsSeparableContractionproof · cited by 7
- IntermediateField.isSeparable_of_mem_isSeparableproof · cited by 7
- Irreducible.separablestatement · cited by 6
- Polynomial.separable_X_pow_sub_Cstatement · cited by 6
- Polynomial.separable_mapstatement and proof · cited by 6
- Polynomial.Separable.aeval_derivative_ne_zerostatement and proof · cited by 6