Theorems · Theorem · field theory
Polynomial.Separable.aeval_derivative_ne_zero
∀ {R : Type u} [inst : CommSemiring R] {S : Type v} [inst_1 : CommSemiring S] [Nontrivial S] [inst_3 : Algebra R S]
{p : Polynomial R},
p.Separable → ∀ {x : S}, (Polynomial.aeval x) p = 0 → (Polynomial.aeval x) (Polynomial.derivative p) ≠ 0- Defined in
- Mathlib.FieldTheory.Separable
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- RingHom.idstatement · cited by 18,349
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- LinearMapstatement · cited by 10,215
- Polynomialstatement and proof · cited by 5,681
- Algebra.algebraMapproof · cited by 4,706
- AlgHomstatement · cited by 3,236
- Nontrivialstatement and proof · cited by 2,416
- Polynomial.aevalstatement and proof · cited by 615
- Polynomial.derivativestatement · cited by 331
- Polynomial.Separablestatement and proof · cited by 117
Cited by6
Results whose statement or proof uses this declaration.
- Algebra.FormallyUnramified.of_isSeparableproof · cited by 5
- Differential.algHom_derivproof · cited by 2
- conductor_mul_differentIdealproof · cited by 1
- sum_smul_minpolyDiv_eq_X_powproof · cited by 1
- Algebra.FormallyEtale.of_isSeparable_auxproof · cited by 1
- IsLocalRing.isUnit_aeval_derivative_minpoly_of_adjoin_eq_topproof · cited by 0