Theorems · Theorem · field theory
Polynomial.separable_def
∀ {R : Type u} [inst : CommSemiring R] (f : Polynomial R), f.Separable ↔ IsCoprime f (Polynomial.derivative f)- Defined in
- Mathlib.FieldTheory.Separable
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- RingHom.idstatement · cited by 18,349
- CommSemiringstatement and proof · cited by 10,911
- LinearMapstatement · cited by 10,215
- Polynomialstatement and proof · cited by 5,681
- Polynomial.derivativestatement · cited by 331
- IsCoprimestatement · cited by 321
- Polynomial.Separablestatement · cited by 117
Cited by7
Results whose statement or proof uses this declaration.
- Polynomial.separable_mapproof · cited by 6
- FiniteField.roots_X_pow_card_sub_Xproof · cited by 2
- Polynomial.isUnit_or_eq_zero_of_separable_expandproof · cited by 2
- Polynomial.separable_Cproof · cited by 1
- Polynomial.separable_X_add_Cproof · cited by 1
- Polynomial.Separable.mulproof · cited by 1
- Polynomial.separable_Xproof · cited by 0