Theorems · Theorem · field theory
Polynomial.natSepDegree_eq_zero_iff
∀ {F : Type u} [inst : Field F] (f : Polynomial F), f.natSepDegree = 0 ↔ f.natDegree = 0A polynomial has zero separable degree if and only if it is constant.
- Defined in
- Mathlib.FieldTheory.SeparableDegree
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 156 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Polynomial.natDegreestatement · cited by 1,105
- Polynomial.natSepDegreestatement · cited by 53
- Function.mtrproof · cited by 12
- Polynomial.natSepDegree_eq_zeroproof · cited by 2
- Polynomial.natSepDegree_ne_zeroproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- Polynomial.natSepDegree_ne_zero_iffproof · cited by 2
- Polynomial.natSepDegree_mul_eq_iffproof · cited by 1
- Polynomial.Monic.eq_X_pow_char_pow_sub_C_pow_of_natSepDegree_eq_oneproof · cited by 1