Theorems · Theorem · field theory
Polynomial.natSepDegree_expand
∀ {F : Type u} [inst : Field F] (f : Polynomial F) (q : ℕ) [hF : ExpChar F q] {n : ℕ},
((Polynomial.expand F (q ^ n)) f).natSepDegree = f.natSepDegreeIf a field F is of exponential characteristic q, then Polynomial.expand F (q ^ n) f
and f have the same separable degree.
- Defined in
- Mathlib.FieldTheory.SeparableDegree
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 180 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites28
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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Cited by4
Results whose statement or proof uses this declaration.
- Irreducible.natSepDegree_eq_one_iff_of_monic'proof · cited by 3
- Polynomial.natSepDegree_X_pow_char_pow_sub_Cproof · cited by 3
- minpoly.natSepDegree_eq_one_iff_eq_expand_X_sub_Cproof · cited by 1
- Polynomial.IsSeparableContraction.natSepDegree_eqproof · cited by 1