Theorems · Theorem · field theory
Polynomial.natSepDegree_pow
∀ {F : Type u} [inst : Field F] (f : Polynomial F) {n : ℕ}, (f ^ n).natSepDegree = if n = 0 then 0 else f.natSepDegree- Defined in
- Mathlib.FieldTheory.SeparableDegree
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 180 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.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Algebraproof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement and proof · cited by 5,681
- Multisetproof · cited by 2,627
- Finset.cardproof · cited by 2,327
- zero_smulproof · cited by 716
- Multiset.toFinsetproof · cited by 230
- IsAlgClosedproof · cited by 150
- Polynomial.arootsproof · cited by 89
- AlgebraicClosureproof · cited by 53
- Polynomial.natSepDegreestatement · cited by 53
- Polynomial.natSepDegree_eq_of_isAlgClosedproof · cited by 9
Cited by4
Results whose statement or proof uses this declaration.
- Polynomial.natSepDegree_X_sub_C_powproof · cited by 1
- Polynomial.natSepDegree_pow_of_ne_zeroproof · cited by 1
- Polynomial.Monic.natSepDegree_eq_one_iffproof · cited by 0
- Polynomial.natSepDegree_X_powproof · cited by 0