Theorems · Definition · field theory
Polynomial.IsSeparableContraction
{F : Type u_1} → [inst : CommSemiring F] → ℕ → Polynomial F → Polynomial F → PropA separable contraction of a polynomial f is a separable polynomial g such that
g(x^(q^m)) = f(x) for some m : ℕ.
- 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.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommSemiringstatement and proof · cited by 10,911
- Polynomialstatement and proof · cited by 5,681
- Polynomial.Separableproof · cited by 117
- Polynomial.expandproof · cited by 90
Cited by8
Results whose statement or proof uses this declaration.
- isPurelyInseparable_iff_pow_memproof · cited by 10
- Polynomial.HasSeparableContractionproof · cited by 8
- Irreducible.natSepDegree_eq_one_iff_of_monic'proof · cited by 3
- Algebra.trace_eq_zero_of_not_isSeparableproof · cited by 2
- Polynomial.HasSeparableContraction.isSeparableContractionstatement · cited by 1
- Polynomial.IsSeparableContraction.dvd_degree'statement and proof · cited by 1
- Polynomial.IsSeparableContraction.natSepDegree_eqstatement and proof · cited by 1
- Polynomial.IsSeparableContraction.degree_eqstatement and proof · cited by 0