Theorems · Theorem · field theory
Polynomial.Gal.splits_in_splittingField_of_comp
∀ {F : Type u_1} [inst : Field F] (p q : Polynomial F),
q.natDegree ≠ 0 → (Polynomial.map (algebraMap F (p.comp q).SplittingField) p).Splitsp splits in the splitting field of p ∘ q, for q non-constant.
- Cited by
- 1 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.
Cites51
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement and proof · cited by 5,681
- Algebra.algebraMapstatement and proof · cited by 4,706
- LE.le.transproof · cited by 3,151
- MulZeroClass.mul_zeroproof · cited by 2,091
- MulZeroClass.zero_mulproof · cited by 1,625
- IsUnitproof · cited by 1,602
- Polynomial.Cproof · cited by 1,598
- WithBotproof · cited by 1,498
- Polynomial.natDegreestatement and proof · cited by 1,105
- Polynomial.coeffproof · cited by 1,045
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.Gal.restrictComp_surjectiveproof · cited by 0