Theorems · Theorem · field theory
Polynomial.exists_finset_of_splits
∀ {F : Type u} [inst : Field F] {K : Type v} [inst_1 : Field K] (i : F →+* K) {f : Polynomial F},
f.Separable →
(Polynomial.map i f).Splits →
∃ s, Polynomial.map i f = Polynomial.C (i f.leadingCoeff) * ∏ a ∈ s, (Polynomial.X - Polynomial.C a)- Defined in
- Mathlib.FieldTheory.Separable
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 115 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites24
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Finsetstatement and proof · cited by 13,712
- RingHomstatement and proof · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement and proof · cited by 5,681
- Multisetproof · cited by 2,627
- Finset.prodstatement and proof · cited by 2,356
- Polynomial.Xstatement and proof · cited by 1,639
- Polynomial.Cstatement and proof · cited by 1,598
- Multiset.mapproof · cited by 876
- Polynomial.mapstatement and proof · cited by 806
- Multiset.prodproof · cited by 528
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