Theorems · Theorem · field theory
Polynomial.Splits.eq_X_sub_C_of_single_root
∀ {R : Type u_1} [inst : CommRing R] {f : Polynomial R} [inst_1 : IsDomain R],
f.Splits → ∀ {x : R}, f.roots = {x} → f = Polynomial.C f.leadingCoeff * (Polynomial.X - Polynomial.C x)- Defined in
- Mathlib.Algebra.Polynomial.Splits
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 138 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
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
- CommRingstatement and proof · cited by 17,173
- RingHomstatement · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- mul_oneproof · cited by 3,885
- Multisetstatement and proof · cited by 2,627
- IsDomainstatement and proof · cited by 2,196
- Polynomial.Xstatement and proof · cited by 1,639
- Polynomial.Cstatement and proof · cited by 1,598
- Multiset.mapproof · cited by 876
- Multiset.prodproof · cited by 528
- Polynomial.leadingCoeffstatement and proof · cited by 498
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.eq_X_sub_C_of_separable_of_root_eqproof · cited by 1