Theorems · Theorem · field theory
Polynomial.splits_X_sub_C_mul_iff
∀ {R : Type u_1} [inst : CommRing R] {f : Polynomial R} [IsDomain R] {a : R},
((Polynomial.X - Polynomial.C a) * f).Splits ↔ f.Splits- 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.
Cites29
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
- one_mulproof · cited by 2,841
- Multisetproof · 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
- Polynomial.evalproof · cited by 796
- Multiset.prodproof · cited by 528
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.splits_mulproof · cited by 4