Theorems · Theorem · commutative algebra
Polynomial.Splits.scaleRoots
∀ {R : Type u_1} [inst : CommSemiring R] {p : Polynomial R}, p.Splits → ∀ (r : R), (p.scaleRoots r).Splits- Defined in
- Mathlib.RingTheory.Polynomial.ScaleRoots
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 112 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.
Cites34
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
- mul_oneproof · cited by 3,885
- one_mulproof · cited by 2,841
- Multisetproof · cited by 2,627
- Nontrivialproof · cited by 2,416
- Polynomial.Xproof · cited by 1,639
- Polynomial.Cproof · cited by 1,598
- eq_or_neproof · cited by 1,117
- Multiset.mapproof · cited by 876
- Multiset.prodproof · cited by 528
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.resultant_scaleRootsproof · cited by 1