Theorems · Theorem · commutative algebra
Polynomial.rootMultiplicity_scaleRoots
∀ {R : Type u_1} [inst : CommRing R] (p : Polynomial R) {r a : R},
IsLeftRegular r → Polynomial.rootMultiplicity (r * a) (p.scaleRoots r) = Polynomial.rootMultiplicity a p- Defined in
- Mathlib.RingTheory.Polynomial.ScaleRoots
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 125 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites33
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Polynomialstatement and proof · cited by 5,681
- one_mulproof · cited by 2,841
- Nontrivialproof · cited by 2,416
- mul_commproof · cited by 2,262
- Polynomial.Xproof · cited by 1,639
- Polynomial.Cproof · cited by 1,598
- eq_or_neproof · cited by 1,117
- Polynomial.natDegreeproof · cited by 1,105
- Polynomial.evalproof · cited by 796
- one_powproof · cited by 521
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.roots_scaleRootsproof · cited by 1