Theorems · Theorem · field theory
Polynomial.rootMultiplicity_mul_X_sub_C_pow
∀ {R : Type u} [inst : CommRing R] {p : Polynomial R} {a : R} {n : ℕ},
p ≠ 0 → Polynomial.rootMultiplicity a (p * (Polynomial.X - Polynomial.C a) ^ n) = Polynomial.rootMultiplicity a p + n- Defined in
- Mathlib.Algebra.Polynomial.RingDivision
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 120 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.
Cites21
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
- le_antisymmproof · cited by 2,068
- Polynomial.Xstatement and proof · cited by 1,639
- Polynomial.Cstatement and proof · cited by 1,598
- add_commproof · cited by 1,535
- add_assocproof · cited by 746
- pow_addproof · cited by 315
- Polynomial.rootMultiplicitystatement and proof · cited by 79
- Polynomial.monic_X_sub_Cproof · cited by 41
Cited by3
Results whose statement or proof uses this declaration.
- Polynomial.rootMultiplicity_expand_powproof · cited by 2
- Polynomial.rootMultiplicity_scaleRootsproof · cited by 1
- Polynomial.rootMultiplicity_X_sub_C_powproof · cited by 1