Theorems · Definition · field theory
Polynomial.rootMultiplicity
{R : Type u} → [inst : Ring R] → R → Polynomial R → ℕThe largest power of X - C a which divides p.
- Defined in
- Mathlib.Algebra.Polynomial.Div
- Cited by
- 79 results in Mathlib
- Foundations
- Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Ring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Ringstatement and proof · cited by 7,463
- Polynomialstatement and proof · cited by 5,681
- Polynomial.Xproof · cited by 1,639
- Polynomial.Cproof · cited by 1,598
- Nat.findproof · cited by 139
- Classical.decPredproof · cited by 26
- Polynomial.finiteMultiplicity_X_sub_Cproof · cited by 7
Cited by80
Results whose statement or proof uses this declaration.
- Polynomial.count_rootsstatement and proof · cited by 19
- Polynomial.roots_mulproof · cited by 12
- Polynomial.rootMultiplicity_zerostatement · cited by 11
- Polynomial.le_rootMultiplicity_iffstatement · cited by 10
- Polynomial.roots_Cproof · cited by 9
- Polynomial.pow_rootMultiplicity_dvdstatement and proof · cited by 9
- Polynomial.rootMultiplicity_eq_multiplicitystatement · cited by 8
- Polynomial.exists_eq_pow_rootMultiplicity_mul_and_not_dvdstatement · cited by 7
- Polynomial.rootMultiplicity_eq_zerostatement · cited by 6
- Polynomial.prod_multiset_X_sub_C_dvdproof · cited by 5
- Polynomial.rootMultiplicity_le_iffstatement and proof · cited by 4
- Polynomial.rootMultiplicity_posstatement · cited by 4