Theorems · Theorem · field theory
Polynomial.rootMultiplicity_eq_zero_iff
∀ {R : Type u} [inst : CommRing R] {p : Polynomial R} {x : R}, Polynomial.rootMultiplicity x p = 0 ↔ p.IsRoot x → p = 0- Defined in
- Mathlib.Algebra.Polynomial.Div
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 123 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.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Polynomialstatement and proof · cited by 5,681
- Polynomial.IsRootstatement and proof · cited by 152
- Polynomial.rootMultiplicitystatement · cited by 79
- Polynomial.rootMultiplicity_eq_multiplicityproof · cited by 8
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.rootMultiplicity_eq_zeroproof · cited by 6
- Polynomial.rootMultiplicity_pos'proof · cited by 2