Theorems · Theorem · field theory
Polynomial.one_lt_rootMultiplicity_iff_isRoot
∀ {R : Type u} [inst : CommRing R] {p : Polynomial R} {t : R},
p ≠ 0 → (1 < Polynomial.rootMultiplicity t p ↔ p.IsRoot t ∧ (Polynomial.derivative p).IsRoot t)- Defined in
- Mathlib.Algebra.Polynomial.FieldDivision
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 126 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.
Cites10
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
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- LinearMapstatement · cited by 10,215
- Polynomialstatement and proof · cited by 5,681
- Nat.iterateproof · cited by 740
- Polynomial.derivativestatement and proof · cited by 331
- Polynomial.IsRootstatement and proof · cited by 152
- Polynomial.rootMultiplicitystatement · cited by 79
- Polynomial.one_lt_rootMultiplicity_iff_isRoot_iterate_derivativeproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.one_lt_rootMultiplicity_iff_isRoot_gcdproof · cited by 1