Theorems · Theorem · field theory
Polynomial.one_lt_rootMultiplicity_iff_isRoot_iterate_derivative
∀ {R : Type u} [inst : CommRing R] {p : Polynomial R} {t : R},
p ≠ 0 → (1 < Polynomial.rootMultiplicity t p ↔ ∀ m ≤ 1, ((⇑Polynomial.derivative)^[m] p).IsRoot t)- Defined in
- Mathlib.Algebra.Polynomial.FieldDivision
- 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.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · 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.cast_oneproof · cited by 2,501
- nonZeroDivisorsproof · cited by 895
- Nat.iteratestatement · cited by 740
- Polynomial.derivativestatement · cited by 331
- Polynomial.IsRootstatement · cited by 152
- Polynomial.rootMultiplicitystatement · cited by 79
- Submonoid.one_memproof · cited by 28
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.one_lt_rootMultiplicity_iff_isRootproof · cited by 1