Theorems · Theorem · field theory
Polynomial.isRoot_iterate_derivative_of_lt_rootMultiplicity
∀ {R : Type u} [inst : CommRing R] {p : Polynomial R} {t : R} {n : ℕ},
n < Polynomial.rootMultiplicity t p → ((⇑Polynomial.derivative)^[n] p).IsRoot t- Defined in
- Mathlib.Algebra.Polynomial.FieldDivision
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 122 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.
Cites16
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
- Polynomial.Xproof · cited by 1,639
- Polynomial.Cproof · cited by 1,598
- Nat.iteratestatement · cited by 740
- Polynomial.derivativestatement · cited by 331
- Polynomial.IsRootstatement · cited by 152
- Dvd.dvd.transproof · cited by 148
- Polynomial.rootMultiplicitystatement and proof · cited by 79
Cited by3
Results whose statement or proof uses this declaration.