Theorems · Theorem · field theory
Polynomial.one_lt_rootMultiplicity_iff_isRoot_gcd
∀ {R : Type u} [inst : CommRing R] [inst_1 : GCDMonoid (Polynomial R)] {p : Polynomial R} {t : R},
p ≠ 0 → (1 < Polynomial.rootMultiplicity t p ↔ (gcd p (Polynomial.derivative p)).IsRoot t)- Defined in
- Mathlib.Algebra.Polynomial.FieldDivision
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 127 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- Polynomial.derivativestatement and proof · cited by 331
- Polynomial.IsRootstatement and proof · cited by 152
- GCDMonoid.gcdstatement and proof · cited by 143
- GCDMonoidstatement and proof · cited by 96
- Polynomial.rootMultiplicitystatement · cited by 79
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.nodup_roots_iff_of_splitsproof · cited by 1