Theorems · Theorem · field theory

Polynomial.count_map_roots

∀ {A : Type u_1} {B : Type u_2} [inst : CommRing A] [inst_1 : CommRing B] [inst_2 : IsDomain A] [inst_3 : DecidableEq B]
  {p : Polynomial A} {f : A →+* B},
  Polynomial.map f p ≠ 0 →
    ∀ (b : B), Multiset.count b (Multiset.map (⇑f) p.roots) ≤ Polynomial.rootMultiplicity b (Polynomial.map f p)

Defined in

Mathlib.Algebra.Polynomial.Roots

Cited by

2 results in Mathlib

Foundations

Depth 134 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingIsDomainDecidableEq