Theorems · Theorem · field theory

Polynomial.roots_map_of_map_ne_zero_of_card_eq_natDegree

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

Defined in

Mathlib.Algebra.Polynomial.Roots

Cited by

1 results in Mathlib

Foundations

Depth 136 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingIsDomainIsDomain