Theorems · Theorem · field theory

Polynomial.eq_one_of_roots_le

∀ {F : Type u_3} {K : Type u_4} [inst : CommRing F] [inst_1 : NormedField K] {p : Polynomial F} {f : F →+* K} {B : ℝ},
  B < 0 → p.Monic → (Polynomial.map f p).Splits → (∀ z ∈ (Polynomial.map f p).roots, ‖z‖ ≤ B) → p = 1

Defined in

Mathlib.Topology.Algebra.Polynomial

Cited by

2 results in Mathlib

Foundations

Depth 139 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingNormedField