isAlgClosed — Mathlib

English

The field ℂ is algebraically closed; every nonconstant polynomial with complex coefficients has a root in ℂ (the Fundamental Theorem of Algebra).

Русский

Поле ℂ алгебраически замкнуто; любой ненулевой многочлен с коэффициентами в ℂ имеет корень в ℂ (ФТА).

LaTeX

$$$$ \\forall p \\in \\mathbb{C}[X],\\ p \\text{ nonconstant } \\Rightarrow \\exists z \\in \\mathbb{C}, p(z)=0. $$$$

Lean4

instance isAlgClosed : IsAlgClosed ℂ :=
  IsAlgClosed.of_exists_root _ fun _p _ hp => Complex.exists_root <| degree_pos_of_irreducible hp

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