fundamentalDomain_stdBasis — Mathlib

English

The norm of the constant vector (c, c) equals |c|^{finrank(K/ℚ)}.

Русский

Норма константного вектора (c, c) равна |c|^{finrank(K/ℚ)}.

LaTeX

$$$ \| (c, c) \| = |c|^{\operatorname{finrank}_{\mathbb{Q}} K} $$$

Lean4

theorem fundamentalDomain_stdBasis :
    fundamentalDomain (stdBasis K) =
      (Set.univ.pi fun _ => Set.Ico 0 1) ×ˢ
        (Set.univ.pi fun _ => Complex.measurableEquivPi ⁻¹' (Set.univ.pi fun _ => Set.Ico 0 1)) :=
  by
  ext
  simp [stdBasis, mem_fundamentalDomain, Complex.measurableEquivPi]

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