smulAux' — Mathlib

English

For g ∈ GL(2,R) and z ∈ ℂ, the imaginary part of smulAux'(g,z) equals |det g| · Im(z) divided by |denom g z|^2.

Русский

Мнимая часть smulAux'(g,z) равна |\u2206det g| · Im(z) / |denom(g,z)|^2.

LaTeX

$$$\\\\operatorname{Im}(\\\\text{smulAux}'(g,z)) = \\\\frac{|\\\\det g| \\\\cdot z.im}{\\\\lvert \\\\operatorname{denom}(g,z)\\\\rvert^{2}}$$$

Lean4

/-- Fractional linear transformation, also known as the Moebius transformation -/
def smulAux' (g : GL (Fin 2) ℝ) (z : ℂ) : ℂ :=
  σ g (num g z / denom g z)

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