openAI-math-dataset / lean /OAI /Geometry /CylinderCovering /Angular /ApertureDefinitions.lean
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import Mathlib
namespace OAI
noncomputable section
namespace AngularAperture
def transverse (y : ℝ) : ℝ := y ^ 2 / 4 + y ^ 4
def profile (q : ℝ) : ℝ := (q ^ 2 + q ^ 4) / 16
def level (τ η q s : ℝ) : ℝ := s - 1 / 2 - τ ^ 2 * (transverse (q * s) + η)
def aperture (τ η b q : ℝ) : Set ℝ :=
{s | 0 ≤ s ∧ s ≤ b ∧ s ≤ 1 / 2 + τ ^ 2 * (transverse (q * s) + η)}
end AngularAperture
end
end OAI