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785c727 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 | import OAI.Geometry.RuledCovering.Model
namespace OAI
open Filter Topology
namespace CylinderCovering.SingularParameterRange
open RuledApproximation
structure Statement : Prop where
negative_range : ∀ p : ℝ, 1 < p →
(singularCoefficient p < 0 ↔ p < (Real.sqrt 51 - 5) / 2)
critical_zero : singularCoefficient ((Real.sqrt 51 - 5) / 2) = 0
endpoint_value : singularCoefficient 1 = -(1 / 480 : ℝ)
endpoint_limit : Tendsto singularCoefficient (𝓝 1) (𝓝 (-(1 / 480 : ℝ)))
cutoff_window : ∀ p : ℝ,
(∃ γ : ℝ, 1 < γ ∧ γ < 1 / (2 - p)) ↔ 1 < p ∧ p < 2
endpoint_degenerate : ∀ z : Plane, 0 < z 1 →
LinearMap.det (fderiv ℝ (singularField 1) z).toLinearMap = 0 ∧
∀ μ : ℝ, Module.End.HasEigenvalue (fderiv ℝ (singularField 1) z).toLinearMap μ → μ = 0
end CylinderCovering.SingularParameterRange
end OAI
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