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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 | import OAI.Geometry.RuledCovering.Model
namespace OAI
noncomputable section
namespace RuledApproximation
def OrthogonalZeroDiagonalStatement : Prop :=
∀ A : Plane →L[ℝ] Plane, LinearMap.trace ℝ Plane A.toLinearMap = 0 →
LinearMap.det A.toLinearMap < 0 →
∃ R : Plane ≃ₗᵢ[ℝ] Plane, ∃ b c : ℝ,
(∀ z : Plane, R.symm (A (R z)) = vec2 (b * z 1) (c * z 0)) ∧
b * c = -LinearMap.det A.toLinearMap ∧ 0 < b * c ∧
|b| ≤ ‖A‖ ∧ |c| ≤ ‖A‖
end RuledApproximation
end
end OAI
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