| 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 | |