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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 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 | import OAI.Geometry.CylinderCovering.Singular.EdgeOneGeometryDefinitions
namespace OAI
noncomputable section
namespace SingularEdgeOne
open RuledApproximation
def labelLinear : Plane ≃ₗ[ℝ] Plane where
toFun := labelMap
invFun z := vec2 (2 * z 0) (z 1)
left_inv := by
intro z
ext i
fin_cases i <;> simp [labelMap, vec2]
ring
right_inv := by
intro z
ext i
fin_cases i <;> simp [labelMap, vec2]
map_add' := by
intro x y
ext i
fin_cases i <;> simp [labelMap, vec2]
ring
map_smul' := by
intro c z
ext i
fin_cases i <;> simp [labelMap, vec2]
ring
def labelContinuous : Plane ≃L[ℝ] Plane := labelLinear.toContinuousLinearEquiv
def edgeHamiltonian (p w l : ℝ) : ℝ :=
(2 : ℝ) ^ (p - 3) * (w ^ 2 * l ^ (p - 2) - l ^ p / 4)
end SingularEdgeOne
end
end OAI
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