openAI-math-dataset / lean /OAI /Geometry /CylinderCovering /Rational /EnergyIntegralDefinitions.lean
| import OAI.Geometry.CylinderCovering.Rational.FieldDefinitions | |
| namespace OAI | |
| open MeasureTheory | |
| noncomputable section | |
| namespace SlopeRational | |
| def baseDomain : Set Plane := wedge ∩ {z | 0 ≤ z 1} | |
| def energyDensity (d : ℝ) (z : Plane) : ℝ := | |
| (a d (z 0) (z 1))^2 + (1/2)*(b d (z 0) (z 1))^2 | |
| def energyIntegral (d : ℝ) : ℝ := (1/2) * ∫ z in baseDomain, energyDensity d z | |
| end SlopeRational | |
| end | |
| end OAI | |