| import OAI.Geometry.ProjectionBody.SimplexVolume |
| import OAI.Geometry.ProjectionBody.ProductFacetCharts |
|
|
| namespace OAI |
|
|
| noncomputable section |
| open Set MeasureTheory |
|
|
| namespace ProjectionCounterexample |
|
|
| theorem volume_productBody : |
| volume productBody = ENNReal.ofReal (1 / ((Nat.factorial 10 : ℝ) * Nat.factorial 10)) := by |
| simpa only [productBody, simplex_eq_coordinates, firstBlock, secondBlock, |
| Set.mem_ofPred_eq, WithLp.ofLp_toLp] using |
| volume_euclideanSimplexProduct 10 10 |
|
|
| theorem volume_productFacetDomain (b : Bool) : |
| volume (productFacetDomain b) = |
| ENNReal.ofReal (1 / ((Nat.factorial 9 : ℝ) * Nat.factorial 10)) := by |
| cases b |
| · simpa only [productFacetDomain, simplex_eq_coordinates, Set.preimage, |
| Set.mem_prod, Set.mem_ofPred_eq, DiagonalZonotope.finAddEquivProd_apply, |
| WithLp.ofLp_toLp] using |
| volume_euclideanSimplexProduct 9 10 |
| · simpa only [productFacetDomain, simplex_eq_coordinates, Set.preimage, |
| Set.mem_prod, Set.mem_ofPred_eq, DiagonalZonotope.finAddEquivProd_apply, WithLp.ofLp_toLp, |
| mul_comm] using |
| volume_euclideanSimplexProduct 10 9 |
|
|
| theorem productFacetDomain_compact (b : Bool) : IsCompact (productFacetDomain b) := by |
| cases b |
| · exact (@EuclideanSpace.finAddEquivProd ℝ _ 9 10).toHomeomorph.isCompact_preimage.mpr |
| ((simplex_compact 9).prod (simplex_compact 10)) |
| · exact (@EuclideanSpace.finAddEquivProd ℝ _ 10 9).toHomeomorph.isCompact_preimage.mpr |
| ((simplex_compact 10).prod (simplex_compact 9)) |
|
|
| end ProjectionCounterexample |
|
|
| end |
|
|
| end OAI |
|
|
