| import Mathlib | |
| import OAI.Combinatorics.MatchingPSD.Model | |
| namespace OAI | |
| namespace PerfectMatchingPSD | |
| noncomputable def matchingPoint {n : ℕ} (M : PerfectMatching n) : Edge n → ℝ := by | |
| classical | |
| exact fun e => if e ∈ M.1 then 1 else 0 | |
| noncomputable def matchingPolytope (n : ℕ) : Set (Edge n → ℝ) := | |
| convexHull ℝ (Set.range (matchingPoint (n := n))) | |
| def HasAffineLift (n r : ℕ) : Prop := | |
| ∃ (L : AffineSubspace ℝ (Matrix (Fin r) (Fin r) ℝ)) | |
| (T : Matrix (Fin r) (Fin r) ℝ →ᵃ[ℝ] (Edge n → ℝ)), | |
| T '' {X | X ∈ L ∧ X.PosSemidef} = matchingPolytope n | |
| end PerfectMatchingPSD | |
| end OAI | |