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e5a97c6 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 | 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
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