| import Mathlib | |
| namespace OAI | |
| namespace SymmetricMahler | |
| variable {I : Type*} [Fintype I] | |
| def coordinatePolar (K : Set (I → ℝ)) : Set (I → ℝ) := | |
| {p | ∀ v ∈ K, (∑ i, p i*v i) ≤ 1} | |
| noncomputable section | |
| open Set MeasureTheory | |
| theorem symmetric_mahler {n : ℕ} (hn : 1 ≤ n) | |
| {K : Set (Fin n → ℝ)} (hK : IsCompact K) (hconv : Convex ℝ K) | |
| (hsym : ∀ x ∈ K, -x ∈ K) (hint : (interior K).Nonempty) : | |
| (4:ℝ)^n/(Nat.factorial n:ℝ) ≤ | |
| (volume K).toReal*(volume (coordinatePolar K)).toReal := by | |
| sorry | |
| end | |
| end SymmetricMahler | |
| end OAI | |