| import Mathlib | |
| namespace OAI | |
| namespace CirculantHadamard | |
| universe u | |
| def IsSign {R : Type u} [One R] [Neg R] (x : R) : Prop := | |
| x = 1 ∨ x = -1 | |
| abbrev RealMatrix (n : ℕ) := Matrix (Fin n) (Fin n) ℝ | |
| def IsCirculant {n : ℕ} (H : RealMatrix n) : Prop := | |
| ∃ h : Fin n → ℝ, ∀ i j, H i j = h (j - i) | |
| def IsSignHadamard {n : ℕ} (H : RealMatrix n) : Prop := | |
| (∀ i j, IsSign (H i j)) ∧ | |
| H * H.transpose = (n : ℝ) • (1 : RealMatrix n) | |
| def ExistsRealCirculantHadamard (n : ℕ) : Prop := | |
| ∃ H : RealMatrix n, IsCirculant H ∧ IsSignHadamard H | |
| end CirculantHadamard | |
| end OAI | |