openAI-math-dataset / lean /OAI /Combinatorics /ContingencyTables /Dense /DenseGridExponentProgram.lean
| import OAI.Combinatorics.ContingencyTables.Dense.DenseScaleMatrixProgram | |
| namespace OAI | |
| /-! # Computing the dense exponent directly from a binary grid matrix -/ | |
| namespace ContingencyTables.DensePrograms | |
| open MatchingFPRAS.TreeTyped GridBoundary | |
| def scaledData (z : ExponentData) : ExponentData := ((z.1.1,scaleMatrix z),z.2) | |
| def scaledDataRealizer : Realizer scaledData := | |
| pair (pair (composition first first) scaleMatrixRealizer) second | |
| theorem polynomial_scaledData : PolynomialTime scaledDataRealizer := | |
| polynomial_pair (polynomial_pair (polynomial_composition polynomial_first polynomial_first) | |
| polynomial_scaleMatrix) polynomial_second | |
| def gridExponent (z : ExponentData) : ℕ := fullExponent (scaledData z) | |
| def gridExponentRealizer : Realizer gridExponent := | |
| composition scaledDataRealizer fullExponentRealizer | |
| theorem polynomial_gridExponent : PolynomialTime gridExponentRealizer := | |
| polynomial_composition polynomial_scaledData polynomial_fullExponent | |
| theorem gridExponent_code {m n q K : ℕ} (R : Option (Fin m) → ℕ) | |
| (P : Option (Fin n) → ℕ) (d : ℕ) (a : Grid (I := Fin q) K) | |
| (e : Fin m×Fin n ≃ Fin q) : | |
| gridExponent (exponentDataCode R P d (fun i j => (corner a (e (i,j))).toNat))= | |
| denseExponent R P d e a := by | |
| unfold gridExponent scaledData | |
| rw [scaleMatrix_code] | |
| exact fullExponent_code R P d e a | |
| end ContingencyTables.DensePrograms | |
| end OAI | |