openAI-math-dataset / lean /OAI /Combinatorics /ContingencyTables /Dense /DenseFlatExponentProgram.lean
| import OAI.Combinatorics.ContingencyTables.Dense.DenseMatrixLayoutProgram | |
| namespace OAI | |
| /-! # Evaluating the dense exponent on the flat coordinate encoding -/ | |
| namespace ContingencyTables.DensePrograms | |
| open MatchingFPRAS.TreeTyped GridBoundary | |
| abbrev FlatExponentData := GridFlatData×ℕ | |
| def flatToGridData (z : FlatExponentData) : ExponentData := | |
| ((z.1.1,unflattenGrid z.1),z.2) | |
| def flatToGridDataRealizer : Realizer flatToGridData := | |
| pair (pair (composition first first) (composition first unflattenGridRealizer)) second | |
| theorem polynomial_flatToGridData : PolynomialTime flatToGridDataRealizer := | |
| polynomial_pair (polynomial_pair (polynomial_composition polynomial_first polynomial_first) | |
| (polynomial_composition polynomial_first polynomial_unflattenGrid)) polynomial_second | |
| def flatExponent (z : FlatExponentData) : ℕ := gridExponent (flatToGridData z) | |
| def flatExponentRealizer : Realizer flatExponent := composition flatToGridDataRealizer gridExponentRealizer | |
| theorem polynomial_flatExponent : PolynomialTime flatExponentRealizer := | |
| polynomial_composition polynomial_flatToGridData polynomial_gridExponent | |
| theorem flatExponent_code {m n K : ℕ} (R : Option (Fin m) → ℕ) | |
| (P : Option (Fin n) → ℕ) (d : ℕ) (a : Grid (I := Fin (m*n)) K) : | |
| flatExponent (((marginCode R,marginCode P),gridNatCode a),d)= | |
| denseExponent R P d finProdFinEquiv a := by | |
| unfold flatExponent flatToGridData gridNatCode | |
| rw [unflattenGrid_code] | |
| exact gridExponent_code R P d a finProdFinEquiv | |
| end ContingencyTables.DensePrograms | |
| end OAI | |