openAI-math-dataset / lean /OAI /NumberTheory /Catalan /FiniteMatrices /FixedCanonicalModularForm.lean
| import OAI.NumberTheory.Catalan.Arithmetic.FixedCanonicalIntegerBase | |
| import OAI.NumberTheory.Catalan.Polynomial.FixedCanonicalCoefficientTables | |
| namespace OAI | |
| section | |
| noncomputable section | |
| open scoped BigOperators | |
| namespace InternalCatalan | |
| theorem fixedIntegerBaseCanonical_mod_coefficients (r : Fin 49) (k : Fin 48) : | |
| (fixedIntegerBaseCanonical r k : ZMod 101) = | |
| 2 * (∑ i ∈ Finset.range 65, | |
| (fixedCanonicalPCoeff r i : ZMod 101) * (fixedClearedMoment i k : ZMod 101)) - | |
| 3 * (∑ i ∈ Finset.range 65, | |
| (fixedCanonicalDCoeff r i : ZMod 101) * (fixedClearedZeta i k : ZMod 101)) := by | |
| simp only [fixedIntegerBaseCanonical, fixedCanonicalPCoeff_eq, fixedCanonicalDCoeff_eq, | |
| Int.cast_sub, Int.cast_mul, Int.cast_sum, Int.cast_ofNat] | |
| end InternalCatalan | |
| end | |
| end | |
| end OAI | |