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9eeb9c7 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 | import Mathlib
namespace OAI
namespace InvariantProjection.FiniteConvolution
abbrev Coefficients (K : ℕ) := Fin (2 * K + 1) → ℂ
def center (K : ℕ) : Fin (2 * K + 1) := ⟨K, by omega⟩
noncomputable def polynomial {K : ℕ} (a : Coefficients K) : Polynomial ℂ :=
∑ i : Fin (2 * K + 1), Polynomial.monomial (i : ℕ) (a i)
noncomputable def lowProduct {K : ℕ} (a b : Coefficients K) : Coefficients K :=
fun n => (polynomial a * polynomial b).coeff (n : ℕ)
end InvariantProjection.FiniteConvolution
end OAI
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