The Lean 4 theorem `quadPolyMat_apply` in the `ChapterQuadraticRotationEsa` chapter of the timepiece formalization

-- Generated from ChapterQuadraticRotationEsa.lean — theorem BookProof.QuadraticRotation.quadPolyMat_apply
import Definitions.Def_ChapterHermiteProductCore
import Definitions.Def_ChapterHermiteProductBasis
import Definitions.Def_ChapterFarisLavine
import Definitions.Def_ChapterHyperbolicQuadraticEsa
import Mathlib
import Definitions.Def_ChapterQuadraticRotationEsa
import Definitions.Def_ChapterNavierStokesDifferentialL2
open BookProof.NavierStokesFlow.DifferentialL2
open BookProof.QuadraticRotation



open MeasureTheory MvPolynomial Matrix
open BookProof.HermiteProductCore BookProof.HermiteProductBasis
open BookProof.FarisLavine
open BookProof.NavierStokesFlow.DifferentialL2
open BookProof.HyperbolicQuadratic

noncomputable section

variable {d : ℕ}

theorem BookProof.QuadraticRotation.quadPolyMat_apply (A : Matrix (Fin d) (Fin d) ℝ) (p : MvPolynomial (Fin d) ℂ) :
    quadPolyMat A p = ∑ k, ∑ l, ((A k l : ℝ) : ℂ) •
      (momPoly k (momPoly l p) + (1/4 : ℂ) • (X k * (X l * p))) := by sorry