Polynomial det eq monomial of residual

import Mathlib.Algebra.Polynomial.Div
import Mathlib.LinearAlgebra.Matrix.Polynomial

section
open Finset Polynomial Matrix

namespace D1Bound5

/-!
This module isolates an intermediate step in the all-orders Bennett determinant
argument. It does not define the residue polynomials or prove their cancellation.
The required cancellation is an explicit hypothesis of the final theorem.
-/

section CommRing

variable {R ι : Type*} [CommRing R] [Fintype ι] [DecidableEq ι]








theorem _root_.D1Bound5.polynomial_det_eq_monomial_of_residual (P : Matrix ι ι R[X])
    (d : ι → ℕ) (θ : ι → R[X]) (q : ι) (hθ : θ q = 1)
    (hdeg : ∀ i j, (P i j).natDegree ≤ d j)
    (hres : ∀ i, (X : R[X]) ^ (∑ j, d j) ∣ ∑ j, θ j * P i j) :
    P.det = C (P.det.coeff (∑ j, d j)) * X ^ (∑ j, d j) := by sorry



end CommRing

end D1Bound5
end