Example

Let R = Z/2Z and d = X² + X + 1 R[X]. The matrix of the map mod d restricted to R[X]_<5 with respect to the basis 1, X, X², X³, X⁴ of R[X]_<5 and 1, X of R[X]/(d) is

1 0 1 1 0 0 1 1 0 1

.