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There are natural projections from $D^{k+1}(f)$ to $D^k(f)$, determined by forgetting one member of the (k+1)-tuple. We prove that the matrix of a presentation of $\\OO_{D^{k+1}(f)}$ over $\\OO_{D^k(f)}$ appears as a certain submatrix of the matrix of a suitable presentation of $\\OO_{\\CC^n}$ over $\\OO_{\\CC^{n+1}}$. 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There are natural projections from $D^{k+1}(f)$ to $D^k(f)$, determined by forgetting one member of the (k+1)-tuple. We prove that the matrix of a presentation of $\\OO_{D^{k+1}(f)}$ over $\\OO_{D^k(f)}$ appears as a certain submatrix of the matrix of a suitable presentation of $\\OO_{\\CC^n}$ over $\\OO_{\\CC^{n+1}}$. 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