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Let M be a sparse $n\times m$ integral matrix, where $nm$ is very large. The goal is to compute its invariant factors. The naïve approach Diagonal[SmithDecomposition[M][[2]]] is presumably not ideal, as it is computing more information than what I acctually need. Is there a better approach?

Note: I only care about the non-zero factors; does this simplify the problem?

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