A Las Vegas randomized algorithm computes the n by n Hermite normal form basis of the integer lattice of rows p where pF lies in the row lattice generated by M, with bit complexity matching matrix multiplication when M is square and F is the identity.
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C implementation of the Smith massager algorithm achieves practical performance equivalent to matrix multiplication for Smith normal form of integer matrices up to dimension 10007.
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Computing bases in Hermite normal form of lattices of integer relations
A Las Vegas randomized algorithm computes the n by n Hermite normal form basis of the integer lattice of rows p where pF lies in the row lattice generated by M, with bit complexity matching matrix multiplication when M is square and F is the identity.
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A C implementation of the Smith massager algorithm
C implementation of the Smith massager algorithm achieves practical performance equivalent to matrix multiplication for Smith normal form of integer matrices up to dimension 10007.