Fast Computation of Hermite Normal Forms of Random Integer Matrices

by William Stein

July 2010

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This paper is about how to compute the Hermite normal form of a random integer matrix in practice. We propose significant improvements to the algorithm by Micciancio and Warinschi, and extend these techniques to the computation of the saturation of a matrix. Tables of timings confirm the efficiency of this approach. To our knowledge, our implementation is the fastest implementation for computing Hermite normal form for large matrices with large entries.