Abstract : 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. We describe the fastest implementation for computing Hermite normal form for large matrices with large entries.
Clément Pernet, William Stein. Fast computation of Hermite normal forms of random integer matrices. Journal of Number Theory, Elsevier, 2010, 130 (7), pp.1675―1683. ⟨10.1016/j.jnt.2010.01.017⟩. ⟨hal-00798442⟩