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Fast computation of Hermite normal forms of random integer matrices

Clement Pernet 1, * William Stein 2
* Corresponding author
1 MOAIS - PrograMming and scheduling design fOr Applications in Interactive Simulation
Inria Grenoble - Rhône-Alpes, LIG - Laboratoire d'Informatique de Grenoble
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.
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https://hal.inria.fr/hal-00798442
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Submitted on : Friday, March 8, 2013 - 3:31:46 PM
Last modification on : Tuesday, February 9, 2021 - 3:24:23 PM

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Clement 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⟩

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