Complexity of the Havas, Majewski, Matthews LLL Hermite Normal Form algorithm
Abstract
We show that the integers in the HMM LLL HNF algorithm have bit length O(m.log(m.B)), where m is the number of rows and B is the maximum square length of a row of the input matrix. This is only a little worse than the estimate O(m.log(B)) in the LLL algorithm.
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