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Hermite normal form computation using modulo determinant arithmetic. (English) Zbl 0624.65036
One presents some algorithms for Hermite normal form computation in which all arithmetic operations are performed modulo det(A). As a result, the number of bits which are needed to represent any matrix entry during the computation is bounded above by \(n(\log_ 2n+\log_ 2a)\) where a denote the maximum value of the element \(a_{ij}\) of the matrix. Computational experiences are displayed.
Reviewer: G.Jumarie

65F30 Other matrix algorithms (MSC2010)
15A21 Canonical forms, reductions, classification
15B36 Matrices of integers
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