Hermite normal form computation using modulo determinant arithmetic. (English) Zbl 0624.65036

Domich, P. D.; Kannan, R.; Trotter, L. E. jun.

Math. Oper. Res. 12, 50-59 (1987).

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

MSC:

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

Keywords:

unimodular matrix; Hermite normal form; Computational experiences