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Algorithms for large integer matrix problems. (English) Zbl 1056.11078
Boztaş, Serdar (ed.) et al., Applied algebra, algebraic algorithms and error-correcting codes. 14th international symposium, AAECC-14, Melbourne, Australia, November 26–30, 2001.
Proceedings. Berlin: Springer (ISBN 3-540-42911-5). Lect. Notes Comput. Sci. 2227, 297-307 (2001).
Summary: New algorithms are described and analysed for solving various problems associated with a large integer matrix: computing the Hermite form, computing a kernel basis, and solving a system of linear Diophantine equations. The algorithms are space-efficient and for certain types of input matrices – for example, those arising during the computation of class groups and regulators – are faster than previous methods. Experiments with a prototype implementation support the running time analyses.
For the entire collection see [Zbl 0983.00064].
Reviewer: Reviewer (Berlin)

11Y16 Number-theoretic algorithms; complexity
11D04 Linear Diophantine equations
11E39 Bilinear and Hermitian forms
11Y40 Algebraic number theory computations
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