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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2024 MCQ for Mathematics of Computation is 1.78.

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Hermite and Smith normal form algorithms over Dedekind domains
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by Henri Cohen PDF
Math. Comp. 65 (1996), 1681-1699 Request permission

Abstract:

We show how the usual algorithms valid over Euclidean domains, such as the Hermite Normal Form, the modular Hermite Normal Form and the Smith Normal Form can be extended to Dedekind rings. In a sequel to this paper, we will explain the use of these algorithms for computing in relative extensions of number fields.
References
  • W. Bosma and M. Pohst, Computations with finitely generated modules over Dedekind rings, Proceedings ISSAC’91 (1991), 151–156.
  • Henri Cohen, A course in computational algebraic number theory, Graduate Texts in Mathematics, vol. 138, Springer-Verlag, Berlin, 1993. MR 1228206, DOI 10.1007/978-3-662-02945-9
  • H. Cohen, F. Diaz y Diaz and M. Olivier, Algorithmic computations in relative extensions of number fields, in preparation.
  • P. D. Domich, R. Kannan, and L. E. Trotter Jr., Hermite normal form computation using modulo determinant arithmetic, Math. Oper. Res. 12 (1987), no. 1, 50–59. MR 882842, DOI 10.1287/moor.12.1.50
  • James L. Hafner and Kevin S. McCurley, Asymptotically fast triangularization of matrices over rings, SIAM J. Comput. 20 (1991), no. 6, 1068–1083. MR 1135749, DOI 10.1137/0220067
  • G. Havas and B. Majewski, Hermite normal form computation for integer matrices, Congr. Numer. 105 (1994), 184–193.
  • Ravindran Kannan and Achim Bachem, Polynomial algorithms for computing the Smith and Hermite normal forms of an integer matrix, SIAM J. Comput. 8 (1979), no. 4, 499–507. MR 573842, DOI 10.1137/0208040
  • P. Montgomery, in preparation.
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Additional Information
  • Henri Cohen
  • Affiliation: Laboratoire A2X, UMR 9936 du C.N.R.S., Université Bordeaux I, 351 Cours de la Libération, 33405 Talence Cedex, France
  • Email: cohen@math.u-bordeaux.fr
  • Received by editor(s): January 11, 1995
  • Received by editor(s) in revised form: July 19, 1995
  • © Copyright 1996 American Mathematical Society
  • Journal: Math. Comp. 65 (1996), 1681-1699
  • MSC (1991): Primary 11Y40
  • DOI: https://doi.org/10.1090/S0025-5718-96-00766-1
  • MathSciNet review: 1361805