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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 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Algorithms for Hermite and Smith normal matrices and linear Diophantine equations
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by Gordon H. Bradley PDF
Math. Comp. 25 (1971), 897-907 Request permission


New algorithms for constructing the Hermite normal form (triangular) and Smith normal form (diagonal) of an integer matrix are presented. A new algorithm for determining the set of solutions to a system of linear diophantine equations is presented. A modification of the Hermite algorithm gives an integer-preserving algorithm for solving linear equations with real-valued variables. Rough bounds for the number of operations are cubic polynomials involving the order of the matrix and the determinant of the matrix. The algorithms are valid if the elements of the matrix are in a principal ideal domain.
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Additional Information
  • © Copyright 1971 American Mathematical Society
  • Journal: Math. Comp. 25 (1971), 897-907
  • MSC: Primary 65F30
  • DOI:
  • MathSciNet review: 0301909