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Algorithms for Hermite and Smith Normal Matrices and Linear Diophantine Equations
Gordon H. Bradley
Mathematics of Computation
Vol. 25, No. 116 (Oct., 1971), pp. 897-907
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/2004354
Page Count: 11
You can always find the topics here!Topics: Algorithms, Integers, Matrices, Diophantine equation, Gaussian elimination, Mathematical problems, Linear programming, Linear equations, Mathematical congruence, Subroutines
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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.
Mathematics of Computation © 1971 American Mathematical Society