# Smith Normal Form Using Scaled Extended Integer ABS Algorithms

Conference paper
Part of the Advances in Intelligent and Soft Computing book series (AINSC, volume 145)

## Abstract

Classes of integer ABS methods have recently been introduced for solving linear systems of Diophantine equations. The Smith normal form of a general integermatrix is a diagonal integer matrix, obtained by elementary nonsingular (unimodular) operations. Such a form may conveniently be used in solving integer systems of equations and integer linear programming problems. Here, we present a class of algorithms for computing the Smith normal form of an integer matrix. In doing this, we propose new ideas to develop a new class of extended integer ABS algorithms generating an integer basis for the integer null space of the matrix. Finally, we test our algorithms and report the obtained numerical results on randomly generated test problems.

## Keywords

Integer Solution Diophantine Equation Integer Matrix Integer Linear Programming Problem Unimodular Matrix
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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