Abstract
Two algorithms for the solution of linear Diophantine systems, which well restrain intermediate expression swell, are presented. One is an extension and improvement of Kannan and Bachem’s algorithm for the Smith and the Hermite normal forms of a nonsingular square integral matrix. The complexity of this algorithm is investigated and a polynomial time bound is derived. Also a much better coefficient bound is obtained compared to Kannan and Bachem’s analysis. The other is based on ideas of Rosser, which were originally used in finding a general solution with smaller coefficients to a linear Diophantine equation and in computing the exact inverse of a nonsingular square integral matrix. These algorithms are implemented by using the infinite precision integer arithmetic capabilities of the SAC-2 system. Their performances are compared. Finally future studies are mentioned.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
