Solving Systems of Linear Diophantine Equations: An Algebraic Approach (1991)
| Venue: | IN PROC. 16TH MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCE, WARSAW, LNCS 520 |
| Citations: | 18 - 1 self |
BibTeX
@INPROCEEDINGS{Domenjoud91solvingsystems,
author = {Eric Domenjoud},
title = {Solving Systems of Linear Diophantine Equations: An Algebraic Approach},
booktitle = {IN PROC. 16TH MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCE, WARSAW, LNCS 520},
year = {1991},
pages = {141--150},
publisher = {Springer-Verlag}
}
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Abstract
We describe through an algebraic and geometrical study, a new method for solving systems of linear diophantine equations. This approach yields an algorithm which is intrinsically parallel. In addition to the algorithm, we give a geometrical interpretation of the satisfiability of an homogeneous system, as well as upper bounds on height and length of all minimal solutions of such a system. We also show how our results apply to inhomogeneous systems yielding necessary conditions for satisfiability and upper bounds on the minimal solutions.
