A Bound on Solutions of Linear Integer Equalities and Inequalities
- 1 October 1978
- journal article
- Published by JSTOR in Proceedings of the American Mathematical Society
- Vol. 72 (1) , 155-158
- https://doi.org/10.2307/2042554
Abstract
Consider a system of linear equalities and inequalities with integer coefficients. We describe the set of rational solutions by a finite generating set of solution vectors. The entries of these vectors can be bounded by the absolute value of a certain subdeterminant. The smallest integer solution of the system has coefficients not larger than this subdeterminant times the number of indeterminates. Up to the latter factor, the bound is sharp.Keywords
This publication has 2 references indexed in Scilit:
- Bounds on Positive Integral Solutions of Linear Diophantine EquationsProceedings of the American Mathematical Society, 1976
- Convexity and Optimization in Finite Dimensions IPublished by Springer Nature ,1970