A bound on solutions of linear integer equalities and inequalities-Reference-Cited by-同舟云学术

A bound on solutions of linear integer equalities and inequalities

Published:1978 Issue:1 Volume:72 Page:155-158
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

von zur Gathen Joachim,Sieveking Malte

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.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1978-072-01/S0002-9939-1978-0500555-0/S0002-9939-1978-0500555-0.pdf

Reference6 articles.

1. A sharp bound for positive solutions of homogeneous linear Diophantine equations;Borosh, I.;Proc. Amer. Math. Soc.,1976

2. Bounds on positive integral solutions of linear Diophantine equations;Borosh, I.;Proc. Amer. Math. Soc.,1976

3. \bysame, Bounds on positive integral solutions of linear diophantine equations. II, Texas A & M University, (preprint).

4. S. A. Cook, A proof that the linear diophantine problem is in NP, unpublished manuscript, September 13, 1976.

5. Lecture Notes in Computer Science, Vol. 43,1976

Cited by 71 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Trees;Fragments of First-Order Logic;2023-03-30

2. Transitivity;Fragments of First-Order Logic;2023-03-30

3. Equivalence and counting;Fragments of First-Order Logic;2023-03-30

4. Equivalence;Fragments of First-Order Logic;2023-03-30

5. Modalities;Fragments of First-Order Logic;2023-03-30