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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

A bound on solutions of linear integer equalities and inequalities


Authors: Joachim von zur Gathen and Malte Sieveking
Journal: Proc. Amer. Math. Soc. 72 (1978), 155-158
MSC: Primary 52A40; Secondary 15A39, 90C10
MathSciNet review: 0500555
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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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1978-0500555-0
PII: S 0002-9939(1978)0500555-0
Article copyright: © Copyright 1978 American Mathematical Society