On computing Hilbert bases via the Elliot–MacMahon algorithm

The ways of using the Elliot–MacMahon algorithm to compute the Hilbert base of a system of linear Diophantine equations known so far are either not efficient or can fail to terminate. We present a version of an algorithm exploiting this range of ideas, which however is reasonably efficient as well a...

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Bibliographic Details
Published in:Theoretical computer science 2001, Vol.263 (1), p.37-46
Main Author: Pasechnik, Dmitrii V.
Format: Article
Language:English
Subjects:
Algebra
Algebraic geometry
Elliot–MacMahon algorithm
Exact sciences and technology
Hilbert basis
Linear Diophantine equations
Mathematics
Number theory
Sciences and techniques of general use
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Summary:The ways of using the Elliot–MacMahon algorithm to compute the Hilbert base of a system of linear Diophantine equations known so far are either not efficient or can fail to terminate. We present a version of an algorithm exploiting this range of ideas, which however is reasonably efficient as well as finite.
ISSN:0304-3975
1879-2294
DOI:10.1016/S0304-3975(00)00229-2