Efficient computing of n-dimensional simultaneous Diophantine approximation problems

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Abstract

In this paper we consider two algorithmic problems of simultaneous Diophantine approximations. The first algorithm produces a full solution set for approximating an irrational number with rationals with common denominators from a given interval. The second one aims at finding as many simultaneous solutions as possible in a given time unit. All the presented algorithms are implemented, tested and the PariGP version made publicly available.

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Acta Universitatis Sapientiae, Informatica

The Journal of "Sapientia" Hungarian University of Transylvania

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