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Finding simultaneous
Diophantine approximations with prescribed quality
Wieb Bosma and Ionica Smeets |
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Vol. 1 (2013), No. 1, 167–185
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Abstract |
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We give an algorithm that finds a sequence of approximations with Dirichlet coefficients bounded by a constant only depending on the dimension. The algorithm uses LLL lattice basis reduction. We present a version of the algorithm that runs in polynomial time of the input. |
Keywords
simultaneous Diophantine approximation, LLL lattice
reduction
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Mathematical Subject Classification 2010
Primary: 11J13
Secondary: 11Y16, 11J70
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Milestones
Published: 14 November 2013
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Authors |
| Wieb Bosma | |
| Mathematics Department Radboud University Nijmegen PO Box 9010 6500 Nijmegen The Netherlands |
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| Ionica Smeets | |
| Mathematical Institute Leiden University Niels Bohrweg 1 2333 CA Leiden The Netherlands |
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