Does LatticeReduce work with arbitrary precision arithmetic? That is, if I give it a linearly independent integer basis, but the integers are 40 decimal digits long and SVD says the largest singular value is 10^16 times larger than the smallest singular value, will it still give me a good LLL reduced basis?

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    $\begingroup$ Try it and see! $\endgroup$ – David G. Stork Dec 14 '15 at 21:32
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    $\begingroup$ Yes and yes, in that order. $\endgroup$ – Daniel Lichtblau Dec 14 '15 at 21:32
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    $\begingroup$ Of course, you need to indicate the precision of all the numbers you use in order for Mathematica to actually apply arbitrary precision arithmetic. $\endgroup$ – Sjoerd C. de Vries Dec 14 '15 at 21:46

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