It seems to be what most people use in practice; though the reformulation in terms of lattices is a little indirect. In particular, the irrational ratios have to be replaced by (large) integer ratios. I don't have a reference easily to hand ---- but a web search for the original paper (Lenstra, Lenstra & Lov'acs) should turn one up. Personally, I prefer to use my own, non-kosher matrix-based algorithm, which seems to give useful results in practice --- even if I can't (be bothered to) prove it! Fred Lunnon On 9/11/09, Mike Stay <metaweta@gmail.com> wrote:
I'm thinking about the problem of designing gear trains for a lego orrery which I'd like to be fairly accurate. The standard gear sizes are 8, 16, 24, 40, so I have ratios of 1:2:3:5 to work with. I figure that since lg(3) (where lg is log base 2) is irrational, you can get arbitrary accuracy out of a gear train. I think I need a + b lg(3) + c lg(5) ~= lg(period), with a, b, c small. Is LLL the right tool for solving this kind of thing?
-- Mike Stay - metaweta@gmail.com http://math.ucr.edu/~mike http://reperiendi.wordpress.com
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