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Jan 6, 2010 at 15:01 history edited Richard CC BY-SA 2.5
Added note that dimension must be fixed to have a polynomial time algorithm.
Jan 6, 2010 at 14:51 comment added Richard David, good point about Barvinok's algorithm. I'll update the post when/if I run across the reference for the problem being #P-complete.
Jan 6, 2010 at 12:13 comment added David E Speyer And, yes, if you want to solve problems like this in practice, I recommend LattE.
Jan 6, 2010 at 12:13 comment added David E Speyer One should note that Barvinok's algorithm in polynomial in $\log a_i$, for fixed $n$; it is exponential in $n$. I think that, if we are allowed to change $n$, this problem should be #P complete, but I don't know a reference.
Jan 6, 2010 at 1:32 history edited Richard CC BY-SA 2.5
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Jan 6, 2010 at 1:21 history edited Richard CC BY-SA 2.5
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Jan 5, 2010 at 14:18 history edited Richard CC BY-SA 2.5
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Jan 5, 2010 at 13:51 history answered Richard CC BY-SA 2.5