On Mon, Jul 12, 2004 at 10:46:33AM -0600, Schroeppel, Richard wrote:
I think DTs formula below isn't quite right; taking each clause as a 50:50 coin flip, the conjunctions are 1/8 true, and the disjunction only 1/4, while I'd expect 50%.
Umm, right, it should be (p-r > 0 && q-s < 0) || (p-r > 0 && q-s > 0 && (p-r)^2 < k*(q-s)^2) || (p-r < 0 && q-s < 0 && (p-r)^2 > k*(q-s)^2) Sorry for the missing branch. The reason this is complicated should be related to the fact that we're in a quadratic extension of Q, and the answer is very different if you take the other square root. I can't make that precise at the moment, however. [On writing a+bx in order]
... and the appropriate generalization to 3D.
I'm not sure why you're thinking about this, but it's almost guaranteed to be much harder: there is no really nice notion of 3D continued fractions. I bet there won't be a bounded number of possible successive differences you need to keep track of, for instance. Peace, Dylan