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Old 2008-03-22, 15:50   #3
xilman's Avatar
May 2003
Down not across

1068310 Posts

Originally Posted by fivemack View Post
I suppose I usually sieve over algebraic special-Q out of habit; if asked to justify myself, the algebraic side for GNFS jobs is generally much larger than the rational side, and I believe it makes sense to use the special-Q to render effectively smaller the numbers which started off largest, but that's not an answer for why I use -a pretty much universally in SNFS cases.

I haven't done the experiments to see how much duplication there is in a case with roughly equal-sized rational and algebraic side if you sieve on both sides; it might be sensible as a way to push yields up on SNFS problems with particularly intractable polynomials.
I generally sieve with special-Q on the side which has the typically larger norms. As the side with the special-q is guaranteed to be divisible by q, the remaining portion required to be smooth is correspondingly reduced.

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