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 mickfrancis 2014-05-20 13:47

Distribution of relations over the sieving interval in SIQS

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I was wondering whether anyone might know why the distribution, over the sieving interval, of relations found by SIQS seems to have 2 narrow spikes round about 0.7M either side of 0 (though not quite symmetrical, presumably due to asymmetrical parabolas?) See attachment. The peaks are around 3 times the general level. This is true of full relations, 1-partials and 2-partials.

Is this a well-known phenomena? Could it be used in any way to tune the QS algorithms?

Cheers,

Mick.

 xilman 2014-05-20 15:22

[QUOTE=mickfrancis;373864]I was wondering whether anyone might know why the distribution, over the sieving interval, of relations found by SIQS seems to have 2 narrow spikes round about 0.7M either side of 0 (though not quite symmetrical, presumably due to asymmetrical parabolas?) See attachment. The peaks are around 3 times the general level. This is true of full relations, 1-partials and 2-partials.

Is this a well-known phenomena? Could it be used in any way to tune the QS algorithms?

Cheers,

Mick.[/QUOTE]Hint: how many real roots does a quadratic have?

The term "chicken feet" is also relevant, though it may not appear so at first!

 bsquared 2014-05-20 15:26

[QUOTE=mickfrancis;373864]I was wondering whether anyone might know why the distribution, over the sieving interval, of relations found by SIQS seems to have 2 narrow spikes round about 0.7M either side of 0 (though not quite symmetrical, presumably due to asymmetrical parabolas?) See attachment. The peaks are around 3 times the general level. This is true of full relations, 1-partials and 2-partials.

Is this a well-known phenomena? Could it be used in any way to tune the QS algorithms?

Cheers,

Mick.[/QUOTE]

It is well known and has a simple origin as Xilman points out. Klechibar talks about it in "The Quadratic Sieve - introduction to theory with regard to implementation issues".

Early versions of YAFU tried to take advantage of it, but I don't believe the improvement (if any) amounted to much. It is too expensive to check every 'x' to see if you are close to a root or not. As a compromise I think I put a little more effort into all sieve hits within the block containing the root, but the gain at the root offsets the loss away from the root within the block...

 mickfrancis 2014-05-20 15:45

Thanks for the replies, guys - interesting.

Mick.

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