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Old 2006-08-11, 23:11   #1
ATH
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I'm wondering about polyselect.exe for gnfs. What is the formula for the score E(F1,F2) of the polynominals?

I thought it was a function of the coefficients only but the same polynominal can have slightly different score if the search parameters was different:

bestpoly1.txt bestpoly2.txt

Scores are 8.024327e-007 and 8.121436e-007 for the same polynomial and only difference is maxS1 70 or 72 which should only be the stage1 "cutoff" value.




What about the skew? I read in another post here it should be (c_0/c_d)^(1/d). But skewness in my example file is 464.436 while:
(c_0/c_d)^(1/d) = (27473397726011234846439353544/10516227540)^(1/6) = 1173.569.
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Old 2006-08-12, 05:17   #2
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Quote:
Originally Posted by ATH
I'm wondering about polyselect.exe for gnfs. What is the formula for the score E(F1,F2) of the polynominals?
I thought it was a function of the coefficients only but the same polynominal can have slightly different score if the search parameters was different:
E depends on the size of the coefficients, and also on the behavior of the coefficients modulo small primes. Unfortunately the latter property is hard to measure exactly, and so the code creates a few thousand random sample values of the polynomial and tests them for divisibility by the small primes. This means E will vary from run to run, unless you use the same random seed.

The formula for E is equation 5.7 of Murphy's 'Polynomial Selection for the Number Field Sieve'. The root properties are determined by the function alpha(F)

Quote:
Originally Posted by ATH
What about the skew? I read in another post here it should be (c_0/c_d)^(1/d). But skewness in my example file is 464.436 while:
(c_0/c_d)^(1/d) = (27473397726011234846439353544/10516227540)^(1/6) = 1173.569.
I think the skewness is the result of a 1-dimensional minimization procedure given the polynomial coefficients.

jasonp

Last fiddled with by jasonp on 2006-08-12 at 05:23
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Old 2006-08-12, 08:52   #3
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Quote:
I'm wondering about polyselect.exe for gnfs.
Not an answer to your question, but you shouldn't use polyselect anymore. The pol51xxx.exe programs produces much better polynomials.
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Old 2006-08-12, 22:50   #4
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Thanks.

Last fiddled with by ATH on 2006-08-12 at 23:02
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