SNFS polynomials.

chris2be8 · 2012-03-10, 16:06

I had a look at the SNFS polynomials generated by factordb and noticed it generates very bad ones. Eg: http://factorization.ath.cx/index.ph...00000487178750 which is (14754135833^11-1)/132772468352168 gets:

Code:

 n: 54317968970751484973310399914288545196091168576179094060078804933353377706605252225479726219559637
m: 217684524178614603889
deg: 4
skew: 0
type: snfs
c4: 3211747038473252619535796054537
c0: -1
rlim: 343800
alim: 343800
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2

An inverted quintic would be much better.

And http://factorization.ath.cx/index.ph...00000479069951 which is (6638^31+1)/2316174361302856299249 gets:

Code:

 n: 13133589571432270898222759874366292680873211449040207724769678781837619196179064309751019775966737
m: 567885443330209974916203392
deg: 4
skew: 0
type: snfs
c4: 292490486072
c0: 1
rlim: 343800
alim: 343800
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.2
alambda: 2.2

A quartic for a^b+1 with b of the form 4n+3 wants something like:

Code:

 m: a^(n+1)
c4: 1
c0: a

The skew should not be 0 either! I've not looked at alim etc but would not trust them.

Chris

firejuggler · 2012-03-10, 16:49

it's auto-generated, give it some slack!
I think that the original idea was more like to give an idea of what the snfs poly should look like.

2012-03-10, 16:06	#1
chris2be8 Sep 2009 2⁴·5·31 Posts	SNFS polynomials. I had a look at the SNFS polynomials generated by factordb and noticed it generates very bad ones. Eg: http://factorization.ath.cx/index.ph...00000487178750 which is (14754135833^11-1)/132772468352168 gets: Code: n: 54317968970751484973310399914288545196091168576179094060078804933353377706605252225479726219559637 m: 217684524178614603889 deg: 4 skew: 0 type: snfs c4: 3211747038473252619535796054537 c0: -1 rlim: 343800 alim: 343800 lpbr: 25 lpba: 25 mfbr: 45 mfba: 45 rlambda: 2.2 alambda: 2.2 An inverted quintic would be much better. And http://factorization.ath.cx/index.ph...00000479069951 which is (6638^31+1)/2316174361302856299249 gets: Code: n: 13133589571432270898222759874366292680873211449040207724769678781837619196179064309751019775966737 m: 567885443330209974916203392 deg: 4 skew: 0 type: snfs c4: 292490486072 c0: 1 rlim: 343800 alim: 343800 lpbr: 25 lpba: 25 mfbr: 45 mfba: 45 rlambda: 2.2 alambda: 2.2 A quartic for a^b+1 with b of the form 4n+3 wants something like: Code: m: a^(n+1) c4: 1 c0: a The skew should not be 0 either! I've not looked at alim etc but would not trust them. Chris

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2012-03-10, 16:49	#2
firejuggler "Vincent" Apr 2010 Over the rainbow 37·79 Posts	it's auto-generated, give it some slack! I think that the original idea was more like to give an idea of what the snfs poly should look like.