GGNFS questions and Answers - Page 7

fetofs · 2005-12-12, 18:17

How do you calculate the cyclotomic polynomials for the special numbers?

VJS · 2005-12-12, 20:41

Personally I don't know how to calculate it yet and havn't had the time to investigate how. ... I generally use m instead of Y1 Y0.

So how did I do it... Little black box from ??? Xilman ??? ... the phi.exe program.

I used it a couple times to check my calculations for the last few polynomials generally it produces the obvious degree 5 polys and m values. However from time to time it will generate polynomials like the c112 above, I've been using them with great success.

Perhaps I'm doing something wrong but it's certainly working well for me, and the odd 4 hour factorization of a c112+ it's like christmas.

Mystwalker · 2005-12-12, 21:25

Quote:

Originally Posted by VJS

So how did I do it... Little black box from ??? Xilman ??? ... the phi.exe program.

I think it's Alex.

fetofs · 2005-12-12, 21:29

Quote:

Originally Posted by VJS

Personally I don't know how to calculate it yet and havn't had the time to investigate how. ... I generally use m instead of Y1 Y0.

So how did I do it... Little black box from ??? Xilman ??? ... the phi.exe program.

I used it a couple times to check my calculations for the last few polynomials generally it produces the obvious degree 5 polys and m values. However from time to time it will generate polynomials like the c112 above, I've been using them with great success.

Perhaps I'm doing something wrong but it's certainly working well for me, and the odd 4 hour factorization of a c112+ it's like christmas.

I think you didn't understand the question...

Phi asks for the n and x values for the polynomial. How do you calculate those?

VJS · 2005-12-12, 22:26

Quote:

Originally Posted by Mystwalker

I think it's Alex.

Not sure Mystwalker sounds like an Alex program... I downloaded it once while searching this forum on poly selection.

fetofs,

Like I said black box for me so far, if you just run phi it give you switches, correct.

All of the numbers that I have been trying thus far have been of the

x^n-1 type so I'm simply entering the base and exponent. For N you can always use 1 right, it divides everything

. I havn't seen a difference using anything other than 1 for N anyways.

Maybe I need to ask a few question...

1. You know that inorder to do snfs as opposed to ggnfs you need the equation from which the composite orginated.

2. In addition to this N: doesn't have to be N for the entire expression

Maybe I'm still not understanding your question... for the above number a c112 it orginated from the expression.

Ahh sorry I noticed the forum butchered the number..

713406215047 hat 13 - 1

so phi 13 713406215047 1

smh · 2005-12-12, 22:59

Quote:

Originally Posted by Mystwalker

I think it's Alex.

Yes it is Alex' program.

I'm wondering if there's a newer version available. Latest i could find is 0.1.2

ValerieVonck · 2005-12-13, 16:56

Here is the phi program

VJS · 2005-12-13, 17:49

If during sieving you get a report of "too many relations" I know this can be avoided by reducing your sieve range.

My question is...

What does it matter if you get too many relations 90% through your sieving chunk. Are those "extra" relations thrown out or does it just make the bin file too large --> more difficult to process later ?

Just curious.

ValerieVonck · 2005-12-13, 17:58

For me its no problem.... I only wondered it woulnd't interfere with the program.

C.

ValerieVonck · 2005-12-16, 16:51

Hi group,

I am doing my first SNFS factorization.
But I have a question about "degree".

I run the program phi.exe & I choose a polynomial of the 6th degree.
But I can also choose a 4 & 5 degree one!

What is better to choose? a 6 or a 4 degree poly?
Sorry about the st00pid question .... but I try understand it...

Best Regards
C.

akruppa · 2005-12-16, 17:08

Depends on how large your number is, that is, on the SNFS difficulty. Grossly simplified, for difficulty ~100, degree 4 is optimal, for ~150, degree 5 and for ~240, degree 6. Sometimes the difficulty can be reduced by dividing out algebraic factors. Run phi without -deg4 or -deg6 first and see what difficulty you get. Without a -degx parameter, phi will try to minimise the difficulty by dividing out the largest algebraic factors that can be used.
Then. if your number is very small (difficulty <120) try -deg4, if it is very large (>190) try -deg6. If the difficulty you now get is no (or only marginally) higher than the default one, use -deg4 or -deg6, resp. Otherwise stick with the default.

For composite sizes beginners of SNFS will typically attempt, the default polynomial produced by phi is usually very reasonable.

Alex

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2005-12-12, 18:17	#67
fetofs Aug 2005 Brazil 2×181 Posts	How do you calculate the cyclotomic polynomials for the special numbers?

2005-12-12, 20:41	#68
VJS Dec 2004 100101011₂ Posts	Personally I don't know how to calculate it yet and havn't had the time to investigate how. ... I generally use m instead of Y1 Y0. So how did I do it... Little black box from ??? Xilman ??? ... the phi.exe program. I used it a couple times to check my calculations for the last few polynomials generally it produces the obvious degree 5 polys and m values. However from time to time it will generate polynomials like the c112 above, I've been using them with great success. Perhaps I'm doing something wrong but it's certainly working well for me, and the odd 4 hour factorization of a c112+ it's like christmas.

2005-12-13, 17:49	#74
VJS Dec 2004 13·23 Posts	If during sieving you get a report of "too many relations" I know this can be avoided by reducing your sieve range. My question is... What does it matter if you get too many relations 90% through your sieving chunk. Are those "extra" relations thrown out or does it just make the bin file too large --> more difficult to process later ? Just curious.

2005-12-13, 17:58	#75
ValerieVonck Mar 2004 Belgium 29² Posts	For me its no problem.... I only wondered it woulnd't interfere with the program. C.

2005-12-16, 16:51	#76
ValerieVonck Mar 2004 Belgium 29² Posts	Hi group, I am doing my first SNFS factorization. But I have a question about "degree". I run the program phi.exe & I choose a polynomial of the 6th degree. But I can also choose a 4 & 5 degree one! What is better to choose? a 6 or a 4 degree poly? Sorry about the st00pid question .... but I try understand it... Best Regards C.

2005-12-16, 17:08	#77
akruppa "Nancy" Aug 2002 Alexandria 2,467 Posts	Depends on how large your number is, that is, on the SNFS difficulty. Grossly simplified, for difficulty ~100, degree 4 is optimal, for ~150, degree 5 and for ~240, degree 6. Sometimes the difficulty can be reduced by dividing out algebraic factors. Run phi without -deg4 or -deg6 first and see what difficulty you get. Without a -degx parameter, phi will try to minimise the difficulty by dividing out the largest algebraic factors that can be used. Then. if your number is very small (difficulty <120) try -deg4, if it is very large (>190) try -deg6. If the difficulty you now get is no (or only marginally) higher than the default one, use -deg4 or -deg6, resp. Otherwise stick with the default. For composite sizes beginners of SNFS will typically attempt, the default polynomial produced by phi is usually very reasonable. Alex