Running GGNFS

[Batalov]

Sieves nice and fast here. (c2: -1, though, and just a habit, Y1>0, let Y0 be <0)...
total yield: 2529, q=426287 (0.00417 sec/rel)

n: 59637465959020280912357567367209060262303555900277744434999055980903367137477583253307595639414569102520890416866614073
c4: 1
c2: -1
c0: 1
Y0: -909543680129861140820205019889143
Y1: 1818989403545856475830078125
skew: 1
rlim: 850000
alim: 850000
lpbr: 25
lpba: 25
mfbr: 44
mfba: 44
rlambda: 2.3
alambda: 2.3
type: snfs

[Andi47]

Originally Posted by Batalov

c2: -1

- I missed the "-" (and I got the badshed bug, my version is SVN340, seems I have to update)

Now with c2=-1 it sieves good for me too, so I will reserve this number.

BTW: for a^n+b^n with n divisible by 15, I end up with an algebraic factor x^8 + x^7*y - x^5*y^3 - x^4*y^4 - x^3*y^5 + x*y^7 + y^8 (and degree 12 for n divisible by 21); still trying to figure out how to reduce this to something suitable for lasieve.

[Batalov]

Good tips are at http://mersennewiki.org/index.php/SN...mial_Selection
So, similarly, use substitution t = (x^2+y^2)/x/y and then work term by term the expression
(x^8 + x^7*y - x^5*y^3 - x^4*y^4 - x^3*y^5 + x*y^7 + y^8)/x^4/y^4 - (t^4)
the leading coefficient of the remainder will suggest the next term for t^3 to type into last parentheses etc
e.g. in GP/Pari)
...
(00:20) gp > (x^8 + x^7*y - x^5*y^3 - x^4*y^4 - x^3*y^5 + x*y^7 + y^8)/x^4/y^4
- (t^4+t^3-4*t^2-4*t+1)
%6 = 0

Then that's the c#'s for the algebraic
and for rational, Y1: xy, Y0: -(x^2+y^2)
___


[SIZE=1]For the x^15n - y^15n, flip signs for y and for odd terms.
[/SIZE]

[Andi47]

Originally Posted by Batalov

Good tips are at http://mersennewiki.org/index.php/SN...mial_Selection
So, similarly, use substitution t = (x^2+y^2)/x/y and then work term by term the expression
(x^8 + x^7*y - x^5*y^3 - x^4*y^4 - x^3*y^5 + x*y^7 + y^8)/x^4/y^4 - (t^4)
the leading coefficient of the remainder will suggest the next term for t^3 to type into last parentheses etc
e.g. in GP/Pari)
...
(00:20) gp > (x^8 + x^7*y - x^5*y^3 - x^4*y^4 - x^3*y^5 + x*y^7 + y^8)/x^4/y^4
- (t^4+t^3-4*t^2-4*t+1)
%6 = 0

Then that's the c#'s for the algebraic
and for rational, Y1: xy, Y0: -(x^2+y^2)
___


[SIZE=1]For the x^15n - y^15n, flip signs for y and for odd terms.
[/SIZE]

Thanks.
I guess for x^n+y^n with n divisible by 21, giving the algebraic factor x^12 + x^11*y - x^9*y^3 - x^8*y^4 +x^6*y^6 - x^4*y^8 - x^3*y^9 + x*y^11 + y^12, I do again a substitution of t = (x^2+y^2)/x/y?
Unfortunately, the ancient version of Derive, which I have installed, would let me substitute all t's by (x^2+y^2)/x/y, but it won't let my substitute (x^2+y^2)/x/y by t.

(Edit: just installed Pari)

Edit2: How would I do the substitution in Pari? subst(<polynomial>,(x^2+y^2)/(x*y),t) wont't work, as it expects a variable in the second position, and subst(<polynomial>,t,(x^2+y^2)/(x*y)) does nothing as there is no t in the expression to replace.

[fivemack]

I don't think you can do the back-substitution automatically in pari, but you can do it by hand fairly easily:

% A=factor(x^21+1)[4,1]
% t=(x^2+1)/x
% x^6*t^6-A
-x^11 + 6*x^10 + x^9 + 16*x^8 + 19*x^6 + 16*x^4 + x^3 + 6*x^2 - x
% x^6*(t^6+t^5)-A
6*x^10 + 6*x^9 + 16*x^8 + 10*x^7 + 19*x^6 + 10*x^5 + 16*x^4 + 6*x^3 + 6*x^2
% x^6*(t^6+t^5-6*t^4)-A

and so on

[Andi47]

Originally Posted by fivemack

I don't think you can do the back-substitution automatically in pari, but you can do it by hand fairly easily:
<snip>

and so on

So I get t^6+t^5-6*t^4-6*t^3+8*t^2+8*t+1 and thus for homogeneous cunninghams:

c6: 1
c5: 1
c4: -6
c3: -6
c2: 8
c1: 8
c0: 1
Y1: x*y
Y0: -(x^2+y^2)

Thanks!

[Andi47]

Originally Posted by FactorEyes

Just leave all the quartics and sextics, except for those with remaining composite no more than 10 digits smaller than the SNFS difficulty. And the number of composites remaining should not be divisible by 11 or 13.

*gg*

Originally Posted by Batalov

Good tips are at http://mersennewiki.org/index.php/SN...mial_Selection

So for a^11k-b^11k the poly would be

c5: 1
c4: 1
c3: -4
c2: -3
c1: 3
c0: 1
Y1: a^k*b^k
Y0: -(a^2k+b^2k)

...but I guess, for things like 4³⁶³-3³⁶³ it would be better to use the algebraic factor x^2 + xy + y^2 of a^3j-b^3j (=:x^3-y^3)?

Edit: Obviously yes: 13e, sieving on the rational side from 1.3M to 1.3M+200 with the parameters

rlim: 1300000
alim: 1300000
lpbr: 26
lpba: 26
mfbr: 45
mfba: 45
rlambda: 2.3
alambda: 2.3
skew: 1
type: snfs

yields:
total yield: 18, q=1300237 (1.67706 sec/rel) with the quintic
and
total yield: 563, q=1300237 (0.05648 sec/rel) with the quartic

[Batalov]

yes. the only easily combinable prime factors of the exponent are 3*5 and 3*7.
3*11 doesn't help, so one will have to go with the reduction by 3.
3/5/7-free 11-ers and 13-ers are working as you've mentioned.

In the LM factors, there are a few less tricks. (e.g. cannot make use of 3*5 and similar, and cannot use divisibility by 11, but still can make use of 5, 7, 3, and especially 3^2 for a 2LM; there's one instance left of the latter, afair)

[Mini-Geek]

I'm getting "matrix is corrupt; skipping linear algebra" on a c103 after running aliqueit/factMsieve.pl. The only thing different about how I ran this is that I stopped the poly selection after 12 minutes, instead of letting it finish (usually about 20 minutes). When I started again, it apparently used the best poly it had found so far instead of finishing the poly selection. It sieved from 1150000 to 1650000 (using 12e) before running the final filtering run with 4.1 million raw relations. The full ggnfs.log file is attached.

C:\Files\Prime\aliquot\2\ggnfs_343857915597986780213425239029906727961696952919820045330471843628789
6911589739564410066178777106209487>msieve142 -s test.dat -l ggnfs.log -i test.ini -v -nf test.fb -t
2 -nc2

Msieve v. 1.42
...

commencing linear algebra
read 31006 cycles
cycles contain 195702 unique relations
read 195702 relations
using 20 quadratic characters above 67035434
building initial matrix
memory use: 22.3 MB
read 31006 cycles
matrix is 135216 x 31006 (16.4 MB) with weight 5123514 (165.24/col)
sparse part has weight 4094116 (132.04/col)
matrix is corrupt; skipping linear algebra
elapsed time 00:00:11

test.fb is

N 3438579155979867802134252390299067279616969529198200453304718436287896911589739564410066178777106209487
SKEW 15495.41
A5 2100
A4 138988096
A3 -1137721010353
A2 -36730464843574278
A1 150510188120162884360
A0 349966578011471724802352
R1 33425399069
R0 -69635257666296082431
FAMAX 2300000
FRMAX 2300000
SALPMAX 67108864
SRLPMAX 67108864

Anyone know if this run is salvageable or not?

[fivemack]

The run's definitely salvageable, just do a bit more sieving.

The problem is that, even if the number of cycles isn't enough to form a useful matrix, msieve sometimes continues and tries to make the matrix anyway.

[Mini-Geek]

Originally Posted by fivemack

The run's definitely salvageable, just do a bit more sieving.

The problem is that, even if the number of cycles isn't enough to form a useful matrix, msieve sometimes continues and tries to make the matrix anyway.

Thanks, I was hoping it'd be that simple, but really had no clue why it was failing and didn't want to waste CPU time. I'm currently doing more sieving, I'll edit or post again when I finish or run into another problem.