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Old 2021-06-05, 13:12   #23
EdH
 
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"Ed Hall"
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OK! I've commented about running SIQS on lines 60 and 75. I will run those in a little while, if no one else has claimed them.
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Old 2021-06-05, 13:13   #24
Max0526
 
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Quote:
Originally Posted by bur View Post
I'd gladly do some factoring, but admittedly I'm not 100% clear on what to do...


Do I just factor the numbers from your sheet? What about the magma script, is it used on the prime factors after factorization?


I could start with the C127 & C139 (5,-6).
Yes, just factors the numbers from the sheet. The posted Magma script is for generating the initial records on factordb, and also for creating suitable SNFS polys.

That C127 is already factored by fivemack. I am writing a post on how to generate SNFS polys with the C139 as an example.
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Old 2021-06-05, 13:15   #25
Max0526
 
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Quote:
Originally Posted by EdH View Post
OK! I've commented about running SIQS on lines 60 and 75. I will run those in a little while, if no one else has claimed them.
Updated in the sheet, thank you!
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Old 2021-06-05, 13:18   #26
fivemack
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(5,-6) finished - the C139 has a P26 by ecm
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Old 2021-06-05, 13:46   #27
Max0526
 
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Quote:
Originally Posted by fivemack View Post
I'll take the two (5,-6) ones to start with; this is a research direction I've been interested in since my PhD in early 2000s.

Could you also send me the SNFS polynomial for (3,-7) ?

I am also throwing a core-month of ECM at the (6,-7) cofactors
This is how to generate the SNFS polys from the attached Magma script, c126 / snfs144 from (3, -7) is used as an example.

Edit the script to say [3, -7]
Code:
m := [3, 7]; ////////////////////// edit the plot point here /////////////////////
and uncomment the ouput for a
Code:
 a; " "; // uncomment this to get Y0 and Y1 for the SNFS poly, if necessary //
Run the script in Magma Calculator (http://magma.maths.usyd.edu.au/calc/).
Take the first value from the output (a-value) to produce Y0 and Y1 --> a = -Y0/Y1
Code:
a = 2625497112988581533564774729619428753/581569296010330112388333512013248048
Code:
Y0: -2625497112988581533564774729619428753
Y1: 581569296010330112388333512013248048
Now look through the numerators at the bottom of the output and find the one that has c126 as a cofactor: http://factordb.com/index.php?id=1100000002597811273
It was the second numerator from the top (ignore or comment all denominators in the output for now), generated by the second degree 4 poly on the list
Code:
    x^4 - 24*x^3 + 152*x^2 - 336*x + 196,
    2*x^4 - 30*x^3 + 169*x^2 - 420*x + 196*2, <-- this poly
    x^4 - 12*x^3 + 62*x^2 - 168*x + 196,
    x^4 - 6*x^3 + 17*x^2 - 84*x + 196
which creates the block for c0-c4
Code:
c0: 392
c1: -420
c2: 169
c3: -30
c4: 2
Get these 7 lines (c0-c4, Y0, Y1) through the http://cownoise.com/ / Calculators / Optimal Skew to produce the values for the skew and E
Code:
skew: 3.99192
# E = 2.36121084e-09
Add the n-value (c126) at the top of the poly file. The first one is ready! (There will be a second one too, for a different a-value [Y0, Y1, rational side] but the same c0-c4 [algebraic side], will explain it in a bit, need to derive the formula first).
Code:
n: 665346346066322380069828663638962277265700573377334838072153685493190817971091678723311076185411447868488601711575118621654489
skew: 3.99192
c0: 392
c1: -420
c2: 169
c3: -30
c4: 2
Y0: -2625497112988581533564774729619428753
Y1: 581569296010330112388333512013248048
# E = 2.36121084e-09
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Old 2021-06-05, 13:48   #28
Max0526
 
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Quote:
Originally Posted by fivemack View Post
(5,-6) finished - the C139 has a P26 by ecm
Could you please post a P26 to FactorDB for this C139?
EDIT: Ignore it please, marked as done for fivemack.

Last fiddled with by Max0526 on 2021-06-05 at 13:57
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Old 2021-06-05, 14:10   #29
EdH
 
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Line 60 is completed by SIQS and the db updated. What else may be needed?
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Old 2021-06-05, 14:11   #30
Max0526
 
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Quote:
Originally Posted by fivemack View Post
I'll take the two (5,-6) ones to start with; this is a research direction I've been interested in since my PhD in early 2000s.

Could you also send me the SNFS polynomial for (3,-7) ?

I am also throwing a core-month of ECM at the (6,-7) cofactors
The second SNFS poly is created by calculating
Code:
a2 =  7*(a1-4)/(2*a1-7) = 299219928947261084011440681566436561/168572736272121754344459267878017310,
where a1 = 2625497112988581533564774729619428753/581569296010330112388333512013248048
from the Magma script. It gives us
Code:
n: 665346346066322380069828663638962277265700573377334838072153685493190817971091678723311076185411447868488601711575118621654489
skew:  3.01798 # different for a2
c0: 392
c1: -420
c2: 169
c3: -30
c4: 2
Y0: -299219928947261084011440681566436561 # for a2
Y1: 168572736272121754344459267878017310 # for a2
# E = 3.14999605e-09 # different and _better_ poly for a2 !!!
There should be a3 and a4 values, but I didn't get to them yet. If/when I do, I'll post the additions.
Then there could be spin of course, and I am working on it too.
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Old 2021-06-05, 14:19   #31
Max0526
 
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Quote:
Originally Posted by EdH View Post
Line 60 is completed by SIQS and the db updated. What else may be needed?
I updated the sheet, thank you! Are you up for the c93 from here? http://factordb.com/index.php?id=1100000002598197699
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Old 2021-06-05, 14:23   #32
EdH
 
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Quote:
Originally Posted by Max0526 View Post
I updated the sheet, thank you! Are you up for the c93 from here? http://factordb.com/index.php?id=1100000002598197699
Sure! But, I might wait for the LA square root of a different project to complete. . .
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Old 2021-06-05, 14:40   #33
Max0526
 
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Quote:
Originally Posted by EdH View Post
Sure! But, I might wait for the LA square root of a different project to complete. . .
The c93 is done now.
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