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2020-05-21, 12:58   #45
swellman

Jun 2012

323910 Posts

Quote:
 Originally Posted by EdH What is done to "spin" a polynomial? Is it something I can learn and/or implement with my archaic machinery and limited knowledge?
It’s a technique developed by Max. It uses CADO with some tricks to bump a found poly to a higher e-score. I am not familiar with the actual mechanics but Max did send me his recipe in a series of PMs some times ago. I will ask him if these can be published.

Max has also stated that he has found a way to lower the skew while keeping the e-score constant for a given poly. Sounded promising but I have no details.

Keep in mind that not every poly can be spun, and even when it can the spin doesn’t always improve the e-score all that much. But it is a very cool innovation which is definitely a +1 to the art of poly searching.

2020-05-21, 14:01   #46
EdH

"Ed Hall"
Dec 2009

100138 Posts

Quote:
 Originally Posted by swellman It’s a technique developed by Max. It uses CADO with some tricks to bump a found poly to a higher e-score. I am not familiar with the actual mechanics but Max did send me his recipe in a series of PMs some times ago. I will ask him if these can be published. Max has also stated that he has found a way to lower the skew while keeping the e-score constant for a given poly. Sounded promising but I have no details. Keep in mind that not every poly can be spun, and even when it can the spin doesn’t always improve the e-score all that much. But it is a very cool innovation which is definitely a +1 to the art of poly searching.
Thanks. If he'd rather not publish it openly, but would allow me the info, i wouldn't mind PMs from him. I might lack the knowledge to implement it though. I would try to create some scripts.

 2020-05-27, 11:19 #47 swellman     Jun 2012 41×79 Posts My best so far in the 60-70M range is only 2.23e-15. But I am still plugging away. Still collecting data on my various CADO runs on a separate machine. One thing that pops out is that P=8M consistently produces higher scoring polynomials than P=14M for reasons unknown to me. Maybe CADO hits an internal deadline before fully exploring all candidates with the higher P? I’ll post some data by the weekend but it will take another month fo fully fill the test matrix.
2020-05-27, 14:05   #48
EdH

"Ed Hall"
Dec 2009

3×372 Posts

Quote:
 Originally Posted by swellman My best so far in the 60-70M range is only 2.23e-15. But I am still plugging away. Still collecting data on my various CADO runs on a separate machine. One thing that pops out is that P=8M consistently produces higher scoring polynomials than P=14M for reasons unknown to me. Maybe CADO hits an internal deadline before fully exploring all candidates with the higher P? I’ll post some data by the weekend but it will take another month fo fully fill the test matrix.
I wonder if a different, specific parameter needs to be matched with P=14M or higher. My P=16M is similarly lower than my P=2M runs for the same search spaces.

2020-05-27, 18:17   #49
swellman

Jun 2012

41·79 Posts

Quote:
 Originally Posted by EdH I wonder if a different, specific parameter needs to be matched with P=14M or higher. My P=16M is similarly lower than my P=2M runs for the same search spaces.
Maybe sopteffort? I’ve intentionally kept it to the default value of 0 just to limit my test space, but it seems likely to be involved (size optimization time is proportional to sopteffort+1). I believe Ed varied it and got differing results, e.g. the place of the final winning polynomial at the end of size optimization varied wildly with higher values of sopteffort while this “n-place” metric was single digits for default values of sopteffort.

Should sopteffort = k * ropteffort, say with k near 1? 0.5?

 2020-05-28, 18:07 #50 VBCurtis     "Curtis" Feb 2005 Riverside, CA 506510 Posts size-opt effort and root-opt effort should be unrelated in principle. I haven't found a use yet for sopteffort, nor does the CADO default poly select params. However, ropteffort is invoked on every CADO default params file, and is usually rather high (10 as early as c130, from what I recall- I don't have the stock params handy). playing with sopteffort = 1 may be fruitful, but I wouldn't relate it to ropteffort at all.
2020-05-28, 20:21   #51
swellman

Jun 2012

41×79 Posts

Quote:
 Originally Posted by VBCurtis size-opt effort and root-opt effort should be unrelated in principle. I haven't found a use yet for sopteffort, nor does the CADO default poly select params. However, ropteffort is invoked on every CADO default params file, and is usually rather high (10 as early as c130, from what I recall- I don't have the stock params handy). playing with sopteffort = 1 may be fruitful, but I wouldn't relate it to ropteffort at all.
I have some as yet unposted data showing a value of 8M for P produces consistently higher scoring polynomials than P of 14M with all else equal. P=4M produces the lowest scores. We were just speculating on the interaction of P and sopteffort, that’s all. Testing will show the way!

2020-06-08, 05:03   #52
Max0526

"Max"
Jun 2016
Toronto

90610 Posts
C204 poly

Quote:
 Originally Posted by EdH Code: n: 533439167600904850230361756102700151678687933392166847323827307497363839257031077774321424872955045754669625577486179222154434651598903112919949771321416511589029559325246084363632977829645558547714072241 skew: 61173787.626 c0: -84551986041964239497940179882870301230255594832 c1: -1390964012076111490370063297140812459596 c2: 522002006121443981512032398747760 c3: 1762901709293407365122057 c4: -15943093281758022 c5: -318686760 Y0: -1380919702784425269323122024964712327251 Y1: 237213586863942644893691 # MurphyE (Bf=8.590e+09,Bg=4.295e+09,area=2.684e+16) = 4.390e-09 # f(x) = -318686760*x^5-15943093281758022*x^4+1762901709293407365122057*x^3+522002006121443981512032398747760*x^2-1390964012076111490370063297140812459596*x-84551986041964239497940179882870301230255594832 # g(x) = 237213586863942644893691*x-1380919702784425269323122024964712327251 cownoise says: Code: 71610307.84090 2.60680364e-15
After msieve rerun, just for future CADO spin
Code:
Y0: -1380919701727219820649855819252436663945
Y1: 237213586863942644893691
c0: 80233576744915037044865695237775462973210633888
c1: -3360691848973590722240522959473879950752
c2: -543390370730403386816602011237354
c3: -1415383168580686569709049
c4: 23044654864848822
c5: 318686760
skew: 71702279.00367
# size 4.734e-20, alpha -7.634, combined = 2.607e-15 rroots = 3

2020-06-08, 05:24   #53
Max0526

"Max"
Jun 2016
Toronto

2·3·151 Posts

Quote:
 Originally Posted by EdH Here's the 2.3 poly: Code: n: 533439167600904850230361756102700151678687933392166847323827307497363839257031077774321424872955045754669625577486179222154434651598903112919949771321416511589029559325246084363632977829645558547714072241 skew: 10042040.26 c0: -627354527254627652475332655176329358596636356 c1: 213018845490759638721666401827674851417 c2: 95937374251117784023748647685013 c3: -5623556931527657096482154 c4: -479102663461196184 c5: -2511784800 Y0: -1385041351159270154396558379928364326380 Y1: 262954605447105862796669 # MurphyE (Bf=8.590e+09,Bg=4.295e+09,area=2.684e+16) = 4.040e-09 # f(x) = -2511784800*x^5-479102663461196184*x^4-5623556931527657096482154*x^3+95937374251117784023748647685013*x^2+213018845490759638721666401827674851417*x-627354527254627652475332655176329358596636356 # g(x) = 262954605447105862796669*x-1385041351159270154396558379928364326380 cownoise says: Code: 16158683.33848 2.31283325e-15
Code:
R0: -1385041351659143177987030365622752942014
R1: 262954605447105862796669
A0: 653169167883331137294520872848350376000509290
A1: 199697587868029354778396563237441296355
A2: -117792697822385272998589389784161
A3: 2071256675570232894540458
A4: 455228324762132184
A5: 2511784800
skew: 16424161.34054
# size 3.958e-20, alpha -6.662, combined = 2.315e-15 rroots = 5

 2021-09-04, 14:46 #54 swellman     Jun 2012 1100101001112 Posts Bumping this thread. Reviewing the past work, it seems ad was searched up to 70M. I did many CADO searches in the 60-70M range playing with parameters and never found any poly worth reporting. Folks can go back and rerun searches with different parameters but the best e-score for this composite (2.607e-15 found by EdH) is pretty good. I think it is ready to sieve. Last fiddled with by swellman on 2021-09-05 at 11:16
 2021-09-08, 00:08 #55 charybdis     Apr 2020 541 Posts I used some top secret methods to figure out the pre-sizeopt leading coefficients of Ed's polys, and he appears to have searched some range from 100M upwards - perhaps to 110M? - at incr=420 and a very large P value of 16M. I'm not convinced we can't do better here. 2.6 feels a bit low, and the sample size of c204s is too small for the record to be particularly meaningful. The switch to incr=4620 was made quite early, so I'm going to break one of the fundamental rules of poly selection and duplicate some existing work by doing 500k-5M at P=8M, incr=420. I may go further if this looks promising.

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