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2021-09-25, 18:39   #78
EdH

"Ed Hall"
Dec 2009

10000000101102 Posts

Quote:
 Originally Posted by Max0526 Scaled Plutie's poly with a lower skew. The only one so far with a 3-handle. EdH is welcome to try the CADO script on it. . . .
I'll run it, but I don't have a lot of confidence in the script any longer.

2021-09-26, 14:59   #79
Max0526

"Max"
Jun 2016
Toronto

22·227 Posts

Quote:
 Originally Posted by Plutie Found this one! No spin done yet apart from EdH's script, which produced no better results. Code: n: 533439167600904850230361756102700151678687933392166847323827307497363839257031077774321424872955045754669625577486179222154434651598903112919949771321416511589029559325246084363632977829645558547714072241 Y0: -5364063517160195101439064344720425686774 Y1: 38191391760434248123003 c0: -515349887751874687116560925109512114626453230780 c1: 17974344725264404895365666536735938178777 c2: -101346622782727207541871449878174 c3: -1497180969353527609911507 c4: 1395152266302128 c5: 240240 skew: 428721961.354 # lognorm 62.56, E 54.79, alpha -7.77 (proj -2.37), 3 real roots # MurphyE(Bf=1.000e+07,Bg=5.000e+06,area=1.000e+16)=3.496e-15
Another 3-handle spin-off for EdH. Too bad the skew is so high.
Code:
Y0: -10728127031432018094778041711124528492914
Y1: 38191391760434248123003
c0: -469306450383673786154179958923768036883220558848
c1: 16764898040765810552874639420851915901168
c2: -518184119670233545764543818527130
c3: -1282718100125517456876339
c4: 720287485214464
c5: 60060
skew: 925525618.81
# size 6.010e-20, alpha -7.767, combined = 3.022e-15 rroots = 3

 2021-09-26, 15:09 #80 Max0526   "Max" Jun 2016 Toronto 22·227 Posts The last one before I fire up my CADO. Code: Y0: -2682031757909474203063733054205920498761 Y1: 38191391760434248123003 c0: -35908619240718506542028162576570459628200092008 c1: 5559845291855259938458828146982323985017 c2: -497314341623175258490396369880660 c3: -5192928362539057069336396 c4: 11498698480023424 c5: 3843840 skew: 215953735.30 # size 6.029e-20, alpha -7.765, combined = 2.981e-15 rroots = 3
 2021-09-26, 18:01 #81 EdH     "Ed Hall" Dec 2009 Adirondack Mtns 2·29·71 Posts For some reason, my machine I turned loose is still churning. It hasn't found anything better, but I'm wondering why it's still trying. I might have to try the latest ones on a different machine. . .
 2021-09-27, 15:00 #82 EdH     "Ed Hall" Dec 2009 Adirondack Mtns 2·29·71 Posts I tried the last two Max posted, but didn't get anything to be excited about: Code: Y0: -2682031753193739554089051909692707821633 Y1: 38191391760434248123003 c0: -2558958882078862036416567911929050848051646810840 c1: 14288895390205752696754550185547792236194 c2: 1296679606343231125776054513987683 c3: -1072389920449047317227700 c4: -13871815645642624 c5: -3843840 skew: 225516970.018 # lognorm 63.80, E 55.60, alpha -8.20 (proj -2.75), 5 real roots # MurphyE(Bf=1.000e+07,Bg=5.000e+06,area=1.000e+16)=3.094e-15 cownoise: Code: 316412275.01640 3.10650558e-15
 2021-09-27, 20:59 #83 swellman     Jun 2012 62708 Posts Lot of high e-scoring candidates! How critical is the skew wrt sieving efficiency for these bigger GNFS jobs? Cownoise (and presumably msieve) doesn’t use an input value for skew in the score calculation, what’s to stop someone from using the highest scoring poly and cutting the skew in half or a third? Sieving efficiency could suffer but would the high e-score carry the day? I noted that with Plutie’s record poly, the skew was ~210M per CADO but cownoise said 489.7M. What would be the effect(s) be if we ignore this suggestion from cownoise? Or set skew to say 290M? Most of us seem to use the output value for skew, often > 1e8, to two decimals places of precision. Is this strictly necessary? Just random musings. I know skew has been discussed before, likely numerous times but looking at the list of polys in this thread the proper method of selecting the “best one” is not obvious to me.
 2021-09-27, 21:53 #84 VBCurtis     "Curtis" Feb 2005 Riverside, CA 52·7·29 Posts cownoise is testing a bunch of skew values to see which one results in the highest e-score. If you use a non-optimal skew, the poly will generally sieve less efficiently. But, this "efficiency" is not very sensitive; you might test-sieve that Plutie poly with the CADO skew and the cownoise skew, and see the effect for yourself. 8+ sig-figs is definitely not important for skew.
 2021-09-27, 22:08 #85 charybdis     Apr 2020 22·137 Posts The 3.496e-15 poly scores so highly that it ought to beat all the others as long as the skew selected is vaguely sensible. Cownoise chooses the skew that produces the best Murphy-E score as calculated by msieve with its default parameters. I'm not sure what CADO does, but in practice the difference in performance is going to be pretty small.
2021-09-27, 22:40   #86
swellman

Jun 2012

23·11·37 Posts

Quote:
 Originally Posted by VBCurtis cownoise is testing a bunch of skew values to see which one results in the highest e-score. If you use a non-optimal skew, the poly will generally sieve less efficiently. But, this "efficiency" is not very sensitive; you might test-sieve that Plutie poly with the CADO skew and the cownoise skew, and see the effect for yourself. 8+ sig-figs is definitely not important for skew.
No doubt. In the past I’ve compared the skew values as generated by msieve/CADO with the one suggested by cownoise and honestly found little difference. But that’s hardly authoritative. My point is with what methodology do we select the best poly? Test sieve each candidate over a range of skews, tabulate and declare a winner? Or only use the skew from cownoise (or msieve/CADO) in order to simplify things?

I’ve heard the rule of thumb never use a skew > 3e8. (Not sure if this is still true.) At least one of the high scoring polys in this thread had a skew exceeding this limit - dropping the skew to a lower value may help. Or not. Or do we filter out such polys from the list of finalists?

Bottom line: how important is skew in a GNFS 204 job?

[/babble]

 2021-09-27, 23:01 #87 charybdis     Apr 2020 22416 Posts I'd say test-sieve each poly with whatever skew it came with (ideally these would be consistent i.e. all cownoise or all CADO, but this won't matter) and only try different skews if it's very close between the top two. I see absolutely no mathematical reason to avoid skew > 3e8. For very large degree 5 jobs like this, a large skew is to be expected. Did the GGNFS sievers have trouble with huge skews perhaps? Extremely small skews (<< 1), sometimes seen with SNFS, pose a bigger problem, because on very large jobs they will produce lots of relations with b > 2^32 which msieve filtering can't deal with.
2021-09-27, 23:15   #88
swellman

Jun 2012

23·11·37 Posts

Quote:
 Originally Posted by charybdis I see absolutely no mathematical reason to avoid skew > 3e8. For very large degree 5 jobs like this, a large skew is to be expected. Did the GGNFS sievers have trouble with huge skews perhaps?
Yes I think that rule of thumb was associated with ggnfs. I believe this rule was more computational then mathematical in nature but it was years ago. Can’t find any old posts but I’ll dig some more. Perhaps the greybeards around here remember. Or confirm how confused I really am!

Quote:
 Extremely small skews (<< 1), sometimes seen with SNFS, pose a bigger problem, because on very large jobs they will produce lots of relations with b > 2^32 which msieve filtering can't deal with.
I’ve changed very small skew values to 1 in the past but I don’t remember it happening very often. Or if it worked…

Last fiddled with by swellman on 2021-09-27 at 23:16

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