Discussion related to cado-nfs

[Shi Bai <shih.bai@gmail.com>]

Dear Jayson,

On Mon, Oct 1, 2012 at 9:36 AM, Jayson King <w@jaysonking.com> wrote:
> On 09/30/2012 05:49 AM, Shi Bai wrote:
>> Could you please specify this? To my knowledge, Lemma 2.1 provides an
>> upper bound for the size of A_{d-2}. But Kleinjung 2008 method has a
>> tighter control for A_{d-2}.
>
> Thanks for the prompt reply.
>
> My understanding is that the coefficient gets a correction of size l
> when the polynomial is expanded.
Thanks for the reply. I see -- it happens due to the O(Y1) correction term.

>> I've just tried similar parameters and the  |A_{d-2}| seemed to be
>> similar to m0/P^2 ~= 8.17e17. For instance,
>>
>> # ./polyselect2l -nq 1000 -lq 4 -degree 5 -incr 60 -t 1 -maxnorm
>> 5.18e21 -admin 30030 -admax 30090 -N
>> 10941738641570527421809707322040357612003732945449205990913842131476349984288934784717997257891267332497625752899781833797076537244027146743531593354333897
>> -seed 1 -r -v 1000000
>>
>> gives,
>>
>> # Raw polynomial:
>> n: 
>> 10941738641570527421809707322040357612003732945449205990913842131476349984288934784717997257891267332497625752899781833797076537244027146743531593354333897
>> Y1: 831722133106132709
>> Y0: -816995138187784191741495318541
>> c5: 30060
>> c4: -67649
>> c3: -48826259812817663
>> c2: -373148919050557847685847416834
>> c1: 310280494743488312115747320918
>> c0: -147684545208073702062614789699
>> # raw lognorm 56.39, skew 106594304.00, alpha 0.48, E 56.87,  exp_E
>> 46.37, 1 rroots
>> # Optimized polynomial:
>> n: 
>> 10941738641570527421809707322040357612003732945449205990913842131476349984288934784717997257891267332497625752899781833797076537244027146743531593354333897
>> Y1: 831722133106132709
>> Y0: -816954505341985579904820952002
>> c5: 30060
>> c4: 7342736743651
>> c3: 717393394452928189821
>> c2: -338136683555324576839519112348
>> c1: -5707047913428722097254810411379129079
>> c0: -185794434636076988046000736254603634997227981
>> # lognorm 56.32, skew 110723072.00, alpha -1.36, E 54.95,  exp_E 46.29, 1 
>> rroots
>> # Murphy's E(Bf=10000000,Bg=5000000,area=1.00e+16)=2.02e-13 (best so
>> far 2.02e-13)
>>
>> And the c3 in the raw polynomial is about 10^17.
>> log(48826259812817663)/log(10.0)=16.68
>>
>> What parameters did you use?
>
> That's testing only the first 1000 q. The issue occurs when q is large
Sorry, it's perhaps caused by my codes. The default nq (without giving
the -nq in option) could be very large. So the issue is likely to
occur when the param/param* doesn't contain a nq option.

PS: Paul Zimmermann did notice this (e.g. to use small lq) before,
which I overlooked in our emails.

For the fix, it's easy to bound each q when -lq is normal. I'm still
thinking how to deal with large -lq and any suggestions/ideas would be
more than welcome.

Best regards,
Shi