Re: foursquares.gp

[hermann@stamm-wilbrandt.de]

On 2023-11-19 00:28, hermann@stamm-wilbrandt.de wrote:
> Bill did develop and tuned foursquares.gp based on this thread:
> https://pari.math.u-bordeaux.fr/archives/pari-users-2310/msg00003.html
>
> You can find foursquares.gp in contributed GP scripts section:
> https://pari.math.u-bordeaux.fr/Scripts/
> https://pari.math.u-bordeaux.fr/Scripts/foursquares.gp
>
>
> It does outperform my approach based on ternary quadratic forms to
> determine sum of 3 suqares as of now by far:
> https://pari.math.u-bordeaux.fr/archives/pari-users-2311/msg00018.html
I had a hard time to find any example where ternary quadratic form 
"squares34()" outperforms Bill's "foursquares()".
Here is one; I determined RSA-480 as largest unfactored RSA number =7 
(mod 8) and used that:

hermann@7600x:~/RSA_numbers_factored/pari$ gp -q foursquares.gp tqf.gp 
RSA_numbers_factored.gp
? foreach(RSA.unfactored(3),r,print1(r[1]," "))
260 270 896 290 300 1024 330 350 380 410 420 440 480 490
? n=RSA.get(490)[2];
? n%8
3
? n=RSA.get(480)[2];
? n%8
7
? sq=squares34(n);
? ##
  ***   last result computed in 6 ms.
? #sq
4
? norml2(sq)==n
1
? sq=foursquares(n);
? ##
  ***   last result computed in 52 ms.
? #sq
4
? norml2(sq)==n
1
?

Regaards,

Hermann.