Re: Question on ternary quadratic form

[hermann@stamm-wilbrandt.de]

On 2023-11-16 23:28, Bill Allombert wrote:
> If you want all the solutions, no, there are too many of them.
> If you need only one solution, you can use my script
> <https://pari.math.u-bordeaux.fr/Scripts/foursquares.gp>
>
> Cheers,
> Bill.
I think your "threesquares()" in that script is faster than American 
Citizen's code.


But I determined sum of 4 squares for Mersenne primes M_p=2^p-1
(they do not have sum of 3 squares representation).

Your "foursquares()" takes 21ms for M_1279.
But I had to stop it after more than an hour for M_2203 on i7-11850H 
CPU.

Latest tqf.gp gist
https://gist.github.com/Hermann-SW/f13b8adf7d7e3094f0b6db0bce29a7b8
takes less than 1s for M_p with p<=9689(!).

For bigger Mersenne primes find runtime table here:
https://gist.github.com/Hermann-SW/f13b8adf7d7e3094f0b6db0bce29a7b8?permalink_comment_id=4763152#gistcomment-4763152
(as well as next tuning step for processing even larger Mersenne primes)

Regards,

Hermann.