|
Bill Allombert on Mon, 18 Dec 2023 18:39:03 +0100
|
[Date Prev] [Date Next] [Thread Prev] [Thread Next] [Date Index] [Thread Index]
|
Re: Question on "qfminim()" for quadratic form
|
- To: pari-users@pari.math.u-bordeaux.fr
- Subject: Re: Question on "qfminim()" for quadratic form
- From: Bill Allombert <Bill.Allombert@math.u-bordeaux.fr>
- Date: Mon, 18 Dec 2023 18:38:56 +0100
- Delivery-date: Mon, 18 Dec 2023 18:39:03 +0100
- Dkim-signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=math.u-bordeaux.fr; s=2022; t=1702921138; bh=MUZh/spuO36IqOkS+S4RimMWMN1LwzuDVhJn4ZUIUBE=; h=Date:From:To:Subject:References:In-Reply-To:From; b=oQtvKj5ndS5QzRsm5P/vMrNhxilASiKzApHIac2yTH3kkI6/LaLlIAtdQjHOa2fmw dZu4YjevMN8DTQNyGqqRBvHN8FWJJHV94f/3vPu+AyrLvb58c5rLeUiR4mluxIl8yd oczvuXVVTP1G8BvuuxJyoxbq5MSv8pRNy7oMYqJmnVrqbzRvnTjBwVL2qEksZDzmPq 5uQVnPwVa8tVFY7QA7YYj+Fvt4CFpB/m0jiDPTJfTHQkSHDdAH1y2veuDeB584sGrM zrnxFe5CjzUFuJ28JyusBVP1GZcorNlI1ZfSr6Xp0Q8RKJnOXm4be+vj2pjT9lYtyE HLeM71ds+525xNxcJrSCMX1GSEdhfZeRTq4Sd8UMJxIdSNwHha9HZXCTj9+JbfoUb1 5ctCIrQ2rqxl9hTWbgMCH5jDMLxUoNsjdRd7OAEU26IUWlk5YY2cvn1OgVUFuuOzj8 tIPspm3rrXLMtl6o2ZMSkLLeVZ0AYOYmQtCgfGt3VX6g58PJjqE0wiOPfuf5XlO9Em vBZa90W9FQrJbZlrC/+cQK5TPq+EPSmRa5LqWEYmJCH6M/KmwzSpxIOPoslLaSYBFp MGnZgBcV3nQmVVKl8xKLNh2XtiKRWiommujDjWnWiLDfM890KZsCDQ6o9fE89jxM5c wwxzUDEzpum+ZYC4mRr2YfYQ=
- In-reply-to: <5cf96bf30c0e1c0d0bd7d6446a10d4b1@stamm-wilbrandt.de>
- Mail-followup-to: pari-users@pari.math.u-bordeaux.fr
- References: <5cf96bf30c0e1c0d0bd7d6446a10d4b1@stamm-wilbrandt.de>
On Mon, Dec 18, 2023 at 04:05:39PM +0100, hermann@stamm-wilbrandt.de wrote:
> pi@raspberrypi5:~ $ n=101 gp -q < m2.gp
> 101=[1, 6, 8]
> all asserts OK
> 528979 [711, -153, -7]~ [2, 9, 4]~
> 10232019 [3127, -673, -31]~ [2, 9, -4]~
> ...
> 97549123438 [305322, -65715, -3023]~ [10, 0, -1]~
> 101592175419 [311585, -67063, -3085]~ [10, -1, 0]~
> #S2=168
> 12*h(-4*n)=168
> pi@raspberrypi5:~ $
>
>
> Because "S2=vecsort(concat(S,-S),norml2)", it has 12*h(-4*n) members for
> n!=3 (mod 4):
> https://en.wikipedia.org/wiki/Sum_of_squares_function#k_=_3
>
> S2.gp output is sorted wrt L2 norm of vectors. Is there a method to
> determine either
> minimal norm vector or maximal norm vector in S2 efficiently/"more efficient
> than to
> compute all 12*h(-4*n) elements" ?
I am not sure what you mean by 'maximal norm vector", but it you just want one
solution, you can try this
forqfvec(v,M,n,if(qfeval(M,v)==n,V=v;break()))
Cheers,
Bill.