Re: Find an invertible integer matrix that satisfies given conditions.

[Hongyi Zhao <hongyi.zhao@gmail.com>]

On Mon, Apr 17, 2023 at 5:27 PM Bill Allombert
<Bill.Allombert@math.u-bordeaux.fr> wrote:
>
> On Wed, Apr 12, 2023 at 09:00:00PM +0800, Hongyi Zhao wrote:
> > > The difficult part is obviously 3).
> > > For n=2, the Diophantine equation is a binary quadratic form, so can be solved by PARI.
> > > Hofmann shows that solving the equation can be reduced to solve a set of
> > > norm equations in orders of number fields.
> >
> > I am very grateful to Bill Allombert and Aurel Page for providing me
> > with valuable information and algorithm implementations.
> >
> > Based on the clues here, I checked the works done by Tommy Hofmann
> > [1], and it seems that there are no publically available
> > implementations of his method, such as in open source codes, like GAP
> > or PARI/GP. So, I'm still not sure if it's possible to implement his
> > algorithms based on open source tools solely, and then use them as a
> > starting point to do the further study.
>
> Well, in some case, this can be solved using the GP functions bnfisintnorm
> or bnfunits.

Why this problem can't be in general nicely solved by GP?

> Cheers,
> Bill

Best,
Zhao