Re: Question on completeness of the qfminin() command on finding all vectors for a given positive definite symmetric matrix

[American Citizen <website.reader3@gmail.com>]

Hermann:

You are exactly correct!. I have to add the negative points, since qfminim only supplies the "positive" vectors. Note that I said "positive" vectors, because the entries might < 0.

I know now that Bill wrote this algorithm to give the most efficient answer, and we have to remember to add the "negative" vectors.

Randall

On 3/4/24 15:13, hermann@stamm-wilbrandt.de wrote:

> On
>       2024-03-04 23:31, American Citizen wrote:
>       
> >         
> >         However when I actually used this to find all rational points
> >         < height
> >         
> >         13, I found 18 points which were missing from the 49 which
> >         qfminim()
> >         
> >         gave + torsion points.
> >         
> >         
> >       
>       I ran into this pitfall as well for my application and asked on
>       this list.
>       
>       I learned from Bill that I just had to add the negative values to
>       get all:
>       
>       
>       S=concat(S,-S);
>       
>       
>       You can visually see that in ℤ³ by clicking on the
>       "S=concat(S,-S)" radio button bottom left:
>       
>       https://stamm-wilbrandt.de/tqf_3D.2.gp.n_37.html
>       
>       
>       Regards,
>       
>       
>       Hermann.
>