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

[Bill Allombert <Bill.Allombert@math.u-bordeaux.fr>]

On Mon, Mar 04, 2024 at 05:57:06PM -0800, American Citizen wrote:
> 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.

Thanks but qfminim is older than my involvement with PARI/GP!

When qfminim was written, memory was a serious limitation of computers.
Storing only half the vectors saved a lot of memory for lattices with lots of
minimal vectors like the Leech lattice.

Cheers,
Bill