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Bill Allombert on Sat, 09 Mar 2024 20:32:30 +0100
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Re: Question on completeness of the qfminin() command on finding all vectors for a given positive definite symmetric matrix
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- To: pari-users@pari.math.u-bordeaux.fr
- Subject: Re: Question on completeness of the qfminin() command on finding all vectors for a given positive definite symmetric matrix
- From: Bill Allombert <Bill.Allombert@math.u-bordeaux.fr>
- Date: Sat, 9 Mar 2024 20:32:17 +0100
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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