Karim Belabas on Tue, 05 Mar 2024 08:43:30 +0100


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

* American Citizen [2024-03-05 02:55]:
> I have to point this out to everyone, sorry... but I did read the
> documentation and please find for me the word "negation" ? Please! I beg
> you!
> 
> The documentation (web page https://pari.math.u-bordeaux.fr/dochtml/html/Vectors__matrices__linear_algebra_and_sets.html#qfminim)
> states
> 
> > 
> >         qfminim(x, {B}, {m}, {/flag/ = 0})
> > 
> > x being a square and symmetric matrix of dimension d representing a
> > positive definite quadratic form, this function deals with the vectors
> > of x whose norm is less than or equal to B, enumerated using the
> > Fincke-Pohst algorithm, storing at most m pairs of vectors: only one
> > vector is given for each pair ± v. [...]

Stop right there and re-read the last sentence. The word negation does
not occur indeed, but the idea is there. The current wording was
prefered to "enumerated using the Fincke-Pohst algorithm up to negation,
storing at most m pairs of vectors". (Which wouldn't be quite correct
as vectors are correctly counted, it's only in the stored list that they
appear up to negation.)

Feel free to suggest documentation improvements: that function is very
complicated. I'll add examples shortly.

Cheers,

    K.B.
-- 
Pr. Karim Belabas, U. Bordeaux, Vice-président en charge du Numérique
Institut de Mathématiques de Bordeaux UMR 5251 - (+33) 05 40 00 29 77
http://www.math.u-bordeaux.fr/~kbelabas/