Re: Omitting m in qfminim

["Karim Belabas" <Karim.Belabas@math.u-bordeaux1.fr>]

* Benjamin Benninghofen [2006-02-16 22:51]:
> When I omit m in qfminim the documentation
> says that all vectors are stored.
> 
> However in practice we have:
> 
> ? matsize(qfminim(matid(10),5,,2)[3])
> %11 = [10, 200]
> ? matsize(qfminim(matid(10),5,10000,2)[3])
> %12 = [10, 6482]
> ? 

That problem is now fixed in CVS.

> Furthermore qfminim only stores one of the vectors +X, -X,
> but it still could collect X, 2*X, 3*X, ... depending on b and m.
> would it not be preferable to store at most one of { k*X | k integer} ?
> Depending on the inputs a lot of space could be saved without loosing
> information ? 

I'm not sure:

1) you do lose some information. The norm is not stored, so it must be
recomputed for each primitive vector to find the suitable values of k.

2) storing only primitive vectors roughly saves a further factor zeta(2) ~ 1.64.
This is not such a big improvement.

    K.B.
-- 
Karim Belabas                  Tel: (+33) (0)5 40 00 26 17
Universite Bordeaux 1          Fax: (+33) (0)5 40 00 69 50
351, cours de la Liberation    http://www.math.u-bordeaux.fr/~belabas/
F-33405 Talence (France)       http://pari.math.u-bordeaux.fr/  [PARI/GP]