Karim BELABAS on Thu, 13 Mar 2003 22:11:32 +0100 (MET)

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Re: rnflllgram() regression

On Thu, 13 Mar 2003, Igor Schein wrote:
>> It's still a precision problem but at a higher level: the base nf is not
>> computed to a sufficient accuracy. The natural solution (which I've
>> implemented in CVS) is to increase that accuracy and go on.
>> Since the relative LLL algorithm (even implemented with exact computations)
>> doesn't really work, this produces worse results than immediately using the
>> right accuracy [ in regular LLL, going astray due to accuracy problems
>> is quickly corrected in the following iterations. Here, not at all ].
> I guess by worse results you mean the following:
> ? rnfpolred(nfinit(quadpoly(1297,y)),quadray(1297,1));
>   ***   the PARI stack overflows !
>   current stack size: 512000000 (488.281 Mbytes)
>   [hint] you can increase GP stack with allocatemem()

Errr, no. This is another precision problem which I didn't think of: I
checked the eigenvalues of a supposedly positive definite matrix were
non-zero 0 (meaning complete loss of accuracy, e.g 0.E50).

In fact, they ended up being negative...


> If I set \p163 though, it works fine at default stack.

It does in default precision also now.

> BTW, at \p163 current CVS is 30% faster than 2.2.5 when running this
> command, so it's a significant performance improvement.

I have completely rewritten the routine [ again, the underlying algorithm
doesn't work. Sad... ]

Karim Belabas                     Tel: (+33) (0)1 69 15 57 48
Dép. de Mathématiques, Bât. 425   Fax: (+33) (0)1 69 15 60 19
Université Paris-Sud              http://www.math.u-psud.fr/~belabas/
F-91405 Orsay (France)            http://www.parigp-home.de/  [PARI/GP]