Karim BELABAS on Wed, 29 Jan 2003 12:21:51 +0100 (MET)

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Re: gp: algdep(x,k,0)

On Sun, 19 Jan 2003, Michael Somos wrote:
> pari-dev,
>      I recommend that algdep(x,k,0) never be used, or else the
> default for algdep(x,k) should be changed. The reason is because :
> ? algdep(1+.1^6,1)
> %1 = 1080516752824585954039985431*x - 1080517833341338778625939471
> happens far too often. I fail to see to reason why this is the default
> when it seems that algdep(x,k,default(realprecision,,1)) returns much
> more reasonable results more often.

Because for tough examples, PSLQ should somewhat improve stability.

The real problem here is that PSLQ tried too hard to get a "good" zero, and
eventually operated on random bits introduced by the fact that t_REAL type
handles accuracy by increments of 32 bits [ see the thread started by Walter
Neumann some time ago; the issue is still unresolved ].

I have retuned PSLQ to improve on this aspect (be extra suspicious when only
32 bits of residual accuracy are available). Does it behave better now?


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             Email: Karim.Belabas@math.u-psud.fr
F-91405 Orsay (France)           http://www.math.u-psud.fr/~belabas/
PARI/GP Home Page: http://www.parigp-home.de/