Re: lindep

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

* <Denis.Simon@math.unicaen.fr> [2004-01-28 11:14]:
> maybe my question should be asked in pari-users, 
> but I can't understand the behaviour of lindep:
> ? lindep([0.2527546621, -0.89865858,1.1733994])
> %1 = 66984134.27215961355
> 
> Here, I was expecting 0 or a vector ???
> 
> In the big help, it is written that I can use
> lindep with a matrix if flag <0, but I wasn't able
> to do it !
> 
> ? lindep(matrix(2,2,i,j,1)*1.23456789,-1)
>   ***   incorrect type in lindep.
> ? lindep(matrix(2,2,i,j,1)*1.23456789,-2)
> %2 = [1.234567890000000000000000000, -1.234567890000000000000000000]~
> 
> Here, I was expecting a relation over Z !!
> 
> ? lindep(matrix(2,2,i,j,1)*1.23456789,-3)
>   ***   incorrect type in pslq.
> ? lindep(matrix(2,2,i,j,1)*1.23456789,-4)
>   ***   incorrect type in lindep2.
> ? lindep(matrix(2,2,i,j,1)*1.23456789,-10)
>   ***   incorrect type in lindep2.

The help was completely outdated. I have fixed the long and short help
in CVS.

Note: the PSLQ implementation is not currently in a satisfactory shape. The
original contributor (Henri Cohen) will not maintain that code. I have fixed
some problems and rewrote part of it, but I won't invest much time in it
either. (I don't use it at all and am not that interested in the associated
maths.)

The LLL option is currently, more flexible, reliable and much faster than
PSLQ. This will probably change when (if) somebody improves the PSLQ code...

I have added the "standard" example (2^(1/6)+3^(1/5), from Borwein & Lisonek's
old paper) to algdep doc.

    Karim.
-- 
Karim Belabas                     Tel: (+33) (0)1 69 15 57 48
Dep. de Mathematiques, Bat. 425   Fax: (+33) (0)1 69 15 60 19
Universite Paris-Sud              http://www.math.u-psud.fr/~belabas/ 
F-91405 Orsay (France)            http://pari.math.u-bordeaux.fr/  [PARI/GP]