Re: GP algdep() bug?

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

On Thu, 18 Apr 2002, Michael Somos wrote:
> On Thu, 18 Apr 2002, Karim BELABAS wrote:
>
> > >
> > > Could something have changed in the last few weeks for 'algdep()'?
> >
> > The current CVS version uses PSLQ instead of LLL / HJLS to find integral
> > relations [ undocumented for now, the code is in a _very_ unstable state ].
> >
> > The output means that PSLQ failed and any relation (in algdep context: a
> > minimal polynomial) has height > 20837... I believe the current output is
> > more useful than the former one.
> >
> Perhaps there is a difference of opinion here? Would it be possible to
> have the option of using the old behavior? It would be very useful.

Already there:

(18:57) gp > ??algdep
algdep(x,k,{flag = 0}):
[...]
   If flag is non-zero,  use a standard LLL.   flag then indicates a precision,
which should be between 0.5 and 1.0 times the number of decimal digits to which
x was computed.

===============================================================================

So if you want a "more or less random" polynomial, which is close to 0 at x,
you can use the optional flag.

(18:58) gp > algdep(sin(1),2, 10)
time = 0 ms.
%1 = 258*x^2 - 2*x - 181
(18:58) gp > algdep(sin(1),2, 20)
time = 10 ms.
%2 = 78594*x^2 + 1425003*x - 1254749
(18:58) gp > algdep(sin(1),2, 30)
time = 0 ms.
%3 = 509248885*x^2 - 2125480139*x + 1427944267

The original call (no flag) already tells that these are most probably
artefacts, and not genuine relations.

    Karim.
-- 
Karim Belabas                    Tel: (+33) (0)1 69 15 57 48
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