Re: solving Thue equation

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

* Max Alekseyev [2009-01-29 05:29]:
> Dear pari-users,
> 
> I have some questions about Thue equation solver in pari:
> 
> 1) I often get the following warning:
> 
>   *** thue: Warning: Non trivial conditional class group.
>   *** May miss solutions of the norm equation.
> 
> What does it really mean in terms of the result? That the returned
> solution set may not be complete?

It is complete assuming the GRH is true, otherwise some solutions may be
missing:

(10:29) gp > ??thueinit
[...]
   If flag is non-zero, certify results unconditionally. Otherwise, assume GRH,
this being much faster of course.   In the latter case, the result may still be
unconditionnally correct;  thue prints a Warning if it actually needs to assume
the GRH.

I changed the message to

    *** thue: Warning: Non trivial conditional class group.
    *** The result returned by 'thue' is conditional on the GRH

Use thueinit(, 1) if you do not want to rely on the GRH.

> Is there any way to avoid this kind of problems?

1) proving the GRH :-)

2) certifying unconditionnally the output of bnfinit(); which leads us to:

> 2) Is there any way to disable output of this warning? I have tried
> \g 0
> without any luck.

Use thueinit(, 1).

> 3) In the following equation:
> 
> t = thueinit( 64*x^4 + 64672*x^3 + 14847428*x^2 - 14882644*x + 3389281 );
> thue( t, 4 )
> 
> I am getting an error:
> 
>   *** thue: precision too low in get_arch.
> 
> I've tried to increase the real precision up to a *million* digits but
> that did not help.
> Is there any way to solve this equation in pari?

Not in the version you're using. [ 2.4.3 (development svn-11548) ]

Problem identified, patch in progress...

> Not a question but an occasional bugreport.
> For t defined as above:
> 
> ? thue(t,4,1)
>   ***   at top-level: thue(t,4,1)
>   ***                 ^-----------
>   *** thue: bug in PARI/GP (Segmentation Fault), please report

Added minimal type checking in svn.

    K.B.

P.S: Please, keep unrelated queries to separate emails. (Better, send the
"seemingly obvious" bugs directly to the Bug Tracking System.)

It'll be much simpler for me this way. Thanks!

--
Karim Belabas, IMB (UMR 5251)  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-bordeaux1.fr/~belabas/
F-33405 Talence (France)       http://pari.math.u-bordeaux1.fr/  [PARI/GP]
`