Re: Reducible thue() might be missing solutions

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

* Bill Allombert [2014-05-10 13:01]:
> On Sat, May 10, 2014 at 01:31:14PM +0300, Georgi Guninski wrote:
> > 2.5.5 on linux.
> > 
> > Reducible thue appears to miss solution,
> > as shown:
> > 
> > ? A=10946;B=6765;F=(A*x-B*y)*(x^2+x*y-y^2);th=thueinit(subst(F,y,1),1);so=thue(th,1)
> > %7 = [[4181, 6765], [10946, 17711]]
> > ? so2=[2584, 4181];subst(subst(F,x,so2[1]),y,so2[2])
> > %8 = 1
> > 
> > Same with thueinit(,0).
> 
> also with 2.7.0,
> ? A=10946;B=6765;F=(A*x-B*y)*(x^2+x*y-y^2);th=thueinit(subst(F,y,1),1);so=thue(th,1)
> %1 = []

The root cause (at least in 'master') is the following:

(13:11) gp > R = -y^2 - 24476*y + 119814917;
(13:26) gp > nfroots(,R)   \\ wrong
%25 = []
(13:25) gp > nfroots(,-R)  \\ correct
%24 = [-28657, 4181]

Investigating...

Cheers,

    K.B.
--
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/~kbelabas/
F-33405 Talence (France)       http://pari.math.u-bordeaux1.fr/  [PARI/GP]
`