Re: Reducible thue() might be missing solutions

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

* Bill Allombert [2014-05-10 14:50]:
> 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
> 
> Over the years, a number of various bugs in thue has been reported.
> Unfortunately, neither Karim nor I use it much, so it would be quite useful
> if users of the function provided various families of test-cases.

As I reported, the bug has nothing to do with thue: it lies in nfrootsQ,
which calls ZpX_liftfact with non-monic modular factors, contrary to the
(documented) specifications of the latter.

My first fix was to replace obsolete code in nfrootsQ by a call to the
new ZpX_roots, but ZpX_roots has the same bug. :-(

Am busy fixing the problem in a proper way...

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]
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