Re: Thue equations

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

* John Cremona [2014-11-14 20:34]:
> Thanks for the replies, especially from Guillaume!  (G, I remember you
> giving talks about your work on this many years ago, possibly when you
> were still a student).
> 
> Charles misunderstood the question slightly, I was wondering whether
> the method used was the one which uses S-units (and this might have
> depended on the degree; currently I am only interested in solving
> degree 3 ones).

Ariel Pacetti recently made the interesting remark that replacing the
(arbitrary) model input by the user by a "reduced" one could have a
dramatic effect. E.g.

  ? thue(-1744357*x^3 - 9313887*x^2 - 16576896*x - 9834496, 1)
  time = 8,264 ms.
  %1 = []

  \\ reduced form associated to the same cubic order
  ? thue(196*x^3 - 468*x^2 - 207*x + 228, 1)
  time = 32 ms.
  %2 = []

(Ariel's original example)

I don't think this would affect your computations (I'd expect you
to use reduced models, esp. in the cubic case :-), but I didn't have
time to incorporate that trick yet.

Cheers,

    K.B.
--
Karim Belabas, IMB (UMR 5251)  Tel: (+33) (0)5 40 00 26 17
Universite de Bordeaux         Fax: (+33) (0)5 40 00 69 50
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