Re: Thue equations

[John Cremona <john.cremona@gmail.com>]

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).

John

On 14 November 2014 16:37, Bill Allombert
<Bill.Allombert@math.u-bordeaux.fr> wrote:
> On Fri, Nov 14, 2014 at 05:23:00PM +0100, Guillaume Hanrot wrote:
>> > The algorithm used by thue() is described in Guillaume  Hanrot theis and
>> > published in "Thue Equations of High Degree", by Yu. Bilu and G. Hanrot, J.
>> > Number Theory (1996)
>> >
>> > I do not think it is using S-unit. Also it is not specific to degree 3.
>>
>> Actually, the implementation also uses the trick described in "Solving
>> Thue equations without the full unit group", Math. Comp. (2000) in
>> order to avoid as much as possible calls to bnfcertify in large
>> degree.
>
> Thanks Guillaume, I have added a reference to this paper in thue.c
>
> Cheers,
> Bill.
>