Re: Reducible thue() might be missing solutions

[Georgi Guninski <guninski@guninski.com>]

On Sat, May 10, 2014 at 02:50:42PM +0200, Bill Allombert wrote:
> 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.
>

Hm, one approach is to generate equations with
known solutions by equating coefficients,
search for other small solutions and
compare with the output.
Some heuristic might help too.

Might try to do this, but unless
the current issue is fixed it is
like beating a death horse.

Does thueinit(,0) still depend on GRH?