Max Alekseyev on Thu, 29 Jan 2009 05:29:20 +0100

 solving Thue equation

• To: pari-users <pari-users@list.cr.yp.to>
• Subject: solving Thue equation
• From: Max Alekseyev <maxale@gmail.com>
• Date: Wed, 28 Jan 2009 23:27:37 -0500
• Delivery-date: Thu, 29 Jan 2009 05:29:21 +0100
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```Dear pari-users,

I have some questions about Thue equation solver in pari:

1) I often get the following warning:

*** thue: Warning: Non trivial conditional class group.
*** May miss solutions of the norm equation.

What does it really mean in terms of the result? That the returned
solution set may not be complete?
Is there any way to avoid this kind of problems?

2) Is there any way to disable output of this warning? I have tried
\g 0
without any luck.

3) In the following equation:

t = thueinit( 64*x^4 + 64672*x^3 + 14847428*x^2 - 14882644*x + 3389281 );
thue( t, 4 )

I am getting an error:

*** thue: precision too low in get_arch.

I've tried to increase the real precision up to a *million* digits but
that did not help.
Is there any way to solve this equation in pari?

Please notice that while pari cannot solve this Thue equation, it is
easy to solve it with simple divisibility arguments:
from
64*m^4 + 64672*m^3*n + 14847428*m^2*n^2 - 14882644*m*n^3 + 3389281*n^4 = 4
it follows that n is even, but then the l.h.s. of this equation is
divisible by 16 while the l.h.s. is not.
Hence, this equation does not have integer solutions.

Thanks,
Max

P.S.
Not a question but an occasional bugreport.
For t defined as above:

? thue(t,4,1)
***   at top-level: thue(t,4,1)
***                 ^-----------
*** thue: bug in PARI/GP (Segmentation Fault), please report

This happens in
GP/PARI CALCULATOR Version 2.4.3 (development svn-11548)
amd64 running linux (x86-64/GMP-4.2.4 kernel) 64-bit version

```