Re: qfbclassno

[Bill Allombert <allomber@math.u-bordeaux.fr>]

On Fri, Mar 07, 2003 at 06:58:02PM +0100, Dr. Robert Harley wrote:
> Can this be right?
> 
> > gp
>                   GP/PARI CALCULATOR Version 2.1.4 (released)                   [...]
> (18:56) gp > qfbclassno(-71034143)
> %1 = 0
It could not, but
? ??qfbclassno
qfbclassno(x,{flag = 0}):
...
   Important  warning.  For D < 0,  this function often gives incorrect results
when  the  class  group  is  non-cyclic,   because the authors were too lazy to
implement  Shanks' method completely.   It is therefore strongly recommended to
use  either  the  version  with flag = 1,  the function qfbhclassno(-x) if x is
known to be a fundamental discriminant, or the function quadclassunit.

? qfbclassno(-71034143)
%1 = 0
? qfbhclassno(-71034143)
%2 = 0
? quadclassunit(-71034143)
%3 = [7488, [1872, 2, 2], [Qfb(2, 1, 8879268), Qfb(2363, 2363, 8106), Qfb(23, 23, 772116)], 1, 1.001342826266922034]
? qfbclassno(-71034143,1)
%4 = 7488

Note that the class group is not cyclic which can be predicted since
-71034143 is not prime.

In fact 0 is a good result, since at least we know something wrong happened.
The comment about qfbhclassno leads to believe that there is a bug in
qfbhclassno instead.

(The development version performs no better.)

Cheers,
Bill.