Re: qfbclassno

[Igor Schein <igor@txc.com>]

On Fri, Mar 07, 2003 at 07:50:19PM +0100, Bill Allombert wrote:
> 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.

It doesn't always return zero:

? qfbclassno(-2878367)
1056
? quadclassunit(-2878367)
[1152, [48, 24], [Qfb(647, 189, 1126), Qfb(2, 1, 359796)], 1, 0.9670859857979999927]

This is an example from TODO.

Igor