Re: qfbclassno

[Karim BELABAS <Karim.Belabas@math.u-psud.fr>]

On Fri, 7 Mar 2003, 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
> ? qfbclassno(-71034143)
> %1 = 0
> ? qfbhclassno(-71034143)
> %2 = 0

qfbhclassno takes non-negative arguments [ confusing, but standard, and
expected if you think of it as giving the Fourier coefficients of a modular
form ]:

(19:57) gp >  qfbhclassno(71034143)
%1 = 7488

> ? 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.

Actually, the Shanks BS/GS method is applied to G^2, not to G, in order to
kill trivial non-cyclicity; the two-rank is taken into account later. Here,
G^2 is cyclic of order 936.

> 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.)

It's a weird bug: I can correct it in at least two different ways (modifying
internal parameters), but I still don't understand exactly why it occurs
[ something else is broken which I don't understand yet ], and whether I can
fix it in a "clean" way [ given that the code is heuristic and offers no
guarantee whatsoever ]

    Karim.
-- 
Karim Belabas                     Tel: (+33) (0)1 69 15 57 48
Dép. de Mathématiques, Bât. 425   Fax: (+33) (0)1 69 15 60 19
Université Paris-Sud              http://www.math.u-psud.fr/~belabas/
F-91405 Orsay (France)            http://www.parigp-home.de/  [PARI/GP]