Karim BELABAS on Fri, 7 Mar 2003 20:28:41 +0100 (MET) |
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Re: qfbclassno |
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]