Karim BELABAS on Sat, 8 Mar 2003 16:17:28 +0100 (MET) |
[Date Prev] [Date Next] [Thread Prev] [Thread Next] [Date Index] [Thread Index]
Re: qfbclassno |
On Fri, 7 Mar 2003, Karim BELABAS wrote: [Original bug report by Rob Harley:] > (18:56) gp > qfbclassno(-71034143) > %1 = 0 [...] > 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 ] [Igor later wrote:] > ? qfbclassno(-2878367) > 1056 Both of these are now fixed in development version, by modifying a number of heuristic parameters: as written, the code could run into difficulties if the truncated Euler product approximating the class number did not yield an upper bound. The current code should never return 0. The code still offers no guarantee, since implementing the "correct" BS/GS method (e.g, from GTM 138) would make it generically much slower. At least it does work for all values < 10^6 in absolute value [ didn't bother to check larger ones ]. But it will presumably not work if the exponent of the group is small compared to the class number, and the Euler product doesn't happen to give almost the right value. Note that qfbclassno is often much faster than quadclassunit (which also doesn't give a guaranteed answer, even under GRH, since we cheat on Bach's bound), so there is still some use for this routine. Also note that quadclassunit used to be unreliable for non-fundamental discriminants (another TODO item). I believe I have fixed this also, hence there is no longer a Warning when quadclassunit is fed a non-fundamental discriminant. Cheers, Karim. P.S: All this only applies to the development version (I will probably not backport it, since it doesn't fix a formal bug, only heuristically improve some parameters). So, if someone wants to continue this thread, please move it to pari-dev. I'm interested in bizarre behaviour of either quadclassunit(D non-fundamental) or qfbclassno(D < 0). -- 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]