Karim Belabas on Thu, 29 Jan 2009 14:01:54 +0100 |
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Re: solving Thue equation |
* Max Alekseyev [2009-01-29 05:29]: > Dear pari-users, > > I have some questions about Thue equation solver in pari: > > 1) I often get the following warning: > > *** thue: Warning: Non trivial conditional class group. > *** May miss solutions of the norm equation. > > What does it really mean in terms of the result? That the returned > solution set may not be complete? It is complete assuming the GRH is true, otherwise some solutions may be missing: (10:29) gp > ??thueinit [...] If flag is non-zero, certify results unconditionally. Otherwise, assume GRH, this being much faster of course. In the latter case, the result may still be unconditionnally correct; thue prints a Warning if it actually needs to assume the GRH. I changed the message to *** thue: Warning: Non trivial conditional class group. *** The result returned by 'thue' is conditional on the GRH Use thueinit(, 1) if you do not want to rely on the GRH. > Is there any way to avoid this kind of problems? 1) proving the GRH :-) 2) certifying unconditionnally the output of bnfinit(); which leads us to: > 2) Is there any way to disable output of this warning? I have tried > \g 0 > without any luck. Use thueinit(, 1). > 3) In the following equation: > > t = thueinit( 64*x^4 + 64672*x^3 + 14847428*x^2 - 14882644*x + 3389281 ); > thue( t, 4 ) > > I am getting an error: > > *** thue: precision too low in get_arch. > > I've tried to increase the real precision up to a *million* digits but > that did not help. > Is there any way to solve this equation in pari? Not in the version you're using. [ 2.4.3 (development svn-11548) ] Problem identified, patch in progress... > Not a question but an occasional bugreport. > For t defined as above: > > ? thue(t,4,1) > *** at top-level: thue(t,4,1) > *** ^----------- > *** thue: bug in PARI/GP (Segmentation Fault), please report Added minimal type checking in svn. K.B. P.S: Please, keep unrelated queries to separate emails. (Better, send the "seemingly obvious" bugs directly to the Bug Tracking System.) It'll be much simpler for me this way. Thanks! -- Karim Belabas, IMB (UMR 5251) Tel: (+33) (0)5 40 00 26 17 Universite Bordeaux 1 Fax: (+33) (0)5 40 00 69 50 351, cours de la Liberation http://www.math.u-bordeaux1.fr/~belabas/ F-33405 Talence (France) http://pari.math.u-bordeaux1.fr/ [PARI/GP] `