There are two possibilities: either Sage is sending the wrong input to Simon's script and/or reading its output wrongly; or there's a bug in his script. Both of these have occurred in the past!
One thing you should definitely do in the latter case is to email Denis Simon directly (his web page is http://www.math.unicaen.fr/~simon/). But first you should make sure that the problem is there and not with the Sage interface. Looking at the error messages (and checking that there is still a problem in sage-4.6.1.alpha3 -- you did not say which version you were using!) it looks as if it is caused by the upgrade in Sage from an older pari version to the newer one which happened with sage-4.6. If I am right, then the problem would be solved by changing Simon's script, which seems to mean that this is his bug and not Sage's. John Cremona On Jan 5, 2:28 am, Iwao Kimura <i...@sci.u-toyama.ac.jp> wrote: > Hi list, > > I have noticed that D. Simon's algebraic 2-descent does not > work properly for some elliptic curves defined over real quadratic > fields. So I'd like to forward his message to this list. > > I think that this defect seems similar to those reported in ticket #9322, > #8829, > but I'm not a specialist in these topics, am greatly appreciate your help. > > best regards. > > > > > > > > ---------- Forwarded message ---------- > From: <s-yokoy...@math.kyushu-u.ac.jp> > Date: 2011/1/5 > To: Iwao Kimura <i...@sci.u-toyama.ac.jp> > > Bug-report: Simon's two-descent alg. > > this algorithm does return bounds on the rank of > Mordell-Weil group, and a list of independent points. > So I want to compute when K=QQ(sqrt(43)) : real quad. > However, it doesn't work (nor on Sage Notebook). > > > Q43.<a>=QuadraticField(43); > > eps = UnitGroup(Q43).fundamental_units()[0]; > > E = EllipticCurve(Q43, [0, 1728*eps]); > > dscnt = E.simon_two_descent(verbose=1); dscnt > > :: > > courbe elliptique : Y^2 = x^3 + Mod(917568*y - 6016896, y^2 - 43) > > [ omitted ] > > *** array index (1) out of allowed range [none]: > *** ...iv,r=nfsqrt(nf,norm(zc))[1];if(DEBUGLEVEL_ell > ^-------------------- > ------------------------------------------------------------------------ > --- > NameError Traceback (most recent call > last) > > /Users/yokoemon/<ipython console> in <module>() > > /Applications/sage/local/lib/python2.6/site-packages/sage/schemes/ > elliptic_curves/ell_number_field.pyc in simon_two_descent(self, verbose, > lim1, lim3, limtriv, maxprob, limbigprime) > 196 t = simon_two_descent(self, > 197 verbose=verbose, lim1=lim1, lim3= > lim3, limtriv=limtriv, > --> 198 maxprob=maxprob, limbigprime= > limbigprime) > 199 prob_rank = Integer(t[0]) > 200 two_selmer_rank = Integer(t[1]) > > /Applications/sage/local/lib/python2.6/site-packages/sage/schemes/ > elliptic_curves/gp_simon.pyc in simon_two_descent(E, verbose, lim1, lim3, > limtriv, maxprob, limbigprime) > 110 def _gp_mod(*args): > 111 return args[0] > --> 112 ans = sage_eval(v, {'Mod': _gp_mod, 'y': K.gen(0)}) > 113 inv_transform = F.isomorphism_to(E) > 114 ans[2] = [inv_transform(F(P)) for P in ans[2]] > > /Applications/sage/local/lib/python2.6/site-packages/sage/misc/sage_eval. > pyc in sage_eval(source, locals, cmds, preparse) > 197 return locals['_sage_eval_returnval_'] > 198 else: > --> 199 return eval(source, sage.all.__dict__, locals) > 200 > 201 > > /Applications/sage/local/lib/python2.6/site-packages/sage/all.pyc in < > module>() > NameError: name 'ans' is not defined > > :: > > if K=QQ(sqrt(41)), it works well. > > > Q41.<a>=QuadraticField(41); > > eps = UnitGroup(Q41).fundamental_units()[0]; > > E = EllipticCurve(Q41, [0, 1728*eps]); > > dscnt = E.simon_two_descent(verbose=1); dscnt > > courbe elliptique : Y^2 = x^3 + Mod(8640*y + 55296, y^2 - 41) > points triviaux sur la courbe = [[1, 1, 0]] > point trouve = [Mod(-377788/93025*y - 1952448/93025, y^2 - 41), > Mod(-205379776/28372625*y - 1032512096/28372625, y^2 - 41)] > #S(E/K)[2] = 4 > #E(K)/2E(K) >= 2 > #III(E/K)[2] <= 2 > rang(E/K) >= 1 > III devrait etre un carre, donc > #E(K)/2E(K) = 4 > #III(E/K)[2] = 1 > rang(E/K) = 2 > listpointsmwr = [[Mod(-377788/93025*y - 1952448/93025, y^2 - 41), > Mod(-205379776/28372625*y - 1032512096/28372625, y^2 - 41)]] > (2, 2, [(-377788/93025*a - 1952448/93025 : -205379776/28372625*a - > 1032512096/28372625 : 1)]) > > If someone have any comments, > would you mind telling me about the problem?? > > Best wishes, > > Shun'ichi Yokoyama > Faculty of Mathematics, Kyushu University, Japan > s-yokoy...@math.kyushu-u.ac.jp > > -- > --- > Iwao KIMURA > Dept. Math. University of Toyama, Japan. -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
