Ticket #3674: sage-trac3674new-extra5.patch

File sage-trac3674new-extra5.patch, 5.1 kB (added by cremona, 4 months ago)

  • a/sage/schemes/elliptic_curves/ell_rational_field.py

    old new  
    37983798            e1,e2,e3:  -3.01243037259331 1.06582054769620 1.94660982489710 
    37993799            Minimal eigenvalue of height pairing matrix:  0.472730555831538 
    38003800            x-coords of points on compact component with  -3 <=x<= 1 
    3801             set([0, -1, -3, -2, 1]) 
     3801            [-3, -2, -1, 0, 1] 
    38023802            x-coords of points on non-compact component with  2 <=x<= 6 
    3803             set([2, 3, 4]) 
     3803            [2, 3, 4] 
    38043804            starting search of remaining points using coefficient bound  6 
    38053805            x-coords of extra integral points: 
    3806             set([2, 3, 4, 37, 406, 8, 11, 14, 816, 52, 21, 342, 93]) 
     3806            [2, 3, 4, 8, 11, 14, 21, 37, 52, 93, 342, 406, 816] 
    38073807            Total number of integral points: 18 
    38083808 
    38093809        It is also possible to not specify mw_base, but then the 
    …… 
    39303930                    use_t(P) 
    39313931                return xs 
    39323932             
    3933             # Otherwise is is very very much faster to first compute 
    3934             # the linear combinations over RR, and only compte them as 
    3935             # rational points if they are approximately integral 
     3933            # Otherwise it is very very much faster to first compute 
     3934            # the linear combinations over RR, and only compute them as 
     3935            # rational points if they are approximately integral. 
     3936 
     3937            # Note: making eps larger here will dramatically increase 
     3938            # the running time.  If evidence arises that integral 
     3939            # points are being missed, it would be better to increase 
     3940            # the real precision than to increase eps. 
    39363941 
    39373942            def is_approx_integral(P): 
    3938                 return (abs(P[0]-P[0].round()))<0.1 #one case was 0.09, so 0.001 was too small 
    3939              
    3940             RR = RealField() #(100) 
     3943                eps = 0.0001 
     3944                return (abs(P[0]-P[0].round()))<eps and (abs(P[1]-P[1].round()))<eps 
     3945             
     3946            RR = RealField(100) #(100) 
    39413947            ER = self.change_ring(RR) 
     3948 
     3949# Note: doing [ER(P) for P in mw_base] sometimes fails.  This way is 
     3950# harder since we have to make sure we don't use -P instead of P, but 
     3951# is safer. 
     3952 
    39423953            Rgens = [ER.lift_x(P[0]) for P in mw_base] 
    39433954            for i in range(r): 
    39443955                if abs(Rgens[i][1]-mw_base[i][1])>abs((-Rgens[i])[1]-mw_base[i][1]): 
    39453956                    Rgens[i] = -Rgens[i] 
    3946             #for ni in cartesian_product_iterator([range(-N,N+1) for i in range(r-1)]+[range(N+1)]): ##opt1 
    3947             for mi in range(ceil(((2*H_q+1)**r)/2)): ##opt2 
    3948                 ni = Z(mi).digits(base=2*H_q+1, padto=r, digits=range(-H_q, H_q+1)) ##opt2 
     3957 
     3958            # the ni loop through all tuples (a1,a2,...,ar) with 
     3959            # |ai|<=N, but we stop immediately after using the tuple 
     3960            # (0,0,...,0). 
     3961 
     3962            for ni in cartesian_product_iterator([range(-N,N+1) for i in range(r)]): ##opt1 
     3963 
     3964#  Alternative version not using the fancy iterator: 
     3965#            for mi in range(ceil(((2*H_q+1)**r)/2)): ##opt2 
     3966#                ni = Z(mi).digits(base=2*H_q+1, padto=r, digits=range(-H_q, H_q+1)) ##opt2 
     3967 
     3968                if all([n==0 for n in ni]): 
     3969                    use_t(self(0)) 
     3970                    break 
    39493971                RP=sum([ni[i]*Rgens[i] for i in range(r)],ER(0)) 
    39503972                for T in tors_points: 
    39513973                    if is_approx_integral(RP+ER(T)): 
    …… 
    41584180            x_int_points = integral_x_coords_in_interval(ceil(e1-b2_12), floor(e2-b2_12)+1) 
    41594181            if verbose: 
    41604182                print 'x-coords of points on compact component with ',ceil(e1-b2_12),'<=x<=',floor(e2-b2_12) 
    4161                 print x_int_points 
     4183                L = list(x_int_points) # to have the order  
     4184                L.sort()               # deterministic for doctests! 
     4185                print L 
    41624186        else: 
    41634187            x_int_points = set() 
    41644188             
    …… 
    41694193        x_int_points = x_int_points.union(x_int_points2) 
    41704194        if verbose: 
    41714195            print 'x-coords of points on non-compact component with ',x0,'<=x<=',x1-1 
    4172             print x_int_points2 
     4196            L = list(x_int_points2) 
     4197            L.sort() 
     4198            print L 
    41734199         
    41744200        if verbose: 
    41754201            print 'starting search of remaining points using coefficient bound ',H_q 
    …… 
    41774203        x_int_points = x_int_points.union(x_int_points3) 
    41784204        if verbose: 
    41794205            print 'x-coords of extra integral points:' 
    4180             print x_int_points3 
     4206            L = list(x_int_points3) 
     4207            L.sort() 
     4208            print L 
    41814209 
    41824210        # Now we have all the x-coordinates of integral points, and we 
    41834211        # construct the points, depending on the parameter both_signs: