Attachment '2not4or4not8v3.sage'

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   1 print "start";
   2 li4=[];
   3 li41=[];
   4 li42=[];
   5 li43=[];
   6 li44=[];
   7 li45=[];
   8 li8=[];
   9 li81=[];
  10 li82=[];
  11 li83=[];
  12 li84=[];
  13 li85=[];
  14 li86=[];
  15 li87=[];
  16 li88=[];
  17 li89=[];
  18 li810=[];
  19 li811=[];
  20 li812=[];
  21 li813=[];
  22 li814=[];
  23 li815=[];
  24 li816=[];
  25 li817=[];
  26 li818=[];
  27 c1=vector([ round(1/3,3), round(1/12.0,4), round(1/24.0,4), round( 1/12.0,4), round( 1/4.0,4), round(1/12.0,4), round(1/24.0,4), round(1/12.0 ,2) ]);
  28 c2=vector([ round(1/4,4), round(1/12.0,4), round(1/24.0,4), round(1/12.0,4), round(1/3.0,4), round(1/12,4), round(1/24,4), round(1/12 ,2) ]);
  29 c3=vector([ round(1/4,4), round(1/12,4), round(1/12,4), round(1/12,4), round(1/4,4), round(1/12,4), round(1/12,4), round(1/12 ,2) ]);
  30 c4=vector([ round(7/24,4), round(1/12,4), round(1/24,4), round(1/12,4), round(7/24,4), round(1/12,4), round(1/24,4), round(1/12 ,2) ]);
  31 c5=vector([ round(1/8,4), round(0,4), round(5/24,4), round(1/6,4), round(1/8,4), round(0,4), round(5/24,4), round(1/6 ,2) ]);
  32 c6=vector([ round(1/8,4), round(1/12,4), round(1/6,4), round(1/12,4), round(1/8,4), round(1/12,4), round(1/4,4), round(1/12 ,2) ]);
  33 c7=vector([ round(1/6,4), round(1/12,4), round(1/6,4), round(1/12,4), round(1/6,4), round(1/12,4), round(1/6,4), round(1/12 ,2) ]);
  34 c8=vector([ round(1/2,4), round(0,4), round(1/12,4), round(1/6,4), round(0,4), round(0,4), round(1/12,4), round(1/6 ,2) ]);
  35 c9=vector([ round(1/2,4), round(1/12,4), round(1/6,4), round(1/12,4), round(0,4), round(1/12,4), round(0,4), round(1/12 ,2) ]);
  36 c10=vector([ round(13/24,4), round(1/12,4), round(1/24,4), round(1/12,4), round(1/24,4), round(1/12,4), round(1/24,4), round(1/12 ,2) ]);
  37 c11=vector([ round(1/4,4), round(1/12,4), round(1/6,4), round(1/12,4), round(1/4,4), round(1/12,4), round(0,4), round(1/12 ,2) ]);
  38 c12=vector([ round(1/4,4), round(0,4), round(1/12,4), round(1/6,4), round(1/4,4), round(0,4), round(1/12,4), round(1/6 ,2) ]);
  39 c13=vector([ round(1/8,4), round(1/12,4), round(5/24,4), round(1/12,4), round(1/8,4), round(1/12,4), round(5/24,4), round(1/12 ,2) ]);
  40 c14=vector([ round(3/16,4), round(1/12,4), round(1/6,4), round(1/12,4), round(7/48,4), round(1/12,4), round(1/6,4), round(1/12 ,2) ]);
  41 c15=vector([ round(7/48,4), round(1/12,4), round(1/6,4), round(1/12,4), round(3/16,4), round(1/12,4), round(1/6,4), round(1/12 ,2) ]);
  42 c16=vector([ round(1/2,4), round(1/12,4), round(1/24,4), round(1/12,4), round(1/12,4), round(1/12,4), round(1/24,4), round(1/12 ,2) ]);
  43 c17=vector([ round(7/12,4), round(1/12,4), round(1/24,4), round(1/12,4), round(0,4), round(1/12,4), round(1/24,4), round(1/12 ,2) ]);
  44 c18=vector([ round(1/2,4), round(1/12,4), round(1/12,4), round(1/12,4), round(0,4), round(1/12,4), round(1/12,4), round(1/12 ,2) ]);
  45 d1=vector([round(1/2,4), 0, round(1/6, 2), round(1/3, 2)]);
  46 d2=vector([round(1/2,4), round(1/6, 2), round(1/6, 2), round(1/6, 2)]);
  47 d3=vector([round( 1/4,4), round( 1/6,4), round( 5/12,4), round( 1/6,2) ]);
  48 d4=vector([round( 1/4,4), 0, round(5/12,4), round(1/3,2) ]);
  49 d5=vector([ round(7/12,4), round(1/6,4), round(1/12,4), round(1/6,2) ]);
  50 d6=vector([round( 1/3,4), round(1/6,4), round( 1/3,4), round( 1/6,2) ]);
  51 group41=0;
  52 group42=0;
  53 group43=0;
  54 group44=0;
  55 group45=0;
  56 group4=0;
  57 group81=0;
  58 group82=0;
  59 group83=0;
  60 group84=0;
  61 group85=0;
  62 group86=0;
  63 group87=0;
  64 group88=0;
  65 group89=0;
  66 group810=0;
  67 group811=0;
  68 group812=0;
  69 group813=0;
  70 group814=0;
  71 group815=0;
  72 group816=0;
  73 group817=0;
  74 group818=0;
  75 group8=0;
  76 for E in cremona_curves([10..10000]):
  77     rho=E.galois_representation();
  78     if E.has_cm()==False and  rho.is_surjective(2):
  79         
  80         aps=E.aplist(1000000); 
  81         apsmod4=vector([x%4 for x in aps])
  82         lenaps=n(len(aps))
  83         a0=len([x for x in apsmod4 if x==0])/lenaps;
  84         a1=len([x for x in apsmod4 if x==1])/lenaps;
  85         a2=len([x for x in apsmod4 if x==2])/lenaps;
  86         a3=len([x for x in apsmod4 if x==3])/lenaps;
  87         a=vector([round(a0,4),round(a1,4),round(a2,4),round(a3,2)]);
  88         nm41=norm(a-d1);
  89         nm42=norm(a-d2);
  90         nm43=norm(a-d3);
  91         nm44=norm(a-d4);
  92         nm45=norm(a-d5);
  93         nm46=norm(a-d6);
  94         if nm41<.01:
  95            group41=group41+1; 
  96            group4=group4+1; 
  97            li4.append(E.label());
  98            li41.append(E.label());
  99         elif nm42<.01:
 100             group42=group42+1; 
 101             group4=group4+1; 
 102             li4.append(E.label());
 103             li42.append(E.label());
 104         elif  nm43<.01:
 105             group43=group43+1; 
 106             group4=group4+1; 
 107             li4.append(E.label());
 108             li43.append(E.label());
 109         elif nm44<.01:
 110             group44=group44+1; 
 111             group4=group4+1; 
 112             li4.append(E.label());
 113             li44.append(E.label());
 114         elif nm45<.01:
 115             group45=group45+1; 
 116             group4=group4+1; 
 117             li4.append(E.label());
 118             li45.append(E.label());
 119         else:
 120             apsmod8=vector([x%8 for x in aps]);
 121             lenaps=n(len(aps));
 122             b0=len([x for x in apsmod8 if x==0])/lenaps;
 123             b1=len([x for x in apsmod8 if x==1])/lenaps;
 124             b2=len([x for x in apsmod8 if x==2])/lenaps;
 125             b3=len([x for x in apsmod8 if x==3])/lenaps;
 126             b4=len([x for x in apsmod8 if x==4])/lenaps;
 127             b5=len([x for x in apsmod8 if x==5])/lenaps;
 128             b6=len([x for x in apsmod8 if x==6])/lenaps;
 129             b7=len([x for x in apsmod8 if x==7])/lenaps;
 130             b=vector([round(b0,4),round(b1,3),round(b2,3),round(b3,3), round(b4,3),round(b5,3),round(b6,3),round(b7,3)]);
 131             nm81=norm(b-c1);
 132             nm82=norm(b-c2);
 133             nm83=norm(b-c3);
 134             nm84=norm(b-c4);
 135             nm85=norm(b-c5);
 136             nm86=norm(b-c6);
 137             nm87=norm(b-c7);
 138             nm88=norm(b-c8);
 139             nm89=norm(b-c9);
 140             nm810=norm(b-c10);
 141             nm811=norm(b-c11);
 142             nm812=norm(b-c12);
 143             nm813=norm(b-c13);
 144             nm814=norm(b-c14);
 145             nm815=norm(b-c15);
 146             nm816=norm(b-c16);
 147             nm817=norm(b-c17);
 148             nm818=norm(b-c18);
 149             if nm81<.005:
 150                 group81=group81+1;    
 151                 group8=group8+1;
 152                 li8.append(E.label());
 153                 li81.append(E.label());
 154             elif nm82 <.01:
 155                 group82=group82+1;    
 156                 group8=group8+1;
 157                 li8.append(E.label());
 158                 li82.append(E.label());
 159             elif nm83<.01:
 160                 group83=group83+1;    
 161                 group8=group8+1;
 162                 li8.append(E.label());
 163                 li83.append(E.label());
 164             elif nm84<.01:
 165                 group84=group84+1;    
 166                 group8=group8+1;
 167                 li8.append(E.label());
 168                 li84.append(E.label());
 169             elif nm85<.01:
 170                 group85=group85+1;    
 171                 group8=group8+1;
 172                 li8.append(E.label());
 173                 li85.append(E.label());
 174             elif nm86<.01:
 175                 group86=group86+1;    
 176                 group8=group8+1;
 177                 li8.append(E.label());
 178                 li86.append(E.label());
 179             #elif nm87<.01:
 180                  
 181                 #if b==c7:  
 182                    # print E.label(),"Is E semistable?", E.is_semistable(), E.j_invariant(), "not surjective mod 8 group 7","they are equal";
 183                 
 184                # else:
 185                    # print E.label(),"Is E semistable?", E.is_semistable(), E.j_invariant(),"not surjective mod 8 group 7",":", nm87,":", b,":", c7;
 186             # elif nm88<.01:
 187                 #print E.label(),"Is E semistable?", E.is_semistable(), E.j_invariant(),"not surjective mod 8 group 8";
 188                 #if b==c8:
 189                 #    print E.label(),"Is E semistable?", E.is_semistable(), E.j_invariant(), "not surjective mod 8 group 8","they are equal";
 190                 #else:
 191                  #   print nm88,":", b,":", c8;
 192             elif nm89<.01:
 193                 group89=group89+1;    
 194                 group8=group8+1;
 195                 li8.append(E.label());
 196                 li89.append(E.label());
 197             elif nm810<.01:
 198                 group810=group810+1;    
 199                 group8=group8+1;
 200                 li8.append(E.label());
 201                 li810.append(E.label());
 202             elif nm811<.01:
 203                 group811=group811+1;    
 204                 group8=group8+1;
 205                 li8.append(E.label());
 206                 li811.append(E.label());
 207             elif nm812<.01:
 208                 group812=group812+1;    
 209                 group8=group8+1;
 210                 li8.append(E.label());
 211                 li821.append(E.label());
 212             elif nm813<.01:
 213                 group813=group813+1;    
 214                 group8=group8+1;
 215                 li8.append(E.label());
 216                 li813.append(E.label());
 217             elif nm814<.001:
 218                 group814=group814+1;    
 219                 group8=group8+1;
 220                 li8.append(E.label());
 221                 li814.append(E.label());
 222             elif nm815<.01:
 223                 group815=group815+1;    
 224                 group8=group8+1;
 225                 li8.append(E.label());
 226                 li815.append(E.label());
 227             #elif nm816<.01:
 228                 #print E.label(),"Is E semistable?", E.is_semistable(), E.j_invariant(),"not surjective mod 8 group 16";
 229             #elif nm817<.01:
 230                 #print E.label(),"Is E semistable?", E.is_semistable(), E.j_invariant(),"not surjective mod 8 group 17";  
 231             #elif nm818<.01:
 232                 #print E.label(),"Is E semistable?", E.is_semistable(), E.j_invariant(),"not surjective mod 8 group 18";
 233 statistics=(["group41",group41,"group42",group42, "group43",group43,"group44",group44,"group45",group45,"group4",group4, "percentage:"," group41",group41/group4,"group42",group42/group4, "group43", group43/group4, "group44", group44/group4, "group45",group45/group4,"group81",group81,"group82",group82, "group83",group83,"group84",group84,"group85",group85,"group86",group86,"group87",group87,"group88",group88,"group89",group89,"group810",group810,"group811",group811,"group812",group812,"group813",group813,"group814",group814,"group815",group815,"group816",group816,"group817",group817,"group818",group818, "group8", group8, "percentage:", "group81",group81/group8,"group82", group82/group8, "group83",group83/group8,"group84",group84/group8, "group85",group85/group8, "group86",group86/group8,"group87",group87/group8,"group88",group88/group8,"group89",group89/group8,"group810",group810/group8,"group811",group811/group8,"group812",group812/group8,"group813",group813/group8,"group814",group814/group8,"group815",group815/group8,"group816",group816/group8,"group817",group817/group8,"group818",group818/group8]);
 234 save(statistics,"/Users/sekhon/statistics");
 235 save(li4,"/User/sekhon/li4");
 236 save(li41,"/Users/sekhon/li41");
 237 save(li42,"/Users/sekhon/li42");
 238 save(li43,"/Users/sekhon/li43");
 239 save(li44,"/Users/sekhon/li44");
 240 save(li45,"/Users/sekhon/li45");
 241 save(li8,"/Users/sekhon/li8");
 242 save(li81,"/Users/sekhon/li81");
 243 save(li82,"/Users/sekhon/li82");
 244 save(li83,"/Users/sekhon/li83");
 245 save(li84,"/Users/sekhon/li84");
 246 save(li85,"/Users/sekhon/li85");
 247 save(li86,"/Users/sekhon/li86");
 248 save(li87,"/Users/sekhon/li87");
 249 save(li88,"/Users/sekhon/li88");
 250 save(li89,"/Users/sekhon/li89");
 251 save(li810,"/Users/sekhon/li810");
 252 save(li811,"/Users/sekhon/li811");
 253 save(li812,"/Users/sekhon/li812");
 254 save(li813,"/Users/sekhon/li813");
 255 save(li814,"/Users/sekhon/li814");
 256 save(li815,"/Users/sekhon/li815");
 257 save(li816,"/Users/sekhon/li816");
 258 save(li817,"/Users/sekhon/li817");
 259 save(li818,"/Users/sekhon/li818");
 260 
 261 print "done";

Attached Files

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  • [get | view] (2010-07-02 15:46:50, 20.8 KB) [[attachment:2not4 output.txt]]
  • [get | view] (2010-06-30 15:14:30, 0.8 KB) [[attachment:2not4Galoisapproach.sage]]
  • [get | view] (2010-06-30 16:32:36, 0.8 KB) [[attachment:2not4Galoisapproachv2.sage]]
  • [get | view] (2010-06-30 15:22:48, 0.8 KB) [[attachment:2not4galoisapproach.sage]]
  • [get | view] (2010-06-30 15:14:49, 11.3 KB) [[attachment:2not4or4not8v3.sage]]
  • [get | view] (2010-06-30 15:15:11, 1.7 KB) [[attachment:li4.sobj]]
  • [get | view] (2010-06-30 15:15:27, 1.6 KB) [[attachment:li8.sobj]]
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