Attachment '2not4or4not8v3.sage'
Download 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";
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