forked from JohnCremona/eclib
-
Notifications
You must be signed in to change notification settings - Fork 0
/
checkgens.cc
227 lines (199 loc) · 5.92 KB
/
checkgens.cc
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
// FILE CHECKGENS.CC -- Program to check input gens are Mordell-Weil basis
//////////////////////////////////////////////////////////////////////////
//
// Copyright 1990-2012 John Cremona
//
// This file is part of the eclib package.
//
// eclib is free software; you can redistribute it and/or modify it
// under the terms of the GNU General Public License as published by the
// Free Software Foundation; either version 2 of the License, or (at your
// option) any later version.
//
// eclib is distributed in the hope that it will be useful, but WITHOUT
// ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
// FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
// for more details.
//
// You should have received a copy of the GNU General Public License
// along with eclib; if not, write to the Free Software Foundation,
// Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA
//
//////////////////////////////////////////////////////////////////////////
#include <fstream>
#include <eclib/points.h>
#include <eclib/mwprocs.h>
#include <eclib/sifter.h>
#include <eclib/compproc.h>
#include <eclib/egr.h>
#include <eclib/htconst.h>
#include <eclib/elog.h>
#define INPUT_CLASS_IS_LETTER // we only use letters now!
Curve C;
Curvedata CD;
vector<Point> plist;
int verbose;
string genfile;
string ccode;
#include <eclib/curvesort.h> // for codeletter() function
int main()
{
// cout<<"precision = "<<decimal_precision()<<endl;
set_precision(15);
// cout<<"precision = "<<decimal_precision()<<endl;
cin.flags( cin.flags() | ios::dec ); //force decimal input (bug fix)
int rank, rank2, i;
long cond, ncurve, nclass;
bigfloat reg, hmax;;
cerr<<"verbose (0/1)? "; cin >>verbose;
verbose=0;
// cerr<<"\nLimit on height of search (-1 to just check points are on curve)? ";
// cin >> hmax;
hmax=-1;
cerr <<"\n";
cerr << "input filename for curves and generators? ";
cin >> genfile;
ifstream genin;
genin.open(genfile.c_str());
if(!genin.is_open()) {cerr<<"Unable to open file " << genfile << "\n"; abort();}
cerr<<endl;
while (!genin.eof())
{
genin >> cond;
// cout<<"input conductor="<<cond<<endl;
if(cond==0) break;
#ifdef INPUT_CLASS_IS_LETTER
genin >> ccode;
#else
genin >> nclass;
ccode = codeletter(nclass-1);
// cout<<"After input, nclass="<<nclass<<endl;
#endif
genin >> ncurve;
// cout<<"After input, ncurve="<<ncurve<<endl;
genin>>C;
// cout<<"After input, C="<<C<<endl;
cout << cond<<ccode<<ncurve<<"\t";
cout << C << ":\t";
CD = Curvedata(C);
if(verbose) cout <<endl;
genin >> rank;
cout << "r = "<<rank<<"\t";
if(verbose) cout <<endl;
if (rank==0) {cout<<" OK\n"; continue;}
Point P(CD);
plist.clear();
while(plist.size()<rank)
{
genin >> P;
cout << P;
if(P.isvalid())
{
plist.push_back(P);
cout << " OK ";
}
else
{
cout << " not on curve! "; abort();
}
}
// A test of our division-by-2 code:
for(vector<Point>::const_iterator Pi=plist.begin(); Pi!=plist.end(); Pi++)
{
Point P = *Pi;
Point Q = 2*P;
vector<Point> Qhalves = division_points(CD,Q,2);
if(Qhalves.size()==0)
{
cout<<"ERROR: Q="<<Q<<"=2*P for P="<<P<<" but halving Q failed!"<<endl;
}
}
// Do nothing at all apart from checking points are on curve
// (since we have a separate program for saturation now):
if(hmax<0) {cout<<endl;continue;}
bigfloat ht, maxht = to_bigfloat(0);
for (i=0; i<rank; i++)
{
ht = height(plist[i]);
if(ht>maxht) maxht=ht;
}
mw mwbasis(&CD,verbose,1);
mwbasis.process(plist);
rank2 = mwbasis.getrank();
int rank_under = (rank2<rank);
if(rank_under)
{
cout<<"\nInput points only have rank "<<rank2<<", not "<<rank<<"\n";
// continue;
}
else cout<<" INDEP ";
// Now we check that the points are independent in E(Q)/2E(Q):
long naux=rank;
long r2=0;
while((naux<100)&&(r2<rank))
{
naux+=5;
sifter box(&CD, naux, verbose);
box.process(plist);
r2 = box.getrank();
}
if(r2==rank)
{
cout<<" INDEP_MOD_2 ";
if(verbose)
cout<<"(Points are independent mod 2)"<<endl;
}
else
cout<<"\nPoints may be dependent mod 2, r2 = "<<r2<<endl;
if(hmax<1) {cout<<endl;}
else
{
reg = mwbasis.regulator();
if(verbose) cout<<"\nMax height = "<<maxht<<endl;
if(rank==1)
{
if(r2==rank) maxht/=9; else maxht/=4;
}
// since in this case we know that the index is at least 2 (or 3).
double ht_bound = height_constant(CD);
if(verbose) cout << "height bound = " << ht_bound << "\n";
bigfloat hlim = maxht+ht_bound;
if(verbose||(hlim>hmax))
{
if(!verbose) cout<<"\n";
cout<<"Bound on naive height of extra generators = "<<hlim<<endl;
}
if(hlim>hmax)
{
cout<<"Only searching up to height "<<hmax<<endl;
hlim=hmax;
}
else if(!verbose) cout<<endl;
sieve s(&CD, &mwbasis, 2, 0);
s.search(hlim);
rank2 = mwbasis.getrank();
if(rank2!=rank)
{
cout << "\nPoints found have rank " << rank2<<", not "<<rank<<"\n";
continue;
}
if(rank_under)
cout << "New basis: "<<mwbasis.getbasis()<<endl;
bigfloat reg2 = mwbasis.regulator();
long index = I2long(Iround((sqrt(reg/reg2)+0.01)));
if(index>1)
{
if(!verbose) cout<<"\n";
cout << "Points found contain original with index " << index <<"\n";
vector<Point> b = mwbasis.getbasis();
for (i=0; i<rank; i++)
{ Point P = b[i];
cout << "\nGenerator "<<(i+1)<<" is "<<P<<"; ";
cout << "height "<<height(P);
}
cout<<"\nNew regulator is "<<reg2<<" (old was "<<reg<<")"<<endl<<endl;
}
}
// else cout << "\n";
}
} // end main()