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
|
// indep_test.cc: program to test input points for (in)dependence
//////////////////////////////////////////////////////////////////////////
//
// 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
//
//////////////////////////////////////////////////////////////////////////
// NB This is based on 2-saturation, trying to show points are
// independent in E(Q)/2E(Q), and is now largely obsolete, being
// superceded by general saturation algorithms
#include <eclib/points.h>
#include <eclib/sifter.h>
int main()
{
set_precision(100);
initprimes("PRIMES",0);
int verbose = 1;
long rank, npts, j;
cout<<"verbose (0/1)? ";
cin>>ws; if(cin.eof()) {cout<<endl; exit(0);}
cin >>verbose;
Curve E;
while (1)
{
cout<<"\nInput a curve: ";
cin>>ws; if(cin.eof()) {cout<<endl; exit(0);}
cin >> E;
if ( E.isnull() ) exit(0);
Curvedata C(E);
cout << "Curve " << (Curve)C << endl;
Point P(C);
cout<<"enter number of points: ";
cin>>ws; if(cin.eof()) {cout<<endl; exit(0);}
cin >> npts;
vector<Point> points; points.reserve(npts);
j=0;
while(j<npts)
{
cout<<"\n enter point "<<(j+1)<<" : ";
cin>>ws; if(cin.eof()) {cout<<endl; exit(0);}
cin >> P;
if ( P.isvalid() ) {points.push_back(P); j++;}
else {cout<<"point "<<P<<" not on curve.\n\n"; }
}
if(verbose) cout<<npts<<" points entered.\n";
long naux=npts+10;
cout << "Enter number of primes to use: ";
cin>>ws; if(cin.eof()) {cerr<<endl; exit(0);}
cin>>naux;
sifter box(&C, naux, verbose);
box.process(points);
rank = box.getrank();
if(rank==npts)
cout<<"Points are all independent, their rank is "<<rank<<endl;
else
cout<<"Points may be dependent, rank is at least "<<rank<<endl;
}
}
//end of file indep.cc
|
