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// 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()
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