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point_search.cc
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point_search.cc
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// point_search.cc: program to find points up to given naive height
//////////////////////////////////////////////////////////////////////////
//
// 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 <eclib/interface.h>
#include <eclib/compproc.h>
#include <eclib/matrix.h>
#include <eclib/subspace.h>
#include <eclib/points.h>
#include <eclib/polys.h>
#include <eclib/curvemod.h>
#include <eclib/pointsmod.h>
#include <eclib/ffmod.h>
#include <eclib/divpol.h>
#include <eclib/tlss.h>
#include <eclib/elog.h>
#include <eclib/saturate.h>
#include <eclib/getcurve.h>
#include <eclib/sieve_search.h>
#include <eclib/mwprocs.h>
int main()
{
#ifdef NTL_ALL
set_precision(70);
#endif
initprimes("PRIMES",0);
bigfloat ht_limit;
bigint u,r,s,t;
int verbose = 1, modopt=0, pp=1, change_flag;
long blength, rank, maxrank;
cerr<<"\nenter search limit: "; cin>>ht_limit;
cerr<<"verbose (0/1)? "; cin >>verbose;
cerr<<"process points found (1) or just list them (0): "; cin>>pp;
// cout<<"moduli option (0 (Stoll)/ 1/2/3)?"; cin >> modopt;
int verb=1;
bigint v;
vector<bigrational> ai(5);
while (getcurve(ai,verb))
{
Curvedata C(ai,v);
cout << "Input curve ";
cout <<"["<<ai[0]<<","<<ai[1]<<","<<ai[2]<<","<<ai[3]<<","<<ai[4]<<"]" << endl;
Curvedata C_min = C.minimalize(u,r,s,t);
change_flag = (v!=1) || (((Curve)C_min) != (Curve)C);
if(change_flag)
{
cout<<"Searching on standard minimal model "<<(Curve)C_min<<endl;
cout<<"(points found will be transferred back at end)"<<endl;
cout<<"Transformation: \t[u,r,s,t] = ["<<u<<","<<r<<","<<s<<","<<t<<"]";
if(v!=1) cout<<" with scale factor "<<v;
cout<<endl;
}
P2Point P0;
cerr<<"enter number of known points: "; cin >>blength;
cerr<<"enter max rank to stop when this is reached (-ve for none): ";
cin >>maxrank; if(maxrank<0) maxrank=999;
vector<Point> known_points(blength);
if (blength)
{
for (long j=0; j<blength; j++)
{ cerr<<"\n enter point "<<(j+1);
if(change_flag) cerr<<" on original curve";
cerr<<": ";
cin >> P0;
Point P(C,scale(P0,v,1));
if ( P.isvalid() )
{
Point Q = transform(P,&C_min,u,r,s,t,0);
known_points[j] = Q;
if(change_flag)
{
cout<<P0<<" maps to "<<Q<<" on "<<(Curve)C_min<<", with height "<<height(Q)<<endl;
}
}
else
{
cout<<"Bad point -- not on curve. Start all over again.\n";
break;
}
}
}
mw mwbasis(&C_min, verbose, pp, maxrank);
if(blength)
{
mwbasis.process(known_points);
rank = mwbasis.getrank();
cout<<"Rank of known points is "<<rank
<<" with regulator "<<mwbasis.regulator()<<endl<<endl;
}
mwbasis.search(ht_limit, modopt, verbose);
if(pp)
{
bigint index;
vector<long> unsat;
if(verbose)
{
cout <<"Regulator (before saturation) = "<<mwbasis.regulator()<<"\n";
cout <<"Saturating..." << flush;
}
int sat_ok = mwbasis.saturate(index,unsat);
if(verbose)
{
cout <<"finished saturation (index was " << index << ")\n";
cout <<"Regulator (after saturation) = "<<mwbasis.regulator()<<"\n";
}
if(!sat_ok)
{
cout << "saturation possibly incomplete at primes " << unsat << "\n";
}
rank = mwbasis.getrank();
cout<<"Rank of points found is "<<rank<<endl;
vector<Point> b = mwbasis.getbasis();
vector<P2Point> bb(rank);
for (long i=0; i<rank; i++)
{
Point Q = b[i];
bigfloat hQ = height(Q);
cout << "Generator "<<(i+1)<<" is "<<Q<<"; ";
cout << "height "<<hQ<<endl;
P0 = scale(transform(Q,&C,u,r,s,t,1),v,0);
bb[i] = P0;
if(change_flag)
cout<<"\t--maps back to "<<P0<<" on input curve"<<endl;
}
if(rank>1) cout<<"Regulator = "<<mwbasis.regulator()<<endl;
if(sat_ok)
{
cout<<"Points have been successfully saturated"<<endl;
}
else
{
cout<<"Saturation incomplete "<<endl;
}
cout<<endl;
// Pari output:
cout<<"[";
for(long i=0; i<rank; i++)
{
if(i) cout<<",";
output_pari(cout,bb[i]);
}
cout<<"]\n"<<endl;
}
}
cout<<endl;
}
//end of file findinf.cc