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// FILE ECNF.CC: program for newform construction from an elliptic curve
//////////////////////////////////////////////////////////////////////////
//
// 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/moddata.h>
#include <eclib/symb.h>
#include <eclib/cusp.h>
#include <eclib/homspace.h>
#include <eclib/oldforms.h>
#include <eclib/cperiods.h>
#include <eclib/newforms.h>
#include <eclib/curve.h>
int main(void)
{
int verbose=0;
// Read in the curve, minimise and construct CurveRed (needed for
// conductor and Traces of Frobenius etc.)
Curve C;
cout << "Enter curve: "; cin >> C;
Curvedata CD(C,1); // minimise
CurveRed CR(CD);
bigint N = getconductor(CR);
int n = I2int(N);
cout << ">>> Level = conductor = " << n << " <<<" << endl;
cout << "Minimal curve = " << (Curve)(CR) << endl;
cout<<endl;
// Construct newforms class (this does little work)
int sign=1;
cout<<"Enter sign (1,-1,0 for both):"; cin>>sign;
newforms nf(n,verbose);
// Create the newform from the curve (first create the homspace,
// then split off the eigenspace)
nf.createfromcurve(sign,CR);
// Display newform info
cout << "Newform information:"<<endl;
nf.display();
cout<<endl;
// Display modular symbol info
cout << "Modular symbol map:"<<endl;
nf.display_modular_symbol_map();
// Compute more modular symbols as prompted:
rational r; long nu,de;
cout << "Computation of further modular symbols {0,r} for rational r:"<<endl;
while(1)
{
cout<<"Enter numerator and denominator of r: ";
cin>>ws;
if(cin.eof()) {cout<<endl; break;}
cin >> nu >> de; r=rational(nu,de);
if((nu==0)&&(de==0)) {cout<<endl; break;}
if(sign==+1)
cout<<"{0,"<<r<<"} -> "<< nf.plus_modular_symbol(r)<<endl;
if(sign==-1)
cout<<"{0,"<<r<<"} -> "<< nf.minus_modular_symbol(r)<<endl;
if(sign==0)
{
pair<rational,rational> s = nf.full_modular_symbol(r);
cout<<"{0,"<<r<<"} -> ("<< s.first << "," << s.second << ")" <<endl;
}
}
for(de=1; de<20; de++)
for(nu=0; nu<de; nu++)
{
if(gcd(nu,de)==1)
{
r=rational(nu,de);
if(sign==+1)
cout<<"{0,"<<r<<"} -> "<< nf.plus_modular_symbol(r)<<endl;
if(sign==-1)
cout<<"{0,"<<r<<"} -> "<< nf.minus_modular_symbol(r)<<endl;
if(sign==0)
{
pair<rational,rational> s = nf.full_modular_symbol(r);
cout<<"{0,"<<r<<"} -> ("<< s.first << "," << s.second << ")" <<endl;
}
}
}
} // end of main()
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