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// TCURVE.CC, test program for curve classes
//////////////////////////////////////////////////////////////////////////
//
// 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/curve.h>
int main(void)
{
set_precision(30);
initprimes("PRIMES",0);
Curve E;
cout << "\nEnter a curve: " << endl ;
cin>>ws; if(cin.eof()) {cout<<endl; exit(0);}
cin >> E ;
cout << "The curve is " << E << endl ;
/*
cout << "\nEnter a curve: " << endl ;
E.input(cin);
cout << "The curve is " << E << endl ;
cout << "To test out different constructors: Using all specified:\n" ;
E = Curve(0,0,1,-7,6) ;
cout << "the curve is " << E << "\n" ;
cout << "Using just a4 and a6 specified:\n" ;
E = Curve(78, 89) ;
cout << "the curve is " << E << "\n" ;
E = Curve(0, 0, 1, -7, 6);
cout << "the curve is " << E << "\n" ;
*/
cout << "A test of invariants:\n" ;
Curvedata cd(E,0) ; // the 0 means no minimalization
cout << "The curve is " << cd << endl ;
cd = Curvedata(E,1) ; // the 1 forces minimalization
cout << "The minimal curve is ";
cout << cd;
cout << endl ;
/*
cout << "A test of extended invariants:\n" ;
CurvedataExtra cdx(cd) ;
cout << "The extra curve data is ";
cout << cdx;
cout << endl ;
*/
cout <<"A test of Tate's algorithm:\n";
CurveRed cdr(cd);
cout << cdr << endl;
cout <<"Full display:\n";
cdr.display(cout);
cout <<"Traces of Frobenius:\n";
for(primevar pr(25); pr.ok(); pr++)
{
long p=pr;
cout<<"p="<<p<<": ap="<<Trace_Frob(cdr,BIGINT(p));
if(div(p,getdiscr(cdr))) cout<<" (bad reduction)";
cout<<endl;
}
cout <<"Testing construction from a non-integral model:\n";
bigint a1,a2,a3,a4,a6;
E.getai(a1,a2,a3,a4,a6);
bigrational qa1(a1),qa2(a2),qa3(a3),qa4(a4),qa6(a6);
bigint s=BIGINT(60), scale;
bigint si=s;
qa1/=si; si*=s;
qa2/=si; si*=s;
qa3/=si; si*=s;
qa4/=si; si*=s; si*=s;
qa6/=si;
cout<<"After scaling down by "<<s<<", coeffs are ";
cout<<"["<<qa1<<","<<qa2<<","<<qa3<<","<<qa4<<","<<qa6<<"]"<<endl;
vector<bigrational> qai;
qai.push_back(qa1);
qai.push_back(qa2);
qai.push_back(qa3);
qai.push_back(qa4);
qai.push_back(qa6);
Curvedata Es(qai,scale);
cout<<"Constructed curve is "<<(Curve)Es<<" with scale = "<<scale<<endl;
return 0;
}
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