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// tpoints.cc -- to test points.h/cc
//////////////////////////////////////////////////////////////////////////
//
// Copyright 1990-2023 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/points.h>
int main(){
#ifdef MPFP
set_precision(100);
#else
set_precision("Enter precision in bits");
#endif
initprimes("PRIMES",1);
Curve c(0,0,1,-7,6);
Curvedata cd(c,1);
cout << "Testing some points:\n";
Point P0(cd, bigint(0),bigint(2)) ;
Point P1(cd, bigint(1),bigint(0)) ;
Point P2(cd, bigint(2),bigint(0)) ;
cout << "The points are P0 = " << P0 <<
", P1 = " << P1 << ", and P2 = " << P2 << endl ;
cout << "Now in Pari format:\n";
cout << "The points are P0 = "; output_pari(cout,P0);
cout << ", P1 = "; output_pari(cout,P1);
cout << ", and P2 = "; output_pari(cout,P2); cout << endl ;
if (!P0.isvalid()) cout << "P0 is not on the curve!\n";
if (!P1.isvalid()) cout << "P1 is not on the curve!\n";
if (!P2.isvalid()) cout << "P2 is not on the curve!\n";
cout << "Their negatives are -P0 = " << -P0 <<
", -P1 = " << -P1 << ", and -P2 = " << -P2 << endl ;
cout << "Computing their heights:\n";
bigfloat ht0 = height(P0) ;
bigfloat ht1 = height(P1) ;
bigfloat ht2 = height(P2) ;
cout << "Heights are " << ht0 << ", " << ht1 << ", and " << ht2 << endl ;
Point origin(cd);
cout << "The origin is " << origin << endl;
cout << "Now some additions etc,:\n";
Point sum = P0 + P1 ;
cout << "P0 + P1 = " << sum << endl ;
sum = P0 - P1 ;
cout << "P0 - P1 = " << sum << endl ;
sum -= P2 ;
cout << "P0 - P1 - P2 = " << sum << endl ;
sum = P0.twice();
cout << "P0.twice() = " << sum << endl;
sum = P0 + P0;
cout << "P0 + P0 = " << sum << endl;
sum = 3*P0;
cout << "3*P0 = " << sum << endl;
sum = P0 - P0;
cout << "P0 - P0 = " << sum << endl;
sum = P0 + 3 * P1 - P2 ;
cout << "P0 +3 P1 - P2 = " << sum << endl ;
sum = 2*P0 + 2* P1 + P2 ;
cout << "2P0 +2 P1 + P2 = " << sum << endl ;
cout << "Now we try a systematic exploration" << endl ;
int loop=1;
// cout << "input 0 to skip: "; cin >> loop;
if (loop)
{
Point Q0,Q1,Q2; int i0,i1,i2;
for(i0 = -3, Q0=-3*(P0+P1+P2) ; i0 < 4 ; i0++, Q0+=P0){
for(i1 = -3, Q1=Q0 ; i1 < 4 ; i1++, Q1+=P1){
for(i2 = -3, Q2=Q1 ; i2 < 4 ; i2++, Q2+=P2){
cout << i0 << ", " << i1 <<", " << i2<< ": " << Q2 << endl ;
}
}
}
}
sum = P0 -P1 -P2 ;
cout << "P0 -P1 -P2 = " << sum << endl ;
cout << "Height of P0-P1-P2 = " << flush;
bigfloat htsum = height(sum) ;
cout << htsum << endl ;
cout <<"3 (P0 -P1 -P2) = " << flush;
Point triplesum = 3 * sum ;
cout << triplesum << endl ;
cout << "Height of 3*(P0-P1-P2) = " << flush;
bigfloat ht3sum = height(triplesum) ;
cout << ht3sum << endl ;
cout << "The quotient is " << ht3sum/htsum << endl ;
/*
vector<Point> pointlist(3); // won't initialize
pointlist[0] = P0; pointlist[1] = P1; pointlist[2] = P2 ;
bigfloat reg = regulator(pointlist) ;
cout << "The regulator of P0, P1, P2 is " << reg << endl ;
*/
return 0;
} //ends main
//ends file tpoints.cc
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