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// solve_legendre.cc: program for solving legendre equations
//////////////////////////////////////////////////////////////////////////
//
// 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/marith.h>
#include <eclib/quadratic.h>
#include <eclib/conic.h>
#include <eclib/legendre.h>
#ifndef CONIC_METHOD
#define CONIC_METHOD 4
#endif
#define TEST_PARAM
int main()
{
initprimes("PRIMES");
cout<<"Solving ax^2 + by^2 + cz^2 = 0\n";
cout<<"Using method "<<CONIC_METHOD<<endl<<endl;
bigint a,b,c,x,y,z,zero; zero=0;
quadratic qx, qy, qz;
while(1)
{
cout << "Enter coefficients a b c: ";
cin >> a >> b >> c;
cout<<a<<" "<<b<<" "<<c<<endl;
if(a==0) exit(0);
int use_lll = (CONIC_METHOD==5);
if(!legendre_solve(a,b,c,x,y,z,use_lll))
// if(!solve_conic(a,zero,c,-b,x,y,z,CONIC_METHOD))
{
cout<<"No solution!\n";
}
else
{
cout << "Solution: "; show_xyz(x,y,z);
if(check_leg(a,b,c,x,y,z))
{
cout<<" --OK\n";
#ifdef TEST_PARAM
legendre_param(a,b,c,x,y,z,qx,qy,qz);
// cout<<"Parametric solution:\n";
cout<<"x = "<<qx<<" * [u^2,uv,v^2]\n";
cout<<"y = "<<qy<<" * [u^2,uv,v^2]\n";
cout<<"z = "<<qz<<" * [u^2,uv,v^2]\n";
cout<<"Disc(qx) = "<<qx.disc()<<endl;
cout<<"Disc(qy) = "<<qy.disc()<<endl;
cout<<"Disc(qz) = "<<qz.disc()<<endl;
if(testparamsol(a,zero,c,-b,qx,qy,qz,0))
cout<<"Parametric solution is OK\n";
else
cout<<"Parametric solution is wrong!\n";
#endif
}
else
cout<<" -- wrong!\n";
}
}
}
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