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// quadratic.cc: implementation of class for handling integer quadratics
//////////////////////////////////////////////////////////////////////////
//
// 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/quadratic.h>
void quadratic::transform(const unimod& m)
{
bigint newq0 = eval(m.m11, m.m21);
bigint newq2 = eval(m.m12, m.m22);
coeffs[1] = 2 * (coeffs[0]*m.m11*m.m12 + coeffs[2]*m.m21*m.m22)
+ coeffs[1] * (m.m11*m.m22+m.m12*m.m21);
coeffs[0] = newq0;
coeffs[2] = newq2;
}
void quadratic::x_shift(const bigint& a, unimod& m)
{
const bigint& aq0=a*coeffs[0];
coeffs[2]+= (aq0+coeffs[1])*a;
coeffs[1]+= 2*aq0;
m.x_shift(a);
}
void quadratic::y_shift(const bigint& a, unimod& m)
{
const bigint& aq2=a*coeffs[2];
coeffs[0]+= (aq2+coeffs[1])*a;
coeffs[1]+= 2*aq2;
m.y_shift(a);
}
void quadratic::invert(unimod& m)
{
swap(coeffs[0],coeffs[2]); coeffs[1]=-coeffs[1];
m.invert();
}
void quadratic::reduce(unimod& m)
{
// cout<<"Reducing quadratic "<<(*this)<<endl;
if(coeffs[0]<0)
{
coeffs[0]=-coeffs[0];
coeffs[2]=-coeffs[2];
coeffs[1]=-coeffs[1];
}
bigint a = roundover(-coeffs[1],2*coeffs[0]);
x_shift(a,m);
int reduced = (coeffs[0]<=coeffs[2]);
while(!reduced)
{
invert(m);
a = roundover(-coeffs[1],2*coeffs[0]);
x_shift(a,m);
reduced = (coeffs[0]<=coeffs[2]);
}
// cout<<"Reduced quadratic = "<<(*this)<<endl;
// cout<<" via matrix "<<m<<endl;
// cout<<" of determinant "<<m.det()<<endl;
}
bigint resultant(const quadratic& q1, const quadratic& q2)
{
const bigint&
a1=q1.coeffs[0], b1=q1.coeffs[1], c1=q1.coeffs[2],
a2=q2.coeffs[0], b2=q2.coeffs[1], c2=q2.coeffs[2];
return
sqr(c2*a1) -a1*c2*b2*b1 + (-2*c2*a2 + sqr(b2))*c1*a1 + c2*a2*sqr(b1) - b2*a2*c1*b1 + sqr(a2*c1);
}
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