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// comptest.cc: test program for complex functions
//////////////////////////////////////////////////////////////////////////
//
// 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/compproc.h>
#include <eclib/marith.h>
int main(void)
{
set_precision("Enter number of decimal places");
bigfloat x=to_bigfloat(3.125), y=to_bigfloat(4.25);
bigcomplex z = bigcomplex(x,y);
bigcomplex a = bigcomplex(to_bigfloat(1),to_bigfloat(1));
bigcomplex b = bigcomplex(to_bigfloat(2),to_bigfloat(1));
bigcomplex c;
cout << "z = " << z << "\n";
cout << " has real part = " << real(z) << "\n";
cout << " and imaginary part = " << imag(z) << "i\n";
cout << "z has complex conjugate = " << conj(z) << "\n";
c = cagm(z,to_bigfloat(1));
cout << "AGM(" << z << "," << bigcomplex(to_bigfloat(1)) << ") = ";
cout << c << "\n\n";
cout << "AGM(" << a << "," << b << ") = "<<flush;
c = cagm(a,b);
cout << c << "\n\n";
bigint ia,ib,ic,id,ie; long nr;
vector<bigint> roots;
cout << "Enter Integer coefficients of a (monic) cubic:";
cin>>ia>>ib>>ic;
roots = Introotscubic(ia,ib,ic);
nr=roots.size();
if (nr==0) cout << "No integer roots"<<endl;
else cout << "The "<<nr<<" root(s) are:\n"<<roots<<endl;
// Test of complex cube root
bigcomplex rootz;
bigfloat three(to_bigfloat(3));
bigcomplex w = bigcomplex(to_bigfloat(-1),
sqrt(three))/to_bigfloat(2);
cout << "Enter a real or complex: "; cin >> z;
rootz=exp(log(z)/three);
cout << "Main cube root = " << rootz << endl;
cout << "whose cube is " << pow(rootz,3) << endl;
rootz*=w;
cout << "Next cube root = " << rootz << endl;
cout << "whose cube is " << pow(rootz,3) << endl;
rootz*=w;
cout << "Next cube root = " << rootz << endl;
cout << "whose cube is " << pow(rootz,3) << endl;
// Test for quartic root-finding:
bigfloat xa,xb,xc,xd,xe;
cout << "Enter real coefficients a b c d e of a quartic:";
cin>>xa>>xb>>xc>>xd>>xe;
int iroot;
vector<bigcomplex> croots = solverealquartic((xa), (xb),(xc),(xd),(xe));
cout<<"Quartic [" <<xa << "," << xb << "," << xc << "," << xd << "," << xe
<< "] has roots:\n";
for(iroot=0; iroot<4; iroot++) cout<<croots[iroot]<<"\n";
cout<<endl;
}
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