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// mspace.cc: test program for subspace class with bigint scalars
//////////////////////////////////////////////////////////////////////////
//
// 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/subspace.h>
const bigint MBIGPRIME=to_ZZ("6074000003");
// will convert this string to an bigint
//This is nearly the largest p such that (p/2)^2 < 2^63.
int main()
{
cin.flags( cin.flags() | ios::dec );
cout << "\nM-Subspace package test program\n\n";
int i,r=0;
while (cout << "Enter size of square matrix M: ", cin >> r, r>0 )
{
mat_m m(r,r);
cout << "Enter entries of M: ";
cin >> m;
cout << " M = " << m;
cout << "Trace(M) = " << m.trace() << endl;
//
mat_m mpower=m;
for (i=2; i<=r; i++)
{mpower=mpower*m;
cout << "m^" << i << " = " << mpower;
cout << "Trace(m^" << i << ") = " << mpower.trace() << endl;
}
//
{
vector<bigint> cp = m.charpoly();
cout << "char. poly. of m has coefficients " << cp << endl;
}
cout << "det(M) = " << m.determinant() << endl;
cout << "rank(M) = " << m.rank() << endl;
cout << "nullity(M) = " << m.nullity() << endl;
{
subspace_m ker = kernel(m);
mat_m kerbasis = basis(ker);
cout << "kernel(m) has basis\n" << kerbasis;
vec_i kerpivs = pivots(ker);
cout << "pivots: " << kerpivs << "\n";
bigint kerdenom = denom(ker);
cout << "denom: " << kerdenom << "\n";
}
{
subspace_m im = image(m);
cout << "image(m) has basis\n" << basis(im);
cout << "pivots: " << pivots(im) << "\n";
cout << "denom: " << denom(im) << "\n";
}
{
bigint lambda;
cout << "Enter lambda: "; cin >> lambda;
subspace_m elambda = eigenspace(m,lambda);
cout << "eigenspace for lambda = " << lambda << " has basis\n" << basis(elambda);
cout << "with dimension " << dim(elambda) << endl;
cout << "\nNow repeating eigenspace calculation modulo " << MBIGPRIME << endl;
subspace_m elp;
lift(peigenspace(m,lambda,MBIGPRIME),MBIGPRIME, elp);
cout << "eigenspace for lambda has basis\n" << basis(elp);
cout << "with dimension " << dim(elp) << endl;
}
}
cout<<endl;
}
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