/usr/include/linbox/algorithms/toeplitz-det.h is in liblinbox-dev 1.4.2-3.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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*
*
* ========LICENCE========
* This file is part of the library LinBox.
*
* LinBox is free software: you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation; either
* version 2.1 of the License, or (at your option) any later version.
*
* This library 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
* Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public
* License along with this library; if not, write to the Free Software
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
* ========LICENCE========
*/
#ifndef __LINBOX_toeplitz_det_H
#define __LINBOX_toeplitz_det_H
namespace LinBox
{ // namespace in which all LinBox code resides.
#if 0
template< class Field >
void toeplitz_determinant( ZZ_p& res, const Toeplitz<Field>& A );
#endif
template< class PField >
typename PField::Coeff& toeplitz_determinant
( const PField& F, typename PField::Coeff& res,
const typename PField::Element& T, size_t n )
{
short int sign = 1;
typename PField::Coeff temp;
const typename PField::CoeffField& CField = F.getCoeffField();
CField.assign(res,CField.one);
typename PField::Element f1, f2( T ), fi;
F.setCoeff( f1, 2*n - 1, CField.one );
F.assign( fi, F.one );
while( F.deg(f2) >= n ) {
F.rem( fi, f1, f2 );
CField.mulin
( res, CField.powin( F.leadCoeff( temp, f2 ),
(long)(F.deg(f1) - F.deg(fi)) ) );
if( !((F.deg(f2)-F.deg(f1))%2) && !((F.deg(f1)-n)%2) )
sign = (short)-sign;
f1 = f2;
f2 = fi;
}
if( F.deg(f2) == (n-1) ) {
CField.mulin
( res, CField.powin( F.leadCoeff( temp, f2 ),
(long)(F.deg(f1) - F.deg(f2)) ) );
if( sign == -1 ) {
CField.mulin( res, CField.mOne);
}
}
else CField.assign( res, CField.zero );
return res;
}
} // end of namespace LinBox
#endif //__LINBOX_toeplitz_det_H
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