/** @file prem_uvar.h
 *
 *  Function to calculate the pseudo-remainder. */

/*
 *  GiNaC Copyright (C) 1999-2022 Johannes Gutenberg University Mainz, Germany
 *
 *  This program 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.
 *
 *  This program 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 this program; if not, write to the Free Software
 *  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
 */

#ifndef GINAC_POLYNOMIAL_PREM_H
#define GINAC_POLYNOMIAL_PREM_H

#include "upoly.h"
#include "debug.h"
#include "remainder.h"

namespace GiNaC {

/// Compute the pseudo-remainder of univariate polynomials @a a and @a b
/// Pseudo remainder \f$r(x)\f$ is defined as 
/// \f$\beta^l a(x) = b(x) q(x) + r(x) \f$, where \f$\beta\f$ is leading
/// coefficient of \f$b(x)\f$ and \f$l = degree(a) - degree(b) + 1\f$
/// FIXME: this implementation is extremely dumb.
template<typename T> bool pseudoremainder(T& r, const T& a, const T& b)
{
	typedef typename T::value_type ring_t;
	bug_on(b.size() == 0, "division by zero");
	if (a.size() == 1 && b.size() == 1) {
		r.clear();
		return true;
	}
	if (a.size() == 1) {
		r = b;
		return false;
	}
	if (degree(b) > degree(a)) {
		r = b;
		return false;
	}

	const ring_t one = get_ring_elt(b[0], 1);
	const std::size_t l = degree(a) - degree(b) + 1;
	const ring_t blcoeff = lcoeff(b);
	const ring_t b_lth = expt_pos(blcoeff, l);
	if (b_lth == one)
		return remainder_in_ring(r, a, b);

	T a_(a);
	a_ *= b_lth;
	return remainder_in_ring(r, a_, b);
}

} // namespace GiNaC

#endif // GINAC_POLYNOMIAL_PREM_H