/*
	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.

	---
	Copyright (C) 2011 - 2015, Simon Hampe <simon.hampe@googlemail.com>

	---
	Copyright (c) 2016-2021
	Ewgenij Gawrilow, Michael Joswig, and the polymake team
	Technische Universität Berlin, Germany
	https://polymake.org

	This file includes functions that perform basic linear algebra
	computations
	*/


#pragma once

#include "polymake/Rational.h"
#include "polymake/Matrix.h"

namespace polymake { namespace tropical {


/**
   @brief Takes a vector v and a matrix with column dimension equal to the dimension of v. 
   Assuming that v is in the row span of the matrix, it computes one(!) possible representation of v 
   in these generators. It does this by performing a standard (partial) gaussian reduction algorithm
   @param v The vector supposed to be contained in the row span of the generators
   @param generators  A set of row vectors whose linear span should contain v
   @return A vector (a1,..,an) such that v = (a1,...,an) * generators. It returns a vector of dimension 0, if
   v is not in the span of the generators. An error is thrown if the dimensions of v and the generators mismatch
*/
Vector<Rational> linearRepresentation(Vector<Rational> w, Matrix<Rational> A);

/**
   @brief  This method takes a set of row indices for [[SEPARATED_VERTICES]] and a vector that is supposed 
   to be a ray (i.e. with leading entry 0) in the affine span of these row vectors and 
   the lineality space (see description of [[LATTICE_NORMAL_FCT_VECTOR]]). 
   It then computes the corresponding representation in these vectors
   @param s a set of row indices of [[SEPARATED_VERTICES]]
   @param v a vector supposed to lie in the affine span of [[SEPARATED_VERTICES]] + [[LINEALITY_SPACE]]
   @param rays The matrix of [[SEPARATED_VERTICES]]
   @param linealitySpace A basis of the lineality space
   @return A vector of length [[SEPARATED_VERTICES]]->rows() + [[LINEALITY_DIM]] with linear coefficients 
   of a representation in the generators chosen via s. The last elements always refer to the lineality space.
   @throw std::runtime_error If the vector is not in the affine span of the given vectors
*/
Vector<Rational> functionRepresentationVector(const Set<Int>& rayIndices, const Vector<Rational>& v,
                                              const Matrix<Rational> &rays,
                                              const Matrix<Rational> &linealitySpace);
} }

