// Copyright (c) 2014
// INRIA Saclay-Ile de France (France)
//
// This file is part of CGAL (www.cgal.org)
//
// $URL: https://github.com/CGAL/cgal/blob/v5.1/NewKernel_d/include/CGAL/determinant_of_vectors.h $
// $Id: determinant_of_vectors.h 0779373 2020-03-26T13:31:46+01:00 Sébastien Loriot
// SPDX-License-Identifier: LGPL-3.0-or-later OR LicenseRef-Commercial
//
// Author(s)     : Marc Glisse

#ifndef CGAL_DETVEC_H
#define CGAL_DETVEC_H
#include <CGAL/determinant.h>
#include <CGAL/predicates/sign_of_determinant.h>

namespace CGAL {
  // TODO: determine whether it is better to pass them by lines or columns.

  template <class NT, class Vector> inline
  NT determinant_of_vectors(Vector const&a, Vector const&b){
    return determinant<NT>(a[0],a[1],b[0],b[1]);
  }
  template <class NT, class Vector> inline
  typename Sgn<NT>::result_type
  sign_of_determinant_of_vectors(Vector const&a, Vector const&b){
    return sign_of_determinant<NT>(a[0],a[1],b[0],b[1]);
  }

  template <class NT, class Vector>
  NT determinant_of_vectors(Vector const&a, Vector const&b,
      Vector const&c){
    return determinant<NT>(a[0],a[1],a[2],b[0],b[1],b[2],c[0],c[1],c[2]);
  }
  template <class NT, class Vector>
  typename Sgn<NT>::result_type
  sign_of_determinant_of_vectors(Vector const&a, Vector const&b,
      Vector const&c){
    return sign_of_determinant<NT>(a[0],a[1],a[2],b[0],b[1],b[2],c[0],c[1],c[2]);
  }

  template <class NT, class Vector>
  NT determinant_of_vectors(Vector const&a, Vector const&b,
      Vector const&c, Vector const&d){
    return determinant<NT>(
        a[0],a[1],a[2],a[3],
        b[0],b[1],b[2],b[3],
        c[0],c[1],c[2],c[3],
        d[0],d[1],d[2],d[3]);
  }
  template <class NT, class Vector>
  typename Sgn<NT>::result_type
  sign_of_determinant_of_vectors(Vector const&a, Vector const&b,
      Vector const&c, Vector const&d){
    return sign_of_determinant<NT>(
        a[0],a[1],a[2],a[3],
        b[0],b[1],b[2],b[3],
        c[0],c[1],c[2],c[3],
        d[0],d[1],d[2],d[3]);
  }

  template <class NT, class Vector>
  NT determinant_of_vectors(Vector const&a, Vector const&b,
      Vector const&c, Vector const&d, Vector const&e){
    return determinant<NT>(
        a[0],a[1],a[2],a[3],a[4],
        b[0],b[1],b[2],b[3],b[4],
        c[0],c[1],c[2],c[3],c[4],
        d[0],d[1],d[2],d[3],d[4],
        e[0],e[1],e[2],e[3],e[4]);
  }
  template <class NT, class Vector>
  typename Sgn<NT>::result_type
  sign_of_determinant_of_vectors(Vector const&a, Vector const&b,
      Vector const&c, Vector const&d, Vector const&e){
    return sign_of_determinant<NT>(
        a[0],a[1],a[2],a[3],a[4],
        b[0],b[1],b[2],b[3],b[4],
        c[0],c[1],c[2],c[3],c[4],
        d[0],d[1],d[2],d[3],d[4],
        e[0],e[1],e[2],e[3],e[4]);
  }

  template <class NT, class Vector>
  NT determinant_of_vectors(Vector const&a, Vector const&b,
      Vector const&c, Vector const&d, Vector const&e, Vector const&f){
    return determinant<NT>(
        a[0],a[1],a[2],a[3],a[4],a[5],
        b[0],b[1],b[2],b[3],b[4],b[5],
        c[0],c[1],c[2],c[3],c[4],c[5],
        d[0],d[1],d[2],d[3],d[4],d[5],
        e[0],e[1],e[2],e[3],e[4],e[5],
        f[0],f[1],f[2],f[3],f[4],f[5]);
  }
  template <class NT, class Vector>
  typename Sgn<NT>::result_type
  sign_of_determinant_of_vectors(Vector const&a, Vector const&b,
      Vector const&c, Vector const&d, Vector const&e, Vector const&f){
    return sign_of_determinant<NT>(
        a[0],a[1],a[2],a[3],a[4],a[5],
        b[0],b[1],b[2],b[3],b[4],b[5],
        c[0],c[1],c[2],c[3],c[4],c[5],
        d[0],d[1],d[2],d[3],d[4],d[5],
        e[0],e[1],e[2],e[3],e[4],e[5],
        f[0],f[1],f[2],f[3],f[4],f[5]);
  }

}
#endif