math-octonion.qbk

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[section Template Class octonion]

   namespace boost{ namespace math {
 
   template<typename T>
   class octonion
   {
   public:
      typedef T value_type;

      explicit  ``[link boost_octonions.octonions.octonion_member_functions.constructors octonion]``(T const & requested_a = T(), T const & requested_b = T(), T const & requested_c = T(), T const & requested_d = T(), T const & requested_e = T(), T const & requested_f = T(), T const & requested_g = T(), T const & requested_h = T());
      explicit  ``[link boost_octonions.octonions.octonion_member_functions.constructors octonion]``(::std::complex<T> const & z0, ::std::complex<T> const & z1 = ::std::complex<T>(), ::std::complex<T> const & z2 = ::std::complex<T>(), ::std::complex<T> const & z3 = ::std::complex<T>());
      explicit  ``[link boost_octonions.octonions.octonion_member_functions.constructors octonion]``(::boost::math::quaternion<T> const & q0, ::boost::math::quaternion<T> const & q1 = ::boost::math::quaternion<T>());
      template<typename X> 
      explicit  ``[link boost_octonions.octonions.octonion_member_functions.constructors octonion]``(octonion<X> const & a_recopier);

      T                             ``[link boost_octonions.octonions.octonion_member_functions.real_and_unreal_parts real]``() const;
      octonion<T>                   ``[link boost_octonions.octonions.octonion_member_functions.real_and_unreal_parts unreal]``() const;

      T                             ``[link boost_octonions.octonions.octonion_member_functions.individual_real_components R_component_1]``() const;
      T                             ``[link boost_octonions.octonions.octonion_member_functions.individual_real_components R_component_2]``() const;
      T                             ``[link boost_octonions.octonions.octonion_member_functions.individual_real_components R_component_3]``() const;
      T                             ``[link boost_octonions.octonions.octonion_member_functions.individual_real_components R_component_4]``() const;
      T                             ``[link boost_octonions.octonions.octonion_member_functions.individual_real_components R_component_5]``() const;
      T                             ``[link boost_octonions.octonions.octonion_member_functions.individual_real_components R_component_6]``() const;
      T                             ``[link boost_octonions.octonions.octonion_member_functions.individual_real_components R_component_7]``() const;
      T                             ``[link boost_octonions.octonions.octonion_member_functions.individual_real_components R_component_8]``() const;

      ::std::complex<T>             ``[link boost_octonions.octonions.octonion_member_functions.individual_complex_components C_component_1]``() const;
      ::std::complex<T>             ``[link boost_octonions.octonions.octonion_member_functions.individual_complex_components C_component_2]``() const;
      ::std::complex<T>             ``[link boost_octonions.octonions.octonion_member_functions.individual_complex_components C_component_3]``() const;
      ::std::complex<T>             ``[link boost_octonions.octonions.octonion_member_functions.individual_complex_components C_component_4]``() const;

      ::boost::math::quaternion<T>  ``[link boost_octonions.octonions.octonion_member_functions.individual_quaternion_components H_component_1]``() const;
      ::boost::math::quaternion<T>  ``[link boost_octonions.octonions.octonion_member_functions.individual_quaternion_components H_component_2]``() const;

      octonion<T> & ``[link boost_octonions.octonions.octonion_member_functions.assignment_operators operator =]`` (octonion<T> const  & a_affecter);
      template<typename X> 
      octonion<T> & ``[link boost_octonions.octonions.octonion_member_functions.assignment_operators operator =]`` (octonion<X> const  & a_affecter);
      octonion<T> & ``[link boost_octonions.octonions.octonion_member_functions.assignment_operators operator =]`` (T const  & a_affecter);
      octonion<T> & ``[link boost_octonions.octonions.octonion_member_functions.assignment_operators operator =]`` (::std::complex<T> const & a_affecter);
      octonion<T> & ``[link boost_octonions.octonions.octonion_member_functions.assignment_operators operator =]`` (::boost::math::quaternion<T> const & a_affecter);

      octonion<T> & ``[link boost_octonions.octonions.octonion_member_functions.other_member_operators operator +=]`` (T const & rhs);
      octonion<T> & ``[link boost_octonions.octonions.octonion_member_functions.other_member_operators operator +=]`` (::std::complex<T> const & rhs);
      octonion<T> & ``[link boost_octonions.octonions.octonion_member_functions.other_member_operators operator +=]`` (::boost::math::quaternion<T> const & rhs);
      template<typename X> 
      octonion<T> & ``[link boost_octonions.octonions.octonion_member_functions.other_member_operators operator +=]`` (octonion<X> const & rhs);

      octonion<T> & ``[link boost_octonions.octonions.octonion_member_functions.other_member_operators operator -=]`` (T const & rhs);
      octonion<T> & ``[link boost_octonions.octonions.octonion_member_functions.other_member_operators operator -=]`` (::std::complex<T> const & rhs);
      octonion<T> & ``[link boost_octonions.octonions.octonion_member_functions.other_member_operators operator -=]`` (::boost::math::quaternion<T> const & rhs);
      template<typename X> 
      octonion<T> & ``[link boost_octonions.octonions.octonion_member_functions.other_member_operators operator -=]`` (octonion<X> const & rhs);

      octonion<T> & ``[link boost_octonions.octonions.octonion_member_functions.other_member_operators operator *=]`` (T const & rhs);
      octonion<T> & ``[link boost_octonions.octonions.octonion_member_functions.other_member_operators operator *=]`` (::std::complex<T> const & rhs);
      octonion<T> & ``[link boost_octonions.octonions.octonion_member_functions.other_member_operators operator *=]`` (::boost::math::quaternion<T> const & rhs);
      template<typename X> 
      octonion<T> & ``[link boost_octonions.octonions.octonion_member_functions.other_member_operators operator *=]`` (octonion<X> const & rhs);

      octonion<T> & ``[link boost_octonions.octonions.octonion_member_functions.other_member_operators operator /=]`` (T const & rhs);
      octonion<T> & ``[link boost_octonions.octonions.octonion_member_functions.other_member_operators operator /=]`` (::std::complex<T> const & rhs);
      octonion<T> & ``[link boost_octonions.octonions.octonion_member_functions.other_member_operators operator /=]`` (::boost::math::quaternion<T> const & rhs);
      template<typename X> 
      octonion<T> & ``[link boost_octonions.octonions.octonion_member_functions.other_member_operators operator /=]`` (octonion<X> const & rhs);
   };

   } } // namespaces
   
[endsect]

[section Octonion Specializations]

   namespace boost{ namespace math{
   
   template<>
   class octonion<float>
   {
   public:
      typedef float value_type;

      explicit  ``[link boost_octonions.octonions.octonion_member_functions.constructors octonion]``(float const & requested_a = 0.0f, float const & requested_b = 0.0f, float const & requested_c = 0.0f, float const & requested_d = 0.0f, float const & requested_e = 0.0f, float const & requested_f = 0.0f, float const & requested_g = 0.0f, float const & requested_h = 0.0f);
      explicit  ``[link boost_octonions.octonions.octonion_member_functions.constructors octonion]``(::std::complex<float> const & z0, ::std::complex<float> const & z1 = ::std::complex<float>(), ::std::complex<float> const & z2 = ::std::complex<float>(), ::std::complex<float> const & z3 = ::std::complex<float>());
      explicit  ``[link boost_octonions.octonions.octonion_member_functions.constructors octonion]``(::boost::math::quaternion<float> const & q0, ::boost::math::quaternion<float> const & q1 = ::boost::math::quaternion<float>());
      explicit  ``[link boost_octonions.octonions.octonion_member_functions.constructors octonion]``(octonion<double> const & a_recopier);
      explicit  ``[link boost_octonions.octonions.octonion_member_functions.constructors octonion]``(octonion<long double> const & a_recopier);

      float                             ``[link boost_octonions.octonions.octonion_member_functions.real_and_unreal_parts real]``() const;
      octonion<float>                   ``[link boost_octonions.octonions.octonion_member_functions.real_and_unreal_parts unreal]``() const;

      float                             ``[link boost_octonions.octonions.octonion_member_functions.individual_real_components R_component_1]``() const;
      float                             ``[link boost_octonions.octonions.octonion_member_functions.individual_real_components R_component_2]``() const;
      float                             ``[link boost_octonions.octonions.octonion_member_functions.individual_real_components R_component_3]``() const;
      float                             ``[link boost_octonions.octonions.octonion_member_functions.individual_real_components R_component_4]``() const;
      float                             ``[link boost_octonions.octonions.octonion_member_functions.individual_real_components R_component_5]``() const;
      float                             ``[link boost_octonions.octonions.octonion_member_functions.individual_real_components R_component_6]``() const;
      float                             ``[link boost_octonions.octonions.octonion_member_functions.individual_real_components R_component_7]``() const;
      float                             ``[link boost_octonions.octonions.octonion_member_functions.individual_real_components R_component_8]``() const;

      ::std::complex<float>             ``[link boost_octonions.octonions.octonion_member_functions.individual_complex_components C_component_1]``() const;
      ::std::complex<float>             ``[link boost_octonions.octonions.octonion_member_functions.individual_complex_components C_component_2]``() const;
      ::std::complex<float>             ``[link boost_octonions.octonions.octonion_member_functions.individual_complex_components C_component_3]``() const;
      ::std::complex<float>             ``[link boost_octonions.octonions.octonion_member_functions.individual_complex_components C_component_4]``() const;

      ::boost::math::quaternion<float>  ``[link boost_octonions.octonions.octonion_member_functions.individual_quaternion_components H_component_1]``() const;
      ::boost::math::quaternion<float>  ``[link boost_octonions.octonions.octonion_member_functions.individual_quaternion_components H_component_2]``() const;

      octonion<float> & ``[link boost_octonions.octonions.octonion_member_functions.assignment_operators operator =]`` (octonion<float> const  & a_affecter);
      template<typename X> 
      octonion<float> & ``[link boost_octonions.octonions.octonion_member_functions.assignment_operators operator =]`` (octonion<X> const  & a_affecter);
      octonion<float> & ``[link boost_octonions.octonions.octonion_member_functions.assignment_operators operator =]`` (float const  & a_affecter);
      octonion<float> & ``[link boost_octonions.octonions.octonion_member_functions.assignment_operators operator =]`` (::std::complex<float> const & a_affecter);
      octonion<float> & ``[link boost_octonions.octonions.octonion_member_functions.assignment_operators operator =]`` (::boost::math::quaternion<float> const & a_affecter);

      octonion<float> & ``[link boost_octonions.octonions.octonion_member_functions.other_member_operators operator +=]`` (float const & rhs);
      octonion<float> & ``[link boost_octonions.octonions.octonion_member_functions.other_member_operators operator +=]`` (::std::complex<float> const & rhs);
      octonion<float> & ``[link boost_octonions.octonions.octonion_member_functions.other_member_operators operator +=]`` (::boost::math::quaternion<float> const & rhs);
      template<typename X> 
      octonion<float> & ``[link boost_octonions.octonions.octonion_member_functions.other_member_operators operator +=]`` (octonion<X> const & rhs);

      octonion<float> & ``[link boost_octonions.octonions.octonion_member_functions.other_member_operators operator -=]`` (float const & rhs);
      octonion<float> & ``[link boost_octonions.octonions.octonion_member_functions.other_member_operators operator -=]`` (::std::complex<float> const & rhs);
      octonion<float> & ``[link boost_octonions.octonions.octonion_member_functions.other_member_operators operator -=]`` (::boost::math::quaternion<float> const & rhs);
      template<typename X> 
      octonion<float> & ``[link boost_octonions.octonions.octonion_member_functions.other_member_operators operator -=]`` (octonion<X> const & rhs);

      octonion<float> & ``[link boost_octonions.octonions.octonion_member_functions.other_member_operators operator *=]`` (float const & rhs);
      octonion<float> & ``[link boost_octonions.octonions.octonion_member_functions.other_member_operators operator *=]`` (::std::complex<float> const & rhs);
      octonion<float> & ``[link boost_octonions.octonions.octonion_member_functions.other_member_operators operator *=]`` (::boost::math::quaternion<float> const & rhs);
      template<typename X> 
      octonion<float> & ``[link boost_octonions.octonions.octonion_member_functions.other_member_operators operator *=]`` (octonion<X> const & rhs);

      octonion<float> & ``[link boost_octonions.octonions.octonion_member_functions.other_member_operators operator /=]`` (float const & rhs);
      octonion<float> & ``[link boost_octonions.octonions.octonion_member_functions.other_member_operators operator /=]`` (::std::complex<float> const & rhs);
      octonion<float> & ``[link boost_octonions.octonions.octonion_member_functions.other_member_operators operator /=]`` (::boost::math::quaternion<float> const & rhs);
      template<typename X> 
      octonion<float> & ``[link boost_octonions.octonions.octonion_member_functions.other_member_operators operator /=]`` (octonion<X> const & rhs);
   };

[#boost_octonions.octonion_double]

   template<>
   class octonion<double>
   {
   public:
      typedef double value_type;

      explicit  ``[link boost_octonions.octonions.octonion_member_functions.constructors octonion]``(double const & requested_a = 0.0, double const & requested_b = 0.0, double const & requested_c = 0.0, double const & requested_d = 0.0, double const & requested_e = 0.0, double const & requested_f = 0.0, double const & requested_g = 0.0, double const & requested_h = 0.0);
      explicit  ``[link boost_octonions.octonions.octonion_member_functions.constructors octonion]``(::std::complex<double> const & z0, ::std::complex<double> const & z1 = ::std::complex<double>(), ::std::complex<double> const & z2 = ::std::complex<double>(), ::std::complex<double> const & z3 = ::std::complex<double>());
      explicit  ``[link boost_octonions.octonions.octonion_member_functions.constructors octonion]``(::boost::math::quaternion<double> const & q0, ::boost::math::quaternion<double> const & q1 = ::boost::math::quaternion<double>());
      explicit  ``[link boost_octonions.octonions.octonion_member_functions.constructors octonion]``(octonion<float> const & a_recopier);
      explicit  ``[link boost_octonions.octonions.octonion_member_functions.constructors octonion]``(octonion<long double> const & a_recopier);

      double                             ``[link boost_octonions.octonions.octonion_member_functions.real_and_unreal_parts real]``() const;
      octonion<double>                   ``[link boost_octonions.octonions.octonion_member_functions.real_and_unreal_parts unreal]``() const;

      double                             ``[link boost_octonions.octonions.octonion_member_functions.individual_real_components R_component_1]``() const;
      double                             ``[link boost_octonions.octonions.octonion_member_functions.individual_real_components R_component_2]``() const;
      double                             ``[link boost_octonions.octonions.octonion_member_functions.individual_real_components R_component_3]``() const;
      double                             ``[link boost_octonions.octonions.octonion_member_functions.individual_real_components R_component_4]``() const;
      double                             ``[link boost_octonions.octonions.octonion_member_functions.individual_real_components R_component_5]``() const;
      double                             ``[link boost_octonions.octonions.octonion_member_functions.individual_real_components R_component_6]``() const;
      double                             ``[link boost_octonions.octonions.octonion_member_functions.individual_real_components R_component_7]``() const;
      double                             ``[link boost_octonions.octonions.octonion_member_functions.individual_real_components R_component_8]``() const;

      ::std::complex<double>             ``[link boost_octonions.octonions.octonion_member_functions.individual_complex_components C_component_1]``() const;
      ::std::complex<double>             ``[link boost_octonions.octonions.octonion_member_functions.individual_complex_components C_component_2]``() const;
      ::std::complex<double>             ``[link boost_octonions.octonions.octonion_member_functions.individual_complex_components C_component_3]``() const;
      ::std::complex<double>             ``[link boost_octonions.octonions.octonion_member_functions.individual_complex_components C_component_4]``() const;

      ::boost::math::quaternion<double>  ``[link boost_octonions.octonions.octonion_member_functions.individual_quaternion_components H_component_1]``() const;
      ::boost::math::quaternion<double>  ``[link boost_octonions.octonions.octonion_member_functions.individual_quaternion_components H_component_2]``() const;

      octonion<double> & ``[link boost_octonions.octonions.octonion_member_functions.assignment_operators operator =]`` (octonion<double> const  & a_affecter);
      template<typename X> 
      octonion<double> & ``[link boost_octonions.octonions.octonion_member_functions.assignment_operators operator =]`` (octonion<X> const  & a_affecter);
      octonion<double> & ``[link boost_octonions.octonions.octonion_member_functions.assignment_operators operator =]`` (double const  & a_affecter);
      octonion<double> & ``[link boost_octonions.octonions.octonion_member_functions.assignment_operators operator =]`` (::std::complex<double> const & a_affecter);