math-octonion.qbk

Boost provides free peer-reviewed portable C++ source libraries. We emphasize libraries that work

      octonion<double> & ``[link boost_octonions.octonions.octonion_member_functions.assignment_operators operator =]`` (::boost::math::quaternion<double> const & a_affecter);

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

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

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

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

[#boost_octonions.octonion_long_double]

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

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

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

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

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

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

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

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

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

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

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

   } } // namespaces
   
[endsect]

[section Octonion Member Typedefs]

[*value_type]

Template version:

   typedef T value_type;

Float specialization version:

   typedef float value_type;
   
Double specialization version:

   typedef double value_type;

Long double specialization version:

   typedef long double value_type;

These provide easy acces to the type the template is built upon.

[endsect]

[section Octonion Member Functions]

[h3 Constructors]

Template version:

   explicit  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  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  octonion(::boost::math::quaternion<T> const & q0, ::boost::math::quaternion<T> const & q1 = ::boost::math::quaternion<T>());
   template<typename X> 
   explicit octonion(octonion<X> const & a_recopier);

Float specialization version:

   explicit  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  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  octonion(::boost::math::quaternion<float> const & q0, ::boost::math::quaternion<float> const & q1 = ::boost::math::quaternion<float>());
   explicit  octonion(octonion<double> const & a_recopier); 
   explicit  octonion(octonion<long double> const & a_recopier);

Double specialization version:

   explicit  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  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  octonion(::boost::math::quaternion<double> const & q0, ::boost::math::quaternion<double> const & q1 = ::boost::math::quaternion<double>());
   explicit  octonion(octonion<float> const & a_recopier);
   explicit  octonion(octonion<long double> const & a_recopier);

Long double specialization version:

   explicit  octonion(long double const & requested_a = 0.0L, long double const & requested_b = 0.0L, long double const & requested_c = 0.0L, long double const & requested_d = 0.0L, long double const & requested_e = 0.0L, long double const & requested_f = 0.0L, long double const & requested_g = 0.0L, long double const & requested_h = 0.0L);
   explicit  octonion( ::std::complex<long double> const & z0, ::std::complex<long double> const & z1 = ::std::complex<long double>(), ::std::complex<long double> const & z2 = ::std::complex<long double>(), ::std::complex<long double> const & z3 = ::std::complex<long double>());
   explicit  octonion(::boost::math::quaternion<long double> const & q0, ::boost::math::quaternion<long double> const & q1 = ::boost::math::quaternion<long double>());
   explicit  octonion(octonion<float> const & a_recopier);
   explicit  octonion(octonion<double> const & a_recopier);

A default constructor is provided for each form, which initializes each component 
to the default values for their type (i.e. zero for floating numbers). 
This constructor can also accept one to eight base type arguments. 
A constructor is also provided to build octonions from one to four complex numbers 
sharing the same base type, and another taking one or two quaternions
sharing the same base type. The unspecialized template also sports a 
templarized copy constructor, while the specialized forms have copy 
constructors from the other two specializations, which are explicit 
when a risk of precision loss exists. For the unspecialized form, 
the base type's constructors must not throw.

Destructors and untemplated copy constructors (from the same type) 
are provided by the compiler. Converting copy constructors make use 
of a templated helper function in a "detail" subnamespace.

[h3 Other member functions]

[h4 Real and Unreal Parts]

   T            real()   const;
   octonion<T>  unreal() const;