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boost::math::octonion< T > Singleton Reference

#include <math_fwd.hpp>

Collaboration diagram for boost::math::octonion< T >:
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Public Types

typedef T value_type
 

Public Member Functions

 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())
 
 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 >())
 
 octonion (::boost::math::quaternion< T > const &q0,::boost::math::quaternion< T > const &q1=::boost::math::quaternion< T >())
 
template<typename X >
 octonion (octonion< X > const &a_recopier)
 
T real () const
 
octonion< T > unreal () const
 
T R_component_1 () const
 
T R_component_2 () const
 
T R_component_3 () const
 
T R_component_4 () const
 
T R_component_5 () const
 
T R_component_6 () const
 
T R_component_7 () const
 
T R_component_8 () const
 
::std::complex< T > C_component_1 () const
 
::std::complex< T > C_component_2 () const
 
::std::complex< T > C_component_3 () const
 
::std::complex< T > C_component_4 () const
 
::boost::math::quaternion< T > H_component_1 () const
 
::boost::math::quaternion< T > H_component_2 () const
 
template<typename X >
octonion< T > & operator= (octonion< X > const &a_affecter)
 
octonion< T > & operator= (octonion< T > const &a_affecter)
 
octonion< T > & operator= (T const &a_affecter)
 
octonion< T > & operator= (::std::complex< T > const &a_affecter)
 
octonion< T > & operator= (::boost::math::quaternion< T > const &a_affecter)
 
octonion< T > & operator+= (T const &rhs)
 
octonion< T > & operator+= (::std::complex< T > const &rhs)
 
octonion< T > & operator+= (::boost::math::quaternion< T > const &rhs)
 
template<typename X >
octonion< T > & operator+= (octonion< X > const &rhs)
 
octonion< T > & operator-= (T const &rhs)
 
octonion< T > & operator-= (::std::complex< T > const &rhs)
 
octonion< T > & operator-= (::boost::math::quaternion< T > const &rhs)
 
template<typename X >
octonion< T > & operator-= (octonion< X > const &rhs)
 
octonion< T > & operator*= (T const &rhs)
 
octonion< T > & operator*= (::std::complex< T > const &rhs)
 
octonion< T > & operator*= (::boost::math::quaternion< T > const &rhs)
 
template<typename X >
octonion< T > & operator*= (octonion< X > const &rhs)
 
octonion< T > & operator/= (T const &rhs)
 
octonion< T > & operator/= (::std::complex< T > const &rhs)
 
octonion< T > & operator/= (::boost::math::quaternion< T > const &rhs)
 
template<typename X >
octonion< T > & operator/= (octonion< X > const &rhs)
 

Protected Attributes

T a
 
T b
 
T c
 
T d
 
T e
 
T f
 
T g
 
T h
 

Member Typedef Documentation

template<typename T>
typedef T boost::math::octonion< T >::value_type

Constructor & Destructor Documentation

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

Member Function Documentation

template<typename T>
::std::complex< T > boost::math::octonion< T >::C_component_1 ( ) const
inline
template<typename T>
::std::complex< T > boost::math::octonion< T >::C_component_2 ( ) const
inline
template<typename T>
::std::complex< T > boost::math::octonion< T >::C_component_3 ( ) const
inline
template<typename T>
::std::complex< T > boost::math::octonion< T >::C_component_4 ( ) const
inline
template<typename T>
::boost::math::quaternion< T > boost::math::octonion< T >::H_component_1 ( ) const
inline
template<typename T>
::boost::math::quaternion< T > boost::math::octonion< T >::H_component_2 ( ) const
inline
template<typename T>
octonion<T>& boost::math::octonion< T >::operator*= ( T const &  rhs)
inline

References boost::math::octonion< T >::a, boost::xpressive::at, boost::math::octonion< T >::b, boost::math::octonion< T >::c, boost::math::octonion< T >::d, boost::math::octonion< T >::e, boost::math::octonion< T >::f, boost::math::octonion< T >::g, boost::tuples::detail::gt(), boost::math::octonion< T >::h, and T.

template<typename T>
octonion<T>& boost::math::octonion< T >::operator*= ( ::std::complex< T > const &  rhs)
inline

References boost::math::octonion< T >::a, boost::xpressive::at, boost::math::octonion< T >::b, boost::math::octonion< T >::c, boost::math::octonion< T >::d, boost::math::octonion< T >::e, boost::math::octonion< T >::f, boost::math::octonion< T >::g, boost::tuples::detail::gt(), boost::math::octonion< T >::h, and T.

template<typename T>
octonion<T>& boost::math::octonion< T >::operator*= ( ::boost::math::quaternion< T > const &  rhs)
inline

References boost::math::octonion< T >::a, boost::xpressive::at, boost::math::octonion< T >::b, boost::math::octonion< T >::c, boost::math::octonion< T >::d, boost::math::octonion< T >::e, boost::math::octonion< T >::f, boost::math::octonion< T >::g, boost::tuples::detail::gt(), boost::math::octonion< T >::h, boost::math::quaternion< T >::R_component_1(), boost::math::quaternion< T >::R_component_2(), and T.

template<typename T>
template<typename X >
octonion<T>& boost::math::octonion< T >::operator*= ( octonion< X > const &  rhs)
inline

References boost::math::octonion< T >::a, boost::xpressive::at, boost::math::octonion< T >::b, boost::math::octonion< T >::c, boost::math::octonion< T >::d, boost::math::octonion< T >::e, boost::math::octonion< T >::f, boost::math::octonion< T >::g, boost::numeric::ublas::blas_2::gr(), boost::tuples::detail::gt(), boost::math::octonion< T >::h, boost::numeric::ublas::blas_2::hr(), boost::math::octonion< T >::R_component_1(), boost::math::octonion< T >::R_component_2(), boost::math::octonion< T >::R_component_3(), boost::math::octonion< T >::R_component_4(), boost::math::octonion< T >::R_component_5(), boost::math::octonion< T >::R_component_6(), boost::math::octonion< T >::R_component_7(), boost::math::octonion< T >::R_component_8(), and T.

template<typename T>
octonion<T>& boost::math::octonion< T >::operator+= ( T const &  rhs)
inline

References boost::math::octonion< T >::a, boost::xpressive::at, and T.

template<typename T>
octonion<T>& boost::math::octonion< T >::operator+= ( ::std::complex< T > const &  rhs)
inline

References boost::math::octonion< T >::a, boost::xpressive::at, boost::math::octonion< T >::b, and T.

template<typename T>
octonion<T>& boost::math::octonion< T >::operator+= ( ::boost::math::quaternion< T > const &  rhs)
inline

References boost::math::octonion< T >::a, boost::xpressive::at, boost::math::octonion< T >::b, boost::math::octonion< T >::c, boost::math::octonion< T >::d, boost::math::quaternion< T >::R_component_1(), boost::math::quaternion< T >::R_component_2(), boost::math::quaternion< T >::R_component_3(), boost::math::quaternion< T >::R_component_4(), and T.

template<typename T>
template<typename X >
octonion<T>& boost::math::octonion< T >::operator+= ( octonion< X > const &  rhs)
inline

References boost::math::octonion< T >::a, boost::xpressive::at, boost::math::octonion< T >::b, boost::math::octonion< T >::c, boost::math::octonion< T >::d, boost::math::octonion< T >::e, boost::math::octonion< T >::f, boost::math::octonion< T >::g, boost::tuples::detail::gt(), boost::math::octonion< T >::h, boost::math::octonion< T >::R_component_1(), boost::math::octonion< T >::R_component_2(), boost::math::octonion< T >::R_component_3(), boost::math::octonion< T >::R_component_4(), boost::math::octonion< T >::R_component_5(), boost::math::octonion< T >::R_component_6(), boost::math::octonion< T >::R_component_7(), boost::math::octonion< T >::R_component_8(), and T.

template<typename T>
octonion<T>& boost::math::octonion< T >::operator-= ( T const &  rhs)
inline

References boost::math::octonion< T >::a, boost::xpressive::at, and T.

template<typename T>
octonion<T>& boost::math::octonion< T >::operator-= ( ::std::complex< T > const &  rhs)
inline

References boost::math::octonion< T >::a, boost::xpressive::at, boost::math::octonion< T >::b, and T.

template<typename T>
octonion<T>& boost::math::octonion< T >::operator-= ( ::boost::math::quaternion< T > const &  rhs)
inline

References boost::math::octonion< T >::a, boost::xpressive::at, boost::math::octonion< T >::b, boost::math::octonion< T >::c, boost::math::octonion< T >::d, boost::math::quaternion< T >::R_component_1(), boost::math::quaternion< T >::R_component_2(), boost::math::quaternion< T >::R_component_3(), boost::math::quaternion< T >::R_component_4(), and T.

template<typename T>
template<typename X >
octonion<T>& boost::math::octonion< T >::operator-= ( octonion< X > const &  rhs)
inline

References boost::math::octonion< T >::a, boost::xpressive::at, boost::math::octonion< T >::b, boost::math::octonion< T >::c, boost::math::octonion< T >::d, boost::math::octonion< T >::e, boost::math::octonion< T >::f, boost::math::octonion< T >::g, boost::tuples::detail::gt(), boost::math::octonion< T >::h, boost::math::octonion< T >::R_component_1(), boost::math::octonion< T >::R_component_2(), boost::math::octonion< T >::R_component_3(), boost::math::octonion< T >::R_component_4(), boost::math::octonion< T >::R_component_5(), boost::math::octonion< T >::R_component_6(), boost::math::octonion< T >::R_component_7(), boost::math::octonion< T >::R_component_8(), and T.

template<typename T>
octonion<T>& boost::math::octonion< T >::operator/= ( T const &  rhs)
inline

References boost::math::octonion< T >::a, boost::xpressive::at, boost::math::octonion< T >::b, boost::math::octonion< T >::c, boost::math::octonion< T >::d, boost::math::octonion< T >::e, boost::math::octonion< T >::f, boost::math::octonion< T >::g, boost::tuples::detail::gt(), boost::math::octonion< T >::h, and T.

template<typename T>
octonion<T>& boost::math::octonion< T >::operator/= ( ::std::complex< T > const &  rhs)
inline

References boost::math::octonion< T >::a, boost::xpressive::at, boost::math::octonion< T >::b, boost::math::octonion< T >::c, boost::math::octonion< T >::d, boost::denominator(), boost::math::octonion< T >::e, boost::math::octonion< T >::f, boost::math::octonion< T >::g, boost::tuples::detail::gt(), boost::math::octonion< T >::h, and T.

template<typename T>
octonion<T>& boost::math::octonion< T >::operator/= ( ::boost::math::quaternion< T > const &  rhs)
inline

References boost::math::octonion< T >::a, boost::xpressive::at, boost::math::octonion< T >::b, boost::math::octonion< T >::c, boost::math::octonion< T >::d, boost::denominator(), boost::math::octonion< T >::e, boost::math::octonion< T >::f, boost::math::octonion< T >::g, boost::tuples::detail::gt(), boost::math::octonion< T >::h, boost::math::quaternion< T >::R_component_1(), boost::math::quaternion< T >::R_component_2(), and T.

template<typename T>
template<typename X >
octonion<T>& boost::math::octonion< T >::operator/= ( octonion< X > const &  rhs)
inline

References boost::math::octonion< T >::a, boost::xpressive::at, boost::math::octonion< T >::b, boost::math::octonion< T >::c, boost::math::octonion< T >::d, boost::denominator(), boost::math::octonion< T >::e, boost::math::octonion< T >::f, boost::math::octonion< T >::g, boost::numeric::ublas::blas_2::gr(), boost::tuples::detail::gt(), boost::math::octonion< T >::h, boost::numeric::ublas::blas_2::hr(), boost::math::octonion< T >::R_component_1(), boost::math::octonion< T >::R_component_2(), boost::math::octonion< T >::R_component_3(), boost::math::octonion< T >::R_component_4(), boost::math::octonion< T >::R_component_5(), boost::math::octonion< T >::R_component_6(), boost::math::octonion< T >::R_component_7(), boost::math::octonion< T >::R_component_8(), and T.

template<typename T>
template<typename X >
octonion< T >& boost::math::octonion< T >::operator= ( octonion< X > const &  a_affecter)
inline
template<typename T>
octonion< T >& boost::math::octonion< T >::operator= ( T const &  a_affecter)
inline
template<typename T>
octonion< T >& boost::math::octonion< T >::operator= ( ::boost::math::quaternion< T > const &  a_affecter)
inline
template<typename T>
octonion< T >& boost::math::octonion< T >::operator= ( ::std::complex< T > const &  a_affecter)
inline
template<typename T>
octonion< T >& boost::math::octonion< T >::operator= ( octonion< T > const &  a_affecter)
inline
template<typename T>
T boost::math::octonion< T >::R_component_1 ( ) const
inline

Referenced by boost::math::conj(), boost::math::detail::octonion_type_converter(), boost::math::octonion< T >::operator*=(), boost::math::octonion< T >::operator+=(), boost::math::operator-(), boost::math::octonion< T >::operator-=(), boost::math::octonion< T >::operator/=(), and boost::math::operator==().

template<typename T>
T boost::math::octonion< T >::R_component_2 ( ) const
inline

Referenced by boost::math::conj(), boost::math::cos(), boost::math::exp(), boost::math::detail::octonion_type_converter(), boost::math::octonion< T >::operator*=(), boost::math::octonion< T >::operator+=(), boost::math::operator-(), boost::math::octonion< T >::operator-=(), boost::math::octonion< T >::operator/=(), boost::math::operator==(), and boost::math::sin().

template<typename T>
T boost::math::octonion< T >::R_component_3 ( ) const
inline

Referenced by boost::math::conj(), boost::math::cos(), boost::math::exp(), boost::math::detail::octonion_type_converter(), boost::math::octonion< T >::operator*=(), boost::math::octonion< T >::operator+=(), boost::math::operator-(), boost::math::octonion< T >::operator-=(), boost::math::octonion< T >::operator/=(), boost::math::operator==(), and boost::math::sin().

template<typename T>
T boost::math::octonion< T >::R_component_4 ( ) const
inline

Referenced by boost::math::conj(), boost::math::cos(), boost::math::exp(), boost::math::detail::octonion_type_converter(), boost::math::octonion< T >::operator*=(), boost::math::octonion< T >::operator+=(), boost::math::operator-(), boost::math::octonion< T >::operator-=(), boost::math::octonion< T >::operator/=(), boost::math::operator==(), and boost::math::sin().

template<typename T>
T boost::math::octonion< T >::R_component_5 ( ) const
inline

Referenced by boost::math::conj(), boost::math::cos(), boost::math::exp(), boost::math::detail::octonion_type_converter(), boost::math::octonion< T >::operator*=(), boost::math::octonion< T >::operator+=(), boost::math::operator-(), boost::math::octonion< T >::operator-=(), boost::math::octonion< T >::operator/=(), boost::math::operator==(), and boost::math::sin().

template<typename T>
T boost::math::octonion< T >::R_component_6 ( ) const
inline

Referenced by boost::math::conj(), boost::math::cos(), boost::math::exp(), boost::math::detail::octonion_type_converter(), boost::math::octonion< T >::operator*=(), boost::math::octonion< T >::operator+=(), boost::math::operator-(), boost::math::octonion< T >::operator-=(), boost::math::octonion< T >::operator/=(), boost::math::operator==(), and boost::math::sin().

template<typename T>
T boost::math::octonion< T >::R_component_7 ( ) const
inline

Referenced by boost::math::conj(), boost::math::cos(), boost::math::exp(), boost::math::detail::octonion_type_converter(), boost::math::octonion< T >::operator*=(), boost::math::octonion< T >::operator+=(), boost::math::operator-(), boost::math::octonion< T >::operator-=(), boost::math::octonion< T >::operator/=(), boost::math::operator==(), and boost::math::sin().

template<typename T>
T boost::math::octonion< T >::R_component_8 ( ) const
inline

Referenced by boost::math::conj(), boost::math::cos(), boost::math::exp(), boost::math::detail::octonion_type_converter(), boost::math::octonion< T >::operator*=(), boost::math::octonion< T >::operator+=(), boost::math::operator-(), boost::math::octonion< T >::operator-=(), boost::math::octonion< T >::operator/=(), boost::math::operator==(), and boost::math::sin().

template<typename T>
T boost::math::octonion< T >::real ( ) const
inline

Referenced by boost::math::cos(), boost::math::exp(), boost::math::norm(), boost::math::real(), and boost::math::sin().

template<typename T>
octonion< T > boost::math::octonion< T >::unreal ( ) const
inline

Referenced by boost::math::cos(), boost::math::exp(), boost::math::sin(), and boost::math::unreal().

Member Data Documentation

template<typename T>
T boost::math::octonion< T >::a
protected

Referenced by boost::math::cylindrical(), boost::math::multipolar(), boost::math::octonion< T >::operator*=(), boost::math::octonion< T >::operator+=(), boost::math::octonion< T >::operator-=(), boost::math::octonion< T >::operator/=(), boost::math::operator>>(), and boost::math::spherical().

template<typename T>
T boost::math::octonion< T >::b
protected

Referenced by boost::math::cylindrical(), boost::math::multipolar(), boost::math::octonion< T >::operator*=(), boost::math::octonion< T >::operator+=(), boost::math::octonion< T >::operator-=(), boost::math::octonion< T >::operator/=(), boost::math::operator>>(), and boost::math::spherical().

template<typename T>
T boost::math::octonion< T >::c
protected

Referenced by boost::math::multipolar(), boost::math::octonion< T >::operator*=(), boost::math::octonion< T >::operator+=(), boost::math::octonion< T >::operator-=(), boost::math::octonion< T >::operator/=(), boost::math::operator>>(), and boost::math::spherical().

template<typename T>
T boost::math::octonion< T >::d
protected

Referenced by boost::math::multipolar(), boost::math::octonion< T >::operator*=(), boost::math::octonion< T >::operator+=(), boost::math::octonion< T >::operator-=(), boost::math::octonion< T >::operator/=(), boost::math::operator>>(), and boost::math::spherical().

template<typename T>
T boost::math::octonion< T >::e
protected

Referenced by boost::math::multipolar(), boost::math::octonion< T >::operator*=(), boost::math::octonion< T >::operator+=(), boost::math::octonion< T >::operator-=(), boost::math::octonion< T >::operator/=(), boost::math::operator>>(), and boost::math::spherical().

template<typename T>
T boost::math::octonion< T >::f
protected

Referenced by boost::math::multipolar(), boost::math::octonion< T >::operator*=(), boost::math::octonion< T >::operator+=(), boost::math::octonion< T >::operator-=(), boost::math::octonion< T >::operator/=(), boost::math::operator>>(), and boost::math::spherical().

template<typename T>
T boost::math::octonion< T >::g
protected

Referenced by boost::math::multipolar(), boost::math::octonion< T >::operator*=(), boost::math::octonion< T >::operator+=(), boost::math::octonion< T >::operator-=(), boost::math::octonion< T >::operator/=(), boost::math::operator>>(), and boost::math::spherical().

template<typename T>
T boost::math::octonion< T >::h
protected

Referenced by boost::math::multipolar(), boost::math::octonion< T >::operator*=(), boost::math::octonion< T >::operator+=(), boost::math::octonion< T >::operator-=(), boost::math::octonion< T >::operator/=(), boost::math::operator>>(), and boost::math::spherical().

The documentation for this singleton was generated from the following file: