Boost C++ Libraries

...one of the most highly regarded and expertly designed C++ library projects in the world. Herb Sutter and Andrei Alexandrescu, C++ Coding Standards

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Octonion Non-Member Operators

Unary Plus and Minus Operators
template<typename T> octonion<T> operator + (octonion<T> const & o);

This unary operator simply returns o.

template<typename T> octonion<T> operator - (octonion<T> const & o);

This unary operator returns the opposite of o.

Binary Addition Operators
template<typename T> octonion<T> operator + (T const & lhs, octonion<T> const & rhs);
template<typename T> octonion<T> operator + (octonion<T> const & lhs, T const & rhs);
template<typename T> octonion<T> operator + (::std::complex<T> const & lhs, octonion<T> const & rhs);
template<typename T> octonion<T> operator + (octonion<T> const & lhs, ::std::complex<T> const & rhs);
template<typename T> octonion<T> operator + (::boost::math::quaternion<T> const & lhs, octonion<T> const & rhs);
template<typename T> octonion<T> operator + (octonion<T> const & lhs, ::boost::math::quaternion<T> const & rhs);
template<typename T> octonion<T> operator + (octonion<T> const & lhs, octonion<T> const & rhs);

These operators return octonion<T>(lhs) += rhs.

Binary Subtraction Operators
template<typename T> octonion<T> operator - (T const & lhs, octonion<T> const & rhs);
template<typename T> octonion<T> operator - (octonion<T> const & lhs, T const & rhs);
template<typename T> octonion<T> operator - (::std::complex<T> const & lhs, octonion<T> const & rhs);
template<typename T> octonion<T> operator - (octonion<T> const & lhs, ::std::complex<T> const & rhs);
template<typename T> octonion<T> operator - (::boost::math::quaternion<T> const & lhs, octonion<T> const & rhs);
template<typename T> octonion<T> operator - (octonion<T> const & lhs, ::boost::math::quaternion<T> const & rhs);
template<typename T> octonion<T> operator - (octonion<T> const & lhs, octonion<T> const & rhs);

These operators return octonion<T>(lhs) -= rhs.

Binary Multiplication Operators
template<typename T> octonion<T> operator * (T const & lhs, octonion<T> const & rhs);
template<typename T> octonion<T> operator * (octonion<T> const & lhs, T const & rhs);
template<typename T> octonion<T> operator * (::std::complex<T> const & lhs, octonion<T> const & rhs);
template<typename T> octonion<T> operator * (octonion<T> const & lhs, ::std::complex<T> const & rhs);
template<typename T> octonion<T> operator * (::boost::math::quaternion<T> const & lhs, octonion<T> const & rhs);
template<typename T> octonion<T> operator * (octonion<T> const & lhs, ::boost::math::quaternion<T> const & rhs);
template<typename T> octonion<T> operator * (octonion<T> const & lhs, octonion<T> const & rhs);

These operators return octonion<T>(lhs) *= rhs.

Binary Division Operators
template<typename T> octonion<T> operator / (T const & lhs, octonion<T> const & rhs);
template<typename T> octonion<T> operator / (octonion<T> const & lhs, T const & rhs);
template<typename T> octonion<T> operator / (::std::complex<T> const & lhs, octonion<T> const & rhs);
template<typename T> octonion<T> operator / (octonion<T> const & lhs, ::std::complex<T> const & rhs);
template<typename T> octonion<T> operator / (::boost::math::quaternion<T> const & lhs, octonion<T> const & rhs);
template<typename T> octonion<T> operator / (octonion<T> const & lhs, ::boost::math::quaternion<T> const & rhs);
template<typename T> octonion<T> operator / (octonion<T> const & lhs, octonion<T> const & rhs);

These operators return octonion<T>(lhs) /= rhs. It is of course still an error to divide by zero...

Binary Equality Operators
template<typename T> bool operator == (T const & lhs, octonion<T> const & rhs);
template<typename T> bool operator == (octonion<T> const & lhs, T const & rhs);
template<typename T> bool operator == (::std::complex<T> const & lhs, octonion<T> const & rhs);
template<typename T> bool operator == (octonion<T> const & lhs, ::std::complex<T> const & rhs);
template<typename T> bool operator == (::boost::math::quaternion<T> const & lhs, octonion<T> const & rhs);
template<typename T> bool operator == (octonion<T> const & lhs, ::boost::math::quaternion<T> const & rhs);
template<typename T> bool operator == (octonion<T> const & lhs, octonion<T> const & rhs);

These return true if and only if the four components of octonion<T>(lhs) are equal to their counterparts in octonion<T>(rhs). As with any floating-type entity, this is essentially meaningless.

Binary Inequality Operators
template<typename T> bool operator != (T const & lhs, octonion<T> const & rhs);
template<typename T> bool operator != (octonion<T> const & lhs, T const & rhs);
template<typename T> bool operator != (::std::complex<T> const & lhs, octonion<T> const & rhs);
template<typename T> bool operator != (octonion<T> const & lhs, ::std::complex<T> const & rhs);
template<typename T> bool operator != (::boost::math::quaternion<T> const & lhs, octonion<T> const & rhs);
template<typename T> bool operator != (octonion<T> const & lhs, ::boost::math::quaternion<T> const & rhs);
template<typename T> bool operator != (octonion<T> const & lhs, octonion<T> const & rhs);

These return true if and only if octonion<T>(lhs) == octonion<T>(rhs) is false. As with any floating-type entity, this is essentially meaningless.

Stream Extractor
template<typename T, typename charT, class traits>
::std::basic_istream<charT,traits> & operator >> (::std::basic_istream<charT,traits> & is, octonion<T> & o);

Extracts an octonion o. We accept any format which seems reasonable. However, since this leads to a great many ambiguities, decisions were made to lift these. In case of doubt, stick to lists of reals.

The input values must be convertible to T. If bad input is encountered, calls is.setstate(ios::failbit) (which may throw ios::failure (27.4.5.3)).

Returns is.

Stream Inserter
template<typename T, typename charT, class traits>
::std::basic_ostream<charT,traits> & operator << (::std::basic_ostream<charT,traits> & os, octonion<T> const & o);

Inserts the octonion o onto the stream os as if it were implemented as follows:

template<typename T, typename charT, class traits>
::std::basic_ostream<charT,traits> & operator << ( ::std::basic_ostream<charT,traits> & os,
octonion<T> const & o)
{
   ::std::basic_ostringstream<charT,traits> s;

   s.flags(os.flags());
   s.imbue(os.getloc());
   s.precision(os.precision());

   s << '(' << o.R_component_1() << ','
      << o.R_component_2() << ','
      << o.R_component_3() << ','
      << o.R_component_4() << ','
      << o.R_component_5() << ','
      << o.R_component_6() << ','
      << o.R_component_7() << ','
      << o.R_component_8() << ')';

   return os << s.str();
}

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