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Octonion Value Operations

Real and Unreal
template<typename T> T  real(octonion<T> const & o);
template<typename T> octonion<T> unreal(octonion<T> const & o);

These return o.real() and o.unreal() respectively.

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

This returns the conjugate of the octonion.

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

This return the sup norm (the greatest among abs(o.R_component_1())...abs(o.R_component_8())) of the octonion.

l1
template<typename T> T   l1(octonion<T> const & o);

This return the l1 norm (abs(o.R_component_1())+...+abs(o.R_component_8())) of the octonion.

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

This return the magnitude (Euclidian norm) of the octonion.

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

This return the (Cayley) norm of the octonion. The term "norm" might be confusing, as most people associate it with the Euclidian norm (and quadratic functionals). For this version of (the mathematical objects known as) octonions, the Euclidian norm (also known as magnitude) is the square root of the Cayley norm.


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