sp::UnitOctonions< T > Struct Template Reference

A container for the eight basis unit octonions. More...

#include <Complex.hpp>

Public Types
using	R = UnderlyingRealType< T >

Static Public Attributes
constexpr static Octonion< R >	one = {{{o, z}, {z, z}}, {{z, z}, {z, z}}}
constexpr static Octonion< R >	e1 = {{{z, o}, {z, z}}, {{z, z}, {z, z}}}
constexpr static Octonion< R >	e2 = {{{z, z}, {o, z}}, {{z, z}, {z, z}}}
constexpr static Octonion< R >	e4 = {{{z, z}, {z, o}}, {{z, z}, {z, z}}}
constexpr static Octonion< R >	e0 = {{{z, z}, {z, z}}, {{o, z}, {z, z}}}
constexpr static Octonion< R >	e3 = {{{z, z}, {z, z}}, {{z, -o}, {z, z}}}
constexpr static Octonion< R >	e6 = {{{z, z}, {z, z}}, {{z, z}, {-o, z}}}
constexpr static Octonion< R >	e5 = {{{z, z}, {z, z}}, {{z, z}, {z, -o}}}

Detailed Description

template<typename T>
struct sp::UnitOctonions< T >

A container for the eight basis unit octonions.

They can be accessed in the following manner:

auto one = sp::UnitOctonions<float>::one;
auto  e0 = sp::UnitOctonions<float>::e0;
auto  e1 = sp::UnitOctonions<float>::e1;
auto  e2 = sp::UnitOctonions<float>::e2;
auto  e3 = sp::UnitOctonions<float>::e3;
auto  e4 = sp::UnitOctonions<float>::e4;
auto  e5 = sp::UnitOctonions<float>::e5;
auto  e6 = sp::UnitOctonions<float>::e6;

These obey the multiplicative rules \( e_{i+1} e_{i+2} = e_{i+4} \) for all \( i \in \mathbb{Z} / 7 \mathbb{Z} \), where each rule is antisymmetric when the terms are permuted.