Boost C++ Libraries

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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.

 Copyright © 2006-2010, 2012, 2013 Paul A. Bristow, Christopher Kormanyos, Hubert Holin, Bruno Lalande, John Maddock, Johan Råde, Gautam Sewani, Benjamin Sobotta, Thijs van den Berg, Daryle Walker and Xiaogang Zhang Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)