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<title>Octonion Member Functions</title>
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@@ -133,8 +133,8 @@
<p>
A octonion likewise has four complex components. Actually, octonions are indeed
a (left) vector field over the complexes, but beware, as for any octonion
<span class="emphasis"><em><code class="literal">o = &#945; + &#946;i + &#947;j + &#948;k + &#949;e' + &#950;i' + &#951;j' + &#952;k'</code></em></span> we also have <span class="emphasis"><em><code class="literal">o
= (&#945; + &#946;i) + (&#947; + &#948;i)j + (&#949; + &#950;i)e' + (&#951; - &#952;i)j'</code></em></span> (note the <span class="bold"><strong>minus</strong></span> sign
<span class="emphasis"><em><code class="literal">o = α + βi + γj + δk + εe' + ζi' + ηj' + θk'</code></em></span> we also have <span class="emphasis"><em><code class="literal">o
= (α + βi) + (γ + δi)j + (ε + ζi)e' + (η - θi)j'</code></em></span> (note the <span class="bold"><strong>minus</strong></span> sign
in the last factor). What the C_component_n functions return, however, are
the complexes which could be used to build the octonion using the constructor,
and <span class="bold"><strong>not</strong></span> the components of the octonion on
@@ -149,8 +149,8 @@
<span class="special">::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">H_component_2</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
</pre>
<p>
Likewise, for any octonion <span class="emphasis"><em><code class="literal">o = &#945; + &#946;i + &#947;j + &#948;k + &#949;e' + &#950;i' + &#951;j' + &#952;k'</code></em></span> we
also have <span class="emphasis"><em><code class="literal">o = (&#945; + &#946;i + &#947;j + &#948;k) + (&#949; + &#950;i + &#951;j - &#952;j)e'</code></em></span>, though there is no
Likewise, for any octonion <span class="emphasis"><em><code class="literal">o = α + βi + γj + δk + εe' + ζi' + ηj' + θk'</code></em></span> we
also have <span class="emphasis"><em><code class="literal">o = (α + βi + γj + δk) + (ε + ζi + ηj - θj)e'</code></em></span>, though there is no
meaningful vector-space-like structure based on the quaternions. What the H_component_n
functions return are the quaternions which could be used to build the octonion
using the constructor.
@@ -242,11 +242,11 @@
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
and Xiaogang Zhang<p>
<td align="right"><div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno
Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
Walker and Xiaogang Zhang<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
</p>