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<title>Octonion Value Operations</title>
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<div class="titlepage"><div><div><h3 class="title">
<a name="boost_octonions.octonions.octonion_value_operations"></a><a class="link" href="octonion_value_operations.html" title="Octonion Value Operations">Octonion
      Value Operations</a>
</h3></div></div></div>
<a name="boost_octonions.octonions.octonion_value_operations.real_and_unreal"></a><h5>
<a name="id2673069"></a>
        <a class="link" href="octonion_value_operations.html#boost_octonions.octonions.octonion_value_operations.real_and_unreal">Real
        and Unreal</a>
      </h5>
<pre class="programlisting">
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">T</span>  <span class="identifier">real</span><span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">o</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">unreal</span><span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">o</span><span class="special">);</span>
</pre>
<p>
        These return <code class="computeroutput"><span class="identifier">o</span><span class="special">.</span><span class="identifier">real</span><span class="special">()</span></code>
        and <code class="computeroutput"><span class="identifier">o</span><span class="special">.</span><span class="identifier">unreal</span><span class="special">()</span></code>
        respectively.
      </p>
<a name="boost_octonions.octonions.octonion_value_operations.conj"></a><h5>
<a name="id2673325"></a>
        <a class="link" href="octonion_value_operations.html#boost_octonions.octonions.octonion_value_operations.conj">conj</a>
      </h5>
<pre class="programlisting">
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">conj</span><span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">o</span><span class="special">);</span>
</pre>
<p>
        This returns the conjugate of the octonion.
      </p>
<a name="boost_octonions.octonions.octonion_value_operations.sup"></a><h5>
<a name="id2673451"></a>
        <a class="link" href="octonion_value_operations.html#boost_octonions.octonions.octonion_value_operations.sup">sup</a>
      </h5>
<pre class="programlisting">
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">T</span>   <span class="identifier">sup</span><span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">o</span><span class="special">);</span>
</pre>
<p>
        This return the sup norm (the greatest among <code class="computeroutput"><span class="identifier">abs</span><span class="special">(</span><span class="identifier">o</span><span class="special">.</span><span class="identifier">R_component_1</span><span class="special">())...</span><span class="identifier">abs</span><span class="special">(</span><span class="identifier">o</span><span class="special">.</span><span class="identifier">R_component_8</span><span class="special">()))</span></code> of the octonion.
      </p>
<a name="boost_octonions.octonions.octonion_value_operations.l1"></a><h5>
<a name="id2673624"></a>
        <a class="link" href="octonion_value_operations.html#boost_octonions.octonions.octonion_value_operations.l1">l1</a>
      </h5>
<pre class="programlisting">
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">T</span>   <span class="identifier">l1</span><span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">o</span><span class="special">);</span>
</pre>
<p>
        This return the l1 norm (<code class="computeroutput"><span class="identifier">abs</span><span class="special">(</span><span class="identifier">o</span><span class="special">.</span><span class="identifier">R_component_1</span><span class="special">())+...+</span><span class="identifier">abs</span><span class="special">(</span><span class="identifier">o</span><span class="special">.</span><span class="identifier">R_component_8</span><span class="special">())</span></code>) of the octonion.
      </p>
<a name="boost_octonions.octonions.octonion_value_operations.abs"></a><h5>
<a name="id2673795"></a>
        <a class="link" href="octonion_value_operations.html#boost_octonions.octonions.octonion_value_operations.abs">abs</a>
      </h5>
<pre class="programlisting">
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">T</span>   <span class="identifier">abs</span><span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">o</span><span class="special">);</span>
</pre>
<p>
        This return the magnitude (Euclidian norm) of the octonion.
      </p>
<a name="boost_octonions.octonions.octonion_value_operations.norm"></a><h5>
<a name="id2673908"></a>
        <a class="link" href="octonion_value_operations.html#boost_octonions.octonions.octonion_value_operations.norm">norm</a>
      </h5>
<pre class="programlisting">
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">T</span>  <span class="identifier">norm</span><span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span><span class="keyword">const</span>  <span class="special">&amp;</span> <span class="identifier">o</span><span class="special">);</span>
</pre>
<p>
        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.
      </p>
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<td align="right"><div class="copyright-footer">Copyright  2001 -2003 Hubert Holin<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>)
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