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<div class="titlepage"><div><div><h2 class="title" style="clear: both">
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<a name="math_toolkit.value_op"></a><a class="link" href="value_op.html" title="Quaternion Value Operations">Quaternion Value Operations</a>
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</h2></div></div></div>
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<h5>
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<a name="math_toolkit.value_op.h0"></a>
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<span class="phrase"><a name="math_toolkit.value_op.real_and_unreal"></a></span><a class="link" href="value_op.html#math_toolkit.value_op.real_and_unreal">real
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and unreal</a>
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</h5>
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<pre class="programlisting"><span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">T</span> <span class="identifier">real</span><span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">q</span><span class="special">);</span>
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<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="identifier">unreal</span><span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">q</span><span class="special">);</span>
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</pre>
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<p>
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These return <code class="computeroutput"><span class="identifier">q</span><span class="special">.</span><span class="identifier">real</span><span class="special">()</span></code> and
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<code class="computeroutput"><span class="identifier">q</span><span class="special">.</span><span class="identifier">unreal</span><span class="special">()</span></code>
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respectively.
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</p>
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<h5>
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<a name="math_toolkit.value_op.h1"></a>
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<span class="phrase"><a name="math_toolkit.value_op.conj"></a></span><a class="link" href="value_op.html#math_toolkit.value_op.conj">conj</a>
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</h5>
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<pre class="programlisting"><span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="identifier">conj</span><span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">q</span><span class="special">);</span>
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</pre>
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<p>
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This returns the conjugate of the quaternion.
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</p>
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<h5>
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<a name="math_toolkit.value_op.h2"></a>
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<span class="phrase"><a name="math_toolkit.value_op.sup"></a></span><a class="link" href="value_op.html#math_toolkit.value_op.sup">sup</a>
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</h5>
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<p>
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template<typename T> T sup(quaternion<T> const & q);
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</p>
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<p>
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This return the sup norm (the greatest among <code class="computeroutput"><span class="identifier">abs</span><span class="special">(</span><span class="identifier">q</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">q</span><span class="special">.</span><span class="identifier">R_component_4</span><span class="special">()))</span></code> of the quaternion.
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</p>
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<h5>
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<a name="math_toolkit.value_op.h3"></a>
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<span class="phrase"><a name="math_toolkit.value_op.l1"></a></span><a class="link" href="value_op.html#math_toolkit.value_op.l1">l1</a>
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</h5>
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<pre class="programlisting"><span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">T</span> <span class="identifier">l1</span><span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">q</span><span class="special">);</span>
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</pre>
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<p>
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This return the l1 norm <code class="computeroutput"><span class="special">(</span><span class="identifier">abs</span><span class="special">(</span><span class="identifier">q</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">q</span><span class="special">.</span><span class="identifier">R_component_4</span><span class="special">()))</span></code> of the quaternion.
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</p>
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<h5>
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<a name="math_toolkit.value_op.h4"></a>
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<span class="phrase"><a name="math_toolkit.value_op.abs"></a></span><a class="link" href="value_op.html#math_toolkit.value_op.abs">abs</a>
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</h5>
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<pre class="programlisting"><span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">T</span> <span class="identifier">abs</span><span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">q</span><span class="special">);</span>
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</pre>
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<p>
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This return the magnitude (Euclidian norm) of the quaternion.
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</p>
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<h5>
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<a name="math_toolkit.value_op.h5"></a>
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<span class="phrase"><a name="math_toolkit.value_op.norm"></a></span><a class="link" href="value_op.html#math_toolkit.value_op.norm">norm</a>
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</h5>
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<pre class="programlisting"><span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">T</span> <span class="identifier">norm</span><span class="special">(</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span><span class="keyword">const</span> <span class="special">&</span> <span class="identifier">q</span><span class="special">);</span>
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</pre>
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<p>
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This return the (Cayley) norm of the quaternion. The term "norm"
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might be confusing, as most people associate it with the Euclidian norm (and
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quadratic functionals). For this version of (the mathematical objects known
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as) quaternions, the Euclidian norm (also known as magnitude) is the square
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root of the Cayley norm.
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</p>
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<td align="right"><div class="copyright-footer">Copyright © 2006-2019 Nikhar
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Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
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Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
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Råde, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
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Daryle Walker and Xiaogang Zhang<p>
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Distributed under the Boost Software License, Version 1.0. (See accompanying
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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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