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  26 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
  27 <a name="math_toolkit.value_op"></a><a class="link" href="value_op.html" title="Quaternion Value Operations">Quaternion Value Operations</a>
  28 </h2></div></div></div>
  29 <h5>
  30 <a name="math_toolkit.value_op.h0"></a>
  31       <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
  32       and unreal</a>
  33     </h5>
  34 <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">quaternion</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">q</span><span class="special">);</span>
  35 <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">quaternion</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">quaternion</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">q</span><span class="special">);</span>
  36 </pre>
  37 <p>
  38       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
  39       <code class="computeroutput"><span class="identifier">q</span><span class="special">.</span><span class="identifier">unreal</span><span class="special">()</span></code>
  40       respectively.
  41     </p>
  42 <h5>
  43 <a name="math_toolkit.value_op.h1"></a>
  44       <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>
  45     </h5>
  46 <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">quaternion</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">quaternion</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">q</span><span class="special">);</span>
  47 </pre>
  48 <p>
  49       This returns the conjugate of the quaternion.
  50     </p>
  51 <h5>
  52 <a name="math_toolkit.value_op.h2"></a>
  53       <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>
  54     </h5>
  55 <p>
  56       template&lt;typename T&gt; T sup(quaternion&lt;T&gt; const &amp; q);
  57     </p>
  58 <p>
  59       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.
  60     </p>
  61 <h5>
  62 <a name="math_toolkit.value_op.h3"></a>
  63       <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>
  64     </h5>
  65 <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">quaternion</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">q</span><span class="special">);</span>
  66 </pre>
  67 <p>
  68       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.
  69     </p>
  70 <h5>
  71 <a name="math_toolkit.value_op.h4"></a>
  72       <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>
  73     </h5>
  74 <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">quaternion</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">q</span><span class="special">);</span>
  75 </pre>
  76 <p>
  77       This return the magnitude (Euclidian norm) of the quaternion.
  78     </p>
  79 <h5>
  80 <a name="math_toolkit.value_op.h5"></a>
  81       <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>
  82     </h5>
  83 <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">quaternion</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">q</span><span class="special">);</span>
  84 </pre>
  85 <p>
  86       This return the (Cayley) norm of the quaternion. The term "norm"
  87       might be confusing, as most people associate it with the Euclidian norm (and
  88       quadratic functionals). For this version of (the mathematical objects known
  89       as) quaternions, the Euclidian norm (also known as magnitude) is the square
  90       root of the Cayley norm.
  91     </p>
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