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  26 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
  27 <a name="math_toolkit.oct_non_mem"></a><a class="link" href="oct_non_mem.html" title="Octonion Non-Member Operators">Octonion Non-Member Operators</a>
  28 </h2></div></div></div>
  29 <h5>
  30 <a name="math_toolkit.oct_non_mem.h0"></a>
  31       <span class="phrase"><a name="math_toolkit.oct_non_mem.unary_plus_and_minus_operators"></a></span><a class="link" href="oct_non_mem.html#math_toolkit.oct_non_mem.unary_plus_and_minus_operators">Unary Plus
  32       and Minus Operators</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">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">operator</span> <span class="special">+</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>
  35 </pre>
  36 <p>
  37       This unary operator simply returns o.
  38     </p>
  39 <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="keyword">operator</span> <span class="special">-</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>
  40 </pre>
  41 <p>
  42       This unary operator returns the opposite of o.
  43     </p>
  44 <h5>
  45 <a name="math_toolkit.oct_non_mem.h1"></a>
  46       <span class="phrase"><a name="math_toolkit.oct_non_mem.binary_addition_operators"></a></span><a class="link" href="oct_non_mem.html#math_toolkit.oct_non_mem.binary_addition_operators">Binary
  47       Addition Operators</a>
  48     </h5>
  49 <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="keyword">operator</span> <span class="special">+</span> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</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">rhs</span><span class="special">);</span>
  50 <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="keyword">operator</span> <span class="special">+</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">lhs</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
  51 <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="keyword">operator</span> <span class="special">+</span> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</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">lhs</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">rhs</span><span class="special">);</span>
  52 <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="keyword">operator</span> <span class="special">+</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">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</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">rhs</span><span class="special">);</span>
  53 <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="keyword">operator</span> <span class="special">+</span> <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="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</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">rhs</span><span class="special">);</span>
  54 <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="keyword">operator</span> <span class="special">+</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">lhs</span><span class="special">,</span> <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="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
  55 <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="keyword">operator</span> <span class="special">+</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">lhs</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">rhs</span><span class="special">);</span>
  56 </pre>
  57 <p>
  58       These operators return <code class="computeroutput"><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;(</span><span class="identifier">lhs</span><span class="special">)</span> <span class="special">+=</span>
  59       <span class="identifier">rhs</span></code>.
  60     </p>
  61 <h5>
  62 <a name="math_toolkit.oct_non_mem.h2"></a>
  63       <span class="phrase"><a name="math_toolkit.oct_non_mem.binary_subtraction_operators"></a></span><a class="link" href="oct_non_mem.html#math_toolkit.oct_non_mem.binary_subtraction_operators">Binary
  64       Subtraction Operators</a>
  65     </h5>
  66 <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="keyword">operator</span> <span class="special">-</span> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</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">rhs</span><span class="special">);</span>
  67 <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="keyword">operator</span> <span class="special">-</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">lhs</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
  68 <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="keyword">operator</span> <span class="special">-</span> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</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">lhs</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">rhs</span><span class="special">);</span>
  69 <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="keyword">operator</span> <span class="special">-</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">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</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">rhs</span><span class="special">);</span>
  70 <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="keyword">operator</span> <span class="special">-</span> <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="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</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">rhs</span><span class="special">);</span>
  71 <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="keyword">operator</span> <span class="special">-</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">lhs</span><span class="special">,</span> <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="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
  72 <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="keyword">operator</span> <span class="special">-</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">lhs</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">rhs</span><span class="special">);</span>
  73 </pre>
  74 <p>
  75       These operators return <code class="computeroutput"><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;(</span><span class="identifier">lhs</span><span class="special">)</span> <span class="special">-=</span>
  76       <span class="identifier">rhs</span></code>.
  77     </p>
  78 <h5>
  79 <a name="math_toolkit.oct_non_mem.h3"></a>
  80       <span class="phrase"><a name="math_toolkit.oct_non_mem.binary_multiplication_operators"></a></span><a class="link" href="oct_non_mem.html#math_toolkit.oct_non_mem.binary_multiplication_operators">Binary Multiplication
  81       Operators</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">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">operator</span> <span class="special">*</span> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</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">rhs</span><span class="special">);</span>
  84 <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="keyword">operator</span> <span class="special">*</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">lhs</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
  85 <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="keyword">operator</span> <span class="special">*</span> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</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">lhs</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">rhs</span><span class="special">);</span>
  86 <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="keyword">operator</span> <span class="special">*</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">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</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">rhs</span><span class="special">);</span>
  87 <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="keyword">operator</span> <span class="special">*</span> <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="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</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">rhs</span><span class="special">);</span>
  88 <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="keyword">operator</span> <span class="special">*</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">lhs</span><span class="special">,</span> <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="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
  89 <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="keyword">operator</span> <span class="special">*</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">lhs</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">rhs</span><span class="special">);</span>
  90 </pre>
  91 <p>
  92       These operators return <code class="computeroutput"><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;(</span><span class="identifier">lhs</span><span class="special">)</span> <span class="special">*=</span>
  93       <span class="identifier">rhs</span></code>.
  94     </p>
  95 <h5>
  96 <a name="math_toolkit.oct_non_mem.h4"></a>
  97       <span class="phrase"><a name="math_toolkit.oct_non_mem.binary_division_operators"></a></span><a class="link" href="oct_non_mem.html#math_toolkit.oct_non_mem.binary_division_operators">Binary
  98       Division Operators</a>
  99     </h5>
 100 <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="keyword">operator</span> <span class="special">/</span> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</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">rhs</span><span class="special">);</span>
 101 <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="keyword">operator</span> <span class="special">/</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">lhs</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
 102 <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="keyword">operator</span> <span class="special">/</span> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</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">lhs</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">rhs</span><span class="special">);</span>
 103 <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="keyword">operator</span> <span class="special">/</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">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</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">rhs</span><span class="special">);</span>
 104 <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="keyword">operator</span> <span class="special">/</span> <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="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</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">rhs</span><span class="special">);</span>
 105 <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="keyword">operator</span> <span class="special">/</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">lhs</span><span class="special">,</span> <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="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
 106 <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="keyword">operator</span> <span class="special">/</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">lhs</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">rhs</span><span class="special">);</span>
 107 </pre>
 108 <p>
 109       These operators return <code class="computeroutput"><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;(</span><span class="identifier">lhs</span><span class="special">)</span> <span class="special">/=</span>
 110       <span class="identifier">rhs</span></code>. It is of course still an error
 111       to divide by zero...
 112     </p>
 113 <h5>
 114 <a name="math_toolkit.oct_non_mem.h5"></a>
 115       <span class="phrase"><a name="math_toolkit.oct_non_mem.binary_equality_operators"></a></span><a class="link" href="oct_non_mem.html#math_toolkit.oct_non_mem.binary_equality_operators">Binary
 116       Equality Operators</a>
 117     </h5>
 118 <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="keyword">bool</span> <span class="keyword">operator</span> <span class="special">==</span> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</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">rhs</span><span class="special">);</span>
 119 <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="keyword">bool</span> <span class="keyword">operator</span> <span class="special">==</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">lhs</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
 120 <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="keyword">bool</span> <span class="keyword">operator</span> <span class="special">==</span> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</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">lhs</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">rhs</span><span class="special">);</span>
 121 <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="keyword">bool</span> <span class="keyword">operator</span> <span class="special">==</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">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</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">rhs</span><span class="special">);</span>
 122 <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="keyword">bool</span> <span class="keyword">operator</span> <span class="special">==</span> <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="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</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">rhs</span><span class="special">);</span>
 123 <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="keyword">bool</span> <span class="keyword">operator</span> <span class="special">==</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">lhs</span><span class="special">,</span> <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="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
 124 <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="keyword">bool</span> <span class="keyword">operator</span> <span class="special">==</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">lhs</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">rhs</span><span class="special">);</span>
 125 </pre>
 126 <p>
 127       These return true if and only if the four components of <code class="computeroutput"><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;(</span><span class="identifier">lhs</span><span class="special">)</span></code> are
 128       equal to their counterparts in <code class="computeroutput"><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;(</span><span class="identifier">rhs</span><span class="special">)</span></code>. As
 129       with any floating-type entity, this is essentially meaningless.
 130     </p>
 131 <h5>
 132 <a name="math_toolkit.oct_non_mem.h6"></a>
 133       <span class="phrase"><a name="math_toolkit.oct_non_mem.binary_inequality_operators"></a></span><a class="link" href="oct_non_mem.html#math_toolkit.oct_non_mem.binary_inequality_operators">Binary
 134       Inequality Operators</a>
 135     </h5>
 136 <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="keyword">bool</span> <span class="keyword">operator</span> <span class="special">!=</span> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</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">rhs</span><span class="special">);</span>
 137 <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="keyword">bool</span> <span class="keyword">operator</span> <span class="special">!=</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">lhs</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
 138 <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="keyword">bool</span> <span class="keyword">operator</span> <span class="special">!=</span> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</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">lhs</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">rhs</span><span class="special">);</span>
 139 <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="keyword">bool</span> <span class="keyword">operator</span> <span class="special">!=</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">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</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">rhs</span><span class="special">);</span>
 140 <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="keyword">bool</span> <span class="keyword">operator</span> <span class="special">!=</span> <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="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</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">rhs</span><span class="special">);</span>
 141 <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="keyword">bool</span> <span class="keyword">operator</span> <span class="special">!=</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">lhs</span><span class="special">,</span> <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="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
 142 <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="keyword">bool</span> <span class="keyword">operator</span> <span class="special">!=</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">lhs</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">rhs</span><span class="special">);</span>
 143 </pre>
 144 <p>
 145       These return true if and only if <code class="computeroutput"><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;(</span><span class="identifier">lhs</span><span class="special">)</span> <span class="special">==</span>
 146       <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;(</span><span class="identifier">rhs</span><span class="special">)</span></code> is false. As with any floating-type entity,
 147       this is essentially meaningless.
 148     </p>
 149 <h5>
 150 <a name="math_toolkit.oct_non_mem.h7"></a>
 151       <span class="phrase"><a name="math_toolkit.oct_non_mem.stream_extractor"></a></span><a class="link" href="oct_non_mem.html#math_toolkit.oct_non_mem.stream_extractor">Stream
 152       Extractor</a>
 153     </h5>
 154 <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">,</span> <span class="keyword">typename</span> <span class="identifier">charT</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">traits</span><span class="special">&gt;</span>
 155 <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_istream</span><span class="special">&lt;</span><span class="identifier">charT</span><span class="special">,</span><span class="identifier">traits</span><span class="special">&gt;</span> <span class="special">&amp;</span> <span class="keyword">operator</span> <span class="special">&gt;&gt;</span> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_istream</span><span class="special">&lt;</span><span class="identifier">charT</span><span class="special">,</span><span class="identifier">traits</span><span class="special">&gt;</span> <span class="special">&amp;</span> <span class="identifier">is</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="special">&amp;</span> <span class="identifier">o</span><span class="special">);</span>
 156 </pre>
 157 <p>
 158       Extracts an octonion <code class="computeroutput"><span class="identifier">o</span></code>. We
 159       accept any format which seems reasonable. However, since this leads to a great
 160       many ambiguities, decisions were made to lift these. In case of doubt, stick
 161       to lists of reals.
 162     </p>
 163 <p>
 164       The input values must be convertible to T. If bad input is encountered, calls
 165       <code class="computeroutput"><span class="identifier">is</span><span class="special">.</span><span class="identifier">setstate</span><span class="special">(</span><span class="identifier">ios</span><span class="special">::</span><span class="identifier">failbit</span><span class="special">)</span></code> (which may throw <code class="computeroutput"><span class="identifier">ios</span><span class="special">::</span><span class="identifier">failure</span></code>
 166       (27.4.5.3)).
 167     </p>
 168 <p>
 169       Returns <code class="computeroutput"><span class="identifier">is</span></code>.
 170     </p>
 171 <h5>
 172 <a name="math_toolkit.oct_non_mem.h8"></a>
 173       <span class="phrase"><a name="math_toolkit.oct_non_mem.stream_inserter"></a></span><a class="link" href="oct_non_mem.html#math_toolkit.oct_non_mem.stream_inserter">Stream
 174       Inserter</a>
 175     </h5>
 176 <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">,</span> <span class="keyword">typename</span> <span class="identifier">charT</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">traits</span><span class="special">&gt;</span>
 177 <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_ostream</span><span class="special">&lt;</span><span class="identifier">charT</span><span class="special">,</span><span class="identifier">traits</span><span class="special">&gt;</span> <span class="special">&amp;</span> <span class="keyword">operator</span> <span class="special">&lt;&lt;</span> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_ostream</span><span class="special">&lt;</span><span class="identifier">charT</span><span class="special">,</span><span class="identifier">traits</span><span class="special">&gt;</span> <span class="special">&amp;</span> <span class="identifier">os</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>
 178 </pre>
 179 <p>
 180       Inserts the octonion <code class="computeroutput"><span class="identifier">o</span></code> onto
 181       the stream <code class="computeroutput"><span class="identifier">os</span></code> as if it were
 182       implemented as follows:
 183     </p>
 184 <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">,</span> <span class="keyword">typename</span> <span class="identifier">charT</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">traits</span><span class="special">&gt;</span>
 185 <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_ostream</span><span class="special">&lt;</span><span class="identifier">charT</span><span class="special">,</span><span class="identifier">traits</span><span class="special">&gt;</span> <span class="special">&amp;</span> <span class="keyword">operator</span> <span class="special">&lt;&lt;</span> <span class="special">(</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_ostream</span><span class="special">&lt;</span><span class="identifier">charT</span><span class="special">,</span><span class="identifier">traits</span><span class="special">&gt;</span> <span class="special">&amp;</span> <span class="identifier">os</span><span class="special">,</span>
 186 <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>
 187 <span class="special">{</span>
 188    <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_ostringstream</span><span class="special">&lt;</span><span class="identifier">charT</span><span class="special">,</span><span class="identifier">traits</span><span class="special">&gt;</span> <span class="identifier">s</span><span class="special">;</span>
 189
 190    <span class="identifier">s</span><span class="special">.</span><span class="identifier">flags</span><span class="special">(</span><span class="identifier">os</span><span class="special">.</span><span class="identifier">flags</span><span class="special">());</span>
 191    <span class="identifier">s</span><span class="special">.</span><span class="identifier">imbue</span><span class="special">(</span><span class="identifier">os</span><span class="special">.</span><span class="identifier">getloc</span><span class="special">());</span>
 192    <span class="identifier">s</span><span class="special">.</span><span class="identifier">precision</span><span class="special">(</span><span class="identifier">os</span><span class="special">.</span><span class="identifier">precision</span><span class="special">());</span>
 193
 194    <span class="identifier">s</span> <span class="special">&lt;&lt;</span> <span class="char">'('</span> <span class="special">&lt;&lt;</span> <span class="identifier">o</span><span class="special">.</span><span class="identifier">R_component_1</span><span class="special">()</span> <span class="special">&lt;&lt;</span> <span class="char">','</span>
 195       <span class="special">&lt;&lt;</span> <span class="identifier">o</span><span class="special">.</span><span class="identifier">R_component_2</span><span class="special">()</span> <span class="special">&lt;&lt;</span> <span class="char">','</span>
 196       <span class="special">&lt;&lt;</span> <span class="identifier">o</span><span class="special">.</span><span class="identifier">R_component_3</span><span class="special">()</span> <span class="special">&lt;&lt;</span> <span class="char">','</span>
 197       <span class="special">&lt;&lt;</span> <span class="identifier">o</span><span class="special">.</span><span class="identifier">R_component_4</span><span class="special">()</span> <span class="special">&lt;&lt;</span> <span class="char">','</span>
 198       <span class="special">&lt;&lt;</span> <span class="identifier">o</span><span class="special">.</span><span class="identifier">R_component_5</span><span class="special">()</span> <span class="special">&lt;&lt;</span> <span class="char">','</span>
 199       <span class="special">&lt;&lt;</span> <span class="identifier">o</span><span class="special">.</span><span class="identifier">R_component_6</span><span class="special">()</span> <span class="special">&lt;&lt;</span> <span class="char">','</span>
 200       <span class="special">&lt;&lt;</span> <span class="identifier">o</span><span class="special">.</span><span class="identifier">R_component_7</span><span class="special">()</span> <span class="special">&lt;&lt;</span> <span class="char">','</span>
 201       <span class="special">&lt;&lt;</span> <span class="identifier">o</span><span class="special">.</span><span class="identifier">R_component_8</span><span class="special">()</span> <span class="special">&lt;&lt;</span> <span class="char">')'</span><span class="special">;</span>
 202
 203    <span class="keyword">return</span> <span class="identifier">os</span> <span class="special">&lt;&lt;</span> <span class="identifier">s</span><span class="special">.</span><span class="identifier">str</span><span class="special">();</span>
 204 <span class="special">}</span>
 205 </pre>
 206 </div>
 207 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 208 <td align="left"></td>
 209 <td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
 210       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
 211       Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
 212       R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
 213       Daryle Walker and Xiaogang Zhang<p>
 214         Distributed under the Boost Software License, Version 1.0. (See accompanying
 215         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>)
 216       </p>
 217 </div></td>
 218 </tr></table>
 219 <hr>
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