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<a name="boost_octonions.octonions.octonion_member_functions"></a><a class="link" href="octonion_member_functions.html" title="Octonion Member Functions">Octonion
Member Functions</a>
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<a name="boost_octonions.octonions.octonion_member_functions.constructors"></a><h4>
<a name="id782528"></a>
<a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.constructors">Constructors</a>
</h4>
<p>
Template version:
</p>
<pre class="programlisting"><span class="keyword">explicit</span> <span class="identifier">octonion</span><span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_a</span> <span class="special">=</span> <span class="identifier">T</span><span class="special">(),</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_b</span> <span class="special">=</span> <span class="identifier">T</span><span class="special">(),</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_c</span> <span class="special">=</span> <span class="identifier">T</span><span class="special">(),</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_d</span> <span class="special">=</span> <span class="identifier">T</span><span class="special">(),</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_e</span> <span class="special">=</span> <span class="identifier">T</span><span class="special">(),</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_f</span> <span class="special">=</span> <span class="identifier">T</span><span class="special">(),</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_g</span> <span class="special">=</span> <span class="identifier">T</span><span class="special">(),</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_h</span> <span class="special">=</span> <span class="identifier">T</span><span class="special">());</span>
<span class="keyword">explicit</span> <span class="identifier">octonion</span><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</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">z0</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"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">z1</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"><</span><span class="identifier">T</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"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">z2</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"><</span><span class="identifier">T</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"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">z3</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"><</span><span class="identifier">T</span><span class="special">>());</span>
<span class="keyword">explicit</span> <span class="identifier">octonion</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"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">q0</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"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">q1</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"><</span><span class="identifier">T</span><span class="special">>());</span>
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span>
<span class="keyword">explicit</span> <span class="identifier">octonion</span><span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">X</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_recopier</span><span class="special">);</span>
</pre>
<p>
Float specialization version:
</p>
<pre class="programlisting"><span class="keyword">explicit</span> <span class="identifier">octonion</span><span class="special">(</span><span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_a</span> <span class="special">=</span> <span class="number">0.0f</span><span class="special">,</span> <span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_b</span> <span class="special">=</span> <span class="number">0.0f</span><span class="special">,</span> <span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_c</span> <span class="special">=</span> <span class="number">0.0f</span><span class="special">,</span> <span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_d</span> <span class="special">=</span> <span class="number">0.0f</span><span class="special">,</span> <span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_e</span> <span class="special">=</span> <span class="number">0.0f</span><span class="special">,</span> <span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_f</span> <span class="special">=</span> <span class="number">0.0f</span><span class="special">,</span> <span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_g</span> <span class="special">=</span> <span class="number">0.0f</span><span class="special">,</span> <span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_h</span> <span class="special">=</span> <span class="number">0.0f</span><span class="special">);</span>
<span class="keyword">explicit</span> <span class="identifier">octonion</span><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">z0</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"><</span><span class="keyword">float</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">z1</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"><</span><span class="keyword">float</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"><</span><span class="keyword">float</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">z2</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"><</span><span class="keyword">float</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"><</span><span class="keyword">float</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">z3</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"><</span><span class="keyword">float</span><span class="special">>());</span>
<span class="keyword">explicit</span> <span class="identifier">octonion</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"><</span><span class="keyword">float</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">q0</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"><</span><span class="keyword">float</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">q1</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"><</span><span class="keyword">float</span><span class="special">>());</span>
<span class="keyword">explicit</span> <span class="identifier">octonion</span><span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_recopier</span><span class="special">);</span>
<span class="keyword">explicit</span> <span class="identifier">octonion</span><span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_recopier</span><span class="special">);</span>
</pre>
<p>
Double specialization version:
</p>
<pre class="programlisting"><span class="keyword">explicit</span> <span class="identifier">octonion</span><span class="special">(</span><span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_a</span> <span class="special">=</span> <span class="number">0.0</span><span class="special">,</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_b</span> <span class="special">=</span> <span class="number">0.0</span><span class="special">,</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_c</span> <span class="special">=</span> <span class="number">0.0</span><span class="special">,</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_d</span> <span class="special">=</span> <span class="number">0.0</span><span class="special">,</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_e</span> <span class="special">=</span> <span class="number">0.0</span><span class="special">,</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_f</span> <span class="special">=</span> <span class="number">0.0</span><span class="special">,</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_g</span> <span class="special">=</span> <span class="number">0.0</span><span class="special">,</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_h</span> <span class="special">=</span> <span class="number">0.0</span><span class="special">);</span>
<span class="keyword">explicit</span> <span class="identifier">octonion</span><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">z0</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"><</span><span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">z1</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"><</span><span class="keyword">double</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"><</span><span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">z2</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"><</span><span class="keyword">double</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"><</span><span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">z3</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"><</span><span class="keyword">double</span><span class="special">>());</span>
<span class="keyword">explicit</span> <span class="identifier">octonion</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"><</span><span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">q0</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"><</span><span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">q1</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"><</span><span class="keyword">double</span><span class="special">>());</span>
<span class="keyword">explicit</span> <span class="identifier">octonion</span><span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_recopier</span><span class="special">);</span>
<span class="keyword">explicit</span> <span class="identifier">octonion</span><span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_recopier</span><span class="special">);</span>
</pre>
<p>
Long double specialization version:
</p>
<pre class="programlisting"><span class="keyword">explicit</span> <span class="identifier">octonion</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_a</span> <span class="special">=</span> <span class="number">0.0L</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_b</span> <span class="special">=</span> <span class="number">0.0L</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_c</span> <span class="special">=</span> <span class="number">0.0L</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_d</span> <span class="special">=</span> <span class="number">0.0L</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_e</span> <span class="special">=</span> <span class="number">0.0L</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_f</span> <span class="special">=</span> <span class="number">0.0L</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_g</span> <span class="special">=</span> <span class="number">0.0L</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">requested_h</span> <span class="special">=</span> <span class="number">0.0L</span><span class="special">);</span>
<span class="keyword">explicit</span> <span class="identifier">octonion</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"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">z0</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"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">z1</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"><</span><span class="keyword">long</span> <span class="keyword">double</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"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">z2</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"><</span><span class="keyword">long</span> <span class="keyword">double</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"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">z3</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"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">>());</span>
<span class="keyword">explicit</span> <span class="identifier">octonion</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"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">q0</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"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">q1</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"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">>());</span>
<span class="keyword">explicit</span> <span class="identifier">octonion</span><span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_recopier</span><span class="special">);</span>
<span class="keyword">explicit</span> <span class="identifier">octonion</span><span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_recopier</span><span class="special">);</span>
</pre>
<p>
A default constructor is provided for each form, which initializes each component
to the default values for their type (i.e. zero for floating numbers). This
constructor can also accept one to eight base type arguments. A constructor
is also provided to build octonions from one to four complex numbers sharing
the same base type, and another taking one or two quaternions sharing the
same base type. The unspecialized template also sports a templarized copy
constructor, while the specialized forms have copy constructors from the
other two specializations, which are explicit when a risk of precision loss
exists. For the unspecialized form, the base type's constructors must not
throw.
</p>
<p>
Destructors and untemplated copy constructors (from the same type) are provided
by the compiler. Converting copy constructors make use of a templated helper
function in a "detail" subnamespace.
</p>
<a name="boost_octonions.octonions.octonion_member_functions.other_member_functions"></a><h4>
<a name="id786632"></a>
<a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_functions">Other
member functions</a>
</h4>
<a name="boost_octonions.octonions.octonion_member_functions.real_and_unreal_parts"></a><h5>
<a name="id786654"></a>
<a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.real_and_unreal_parts">Real
and Unreal Parts</a>
</h5>
<pre class="programlisting"><span class="identifier">T</span> <span class="identifier">real</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="identifier">octonion</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="keyword">const</span><span class="special">;</span>
</pre>
<p>
Like complex number, octonions do have a meaningful notion of "real
part", but unlike them there is no meaningful notion of "imaginary
part". Instead there is an "unreal part" which itself is a
octonion, and usually nothing simpler (as opposed to the complex number case).
These are returned by the first two functions.
</p>
<a name="boost_octonions.octonions.octonion_member_functions.individual_real_components"></a><h5>
<a name="id786755"></a>
<a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">Individual
Real Components</a>
</h5>
<pre class="programlisting"><span class="identifier">T</span> <span class="identifier">R_component_1</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="identifier">T</span> <span class="identifier">R_component_2</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="identifier">T</span> <span class="identifier">R_component_3</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="identifier">T</span> <span class="identifier">R_component_4</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="identifier">T</span> <span class="identifier">R_component_5</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="identifier">T</span> <span class="identifier">R_component_6</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="identifier">T</span> <span class="identifier">R_component_7</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="identifier">T</span> <span class="identifier">R_component_8</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
</pre>
<p>
A octonion having eight real components, these are returned by these eight
functions. Hence real and R_component_1 return the same value.
</p>
<a name="boost_octonions.octonions.octonion_member_functions.individual_complex_components"></a><h5>
<a name="id786990"></a>
<a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_complex_components">Individual
Complex Components</a>
</h5>
<pre class="programlisting"><span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="identifier">C_component_1</span><span class="special">()</span> <span class="keyword">const</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"><</span><span class="identifier">T</span><span class="special">></span> <span class="identifier">C_component_2</span><span class="special">()</span> <span class="keyword">const</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"><</span><span class="identifier">T</span><span class="special">></span> <span class="identifier">C_component_3</span><span class="special">()</span> <span class="keyword">const</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"><</span><span class="identifier">T</span><span class="special">></span> <span class="identifier">C_component_4</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
</pre>
<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 = 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
the basis <span class="emphasis"><em><code class="literal">(1, j, e', j')</code></em></span>.
</p>
<a name="boost_octonions.octonions.octonion_member_functions.individual_quaternion_components"></a><h5>
<a name="id787271"></a>
<a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_quaternion_components">Individual
Quaternion Components</a>
</h5>
<pre class="programlisting"><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"><</span><span class="identifier">T</span><span class="special">></span> <span class="identifier">H_component_1</span><span class="special">()</span> <span class="keyword">const</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"><</span><span class="identifier">T</span><span class="special">></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 = 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.
</p>
<a name="boost_octonions.octonions.octonion_member_functions.octonion_member_operators"></a><h4>
<a name="id787445"></a>
<a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.octonion_member_operators">Octonion
Member Operators</a>
</h4>
<a name="boost_octonions.octonions.octonion_member_functions.assignment_operators"></a><h5>
<a name="id787468"></a>
<a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.assignment_operators">Assignment
Operators</a>
</h5>
<pre class="programlisting"><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <span class="keyword">operator</span> <span class="special">=</span> <span class="special">(</span><span class="identifier">octonion</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">a_affecter</span><span class="special">);</span>
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span>
<span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <span class="keyword">operator</span> <span class="special">=</span> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">X</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_affecter</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</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">&</span> <span class="identifier">a_affecter</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</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"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_affecter</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</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"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_affecter</span><span class="special">);</span>
</pre>
<p>
These perform the expected assignment, with type modification if necessary
(for instance, assigning from a base type will set the real part to that
value, and all other components to zero). For the unspecialized form, the
base type's assignment operators must not throw.
</p>
<a name="boost_octonions.octonions.octonion_member_functions.other_member_operators"></a><h5>
<a name="id787939"></a>
<a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">Other
Member Operators</a>
</h5>
<pre class="programlisting"><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</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">&</span> <span class="identifier">rhs</span><span class="special">)</span>
<span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</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"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</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"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span>
<span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <span class="keyword">operator</span> <span class="special">+=</span> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">X</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
</pre>
<p>
These perform the mathematical operation <code class="computeroutput"><span class="special">(*</span><span class="keyword">this</span><span class="special">)+</span><span class="identifier">rhs</span></code>
and store the result in <code class="computeroutput"><span class="special">*</span><span class="keyword">this</span></code>.
The unspecialized form has exception guards, which the specialized forms
do not, so as to insure exception safety. For the unspecialized form, the
base type's assignment operators must not throw.
</p>
<pre class="programlisting"><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</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">&</span> <span class="identifier">rhs</span><span class="special">)</span>
<span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</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"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</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"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span>
<span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <span class="keyword">operator</span> <span class="special">-=</span> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">X</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
</pre>
<p>
These perform the mathematical operation <code class="computeroutput"><span class="special">(*</span><span class="keyword">this</span><span class="special">)-</span><span class="identifier">rhs</span></code>
and store the result in <code class="computeroutput"><span class="special">*</span><span class="keyword">this</span></code>.
The unspecialized form has exception guards, which the specialized forms
do not, so as to insure exception safety. For the unspecialized form, the
base type's assignment operators must not throw.
</p>
<pre class="programlisting"><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</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">&</span> <span class="identifier">rhs</span><span class="special">)</span>
<span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</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"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</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"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span>
<span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <span class="keyword">operator</span> <span class="special">*=</span> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">X</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
</pre>
<p>
These perform the mathematical operation <code class="computeroutput"><span class="special">(*</span><span class="keyword">this</span><span class="special">)*</span><span class="identifier">rhs</span></code>
in this order (order is important as multiplication is not commutative for
octonions) and store the result in <code class="computeroutput"><span class="special">*</span><span class="keyword">this</span></code>. The unspecialized form has exception
guards, which the specialized forms do not, so as to insure exception safety.
For the unspecialized form, the base type's assignment operators must not
throw. Also, for clarity's sake, you should always group the factors in a
multiplication by groups of two, as the multiplication is not even associative
on the octonions (though there are of course cases where this does not matter,
it usually does).
</p>
<pre class="programlisting"><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</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">&</span> <span class="identifier">rhs</span><span class="special">)</span>
<span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</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"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</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"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span>
<span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <span class="keyword">operator</span> <span class="special">/=</span> <span class="special">(</span><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">X</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span>
</pre>
<p>
These perform the mathematical operation <code class="computeroutput"><span class="special">(*</span><span class="keyword">this</span><span class="special">)*</span><span class="identifier">inverse_of</span><span class="special">(</span><span class="identifier">rhs</span><span class="special">)</span></code>
in this order (order is important as multiplication is not commutative for
octonions) and store the result in <code class="computeroutput"><span class="special">*</span><span class="keyword">this</span></code>. The unspecialized form has exception
guards, which the specialized forms do not, so as to insure exception safety.
For the unspecialized form, the base type's assignment operators must not
throw. As for the multiplication, remember to group any two factors using
parenthesis.
</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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