| <html> |
| <head> |
| <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> |
| <title>Octonion Member Functions</title> |
| <link rel="stylesheet" href="../math.css" type="text/css"> |
| <meta name="generator" content="DocBook XSL Stylesheets V1.77.1"> |
| <link rel="home" href="../index.html" title="Math Toolkit 2.2.0"> |
| <link rel="up" href="../octonions.html" title="Chapter 10. Octonions"> |
| <link rel="prev" href="oct_typedefs.html" title="Octonion Member Typedefs"> |
| <link rel="next" href="oct_non_mem.html" title="Octonion Non-Member Operators"> |
| </head> |
| <body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> |
| <table cellpadding="2" width="100%"><tr> |
| <td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td> |
| <td align="center"><a href="../../../../../index.html">Home</a></td> |
| <td align="center"><a href="../../../../../libs/libraries.htm">Libraries</a></td> |
| <td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> |
| <td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> |
| <td align="center"><a href="../../../../../more/index.htm">More</a></td> |
| </tr></table> |
| <hr> |
| <div class="spirit-nav"> |
| <a accesskey="p" href="oct_typedefs.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../octonions.html"><img src="../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="oct_non_mem.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a> |
| </div> |
| <div class="section"> |
| <div class="titlepage"><div><div><h2 class="title" style="clear: both"> |
| <a name="math_toolkit.oct_mem_fun"></a><a class="link" href="oct_mem_fun.html" title="Octonion Member Functions">Octonion Member Functions</a> |
| </h2></div></div></div> |
| <h4> |
| <a name="math_toolkit.oct_mem_fun.h0"></a> |
| <span class="phrase"><a name="math_toolkit.oct_mem_fun.constructors"></a></span><a class="link" href="oct_mem_fun.html#math_toolkit.oct_mem_fun.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> |
| <h4> |
| <a name="math_toolkit.oct_mem_fun.h1"></a> |
| <span class="phrase"><a name="math_toolkit.oct_mem_fun.other_member_functions"></a></span><a class="link" href="oct_mem_fun.html#math_toolkit.oct_mem_fun.other_member_functions">Other |
| member functions</a> |
| </h4> |
| <h5> |
| <a name="math_toolkit.oct_mem_fun.h2"></a> |
| <span class="phrase"><a name="math_toolkit.oct_mem_fun.real_and_unreal_parts"></a></span><a class="link" href="oct_mem_fun.html#math_toolkit.oct_mem_fun.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> |
| <h5> |
| <a name="math_toolkit.oct_mem_fun.h3"></a> |
| <span class="phrase"><a name="math_toolkit.oct_mem_fun.individual_real_components"></a></span><a class="link" href="oct_mem_fun.html#math_toolkit.oct_mem_fun.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> |
| <h5> |
| <a name="math_toolkit.oct_mem_fun.h4"></a> |
| <span class="phrase"><a name="math_toolkit.oct_mem_fun.individual_complex_components"></a></span><a class="link" href="oct_mem_fun.html#math_toolkit.oct_mem_fun.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> |
| <h5> |
| <a name="math_toolkit.oct_mem_fun.h5"></a> |
| <span class="phrase"><a name="math_toolkit.oct_mem_fun.individual_quaternion_components"></a></span><a class="link" href="oct_mem_fun.html#math_toolkit.oct_mem_fun.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> |
| <h4> |
| <a name="math_toolkit.oct_mem_fun.h6"></a> |
| <span class="phrase"><a name="math_toolkit.oct_mem_fun.octonion_member_operators"></a></span><a class="link" href="oct_mem_fun.html#math_toolkit.oct_mem_fun.octonion_member_operators">Octonion |
| Member Operators</a> |
| </h4> |
| <h5> |
| <a name="math_toolkit.oct_mem_fun.h7"></a> |
| <span class="phrase"><a name="math_toolkit.oct_mem_fun.assignment_operators"></a></span><a class="link" href="oct_mem_fun.html#math_toolkit.oct_mem_fun.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> |
| <h5> |
| <a name="math_toolkit.oct_mem_fun.h8"></a> |
| <span class="phrase"><a name="math_toolkit.oct_mem_fun.other_member_operators"></a></span><a class="link" href="oct_mem_fun.html#math_toolkit.oct_mem_fun.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> |
| </div> |
| <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> |
| <td align="left"></td> |
| <td align="right"><div class="copyright-footer">Copyright © 2006-2010, 2012-2014 Nikhar Agrawal, |
| Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert |
| Holin, Bruno Lalande, John Maddock, Johan Råde, Gautam Sewani, Benjamin Sobotta, |
| Thijs van den Berg, Daryle Walker and Xiaogang Zhang<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>) |
| </p> |
| </div></td> |
| </tr></table> |
| <hr> |
| <div class="spirit-nav"> |
| <a accesskey="p" href="oct_typedefs.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../octonions.html"><img src="../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="oct_non_mem.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a> |
| </div> |
| </body> |
| </html> |
