1<html> 2<head> 3<meta http-equiv="Content-Type" content="text/html; charset=UTF-8"> 4<title>Octonion Value Operations</title> 5<link rel="stylesheet" href="../math.css" type="text/css"> 6<meta name="generator" content="DocBook XSL Stylesheets V1.79.1"> 7<link rel="home" href="../index.html" title="Math Toolkit 2.12.0"> 8<link rel="up" href="../octonions.html" title="Chapter 17. Octonions"> 9<link rel="prev" href="oct_non_mem.html" title="Octonion Non-Member Operators"> 10<link rel="next" href="oct_create.html" title="Octonion Creation Functions"> 11</head> 12<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> 13<table cellpadding="2" width="100%"><tr> 14<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td> 15<td align="center"><a href="../../../../../index.html">Home</a></td> 16<td align="center"><a href="../../../../../libs/libraries.htm">Libraries</a></td> 17<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> 18<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> 19<td align="center"><a href="../../../../../more/index.htm">More</a></td> 20</tr></table> 21<hr> 22<div class="spirit-nav"> 23<a accesskey="p" href="oct_non_mem.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_create.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a> 24</div> 25<div class="section"> 26<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 27<a name="math_toolkit.oct_value_ops"></a><a class="link" href="oct_value_ops.html" title="Octonion Value Operations">Octonion Value Operations</a> 28</h2></div></div></div> 29<h5> 30<a name="math_toolkit.oct_value_ops.h0"></a> 31 <span class="phrase"><a name="math_toolkit.oct_value_ops.real_and_unreal"></a></span><a class="link" href="oct_value_ops.html#math_toolkit.oct_value_ops.real_and_unreal">Real 32 and Unreal</a> 33 </h5> 34<pre class="programlisting"><span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">T</span> <span class="identifier">real</span><span class="special">(</span><span class="identifier">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">o</span><span class="special">);</span> 35<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">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="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">o</span><span class="special">);</span> 36</pre> 37<p> 38 These return <code class="computeroutput"><span class="identifier">o</span><span class="special">.</span><span class="identifier">real</span><span class="special">()</span></code> and 39 <code class="computeroutput"><span class="identifier">o</span><span class="special">.</span><span class="identifier">unreal</span><span class="special">()</span></code> 40 respectively. 41 </p> 42<h5> 43<a name="math_toolkit.oct_value_ops.h1"></a> 44 <span class="phrase"><a name="math_toolkit.oct_value_ops.conj"></a></span><a class="link" href="oct_value_ops.html#math_toolkit.oct_value_ops.conj">conj</a> 45 </h5> 46<pre class="programlisting"><span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="identifier">conj</span><span class="special">(</span><span class="identifier">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">o</span><span class="special">);</span> 47</pre> 48<p> 49 This returns the conjugate of the octonion. 50 </p> 51<h5> 52<a name="math_toolkit.oct_value_ops.h2"></a> 53 <span class="phrase"><a name="math_toolkit.oct_value_ops.sup"></a></span><a class="link" href="oct_value_ops.html#math_toolkit.oct_value_ops.sup">sup</a> 54 </h5> 55<pre class="programlisting"><span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">T</span> <span class="identifier">sup</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">o</span><span class="special">);</span> 56</pre> 57<p> 58 This return the sup norm (the greatest among <code class="computeroutput"><span class="identifier">abs</span><span class="special">(</span><span class="identifier">o</span><span class="special">.</span><span class="identifier">R_component_1</span><span class="special">())...</span><span class="identifier">abs</span><span class="special">(</span><span class="identifier">o</span><span class="special">.</span><span class="identifier">R_component_8</span><span class="special">()))</span></code> of the octonion. 59 </p> 60<h5> 61<a name="math_toolkit.oct_value_ops.h3"></a> 62 <span class="phrase"><a name="math_toolkit.oct_value_ops.l1"></a></span><a class="link" href="oct_value_ops.html#math_toolkit.oct_value_ops.l1">l1</a> 63 </h5> 64<pre class="programlisting"><span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">T</span> <span class="identifier">l1</span><span class="special">(</span><span class="identifier">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">o</span><span class="special">);</span> 65</pre> 66<p> 67 This return the l1 norm (<code class="computeroutput"><span class="identifier">abs</span><span class="special">(</span><span class="identifier">o</span><span class="special">.</span><span class="identifier">R_component_1</span><span class="special">())+...+</span><span class="identifier">abs</span><span class="special">(</span><span class="identifier">o</span><span class="special">.</span><span class="identifier">R_component_8</span><span class="special">())</span></code>) of the octonion. 68 </p> 69<h5> 70<a name="math_toolkit.oct_value_ops.h4"></a> 71 <span class="phrase"><a name="math_toolkit.oct_value_ops.abs"></a></span><a class="link" href="oct_value_ops.html#math_toolkit.oct_value_ops.abs">abs</a> 72 </h5> 73<pre class="programlisting"><span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">T</span> <span class="identifier">abs</span><span class="special">(</span><span class="identifier">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">o</span><span class="special">);</span> 74</pre> 75<p> 76 This return the magnitude (Euclidean norm) of the octonion. 77 </p> 78<h5> 79<a name="math_toolkit.oct_value_ops.h5"></a> 80 <span class="phrase"><a name="math_toolkit.oct_value_ops.norm"></a></span><a class="link" href="oct_value_ops.html#math_toolkit.oct_value_ops.norm">norm</a> 81 </h5> 82<pre class="programlisting"><span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">T</span> <span class="identifier">norm</span><span class="special">(</span><span class="identifier">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">o</span><span class="special">);</span> 83</pre> 84<p> 85 This return the (Cayley) norm of the octonion. The term "norm" might 86 be confusing, as most people associate it with the Euclidean norm (and quadratic 87 functionals). For this version of (the mathematical objects known as) octonions, 88 the Euclidean norm (also known as magnitude) is the square root of the Cayley 89 norm. 90 </p> 91</div> 92<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> 93<td align="left"></td> 94<td align="right"><div class="copyright-footer">Copyright © 2006-2019 Nikhar 95 Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, 96 Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan 97 Råde, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, 98 Daryle Walker and Xiaogang Zhang<p> 99 Distributed under the Boost Software License, Version 1.0. (See accompanying 100 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>) 101 </p> 102</div></td> 103</tr></table> 104<hr> 105<div class="spirit-nav"> 106<a accesskey="p" href="oct_non_mem.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_create.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a> 107</div> 108</body> 109</html> 110
