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| 25 | <div class="section" lang="en"> |
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| 26 | <div class="titlepage"><div><div><h2 class="title" style="clear: both"> |
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| 27 | <a name="boost_math.octonions"></a>Octonions</h2></div></div></div> |
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| 28 | <div class="toc"><dl> |
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| 29 | <dt><span class="section"><a href="octonions.html#boost_math.octonions.overview">Overview</a></span></dt> |
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| 30 | <dt><span class="section"><a href="octonions.html#boost_math.octonions.header_file">Header File</a></span></dt> |
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| 31 | <dt><span class="section"><a href="octonions.html#boost_math.octonions.synopsis">Synopsis</a></span></dt> |
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| 32 | <dt><span class="section"><a href="octonions.html#boost_math.octonions.template_class_octonion">Template Class octonion</a></span></dt> |
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| 33 | <dt><span class="section"><a href="octonions.html#boost_math.octonions.octonion_specializations">Octonion Specializations</a></span></dt> |
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| 34 | <dt><span class="section"><a href="octonions.html#boost_math.octonions.octonion_member_typedefs">Octonion Member Typedefs</a></span></dt> |
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| 35 | <dt><span class="section"><a href="octonions.html#boost_math.octonions.octonion_member_functions">Octonion Member Functions</a></span></dt> |
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| 36 | <dt><span class="section"><a href="octonions.html#boost_math.octonions.octonion_non_member_operators">Octonion Non-Member Operators</a></span></dt> |
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| 37 | <dt><span class="section"><a href="octonions.html#boost_math.octonions.octonion_value_operations">Octonion Value Operations</a></span></dt> |
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| 38 | <dt><span class="section"><a href="octonions.html#boost_math.octonions.quaternion_creation_functions">Quaternion Creation Functions</a></span></dt> |
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| 39 | <dt><span class="section"><a href="octonions.html#boost_math.octonions.octonions_transcendentals">Octonions Transcendentals</a></span></dt> |
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| 40 | <dt><span class="section"><a href="octonions.html#boost_math.octonions.test_program">Test Program</a></span></dt> |
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| 41 | <dt><span class="section"><a href="octonions.html#boost_math.octonions.acknowledgements">Acknowledgements</a></span></dt> |
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| 42 | <dt><span class="section"><a href="octonions.html#boost_math.octonions.history">History</a></span></dt> |
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| 43 | <dt><span class="section"><a href="octonions.html#boost_math.octonions.to_do">To Do</a></span></dt> |
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| 44 | </dl></div> |
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| 45 | <div class="section" lang="en"> |
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| 46 | <div class="titlepage"><div><div><h3 class="title"> |
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| 47 | <a name="boost_math.octonions.overview"></a>Overview</h3></div></div></div> |
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| 48 | <p> |
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| 49 | Octonions, like <a href="quaternions.html" title="Quaternions">quaternions</a>, |
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| 50 | are a relative of complex numbers. |
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| 51 | </p> |
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| 52 | <p> |
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| 53 | Octonions see some use in theoretical physics. |
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| 54 | </p> |
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| 55 | <p> |
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| 56 | In practical terms, an octonion is simply an octuple of real numbers ( |
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| 57 | α,β,γ,δ,ε,ζ,η,θ |
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| 58 | ), which we can write in the form <span class="emphasis"><em><code class="literal">o = |
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| 59 | α + βi + γj + δk + εe' + ζi' + ηj' + θk' |
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| 60 | </code></em></span>, where <span class="emphasis"><em><code class="literal">i</code></em></span>, |
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| 61 | <span class="emphasis"><em><code class="literal">j</code></em></span> and <span class="emphasis"><em><code class="literal">k</code></em></span> |
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| 62 | are the same objects as for quaternions, and <span class="emphasis"><em><code class="literal">e'</code></em></span>, |
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| 63 | <span class="emphasis"><em><code class="literal">i'</code></em></span>, <span class="emphasis"><em><code class="literal">j'</code></em></span> |
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| 64 | and <span class="emphasis"><em><code class="literal">k'</code></em></span> are distinct objects which |
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| 65 | play essentially the same kind of role as <span class="emphasis"><em><code class="literal">i</code></em></span> |
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| 66 | (or <span class="emphasis"><em><code class="literal">j</code></em></span> or <span class="emphasis"><em><code class="literal">k</code></em></span>). |
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| 67 | </p> |
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| 68 | <p> |
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| 69 | Addition and a multiplication is defined on the set of octonions, which generalize |
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| 70 | their quaternionic counterparts. The main novelty this time is that <span class="bold"><strong>the multiplication is not only not commutative, is now not even |
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| 71 | associative</strong></span> (i.e. there are quaternions <span class="emphasis"><em><code class="literal">x</code></em></span>, |
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| 72 | <span class="emphasis"><em><code class="literal">y</code></em></span> and <span class="emphasis"><em><code class="literal">z</code></em></span> |
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| 73 | such that <span class="emphasis"><em><code class="literal">x(yz) |
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| 74 | ≠ |
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| 75 | (xy)z</code></em></span>). A way of remembering things is by using the |
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| 76 | following multiplication table: |
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| 77 | </p> |
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| 78 | <p> |
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| 79 | <span class="inlinemediaobject"><img src="../../../libs/math/octonion/graphics/octonion_blurb17.jpeg" alt="octonion_blurb17"></span> |
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| 80 | </p> |
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| 81 | <p> |
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| 82 | Octonions (and their kin) are described in far more details in this other |
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| 83 | <a href="../../../libs/math/quaternion/TQE.pdf" target="_top">document</a> (with <a href="../../../libs/math/quaternion/TQE_EA.pdf" target="_top">errata and addenda</a>). |
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| 84 | </p> |
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| 85 | <p> |
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| 86 | Some traditional constructs, such as the exponential, carry over without |
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| 87 | too much change into the realms of octonions, but other, such as taking a |
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| 88 | square root, do not (the fact that the exponential has a closed form is a |
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| 89 | result of the author, but the fact that the exponential exists at all for |
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| 90 | octonions is known since quite a long time ago). |
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| 91 | </p> |
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| 92 | </div> |
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| 93 | <div class="section" lang="en"> |
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| 94 | <div class="titlepage"><div><div><h3 class="title"> |
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| 95 | <a name="boost_math.octonions.header_file"></a>Header File</h3></div></div></div> |
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| 96 | <p> |
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| 97 | The interface and implementation are both supplied by the header file <a href="../../../boost/math/octonion.hpp" target="_top">octonion.hpp</a>. |
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| 98 | </p> |
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| 99 | </div> |
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| 100 | <div class="section" lang="en"> |
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| 101 | <div class="titlepage"><div><div><h3 class="title"> |
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| 102 | <a name="boost_math.octonions.synopsis"></a>Synopsis</h3></div></div></div> |
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| 103 | <pre class="programlisting"> |
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| 104 | <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span> |
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| 105 | |
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| 106 | <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="keyword">class</span> <a href="octonions.html#boost_math.octonions.template_class_octonion" title="Template Class octonion">octonion</a><span class="special">;</span> |
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| 107 | <span class="keyword">template</span><span class="special"><></span> <span class="keyword">class</span> <a href="octonions.html#boost_math.octonions.octonion_specializations" title="Octonion Specializations">octonion<float></a><span class="special">;</span> |
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| 108 | <span class="keyword">template</span><span class="special"><></span> <span class="keyword">class</span> <a href="octonions.html#boost_math.octonion_double">octonion<double></a><span class="special">;</span> |
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| 109 | <span class="keyword">template</span><span class="special"><></span> <span class="keyword">class</span> <a href="octonions.html#boost_math.octonion_long_double">octonion<long double></a><span class="special">;</span> |
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| 110 | |
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| 111 | <span class="comment">// operators |
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| 112 | </span> |
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| 113 | <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> <a href="octonions.html#boost_math.octonions.octonion_non_member_operators.binary_addition_operators">operator +</a> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</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">rhs</span><span class="special">);</span> |
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| 114 | <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> <a href="octonions.html#boost_math.octonions.octonion_non_member_operators.binary_addition_operators">operator +</a> <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">lhs</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> |
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| 115 | <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> <a href="octonions.html#boost_math.octonions.octonion_non_member_operators.binary_addition_operators">operator +</a> <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">lhs</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">rhs</span><span class="special">);</span> |
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| 116 | <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> <a href="octonions.html#boost_math.octonions.octonion_non_member_operators.binary_addition_operators">operator +</a> <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">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</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> |
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| 117 | <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> <a href="octonions.html#boost_math.octonions.octonion_non_member_operators.binary_addition_operators">operator +</a> <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">lhs</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">rhs</span><span class="special">);</span> |
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| 118 | <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> <a href="octonions.html#boost_math.octonions.octonion_non_member_operators.binary_addition_operators">operator +</a> <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">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</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> |
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| 119 | <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> <a href="octonions.html#boost_math.octonions.octonion_non_member_operators.binary_addition_operators">operator +</a> <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">lhs</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">rhs</span><span class="special">);</span> |
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| 120 | |
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| 121 | <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> <a href="octonions.html#boost_math.octonions.octonion_non_member_operators.binary_subtraction_operators">operator -</a> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</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">rhs</span><span class="special">);</span> |
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| 122 | <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> <a href="octonions.html#boost_math.octonions.octonion_non_member_operators.binary_subtraction_operators">operator -</a> <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">lhs</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> |
|---|
| 123 | <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> <a href="octonions.html#boost_math.octonions.octonion_non_member_operators.binary_subtraction_operators">operator -</a> <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">lhs</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">rhs</span><span class="special">);</span> |
|---|
| 124 | <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> <a href="octonions.html#boost_math.octonions.octonion_non_member_operators.binary_subtraction_operators">operator -</a> <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">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</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> |
|---|
| 125 | <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> <a href="octonions.html#boost_math.octonions.octonion_non_member_operators.binary_subtraction_operators">operator -</a> <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">lhs</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">rhs</span><span class="special">);</span> |
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| 126 | <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> <a href="octonions.html#boost_math.octonions.octonion_non_member_operators.binary_subtraction_operators">operator -</a> <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">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</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> |
|---|
| 127 | <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> <a href="octonions.html#boost_math.octonions.octonion_non_member_operators.binary_subtraction_operators">operator -</a> <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">lhs</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">rhs</span><span class="special">);</span> |
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| 128 | |
|---|
| 129 | <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> <a href="octonions.html#boost_math.octonions.octonion_non_member_operators.binary_multiplication_operators">operator *</a> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</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">rhs</span><span class="special">);</span> |
|---|
| 130 | <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> <a href="octonions.html#boost_math.octonions.octonion_non_member_operators.binary_multiplication_operators">operator *</a> <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">lhs</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> |
|---|
| 131 | <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> <a href="octonions.html#boost_math.octonions.octonion_non_member_operators.binary_multiplication_operators">operator *</a> <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">lhs</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">rhs</span><span class="special">);</span> |
|---|
| 132 | <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> <a href="octonions.html#boost_math.octonions.octonion_non_member_operators.binary_multiplication_operators">operator *</a> <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">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</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> |
|---|
| 133 | <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> <a href="octonions.html#boost_math.octonions.octonion_non_member_operators.binary_multiplication_operators">operator *</a> <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">lhs</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">rhs</span><span class="special">);</span> |
|---|
| 134 | <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> <a href="octonions.html#boost_math.octonions.octonion_non_member_operators.binary_multiplication_operators">operator *</a> <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">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</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> |
|---|
| 135 | <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> <a href="octonions.html#boost_math.octonions.octonion_non_member_operators.binary_multiplication_operators">operator *</a> <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">lhs</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">rhs</span><span class="special">);</span> |
|---|
| 136 | |
|---|
| 137 | <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> <a href="octonions.html#boost_math.octonions.octonion_non_member_operators.binary_division_operators">operator /</a> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</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">rhs</span><span class="special">);</span> |
|---|
| 138 | <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> <a href="octonions.html#boost_math.octonions.octonion_non_member_operators.binary_division_operators">operator /</a> <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">lhs</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> |
|---|
| 139 | <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> <a href="octonions.html#boost_math.octonions.octonion_non_member_operators.binary_division_operators">operator /</a> <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">lhs</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">rhs</span><span class="special">);</span> |
|---|
| 140 | <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> <a href="octonions.html#boost_math.octonions.octonion_non_member_operators.binary_division_operators">operator /</a> <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">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</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> |
|---|
| 141 | <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> <a href="octonions.html#boost_math.octonions.octonion_non_member_operators.binary_division_operators">operator /</a> <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">lhs</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">rhs</span><span class="special">);</span> |
|---|
| 142 | <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> <a href="octonions.html#boost_math.octonions.octonion_non_member_operators.binary_division_operators">operator /</a> <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">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</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> |
|---|
| 143 | <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> <a href="octonions.html#boost_math.octonions.octonion_non_member_operators.binary_division_operators">operator /</a> <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">lhs</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">rhs</span><span class="special">);</span> |
|---|
| 144 | |
|---|
| 145 | <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> <a href="octonions.html#boost_math.octonions.octonion_non_member_operators.unary_plus_and_minus_operators">operator +</a> <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> |
|---|
| 146 | <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> <a href="octonions.html#boost_math.octonions.octonion_non_member_operators.unary_plus_and_minus_operators">operator -</a> <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> |
|---|
| 147 | |
|---|
| 148 | <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="keyword">bool</span> <a href="octonions.html#boost_math.octonions.octonion_non_member_operators.binary_equality_operators">operator ==</a> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</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">rhs</span><span class="special">);</span> |
|---|
| 149 | <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="keyword">bool</span> <a href="octonions.html#boost_math.octonions.octonion_non_member_operators.binary_equality_operators">operator ==</a> <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">lhs</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> |
|---|
| 150 | <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="keyword">bool</span> <a href="octonions.html#boost_math.octonions.octonion_non_member_operators.binary_equality_operators">operator ==</a> <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">lhs</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">rhs</span><span class="special">);</span> |
|---|
| 151 | <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="keyword">bool</span> <a href="octonions.html#boost_math.octonions.octonion_non_member_operators.binary_equality_operators">operator ==</a> <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">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</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> |
|---|
| 152 | <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="keyword">bool</span> <a href="octonions.html#boost_math.octonions.octonion_non_member_operators.binary_equality_operators">operator ==</a> <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">lhs</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">rhs</span><span class="special">);</span> |
|---|
| 153 | <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="keyword">bool</span> <a href="octonions.html#boost_math.octonions.octonion_non_member_operators.binary_equality_operators">operator ==</a> <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">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</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> |
|---|
| 154 | <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="keyword">bool</span> <a href="octonions.html#boost_math.octonions.octonion_non_member_operators.binary_equality_operators">operator ==</a> <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">lhs</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">rhs</span><span class="special">);</span> |
|---|
| 155 | |
|---|
| 156 | <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="keyword">bool</span> <a href="octonions.html#boost_math.octonions.octonion_non_member_operators.binary_inequality_operators">operator !=</a> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</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">rhs</span><span class="special">);</span> |
|---|
| 157 | <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="keyword">bool</span> <a href="octonions.html#boost_math.octonions.octonion_non_member_operators.binary_inequality_operators">operator !=</a> <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">lhs</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> |
|---|
| 158 | <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="keyword">bool</span> <a href="octonions.html#boost_math.octonions.octonion_non_member_operators.binary_inequality_operators">operator !=</a> <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">lhs</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">rhs</span><span class="special">);</span> |
|---|
| 159 | <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="keyword">bool</span> <a href="octonions.html#boost_math.octonions.octonion_non_member_operators.binary_inequality_operators">operator !=</a> <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">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</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> |
|---|
| 160 | <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="keyword">bool</span> <a href="octonions.html#boost_math.octonions.octonion_non_member_operators.binary_inequality_operators">operator !=</a> <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">lhs</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">rhs</span><span class="special">);</span> |
|---|
| 161 | <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="keyword">bool</span> <a href="octonions.html#boost_math.octonions.octonion_non_member_operators.binary_inequality_operators">operator !=</a> <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">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</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> |
|---|
| 162 | <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="keyword">bool</span> <a href="octonions.html#boost_math.octonions.octonion_non_member_operators.binary_inequality_operators">operator !=</a> <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">lhs</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">rhs</span><span class="special">);</span> |
|---|
| 163 | |
|---|
| 164 | <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="keyword">typename</span> <span class="identifier">charT</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">traits</span><span class="special">></span> |
|---|
| 165 | <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_istream</span><span class="special"><</span><span class="identifier">charT</span><span class="special">,</span><span class="identifier">traits</span><span class="special">></span> <span class="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_non_member_operators.stream_extractor">operator >></a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_istream</span><span class="special"><</span><span class="identifier">charT</span><span class="special">,</span><span class="identifier">traits</span><span class="special">></span> <span class="special">&</span> <span class="identifier">is</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="identifier">o</span><span class="special">);</span> |
|---|
| 166 | |
|---|
| 167 | <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="keyword">typename</span> <span class="identifier">charT</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">traits</span><span class="special">></span> |
|---|
| 168 | <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_ostream</span><span class="special"><</span><span class="identifier">charT</span><span class="special">,</span><span class="identifier">traits</span><span class="special">></span> <span class="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_non_member_operators.stream_inserter">operator <<</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_ostream</span><span class="special"><</span><span class="identifier">charT</span><span class="special">,</span><span class="identifier">traits</span><span class="special">></span> <span class="special">&</span> <span class="identifier">os</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> |
|---|
| 169 | |
|---|
| 170 | <span class="comment">// values |
|---|
| 171 | </span> |
|---|
| 172 | <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> <a href="octonions.html#boost_math.octonions.octonion_value_operations.real_and_unreal">real</a><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> |
|---|
| 173 | <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> <a href="octonions.html#boost_math.octonions.octonion_value_operations.real_and_unreal">unreal</a><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> |
|---|
| 174 | |
|---|
| 175 | <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> <a href="octonions.html#boost_math.octonions.octonion_value_operations.sup">sup</a><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> |
|---|
| 176 | <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> <a href="octonions.html#boost_math.octonions.octonion_value_operations.l1">l1</a><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> |
|---|
| 177 | <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> <a href="octonions.html#boost_math.octonions.octonion_value_operations.abs">abs</a><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> |
|---|
| 178 | <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> <a href="octonions.html#boost_math.octonions.octonion_value_operations.norm">norm</a><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> |
|---|
| 179 | <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> <a href="octonions.html#boost_math.octonions.octonion_value_operations.conj">conj</a><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> |
|---|
| 180 | |
|---|
| 181 | <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> <a href="octonions.html#boost_math.octonions.quaternion_creation_functions" title="Quaternion Creation Functions">spherical</a><span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rho</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">theta</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">phi1</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">phi2</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">phi3</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">phi4</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">phi5</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">phi6</span><span class="special">);</span> |
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| 182 | <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> <a href="octonions.html#boost_math.octonions.quaternion_creation_functions" title="Quaternion Creation Functions">multipolar</a><span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rho1</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">theta1</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rho2</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">theta2</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rho3</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">theta3</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rho4</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">theta4</span><span class="special">);</span> |
|---|
| 183 | <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> <a href="octonions.html#boost_math.octonions.quaternion_creation_functions" title="Quaternion Creation Functions">cylindrical</a><span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">r</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">angle</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">h1</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">h2</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">h3</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">h4</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">h5</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">h6</span><span class="special">);</span> |
|---|
| 184 | |
|---|
| 185 | <span class="comment">// transcendentals |
|---|
| 186 | </span> |
|---|
| 187 | <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> <a href="octonions.html#boost_math.octonions.octonions_transcendentals.exp">exp</a><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> |
|---|
| 188 | <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> <a href="octonions.html#boost_math.octonions.octonions_transcendentals.cos">cos</a><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> |
|---|
| 189 | <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> <a href="octonions.html#boost_math.octonions.octonions_transcendentals.sin">sin</a><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> |
|---|
| 190 | <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> <a href="octonions.html#boost_math.octonions.octonions_transcendentals.tan">tan</a><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> |
|---|
| 191 | <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> <a href="octonions.html#boost_math.octonions.octonions_transcendentals.cosh">cosh</a><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> |
|---|
| 192 | <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> <a href="octonions.html#boost_math.octonions.octonions_transcendentals.sinh">sinh</a><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> |
|---|
| 193 | <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> <a href="octonions.html#boost_math.octonions.octonions_transcendentals.tanh">tanh</a><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> |
|---|
| 194 | |
|---|
| 195 | <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> <a href="octonions.html#boost_math.octonions.octonions_transcendentals.pow">pow</a><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> <span class="keyword">int</span> <span class="identifier">n</span><span class="special">);</span> |
|---|
| 196 | |
|---|
| 197 | <span class="special">}</span> <span class="special">}</span> <span class="comment">// namespaces |
|---|
| 198 | </span></pre> |
|---|
| 199 | </div> |
|---|
| 200 | <div class="section" lang="en"> |
|---|
| 201 | <div class="titlepage"><div><div><h3 class="title"> |
|---|
| 202 | <a name="boost_math.octonions.template_class_octonion"></a>Template Class octonion</h3></div></div></div> |
|---|
| 203 | <pre class="programlisting"> |
|---|
| 204 | <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span> <span class="special">{</span> |
|---|
| 205 | <span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> |
|---|
| 206 | <span class="keyword">class</span> <span class="identifier">octonion</span> |
|---|
| 207 | <span class="special">{</span> |
|---|
| 208 | <span class="keyword">public</span><span class="special">:</span> |
|---|
| 209 | <span class="keyword">typedef</span> <span class="identifier">T</span> <span class="identifier">value_type</span><span class="special">;</span> |
|---|
| 210 | |
|---|
| 211 | <span class="keyword">explicit</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.constructors">octonion</a><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> |
|---|
| 212 | <span class="keyword">explicit</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.constructors">octonion</a><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> |
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| 213 | <span class="keyword">explicit</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.constructors">octonion</a><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> |
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| 214 | <span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span> |
|---|
| 215 | <span class="keyword">explicit</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.constructors">octonion</a><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> |
|---|
| 216 | |
|---|
| 217 | <span class="identifier">T</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.real_and_unreal_parts">real</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> |
|---|
| 218 | <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.real_and_unreal_parts">unreal</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> |
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| 219 | |
|---|
| 220 | <span class="identifier">T</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.individual_real_components">R_component_1</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> |
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| 221 | <span class="identifier">T</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.individual_real_components">R_component_2</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> |
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| 222 | <span class="identifier">T</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.individual_real_components">R_component_3</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> |
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| 223 | <span class="identifier">T</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.individual_real_components">R_component_4</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> |
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| 224 | <span class="identifier">T</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.individual_real_components">R_component_5</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> |
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| 225 | <span class="identifier">T</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.individual_real_components">R_component_6</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> |
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| 226 | <span class="identifier">T</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.individual_real_components">R_component_7</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> |
|---|
| 227 | <span class="identifier">T</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.individual_real_components">R_component_8</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> |
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| 228 | |
|---|
| 229 | <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> <a href="octonions.html#boost_math.octonions.octonion_member_functions.individual_complex_components">C_component_1</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> |
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| 230 | <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> <a href="octonions.html#boost_math.octonions.octonion_member_functions.individual_complex_components">C_component_2</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> |
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| 231 | <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> <a href="octonions.html#boost_math.octonions.octonion_member_functions.individual_complex_components">C_component_3</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> |
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| 232 | <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> <a href="octonions.html#boost_math.octonions.octonion_member_functions.individual_complex_components">C_component_4</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> |
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| 233 | |
|---|
| 234 | <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> <a href="octonions.html#boost_math.octonions.octonion_member_functions.individual_quaternion_components">H_component_1</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> |
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| 235 | <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> <a href="octonions.html#boost_math.octonions.octonion_member_functions.individual_quaternion_components">H_component_2</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> |
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| 236 | |
|---|
| 237 | <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.assignment_operators">operator =</a> <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> |
|---|
| 238 | <span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span> |
|---|
| 239 | <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.assignment_operators">operator =</a> <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> |
|---|
| 240 | <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.assignment_operators">operator =</a> <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> |
|---|
| 241 | <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.assignment_operators">operator =</a> <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> |
|---|
| 242 | <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.assignment_operators">operator =</a> <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> |
|---|
| 243 | |
|---|
| 244 | <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.other_member_operators">operator +=</a> <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> |
|---|
| 245 | <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.other_member_operators">operator +=</a> <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> |
|---|
| 246 | <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.other_member_operators">operator +=</a> <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> |
|---|
| 247 | <span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span> |
|---|
| 248 | <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.other_member_operators">operator +=</a> <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> |
|---|
| 249 | |
|---|
| 250 | <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.other_member_operators">operator -=</a> <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> |
|---|
| 251 | <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.other_member_operators">operator -=</a> <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> |
|---|
| 252 | <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.other_member_operators">operator -=</a> <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> |
|---|
| 253 | <span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span> |
|---|
| 254 | <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.other_member_operators">operator -=</a> <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> |
|---|
| 255 | |
|---|
| 256 | <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.other_member_operators">operator *=</a> <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> |
|---|
| 257 | <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.other_member_operators">operator *=</a> <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> |
|---|
| 258 | <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.other_member_operators">operator *=</a> <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> |
|---|
| 259 | <span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span> |
|---|
| 260 | <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.other_member_operators">operator *=</a> <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> |
|---|
| 261 | |
|---|
| 262 | <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.other_member_operators">operator /=</a> <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> |
|---|
| 263 | <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.other_member_operators">operator /=</a> <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> |
|---|
| 264 | <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.other_member_operators">operator /=</a> <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> |
|---|
| 265 | <span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span> |
|---|
| 266 | <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.other_member_operators">operator /=</a> <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> |
|---|
| 267 | <span class="special">};</span> |
|---|
| 268 | |
|---|
| 269 | <span class="special">}</span> <span class="special">}</span> <span class="comment">// namespaces |
|---|
| 270 | </span></pre> |
|---|
| 271 | </div> |
|---|
| 272 | <div class="section" lang="en"> |
|---|
| 273 | <div class="titlepage"><div><div><h3 class="title"> |
|---|
| 274 | <a name="boost_math.octonions.octonion_specializations"></a>Octonion Specializations</h3></div></div></div> |
|---|
| 275 | <pre class="programlisting"> |
|---|
| 276 | <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span> |
|---|
| 277 | |
|---|
| 278 | <span class="keyword">template</span><span class="special"><></span> |
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| 279 | <span class="keyword">class</span> <span class="identifier">octonion</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> |
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| 280 | <span class="special">{</span> |
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| 281 | <span class="keyword">public</span><span class="special">:</span> |
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| 282 | <span class="keyword">typedef</span> <span class="keyword">float</span> <span class="identifier">value_type</span><span class="special">;</span> |
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| 283 | |
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| 284 | <span class="keyword">explicit</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.constructors">octonion</a><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> |
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| 285 | <span class="keyword">explicit</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.constructors">octonion</a><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> |
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| 286 | <span class="keyword">explicit</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.constructors">octonion</a><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> |
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| 287 | <span class="keyword">explicit</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.constructors">octonion</a><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> |
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| 288 | <span class="keyword">explicit</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.constructors">octonion</a><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> |
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| 289 | |
|---|
| 290 | <span class="keyword">float</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.real_and_unreal_parts">real</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> |
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| 291 | <span class="identifier">octonion</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.real_and_unreal_parts">unreal</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> |
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| 292 | |
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| 293 | <span class="keyword">float</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.individual_real_components">R_component_1</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> |
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| 294 | <span class="keyword">float</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.individual_real_components">R_component_2</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> |
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| 295 | <span class="keyword">float</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.individual_real_components">R_component_3</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> |
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| 296 | <span class="keyword">float</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.individual_real_components">R_component_4</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> |
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| 297 | <span class="keyword">float</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.individual_real_components">R_component_5</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> |
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| 298 | <span class="keyword">float</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.individual_real_components">R_component_6</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> |
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| 299 | <span class="keyword">float</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.individual_real_components">R_component_7</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> |
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| 300 | <span class="keyword">float</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.individual_real_components">R_component_8</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> |
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| 301 | |
|---|
| 302 | <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> <a href="octonions.html#boost_math.octonions.octonion_member_functions.individual_complex_components">C_component_1</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> |
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| 303 | <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> <a href="octonions.html#boost_math.octonions.octonion_member_functions.individual_complex_components">C_component_2</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> |
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| 304 | <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> <a href="octonions.html#boost_math.octonions.octonion_member_functions.individual_complex_components">C_component_3</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> |
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| 305 | <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> <a href="octonions.html#boost_math.octonions.octonion_member_functions.individual_complex_components">C_component_4</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> |
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| 306 | |
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| 307 | <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> <a href="octonions.html#boost_math.octonions.octonion_member_functions.individual_quaternion_components">H_component_1</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> |
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| 308 | <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> <a href="octonions.html#boost_math.octonions.octonion_member_functions.individual_quaternion_components">H_component_2</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> |
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| 309 | |
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| 310 | <span class="identifier">octonion</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.assignment_operators">operator =</a> <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_affecter</span><span class="special">);</span> |
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| 311 | <span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span> |
|---|
| 312 | <span class="identifier">octonion</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.assignment_operators">operator =</a> <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> |
|---|
| 313 | <span class="identifier">octonion</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.assignment_operators">operator =</a> <span class="special">(</span><span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_affecter</span><span class="special">);</span> |
|---|
| 314 | <span class="identifier">octonion</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.assignment_operators">operator =</a> <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">a_affecter</span><span class="special">);</span> |
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| 315 | <span class="identifier">octonion</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.assignment_operators">operator =</a> <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">a_affecter</span><span class="special">);</span> |
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| 316 | |
|---|
| 317 | <span class="identifier">octonion</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.other_member_operators">operator +=</a> <span class="special">(</span><span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span> |
|---|
| 318 | <span class="identifier">octonion</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.other_member_operators">operator +=</a> <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">rhs</span><span class="special">);</span> |
|---|
| 319 | <span class="identifier">octonion</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.other_member_operators">operator +=</a> <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">rhs</span><span class="special">);</span> |
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| 320 | <span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span> |
|---|
| 321 | <span class="identifier">octonion</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.other_member_operators">operator +=</a> <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> |
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| 322 | |
|---|
| 323 | <span class="identifier">octonion</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.other_member_operators">operator -=</a> <span class="special">(</span><span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span> |
|---|
| 324 | <span class="identifier">octonion</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.other_member_operators">operator -=</a> <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">rhs</span><span class="special">);</span> |
|---|
| 325 | <span class="identifier">octonion</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.other_member_operators">operator -=</a> <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">rhs</span><span class="special">);</span> |
|---|
| 326 | <span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span> |
|---|
| 327 | <span class="identifier">octonion</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.other_member_operators">operator -=</a> <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> |
|---|
| 328 | |
|---|
| 329 | <span class="identifier">octonion</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.other_member_operators">operator *=</a> <span class="special">(</span><span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span> |
|---|
| 330 | <span class="identifier">octonion</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.other_member_operators">operator *=</a> <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">rhs</span><span class="special">);</span> |
|---|
| 331 | <span class="identifier">octonion</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.other_member_operators">operator *=</a> <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">rhs</span><span class="special">);</span> |
|---|
| 332 | <span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span> |
|---|
| 333 | <span class="identifier">octonion</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.other_member_operators">operator *=</a> <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> |
|---|
| 334 | |
|---|
| 335 | <span class="identifier">octonion</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.other_member_operators">operator /=</a> <span class="special">(</span><span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span> |
|---|
| 336 | <span class="identifier">octonion</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.other_member_operators">operator /=</a> <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">rhs</span><span class="special">);</span> |
|---|
| 337 | <span class="identifier">octonion</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.other_member_operators">operator /=</a> <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">rhs</span><span class="special">);</span> |
|---|
| 338 | <span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span> |
|---|
| 339 | <span class="identifier">octonion</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.other_member_operators">operator /=</a> <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> |
|---|
| 340 | <span class="special">};</span> |
|---|
| 341 | </pre> |
|---|
| 342 | <a name="boost_math.octonion_double"></a><p> |
|---|
| 343 | </p> |
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| 344 | <pre class="programlisting"> |
|---|
| 345 | <span class="keyword">template</span><span class="special"><></span> |
|---|
| 346 | <span class="keyword">class</span> <span class="identifier">octonion</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> |
|---|
| 347 | <span class="special">{</span> |
|---|
| 348 | <span class="keyword">public</span><span class="special">:</span> |
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| 349 | <span class="keyword">typedef</span> <span class="keyword">double</span> <span class="identifier">value_type</span><span class="special">;</span> |
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| 350 | |
|---|
| 351 | <span class="keyword">explicit</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.constructors">octonion</a><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> |
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| 352 | <span class="keyword">explicit</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.constructors">octonion</a><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> |
|---|
| 353 | <span class="keyword">explicit</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.constructors">octonion</a><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> |
|---|
| 354 | <span class="keyword">explicit</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.constructors">octonion</a><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> |
|---|
| 355 | <span class="keyword">explicit</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.constructors">octonion</a><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> |
|---|
| 356 | |
|---|
| 357 | <span class="keyword">double</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.real_and_unreal_parts">real</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> |
|---|
| 358 | <span class="identifier">octonion</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.real_and_unreal_parts">unreal</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> |
|---|
| 359 | |
|---|
| 360 | <span class="keyword">double</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.individual_real_components">R_component_1</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> |
|---|
| 361 | <span class="keyword">double</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.individual_real_components">R_component_2</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> |
|---|
| 362 | <span class="keyword">double</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.individual_real_components">R_component_3</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> |
|---|
| 363 | <span class="keyword">double</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.individual_real_components">R_component_4</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> |
|---|
| 364 | <span class="keyword">double</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.individual_real_components">R_component_5</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> |
|---|
| 365 | <span class="keyword">double</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.individual_real_components">R_component_6</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> |
|---|
| 366 | <span class="keyword">double</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.individual_real_components">R_component_7</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> |
|---|
| 367 | <span class="keyword">double</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.individual_real_components">R_component_8</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> |
|---|
| 368 | |
|---|
| 369 | <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> <a href="octonions.html#boost_math.octonions.octonion_member_functions.individual_complex_components">C_component_1</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> |
|---|
| 370 | <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> <a href="octonions.html#boost_math.octonions.octonion_member_functions.individual_complex_components">C_component_2</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> |
|---|
| 371 | <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> <a href="octonions.html#boost_math.octonions.octonion_member_functions.individual_complex_components">C_component_3</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> |
|---|
| 372 | <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> <a href="octonions.html#boost_math.octonions.octonion_member_functions.individual_complex_components">C_component_4</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> |
|---|
| 373 | |
|---|
| 374 | <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> <a href="octonions.html#boost_math.octonions.octonion_member_functions.individual_quaternion_components">H_component_1</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> |
|---|
| 375 | <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> <a href="octonions.html#boost_math.octonions.octonion_member_functions.individual_quaternion_components">H_component_2</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> |
|---|
| 376 | |
|---|
| 377 | <span class="identifier">octonion</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.assignment_operators">operator =</a> <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_affecter</span><span class="special">);</span> |
|---|
| 378 | <span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span> |
|---|
| 379 | <span class="identifier">octonion</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.assignment_operators">operator =</a> <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> |
|---|
| 380 | <span class="identifier">octonion</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.assignment_operators">operator =</a> <span class="special">(</span><span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">a_affecter</span><span class="special">);</span> |
|---|
| 381 | <span class="identifier">octonion</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.assignment_operators">operator =</a> <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">a_affecter</span><span class="special">);</span> |
|---|
| 382 | <span class="identifier">octonion</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.assignment_operators">operator =</a> <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">a_affecter</span><span class="special">);</span> |
|---|
| 383 | |
|---|
| 384 | <span class="identifier">octonion</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.other_member_operators">operator +=</a> <span class="special">(</span><span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span> |
|---|
| 385 | <span class="identifier">octonion</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.other_member_operators">operator +=</a> <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">rhs</span><span class="special">);</span> |
|---|
| 386 | <span class="identifier">octonion</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.other_member_operators">operator +=</a> <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">rhs</span><span class="special">);</span> |
|---|
| 387 | <span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span> |
|---|
| 388 | <span class="identifier">octonion</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.other_member_operators">operator +=</a> <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> |
|---|
| 389 | |
|---|
| 390 | <span class="identifier">octonion</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.other_member_operators">operator -=</a> <span class="special">(</span><span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span> |
|---|
| 391 | <span class="identifier">octonion</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.other_member_operators">operator -=</a> <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">rhs</span><span class="special">);</span> |
|---|
| 392 | <span class="identifier">octonion</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.other_member_operators">operator -=</a> <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">rhs</span><span class="special">);</span> |
|---|
| 393 | <span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span> |
|---|
| 394 | <span class="identifier">octonion</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.other_member_operators">operator -=</a> <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> |
|---|
| 395 | |
|---|
| 396 | <span class="identifier">octonion</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.other_member_operators">operator *=</a> <span class="special">(</span><span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span> |
|---|
| 397 | <span class="identifier">octonion</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.other_member_operators">operator *=</a> <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">rhs</span><span class="special">);</span> |
|---|
| 398 | <span class="identifier">octonion</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.other_member_operators">operator *=</a> <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">rhs</span><span class="special">);</span> |
|---|
| 399 | <span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span> |
|---|
| 400 | <span class="identifier">octonion</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.other_member_operators">operator *=</a> <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> |
|---|
| 401 | |
|---|
| 402 | <span class="identifier">octonion</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.other_member_operators">operator /=</a> <span class="special">(</span><span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rhs</span><span class="special">);</span> |
|---|
| 403 | <span class="identifier">octonion</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.other_member_operators">operator /=</a> <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">rhs</span><span class="special">);</span> |
|---|
| 404 | <span class="identifier">octonion</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.other_member_operators">operator /=</a> <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">rhs</span><span class="special">);</span> |
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| 405 | <span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span> |
|---|
| 406 | <span class="identifier">octonion</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.other_member_operators">operator /=</a> <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> |
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| 407 | <span class="special">};</span> |
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| 408 | </pre> |
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| 409 | <a name="boost_math.octonion_long_double"></a><p> |
|---|
| 410 | </p> |
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| 411 | <pre class="programlisting"> |
|---|
| 412 | <span class="keyword">template</span><span class="special"><></span> |
|---|
| 413 | <span class="keyword">class</span> <span class="identifier">octonion</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> |
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| 414 | <span class="special">{</span> |
|---|
| 415 | <span class="keyword">public</span><span class="special">:</span> |
|---|
| 416 | <span class="keyword">typedef</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">value_type</span><span class="special">;</span> |
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| 417 | |
|---|
| 418 | <span class="keyword">explicit</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.constructors">octonion</a><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> |
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| 419 | <span class="keyword">explicit</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.constructors">octonion</a><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> |
|---|
| 420 | <span class="keyword">explicit</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.constructors">octonion</a><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">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">z1</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> |
|---|
| 421 | <span class="keyword">explicit</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.constructors">octonion</a><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> |
|---|
| 422 | <span class="keyword">explicit</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.constructors">octonion</a><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> |
|---|
| 423 | |
|---|
| 424 | <span class="keyword">long</span> <span class="keyword">double</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.real_and_unreal_parts">real</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> |
|---|
| 425 | <span class="identifier">octonion</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.real_and_unreal_parts">unreal</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> |
|---|
| 426 | |
|---|
| 427 | <span class="keyword">long</span> <span class="keyword">double</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.individual_real_components">R_component_1</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> |
|---|
| 428 | <span class="keyword">long</span> <span class="keyword">double</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.individual_real_components">R_component_2</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> |
|---|
| 429 | <span class="keyword">long</span> <span class="keyword">double</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.individual_real_components">R_component_3</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> |
|---|
| 430 | <span class="keyword">long</span> <span class="keyword">double</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.individual_real_components">R_component_4</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> |
|---|
| 431 | <span class="keyword">long</span> <span class="keyword">double</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.individual_real_components">R_component_5</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> |
|---|
| 432 | <span class="keyword">long</span> <span class="keyword">double</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.individual_real_components">R_component_6</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> |
|---|
| 433 | <span class="keyword">long</span> <span class="keyword">double</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.individual_real_components">R_component_7</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> |
|---|
| 434 | <span class="keyword">long</span> <span class="keyword">double</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.individual_real_components">R_component_8</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> |
|---|
| 435 | |
|---|
| 436 | <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> <a href="octonions.html#boost_math.octonions.octonion_member_functions.individual_complex_components">C_component_1</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> |
|---|
| 437 | <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> <a href="octonions.html#boost_math.octonions.octonion_member_functions.individual_complex_components">C_component_2</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> |
|---|
| 438 | <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> <a href="octonions.html#boost_math.octonions.octonion_member_functions.individual_complex_components">C_component_3</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> |
|---|
| 439 | <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> <a href="octonions.html#boost_math.octonions.octonion_member_functions.individual_complex_components">C_component_4</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> |
|---|
| 440 | |
|---|
| 441 | <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> <a href="octonions.html#boost_math.octonions.octonion_member_functions.individual_quaternion_components">H_component_1</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> |
|---|
| 442 | <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> <a href="octonions.html#boost_math.octonions.octonion_member_functions.individual_quaternion_components">H_component_2</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> |
|---|
| 443 | |
|---|
| 444 | <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="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.assignment_operators">operator =</a> <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_affecter</span><span class="special">);</span> |
|---|
| 445 | <span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span> |
|---|
| 446 | <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="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.assignment_operators">operator =</a> <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> |
|---|
| 447 | <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="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.assignment_operators">operator =</a> <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">a_affecter</span><span class="special">);</span> |
|---|
| 448 | <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="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.assignment_operators">operator =</a> <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">a_affecter</span><span class="special">);</span> |
|---|
| 449 | <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="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.assignment_operators">operator =</a> <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">a_affecter</span><span class="special">);</span> |
|---|
| 450 | |
|---|
| 451 | <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="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.other_member_operators">operator +=</a> <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">rhs</span><span class="special">);</span> |
|---|
| 452 | <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="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.other_member_operators">operator +=</a> <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">rhs</span><span class="special">);</span> |
|---|
| 453 | <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="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.other_member_operators">operator +=</a> <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">rhs</span><span class="special">);</span> |
|---|
| 454 | <span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span> |
|---|
| 455 | <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="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.other_member_operators">operator +=</a> <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> |
|---|
| 456 | |
|---|
| 457 | <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="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.other_member_operators">operator -=</a> <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">rhs</span><span class="special">);</span> |
|---|
| 458 | <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="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.other_member_operators">operator -=</a> <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">rhs</span><span class="special">);</span> |
|---|
| 459 | <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="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.other_member_operators">operator -=</a> <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">rhs</span><span class="special">);</span> |
|---|
| 460 | <span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span> |
|---|
| 461 | <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="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.other_member_operators">operator -=</a> <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> |
|---|
| 462 | |
|---|
| 463 | <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="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.other_member_operators">operator *=</a> <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">rhs</span><span class="special">);</span> |
|---|
| 464 | <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="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.other_member_operators">operator *=</a> <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">rhs</span><span class="special">);</span> |
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| 465 | <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="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.other_member_operators">operator *=</a> <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">rhs</span><span class="special">);</span> |
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| 466 | <span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span> |
|---|
| 467 | <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="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.other_member_operators">operator *=</a> <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> |
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| 468 | |
|---|
| 469 | <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="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.other_member_operators">operator /=</a> <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">rhs</span><span class="special">);</span> |
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| 470 | <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="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.other_member_operators">operator /=</a> <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">rhs</span><span class="special">);</span> |
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| 471 | <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="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.other_member_operators">operator /=</a> <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">rhs</span><span class="special">);</span> |
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| 472 | <span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span> |
|---|
| 473 | <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="special">&</span> <a href="octonions.html#boost_math.octonions.octonion_member_functions.other_member_operators">operator /=</a> <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> |
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| 474 | <span class="special">};</span> |
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| 475 | |
|---|
| 476 | <span class="special">}</span> <span class="special">}</span> <span class="comment">// namespaces |
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| 477 | </span></pre> |
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| 478 | </div> |
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| 479 | <div class="section" lang="en"> |
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| 480 | <div class="titlepage"><div><div><h3 class="title"> |
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| 481 | <a name="boost_math.octonions.octonion_member_typedefs"></a>Octonion Member Typedefs</h3></div></div></div> |
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| 482 | <p> |
|---|
| 483 | <span class="bold"><strong>value_type</strong></span> |
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| 484 | </p> |
|---|
| 485 | <p> |
|---|
| 486 | Template version: |
|---|
| 487 | </p> |
|---|
| 488 | <pre class="programlisting"> |
|---|
| 489 | <span class="keyword">typedef</span> <span class="identifier">T</span> <span class="identifier">value_type</span><span class="special">;</span> |
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| 490 | </pre> |
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| 491 | <p> |
|---|
| 492 | Float specialization version: |
|---|
| 493 | </p> |
|---|
| 494 | <pre class="programlisting"> |
|---|
| 495 | <span class="keyword">typedef</span> <span class="keyword">float</span> <span class="identifier">value_type</span><span class="special">;</span> |
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| 496 | </pre> |
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| 497 | <p> |
|---|
| 498 | Double specialization version: |
|---|
| 499 | </p> |
|---|
| 500 | <pre class="programlisting"> |
|---|
| 501 | <span class="keyword">typedef</span> <span class="keyword">double</span> <span class="identifier">value_type</span><span class="special">;</span> |
|---|
| 502 | </pre> |
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| 503 | <p> |
|---|
| 504 | Long double specialization version: |
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| 505 | </p> |
|---|
| 506 | <pre class="programlisting"> |
|---|
| 507 | <span class="keyword">typedef</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">value_type</span><span class="special">;</span> |
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| 508 | </pre> |
|---|
| 509 | <p> |
|---|
| 510 | These provide easy acces to the type the template is built upon. |
|---|
| 511 | </p> |
|---|
| 512 | </div> |
|---|
| 513 | <div class="section" lang="en"> |
|---|
| 514 | <div class="titlepage"><div><div><h3 class="title"> |
|---|
| 515 | <a name="boost_math.octonions.octonion_member_functions"></a>Octonion Member Functions</h3></div></div></div> |
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| 516 | <a name="boost_math.octonions.octonion_member_functions.constructors"></a><h3> |
|---|
| 517 | <a name="id1362806"></a> |
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| 518 | Constructors |
|---|
| 519 | </h3> |
|---|
| 520 | <p> |
|---|
| 521 | Template version: |
|---|
| 522 | </p> |
|---|
| 523 | <pre class="programlisting"> |
|---|
| 524 | <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> |
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| 525 | <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> |
|---|
| 526 | <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> |
|---|
| 527 | <span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span> |
|---|
| 528 | <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> |
|---|
| 529 | </pre> |
|---|
| 530 | <p> |
|---|
| 531 | Float specialization version: |
|---|
| 532 | </p> |
|---|
| 533 | <pre class="programlisting"> |
|---|
| 534 | <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> |
|---|
| 535 | <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> |
|---|
| 536 | <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> |
|---|
| 537 | <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> |
|---|
| 538 | <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> |
|---|
| 539 | </pre> |
|---|
| 540 | <p> |
|---|
| 541 | Double specialization version: |
|---|
| 542 | </p> |
|---|
| 543 | <pre class="programlisting"> |
|---|
| 544 | <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> |
|---|
| 545 | <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> |
|---|
| 546 | <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> |
|---|
| 547 | <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> |
|---|
| 548 | <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> |
|---|
| 549 | </pre> |
|---|
| 550 | <p> |
|---|
| 551 | Long double specialization version: |
|---|
| 552 | </p> |
|---|
| 553 | <pre class="programlisting"> |
|---|
| 554 | <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> |
|---|
| 555 | <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> |
|---|
| 556 | <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> |
|---|
| 557 | <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> |
|---|
| 558 | <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> |
|---|
| 559 | </pre> |
|---|
| 560 | <p> |
|---|
| 561 | A default constructor is provided for each form, which initializes each component |
|---|
| 562 | to the default values for their type (i.e. zero for floating numbers). This |
|---|
| 563 | constructor can also accept one to eight base type arguments. A constructor |
|---|
| 564 | is also provided to build octonions from one to four complex numbers sharing |
|---|
| 565 | the same base type, and another taking one or two quaternions sharing the |
|---|
| 566 | same base type. The unspecialized template also sports a templarized copy |
|---|
| 567 | constructor, while the specialized forms have copy constructors from the |
|---|
| 568 | other two specializations, which are explicit when a risk of precision loss |
|---|
| 569 | exists. For the unspecialized form, the base type's constructors must not |
|---|
| 570 | throw. |
|---|
| 571 | </p> |
|---|
| 572 | <p> |
|---|
| 573 | Destructors and untemplated copy constructors (from the same type) are provided |
|---|
| 574 | by the compiler. Converting copy constructors make use of a templated helper |
|---|
| 575 | function in a "detail" subnamespace. |
|---|
| 576 | </p> |
|---|
| 577 | <a name="boost_math.octonions.octonion_member_functions.other_member_functions"></a><h3> |
|---|
| 578 | <a name="id1558871"></a> |
|---|
| 579 | Other member functions |
|---|
| 580 | </h3> |
|---|
| 581 | <a name="boost_math.octonions.octonion_member_functions.real_and_unreal_parts"></a><h4> |
|---|
| 582 | <a name="id1558884"></a> |
|---|
| 583 | Real and Unreal Parts |
|---|
| 584 | </h4> |
|---|
| 585 | <pre class="programlisting"> |
|---|
| 586 | <span class="identifier">T</span> <span class="identifier">real</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> |
|---|
| 587 | <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> |
|---|
| 588 | </pre> |
|---|
| 589 | <p> |
|---|
| 590 | Like complex number, octonions do have a meaningful notion of "real |
|---|
| 591 | part", but unlike them there is no meaningful notion of "imaginary |
|---|
| 592 | part". Instead there is an "unreal part" which itself is a |
|---|
| 593 | octonion, and usually nothing simpler (as opposed to the complex number case). |
|---|
| 594 | These are returned by the first two functions. |
|---|
| 595 | </p> |
|---|
| 596 | <a name="boost_math.octonions.octonion_member_functions.individual_real_components"></a><h4> |
|---|
| 597 | <a name="id1558977"></a> |
|---|
| 598 | Individual Real Components |
|---|
| 599 | </h4> |
|---|
| 600 | <pre class="programlisting"> |
|---|
| 601 | <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> |
|---|
| 602 | <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> |
|---|
| 603 | <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> |
|---|
| 604 | <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> |
|---|
| 605 | <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> |
|---|
| 606 | <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> |
|---|
| 607 | <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> |
|---|
| 608 | <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> |
|---|
| 609 | </pre> |
|---|
| 610 | <p> |
|---|
| 611 | A octonion having eight real components, these are returned by these eight |
|---|
| 612 | functions. Hence real and R_component_1 return the same value. |
|---|
| 613 | </p> |
|---|
| 614 | <a name="boost_math.octonions.octonion_member_functions.individual_complex_components"></a><h4> |
|---|
| 615 | <a name="id1559203"></a> |
|---|
| 616 | Individual Complex Components |
|---|
| 617 | </h4> |
|---|
| 618 | <pre class="programlisting"> |
|---|
| 619 | <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> |
|---|
| 620 | <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> |
|---|
| 621 | <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> |
|---|
| 622 | <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> |
|---|
| 623 | </pre> |
|---|
| 624 | <p> |
|---|
| 625 | A octonion likewise has four complex components. Actually, octonions are |
|---|
| 626 | indeed a (left) vector field over the complexes, but beware, as for any octonion |
|---|
| 627 | <span class="emphasis"><em><code class="literal">o = |
|---|
| 628 | α + βi + γj + δk + εe' + ζi' + ηj' + θk' |
|---|
| 629 | </code></em></span> we also have <span class="emphasis"><em><code class="literal">o = ( |
|---|
| 630 | α + βi) + (γ + δi)j + (ε + ζi)e' + (η - θi)j' |
|---|
| 631 | </code></em></span> (note the <span class="bold"><strong>minus</strong></span> sign |
|---|
| 632 | in the last factor). What the C_component_n functions return, however, are |
|---|
| 633 | the complexes which could be used to build the octonion using the constructor, |
|---|
| 634 | and <span class="bold"><strong>not</strong></span> the components of the octonion on |
|---|
| 635 | the basis <span class="emphasis"><em><code class="literal">(1, j, e', j')</code></em></span>. |
|---|
| 636 | </p> |
|---|
| 637 | <a name="boost_math.octonions.octonion_member_functions.individual_quaternion_components"></a><h4> |
|---|
| 638 | <a name="id1559474"></a> |
|---|
| 639 | Individual Quaternion Components |
|---|
| 640 | </h4> |
|---|
| 641 | <pre class="programlisting"> |
|---|
| 642 | <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> |
|---|
| 643 | <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> |
|---|
| 644 | </pre> |
|---|
| 645 | <p> |
|---|
| 646 | Likewise, for any octonion <span class="emphasis"><em><code class="literal">o = |
|---|
| 647 | α + βi + γj + δk + εe' + ζi' + ηj' + θk' |
|---|
| 648 | </code></em></span> we also have <span class="emphasis"><em><code class="literal">o = ( |
|---|
| 649 | α + βi + γj + δk) + (ε + ζi + ηj - θj)e' |
|---|
| 650 | </code></em></span>, though there is no meaningful vector-space-like structure |
|---|
| 651 | based on the quaternions. What the H_component_n functions return are the |
|---|
| 652 | quaternions which could be used to build the octonion using the constructor. |
|---|
| 653 | </p> |
|---|
| 654 | <a name="boost_math.octonions.octonion_member_functions.octonion_member_operators"></a><h3> |
|---|
| 655 | <a name="id1559640"></a> |
|---|
| 656 | Octonion Member Operators |
|---|
| 657 | </h3> |
|---|
| 658 | <a name="boost_math.octonions.octonion_member_functions.assignment_operators"></a><h4> |
|---|
| 659 | <a name="id1559653"></a> |
|---|
| 660 | Assignment Operators |
|---|
| 661 | </h4> |
|---|
| 662 | <pre class="programlisting"> |
|---|
| 663 | <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> |
|---|
| 664 | <span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span> |
|---|
| 665 | <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> |
|---|
| 666 | <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> |
|---|
| 667 | <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> |
|---|
| 668 | <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> |
|---|
| 669 | </pre> |
|---|
| 670 | <p> |
|---|
| 671 | These perform the expected assignment, with type modification if necessary |
|---|
| 672 | (for instance, assigning from a base type will set the real part to that |
|---|
| 673 | value, and all other components to zero). For the unspecialized form, the |
|---|
| 674 | base type's assignment operators must not throw. |
|---|
| 675 | </p> |
|---|
| 676 | <a name="boost_math.octonions.octonion_member_functions.other_member_operators"></a><h4> |
|---|
| 677 | <a name="id1560117"></a> |
|---|
| 678 | Other Member Operators |
|---|
| 679 | </h4> |
|---|
| 680 | <pre class="programlisting"> |
|---|
| 681 | <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> |
|---|
| 682 | <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> |
|---|
| 683 | <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> |
|---|
| 684 | <span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span> |
|---|
| 685 | <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> |
|---|
| 686 | </pre> |
|---|
| 687 | <p> |
|---|
| 688 | 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> |
|---|
| 689 | and store the result in <code class="computeroutput"><span class="special">*</span><span class="keyword">this</span></code>. |
|---|
| 690 | The unspecialized form has exception guards, which the specialized forms |
|---|
| 691 | do not, so as to insure exception safety. For the unspecialized form, the |
|---|
| 692 | base type's assignment operators must not throw. |
|---|
| 693 | </p> |
|---|
| 694 | <pre class="programlisting"> |
|---|
| 695 | <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> |
|---|
| 696 | <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> |
|---|
| 697 | <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> |
|---|
| 698 | <span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span> |
|---|
| 699 | <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> |
|---|
| 700 | </pre> |
|---|
| 701 | <p> |
|---|
| 702 | 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> |
|---|
| 703 | and store the result in <code class="computeroutput"><span class="special">*</span><span class="keyword">this</span></code>. |
|---|
| 704 | The unspecialized form has exception guards, which the specialized forms |
|---|
| 705 | do not, so as to insure exception safety. For the unspecialized form, the |
|---|
| 706 | base type's assignment operators must not throw. |
|---|
| 707 | </p> |
|---|
| 708 | <pre class="programlisting"> |
|---|
| 709 | <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> |
|---|
| 710 | <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> |
|---|
| 711 | <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> |
|---|
| 712 | <span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span> |
|---|
| 713 | <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> |
|---|
| 714 | </pre> |
|---|
| 715 | <p> |
|---|
| 716 | 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> |
|---|
| 717 | in this order (order is important as multiplication is not commutative for |
|---|
| 718 | octonions) and store the result in <code class="computeroutput"><span class="special">*</span><span class="keyword">this</span></code>. The unspecialized form has exception |
|---|
| 719 | guards, which the specialized forms do not, so as to insure exception safety. |
|---|
| 720 | For the unspecialized form, the base type's assignment operators must not |
|---|
| 721 | throw. Also, for clarity's sake, you should always group the factors in a |
|---|
| 722 | multiplication by groups of two, as the multiplication is not even associative |
|---|
| 723 | on the octonions (though there are of course cases where this does not matter, |
|---|
| 724 | it usually does). |
|---|
| 725 | </p> |
|---|
| 726 | <pre class="programlisting"> |
|---|
| 727 | <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> |
|---|
| 728 | <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> |
|---|
| 729 | <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> |
|---|
| 730 | <span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">></span> |
|---|
| 731 | <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> |
|---|
| 732 | </pre> |
|---|
| 733 | <p> |
|---|
| 734 | 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> |
|---|
| 735 | in this order (order is important as multiplication is not commutative for |
|---|
| 736 | octonions) and store the result in <code class="computeroutput"><span class="special">*</span><span class="keyword">this</span></code>. The unspecialized form has exception |
|---|
| 737 | guards, which the specialized forms do not, so as to insure exception safety. |
|---|
| 738 | For the unspecialized form, the base type's assignment operators must not |
|---|
| 739 | throw. As for the multiplication, remember to group any two factors using |
|---|
| 740 | parenthesis. |
|---|
| 741 | </p> |
|---|
| 742 | </div> |
|---|
| 743 | <div class="section" lang="en"> |
|---|
| 744 | <div class="titlepage"><div><div><h3 class="title"> |
|---|
| 745 | <a name="boost_math.octonions.octonion_non_member_operators"></a>Octonion Non-Member Operators</h3></div></div></div> |
|---|
| 746 | <a name="boost_math.octonions.octonion_non_member_operators.unary_plus_and_minus_operators"></a><h4> |
|---|
| 747 | <a name="id1561781"></a> |
|---|
| 748 | Unary Plus and Minus Operators |
|---|
| 749 | </h4> |
|---|
| 750 | <pre class="programlisting"> |
|---|
| 751 | <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="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">o</span><span class="special">);</span> |
|---|
| 752 | </pre> |
|---|
| 753 | <p> |
|---|
| 754 | This unary operator simply returns o. |
|---|
| 755 | </p> |
|---|
| 756 | <pre class="programlisting"> |
|---|
| 757 | <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="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">o</span><span class="special">);</span> |
|---|
| 758 | </pre> |
|---|
| 759 | <p> |
|---|
| 760 | This unary operator returns the opposite of o. |
|---|
| 761 | </p> |
|---|
| 762 | <a name="boost_math.octonions.octonion_non_member_operators.binary_addition_operators"></a><h4> |
|---|
| 763 | <a name="id1562011"></a> |
|---|
| 764 | Binary Addition Operators |
|---|
| 765 | </h4> |
|---|
| 766 | <pre class="programlisting"> |
|---|
| 767 | <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="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">lhs</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">rhs</span><span class="special">);</span> |
|---|
| 768 | <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="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">lhs</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> |
|---|
| 769 | <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="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">lhs</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">rhs</span><span class="special">);</span> |
|---|
| 770 | <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="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">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</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> |
|---|
| 771 | <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="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">lhs</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">rhs</span><span class="special">);</span> |
|---|
| 772 | <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="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">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</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> |
|---|
| 773 | <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="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">lhs</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">rhs</span><span class="special">);</span> |
|---|
| 774 | </pre> |
|---|
| 775 | <p> |
|---|
| 776 | These operators return <code class="computeroutput"><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">>(</span><span class="identifier">lhs</span><span class="special">)</span> <span class="special">+=</span> <span class="identifier">rhs</span></code>. |
|---|
| 777 | </p> |
|---|
| 778 | <a name="boost_math.octonions.octonion_non_member_operators.binary_subtraction_operators"></a><h4> |
|---|
| 779 | <a name="id1563077"></a> |
|---|
| 780 | Binary Subtraction Operators |
|---|
| 781 | </h4> |
|---|
| 782 | <pre class="programlisting"> |
|---|
| 783 | <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="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">lhs</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">rhs</span><span class="special">);</span> |
|---|
| 784 | <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="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">lhs</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> |
|---|
| 785 | <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="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">lhs</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">rhs</span><span class="special">);</span> |
|---|
| 786 | <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="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">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</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> |
|---|
| 787 | <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="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">lhs</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">rhs</span><span class="special">);</span> |
|---|
| 788 | <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="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">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</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> |
|---|
| 789 | <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="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">lhs</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">rhs</span><span class="special">);</span> |
|---|
| 790 | </pre> |
|---|
| 791 | <p> |
|---|
| 792 | These operators return <code class="computeroutput"><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">>(</span><span class="identifier">lhs</span><span class="special">)</span> <span class="special">-=</span> <span class="identifier">rhs</span></code>. |
|---|
| 793 | </p> |
|---|
| 794 | <a name="boost_math.octonions.octonion_non_member_operators.binary_multiplication_operators"></a><h4> |
|---|
| 795 | <a name="id1564143"></a> |
|---|
| 796 | Binary Multiplication Operators |
|---|
| 797 | </h4> |
|---|
| 798 | <pre class="programlisting"> |
|---|
| 799 | <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="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">lhs</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">rhs</span><span class="special">);</span> |
|---|
| 800 | <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="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">lhs</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> |
|---|
| 801 | <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="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">lhs</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">rhs</span><span class="special">);</span> |
|---|
| 802 | <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="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">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</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> |
|---|
| 803 | <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="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">lhs</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">rhs</span><span class="special">);</span> |
|---|
| 804 | <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="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">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</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> |
|---|
| 805 | <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="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">lhs</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">rhs</span><span class="special">);</span> |
|---|
| 806 | </pre> |
|---|
| 807 | <p> |
|---|
| 808 | These operators return <code class="computeroutput"><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">>(</span><span class="identifier">lhs</span><span class="special">)</span> <span class="special">*=</span> <span class="identifier">rhs</span></code>. |
|---|
| 809 | </p> |
|---|
| 810 | <a name="boost_math.octonions.octonion_non_member_operators.binary_division_operators"></a><h4> |
|---|
| 811 | <a name="id1565208"></a> |
|---|
| 812 | Binary Division Operators |
|---|
| 813 | </h4> |
|---|
| 814 | <pre class="programlisting"> |
|---|
| 815 | <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="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">lhs</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">rhs</span><span class="special">);</span> |
|---|
| 816 | <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="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">lhs</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> |
|---|
| 817 | <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="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">lhs</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">rhs</span><span class="special">);</span> |
|---|
| 818 | <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="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">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</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> |
|---|
| 819 | <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="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">lhs</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">rhs</span><span class="special">);</span> |
|---|
| 820 | <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="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">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</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> |
|---|
| 821 | <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="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">lhs</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">rhs</span><span class="special">);</span> |
|---|
| 822 | </pre> |
|---|
| 823 | <p> |
|---|
| 824 | These operators return <code class="computeroutput"><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">>(</span><span class="identifier">lhs</span><span class="special">)</span> <span class="special">/=</span> <span class="identifier">rhs</span></code>. |
|---|
| 825 | It is of course still an error to divide by zero... |
|---|
| 826 | </p> |
|---|
| 827 | <a name="boost_math.octonions.octonion_non_member_operators.binary_equality_operators"></a><h4> |
|---|
| 828 | <a name="id1566275"></a> |
|---|
| 829 | Binary Equality Operators |
|---|
| 830 | </h4> |
|---|
| 831 | <pre class="programlisting"> |
|---|
| 832 | <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="keyword">bool</span> <span class="keyword">operator</span> <span class="special">==</span> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</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">rhs</span><span class="special">);</span> |
|---|
| 833 | <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="keyword">bool</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">lhs</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> |
|---|
| 834 | <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="keyword">bool</span> <span class="keyword">operator</span> <span class="special">==</span> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</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">rhs</span><span class="special">);</span> |
|---|
| 835 | <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="keyword">bool</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">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</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> |
|---|
| 836 | <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="keyword">bool</span> <span class="keyword">operator</span> <span class="special">==</span> <span class="special">(::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</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">rhs</span><span class="special">);</span> |
|---|
| 837 | <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="keyword">bool</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">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</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> |
|---|
| 838 | <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="keyword">bool</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">lhs</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">rhs</span><span class="special">);</span> |
|---|
| 839 | </pre> |
|---|
| 840 | <p> |
|---|
| 841 | These return true if and only if the four components of <code class="computeroutput"><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">>(</span><span class="identifier">lhs</span><span class="special">)</span></code> are |
|---|
| 842 | equal to their counterparts in <code class="computeroutput"><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">>(</span><span class="identifier">rhs</span><span class="special">)</span></code>. As |
|---|
| 843 | with any floating-type entity, this is essentially meaningless. |
|---|
| 844 | </p> |
|---|
| 845 | <a name="boost_math.octonions.octonion_non_member_operators.binary_inequality_operators"></a><h4> |
|---|
| 846 | <a name="id1567269"></a> |
|---|
| 847 | Binary Inequality Operators |
|---|
| 848 | </h4> |
|---|
| 849 | <pre class="programlisting"> |
|---|
| 850 | <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="keyword">bool</span> <span class="keyword">operator</span> <span class="special">!=</span> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</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">rhs</span><span class="special">);</span> |
|---|
| 851 | <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="keyword">bool</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">lhs</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> |
|---|
| 852 | <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="keyword">bool</span> <span class="keyword">operator</span> <span class="special">!=</span> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</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">rhs</span><span class="special">);</span> |
|---|
| 853 | <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="keyword">bool</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">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</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> |
|---|
| 854 | <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="keyword">bool</span> <span class="keyword">operator</span> <span class="special">!=</span> <span class="special">(::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">lhs</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">rhs</span><span class="special">);</span> |
|---|
| 855 | <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="keyword">bool</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">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special"><</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> |
|---|
| 856 | <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="keyword">bool</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">lhs</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">rhs</span><span class="special">);</span> |
|---|
| 857 | </pre> |
|---|
| 858 | <p> |
|---|
| 859 | These return true if and only if <code class="computeroutput"><span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">>(</span><span class="identifier">lhs</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="identifier">rhs</span><span class="special">)</span></code> is |
|---|
| 860 | false. As with any floating-type entity, this is essentially meaningless. |
|---|
| 861 | </p> |
|---|
| 862 | <a name="boost_math.octonions.octonion_non_member_operators.stream_extractor"></a><h4> |
|---|
| 863 | <a name="id1568264"></a> |
|---|
| 864 | Stream Extractor |
|---|
| 865 | </h4> |
|---|
| 866 | <pre class="programlisting"> |
|---|
| 867 | <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="keyword">typename</span> <span class="identifier">charT</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">traits</span><span class="special">></span> |
|---|
| 868 | <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_istream</span><span class="special"><</span><span class="identifier">charT</span><span class="special">,</span><span class="identifier">traits</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">basic_istream</span><span class="special"><</span><span class="identifier">charT</span><span class="special">,</span><span class="identifier">traits</span><span class="special">></span> <span class="special">&</span> <span class="identifier">is</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="identifier">o</span><span class="special">);</span> |
|---|
| 869 | </pre> |
|---|
| 870 | <p> |
|---|
| 871 | Extracts an octonion <code class="computeroutput"><span class="identifier">o</span></code>. We |
|---|
| 872 | accept any format which seems reasonable. However, since this leads to a |
|---|
| 873 | great many ambiguities, decisions were made to lift these. In case of doubt, |
|---|
| 874 | stick to lists of reals. |
|---|
| 875 | </p> |
|---|
| 876 | <p> |
|---|
| 877 | The input values must be convertible to T. If bad input is encountered, calls |
|---|
| 878 | <code class="computeroutput"><span class="identifier">is</span><span class="special">.</span><span class="identifier">setstate</span><span class="special">(</span><span class="identifier">ios</span><span class="special">::</span><span class="identifier">failbit</span><span class="special">)</span></code> (which may throw <code class="computeroutput"><span class="identifier">ios</span><span class="special">::</span><span class="identifier">failure</span></code> |
|---|
| 879 | (27.4.5.3)). |
|---|
| 880 | </p> |
|---|
| 881 | <p> |
|---|
| 882 | Returns <code class="computeroutput"><span class="identifier">is</span></code>. |
|---|
| 883 | </p> |
|---|
| 884 | <a name="boost_math.octonions.octonion_non_member_operators.stream_inserter"></a><h4> |
|---|
| 885 | <a name="id1568577"></a> |
|---|
| 886 | Stream Inserter |
|---|
| 887 | </h4> |
|---|
| 888 | <pre class="programlisting"> |
|---|
| 889 | <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="keyword">typename</span> <span class="identifier">charT</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">traits</span><span class="special">></span> |
|---|
| 890 | <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_ostream</span><span class="special"><</span><span class="identifier">charT</span><span class="special">,</span><span class="identifier">traits</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">basic_ostream</span><span class="special"><</span><span class="identifier">charT</span><span class="special">,</span><span class="identifier">traits</span><span class="special">></span> <span class="special">&</span> <span class="identifier">os</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> |
|---|
| 891 | </pre> |
|---|
| 892 | <p> |
|---|
| 893 | Inserts the octonion <code class="computeroutput"><span class="identifier">o</span></code> onto |
|---|
| 894 | the stream <code class="computeroutput"><span class="identifier">os</span></code> as if it were |
|---|
| 895 | implemented as follows: |
|---|
| 896 | </p> |
|---|
| 897 | <pre class="programlisting"> |
|---|
| 898 | <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="keyword">typename</span> <span class="identifier">charT</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">traits</span><span class="special">></span> |
|---|
| 899 | <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_ostream</span><span class="special"><</span><span class="identifier">charT</span><span class="special">,</span><span class="identifier">traits</span><span class="special">></span> <span class="special">&</span> <span class="keyword">operator</span> <span class="special"><<</span> <span class="special">(</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_ostream</span><span class="special"><</span><span class="identifier">charT</span><span class="special">,</span><span class="identifier">traits</span><span class="special">></span> <span class="special">&</span> <span class="identifier">os</span><span class="special">,</span> |
|---|
| 900 | <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> |
|---|
| 901 | <span class="special">{</span> |
|---|
| 902 | <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_ostringstream</span><span class="special"><</span><span class="identifier">charT</span><span class="special">,</span><span class="identifier">traits</span><span class="special">></span> <span class="identifier">s</span><span class="special">;</span> |
|---|
| 903 | |
|---|
| 904 | <span class="identifier">s</span><span class="special">.</span><span class="identifier">flags</span><span class="special">(</span><span class="identifier">os</span><span class="special">.</span><span class="identifier">flags</span><span class="special">());</span> |
|---|
| 905 | <span class="identifier">s</span><span class="special">.</span><span class="identifier">imbue</span><span class="special">(</span><span class="identifier">os</span><span class="special">.</span><span class="identifier">getloc</span><span class="special">());</span> |
|---|
| 906 | <span class="identifier">s</span><span class="special">.</span><span class="identifier">precision</span><span class="special">(</span><span class="identifier">os</span><span class="special">.</span><span class="identifier">precision</span><span class="special">());</span> |
|---|
| 907 | |
|---|
| 908 | <span class="identifier">s</span> <span class="special"><<</span> <span class="char">'('</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="special"><<</span> <span class="char">','</span> |
|---|
| 909 | <span class="special"><<</span> <span class="identifier">o</span><span class="special">.</span><span class="identifier">R_component_2</span><span class="special">()</span> <span class="special"><<</span> <span class="char">','</span> |
|---|
| 910 | <span class="special"><<</span> <span class="identifier">o</span><span class="special">.</span><span class="identifier">R_component_3</span><span class="special">()</span> <span class="special"><<</span> <span class="char">','</span> |
|---|
| 911 | <span class="special"><<</span> <span class="identifier">o</span><span class="special">.</span><span class="identifier">R_component_4</span><span class="special">()</span> <span class="special"><<</span> <span class="char">','</span> |
|---|
| 912 | <span class="special"><<</span> <span class="identifier">o</span><span class="special">.</span><span class="identifier">R_component_5</span><span class="special">()</span> <span class="special"><<</span> <span class="char">','</span> |
|---|
| 913 | <span class="special"><<</span> <span class="identifier">o</span><span class="special">.</span><span class="identifier">R_component_6</span><span class="special">()</span> <span class="special"><<</span> <span class="char">','</span> |
|---|
| 914 | <span class="special"><<</span> <span class="identifier">o</span><span class="special">.</span><span class="identifier">R_component_7</span><span class="special">()</span> <span class="special"><<</span> <span class="char">','</span> |
|---|
| 915 | <span class="special"><<</span> <span class="identifier">o</span><span class="special">.</span><span class="identifier">R_component_8</span><span class="special">()</span> <span class="special"><<</span> <span class="char">')'</span><span class="special">;</span> |
|---|
| 916 | |
|---|
| 917 | <span class="keyword">return</span> <span class="identifier">os</span> <span class="special"><<</span> <span class="identifier">s</span><span class="special">.</span><span class="identifier">str</span><span class="special">();</span> |
|---|
| 918 | <span class="special">}</span> |
|---|
| 919 | </pre> |
|---|
| 920 | </div> |
|---|
| 921 | <div class="section" lang="en"> |
|---|
| 922 | <div class="titlepage"><div><div><h3 class="title"> |
|---|
| 923 | <a name="boost_math.octonions.octonion_value_operations"></a>Octonion Value Operations</h3></div></div></div> |
|---|
| 924 | <a name="boost_math.octonions.octonion_value_operations.real_and_unreal"></a><h4> |
|---|
| 925 | <a name="id1569561"></a> |
|---|
| 926 | Real and Unreal |
|---|
| 927 | </h4> |
|---|
| 928 | <pre class="programlisting"> |
|---|
| 929 | <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> |
|---|
| 930 | <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> |
|---|
| 931 | </pre> |
|---|
| 932 | <p> |
|---|
| 933 | These return <code class="computeroutput"><span class="identifier">o</span><span class="special">.</span><span class="identifier">real</span><span class="special">()</span></code> |
|---|
| 934 | and <code class="computeroutput"><span class="identifier">o</span><span class="special">.</span><span class="identifier">unreal</span><span class="special">()</span></code> |
|---|
| 935 | respectively. |
|---|
| 936 | </p> |
|---|
| 937 | <a name="boost_math.octonions.octonion_value_operations.conj"></a><h4> |
|---|
| 938 | <a name="id1569797"></a> |
|---|
| 939 | conj |
|---|
| 940 | </h4> |
|---|
| 941 | <pre class="programlisting"> |
|---|
| 942 | <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> |
|---|
| 943 | </pre> |
|---|
| 944 | <p> |
|---|
| 945 | This returns the conjugate of the octonion. |
|---|
| 946 | </p> |
|---|
| 947 | <a name="boost_math.octonions.octonion_value_operations.sup"></a><h4> |
|---|
| 948 | <a name="id1569912"></a> |
|---|
| 949 | sup |
|---|
| 950 | </h4> |
|---|
| 951 | <pre class="programlisting"> |
|---|
| 952 | <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> |
|---|
| 953 | </pre> |
|---|
| 954 | <p> |
|---|
| 955 | 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. |
|---|
| 956 | </p> |
|---|
| 957 | <a name="boost_math.octonions.octonion_value_operations.l1"></a><h4> |
|---|
| 958 | <a name="id1570069"></a> |
|---|
| 959 | l1 |
|---|
| 960 | </h4> |
|---|
| 961 | <pre class="programlisting"> |
|---|
| 962 | <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> |
|---|
| 963 | </pre> |
|---|
| 964 | <p> |
|---|
| 965 | 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. |
|---|
| 966 | </p> |
|---|
| 967 | <a name="boost_math.octonions.octonion_value_operations.abs"></a><h4> |
|---|
| 968 | <a name="id1570226"></a> |
|---|
| 969 | abs |
|---|
| 970 | </h4> |
|---|
| 971 | <pre class="programlisting"> |
|---|
| 972 | <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> |
|---|
| 973 | </pre> |
|---|
| 974 | <p> |
|---|
| 975 | This return the magnitude (Euclidian norm) of the octonion. |
|---|
| 976 | </p> |
|---|
| 977 | <a name="boost_math.octonions.octonion_value_operations.norm"></a><h4> |
|---|
| 978 | <a name="id1570327"></a> |
|---|
| 979 | norm |
|---|
| 980 | </h4> |
|---|
| 981 | <pre class="programlisting"> |
|---|
| 982 | <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> |
|---|
| 983 | </pre> |
|---|
| 984 | <p> |
|---|
| 985 | This return the (Cayley) norm of the octonion. The term "norm" |
|---|
| 986 | might be confusing, as most people associate it with the Euclidian norm (and |
|---|
| 987 | quadratic functionals). For this version of (the mathematical objects known |
|---|
| 988 | as) octonions, the Euclidian norm (also known as magnitude) is the square |
|---|
| 989 | root of the Cayley norm. |
|---|
| 990 | </p> |
|---|
| 991 | </div> |
|---|
| 992 | <div class="section" lang="en"> |
|---|
| 993 | <div class="titlepage"><div><div><h3 class="title"> |
|---|
| 994 | <a name="boost_math.octonions.quaternion_creation_functions"></a>Quaternion Creation Functions</h3></div></div></div> |
|---|
| 995 | <pre class="programlisting"> |
|---|
| 996 | <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">spherical</span><span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rho</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">theta</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">phi1</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">phi2</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">phi3</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">phi4</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">phi5</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">phi6</span><span class="special">);</span> |
|---|
| 997 | <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">multipolar</span><span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rho1</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">theta1</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rho2</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">theta2</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rho3</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">theta3</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">rho4</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">theta4</span><span class="special">);</span> |
|---|
| 998 | <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">cylindrical</span><span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">r</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">angle</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">h1</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">h2</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">h3</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">h4</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">h5</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">h6</span><span class="special">);</span> |
|---|
| 999 | </pre> |
|---|
| 1000 | <p> |
|---|
| 1001 | These build octonions in a way similar to the way polar builds complex numbers, |
|---|
| 1002 | as there is no strict equivalent to polar coordinates for octonions. |
|---|
| 1003 | </p> |
|---|
| 1004 | <p> |
|---|
| 1005 | <code class="computeroutput"><span class="identifier">spherical</span></code> is a simple transposition |
|---|
| 1006 | of <code class="computeroutput"><span class="identifier">polar</span></code>, it takes as inputs |
|---|
| 1007 | a (positive) magnitude and a point on the hypersphere, given by three angles. |
|---|
| 1008 | The first of these, <span class="emphasis"><em>theta</em></span> has a natural range of -pi |
|---|
| 1009 | to +pi, and the other two have natural ranges of -pi/2 to +pi/2 (as is the |
|---|
| 1010 | case with the usual spherical coordinates in <span class="emphasis"><em><span class="bold"><strong> |
|---|
| 1011 | R<sup>3</sup> |
|---|
| 1012 | </strong></span></em></span>). Due to the many symmetries and periodicities, nothing |
|---|
| 1013 | untoward happens if the magnitude is negative or the angles are outside their |
|---|
| 1014 | natural ranges. The expected degeneracies (a magnitude of zero ignores the |
|---|
| 1015 | angles settings...) do happen however. |
|---|
| 1016 | </p> |
|---|
| 1017 | <p> |
|---|
| 1018 | <code class="computeroutput"><span class="identifier">cylindrical</span></code> is likewise a |
|---|
| 1019 | simple transposition of the usual cylindrical coordinates in <span class="emphasis"><em><span class="bold"><strong> |
|---|
| 1020 | R<sup>3</sup> |
|---|
| 1021 | </strong></span></em></span>, which in turn is another derivative of planar polar |
|---|
| 1022 | coordinates. The first two inputs are the polar coordinates of the first |
|---|
| 1023 | <span class="emphasis"><em><span class="bold"><strong>C</strong></span></em></span> component of the |
|---|
| 1024 | octonion. The third and fourth inputs are placed into the third and fourth |
|---|
| 1025 | <span class="emphasis"><em><span class="bold"><strong>R</strong></span></em></span> components of the |
|---|
| 1026 | octonion, respectively. |
|---|
| 1027 | </p> |
|---|
| 1028 | <p> |
|---|
| 1029 | <code class="computeroutput"><span class="identifier">multipolar</span></code> is yet another |
|---|
| 1030 | simple generalization of polar coordinates. This time, both <span class="emphasis"><em><span class="bold"><strong>C</strong></span></em></span> components of the octonion are given |
|---|
| 1031 | in polar coordinates. |
|---|
| 1032 | </p> |
|---|
| 1033 | <p> |
|---|
| 1034 | In this version of our implementation of octonions, there is no analogue |
|---|
| 1035 | of the complex value operation arg as the situation is somewhat more complicated. |
|---|
| 1036 | </p> |
|---|
| 1037 | </div> |
|---|
| 1038 | <div class="section" lang="en"> |
|---|
| 1039 | <div class="titlepage"><div><div><h3 class="title"> |
|---|
| 1040 | <a name="boost_math.octonions.octonions_transcendentals"></a>Octonions Transcendentals</h3></div></div></div> |
|---|
| 1041 | <p> |
|---|
| 1042 | There is no <code class="computeroutput"><span class="identifier">log</span></code> or <code class="computeroutput"><span class="identifier">sqrt</span></code> provided for octonions in this implementation, |
|---|
| 1043 | and <code class="computeroutput"><span class="identifier">pow</span></code> is likewise restricted |
|---|
| 1044 | to integral powers of the exponent. There are several reasons to this: on |
|---|
| 1045 | the one hand, the equivalent of analytic continuation for octonions ("branch |
|---|
| 1046 | cuts") remains to be investigated thoroughly (by me, at any rate...), |
|---|
| 1047 | and we wish to avoid the nonsense introduced in the standard by exponentiations |
|---|
| 1048 | of complexes by complexes (which is well defined, but not in the standard...). |
|---|
| 1049 | Talking of nonsense, saying that <code class="computeroutput"><span class="identifier">pow</span><span class="special">(</span><span class="number">0</span><span class="special">,</span><span class="number">0</span><span class="special">)</span></code> is "implementation |
|---|
| 1050 | defined" is just plain brain-dead... |
|---|
| 1051 | </p> |
|---|
| 1052 | <p> |
|---|
| 1053 | We do, however provide several transcendentals, chief among which is the |
|---|
| 1054 | exponential. That it allows for a "closed formula" is a result |
|---|
| 1055 | of the author (the existence and definition of the exponential, on the octonions |
|---|
| 1056 | among others, on the other hand, is a few centuries old). Basically, any |
|---|
| 1057 | converging power series with real coefficients which allows for a closed |
|---|
| 1058 | formula in <span class="emphasis"><em><span class="bold"><strong>C</strong></span></em></span> can be |
|---|
| 1059 | transposed to <span class="emphasis"><em><span class="bold"><strong>O</strong></span></em></span>. More |
|---|
| 1060 | transcendentals of this type could be added in a further revision upon request. |
|---|
| 1061 | It should be noted that it is these functions which force the dependency |
|---|
| 1062 | upon the <a href="../../../boost/math/special_functions/sinc.hpp" target="_top">boost/math/special_functions/sinc.hpp</a> |
|---|
| 1063 | and the <a href="../../../boost/math/special_functions/sinhc.hpp" target="_top">boost/math/special_functions/sinhc.hpp</a> |
|---|
| 1064 | headers. |
|---|
| 1065 | </p> |
|---|
| 1066 | <a name="boost_math.octonions.octonions_transcendentals.exp"></a><h4> |
|---|
| 1067 | <a name="id1571481"></a> |
|---|
| 1068 | exp |
|---|
| 1069 | </h4> |
|---|
| 1070 | <pre class="programlisting"> |
|---|
| 1071 | <span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> |
|---|
| 1072 | <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="identifier">exp</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> |
|---|
| 1073 | </pre> |
|---|
| 1074 | <p> |
|---|
| 1075 | Computes the exponential of the octonion. |
|---|
| 1076 | </p> |
|---|
| 1077 | <a name="boost_math.octonions.octonions_transcendentals.cos"></a><h4> |
|---|
| 1078 | <a name="id1571596"></a> |
|---|
| 1079 | cos |
|---|
| 1080 | </h4> |
|---|
| 1081 | <pre class="programlisting"> |
|---|
| 1082 | <span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> |
|---|
| 1083 | <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="identifier">cos</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> |
|---|
| 1084 | </pre> |
|---|
| 1085 | <p> |
|---|
| 1086 | Computes the cosine of the octonion |
|---|
| 1087 | </p> |
|---|
| 1088 | <a name="boost_math.octonions.octonions_transcendentals.sin"></a><h4> |
|---|
| 1089 | <a name="id1571710"></a> |
|---|
| 1090 | sin |
|---|
| 1091 | </h4> |
|---|
| 1092 | <pre class="programlisting"> |
|---|
| 1093 | <span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> |
|---|
| 1094 | <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="identifier">sin</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> |
|---|
| 1095 | </pre> |
|---|
| 1096 | <p> |
|---|
| 1097 | Computes the sine of the octonion. |
|---|
| 1098 | </p> |
|---|
| 1099 | <a name="boost_math.octonions.octonions_transcendentals.tan"></a><h4> |
|---|
| 1100 | <a name="id1571824"></a> |
|---|
| 1101 | tan |
|---|
| 1102 | </h4> |
|---|
| 1103 | <pre class="programlisting"> |
|---|
| 1104 | <span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> |
|---|
| 1105 | <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="identifier">tan</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> |
|---|
| 1106 | </pre> |
|---|
| 1107 | <p> |
|---|
| 1108 | Computes the tangent of the octonion. |
|---|
| 1109 | </p> |
|---|
| 1110 | <a name="boost_math.octonions.octonions_transcendentals.cosh"></a><h4> |
|---|
| 1111 | <a name="id1571939"></a> |
|---|
| 1112 | cosh |
|---|
| 1113 | </h4> |
|---|
| 1114 | <pre class="programlisting"> |
|---|
| 1115 | <span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> |
|---|
| 1116 | <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="identifier">cosh</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> |
|---|
| 1117 | </pre> |
|---|
| 1118 | <p> |
|---|
| 1119 | Computes the hyperbolic cosine of the octonion. |
|---|
| 1120 | </p> |
|---|
| 1121 | <a name="boost_math.octonions.octonions_transcendentals.sinh"></a><h4> |
|---|
| 1122 | <a name="id1572053"></a> |
|---|
| 1123 | sinh |
|---|
| 1124 | </h4> |
|---|
| 1125 | <pre class="programlisting"> |
|---|
| 1126 | <span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> |
|---|
| 1127 | <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="identifier">sinh</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> |
|---|
| 1128 | </pre> |
|---|
| 1129 | <p> |
|---|
| 1130 | Computes the hyperbolic sine of the octonion. |
|---|
| 1131 | </p> |
|---|
| 1132 | <a name="boost_math.octonions.octonions_transcendentals.tanh"></a><h4> |
|---|
| 1133 | <a name="id1572168"></a> |
|---|
| 1134 | tanh |
|---|
| 1135 | </h4> |
|---|
| 1136 | <pre class="programlisting"> |
|---|
| 1137 | <span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> |
|---|
| 1138 | <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="identifier">tanh</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> |
|---|
| 1139 | </pre> |
|---|
| 1140 | <p> |
|---|
| 1141 | Computes the hyperbolic tangent of the octonion. |
|---|
| 1142 | </p> |
|---|
| 1143 | <a name="boost_math.octonions.octonions_transcendentals.pow"></a><h4> |
|---|
| 1144 | <a name="id1572283"></a> |
|---|
| 1145 | pow |
|---|
| 1146 | </h4> |
|---|
| 1147 | <pre class="programlisting"> |
|---|
| 1148 | <span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> |
|---|
| 1149 | <span class="identifier">octonion</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="identifier">pow</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> <span class="keyword">int</span> <span class="identifier">n</span><span class="special">);</span> |
|---|
| 1150 | </pre> |
|---|
| 1151 | <p> |
|---|
| 1152 | Computes the n-th power of the octonion q. |
|---|
| 1153 | </p> |
|---|
| 1154 | </div> |
|---|
| 1155 | <div class="section" lang="en"> |
|---|
| 1156 | <div class="titlepage"><div><div><h3 class="title"> |
|---|
| 1157 | <a name="boost_math.octonions.test_program"></a>Test Program</h3></div></div></div> |
|---|
| 1158 | <p> |
|---|
| 1159 | The <a href="../../../libs/math/octonion/octonion_test.cpp" target="_top">octonion_test.cpp</a> |
|---|
| 1160 | test program tests octonions specialisations for float, double and long double |
|---|
| 1161 | (<a href="../../../libs/math/octonion/output.txt" target="_top">sample output</a>). |
|---|
| 1162 | </p> |
|---|
| 1163 | <p> |
|---|
| 1164 | If you define the symbol BOOST_OCTONION_TEST_VERBOSE, you will get additional |
|---|
| 1165 | output (<a href="../../../libs/math/octonion/output_more.txt" target="_top">verbose output</a>); |
|---|
| 1166 | this will only be helpfull if you enable message output at the same time, |
|---|
| 1167 | of course (by uncommenting the relevant line in the test or by adding --log_level=messages |
|---|
| 1168 | to your command line,...). In that case, and if you are running interactively, |
|---|
| 1169 | you may in addition define the symbol BOOST_INTERACTIVE_TEST_INPUT_ITERATOR |
|---|
| 1170 | to interactively test the input operator with input of your choice from the |
|---|
| 1171 | standard input (instead of hard-coding it in the test). |
|---|
| 1172 | </p> |
|---|
| 1173 | </div> |
|---|
| 1174 | <div class="section" lang="en"> |
|---|
| 1175 | <div class="titlepage"><div><div><h3 class="title"> |
|---|
| 1176 | <a name="boost_math.octonions.acknowledgements"></a>Acknowledgements</h3></div></div></div> |
|---|
| 1177 | <p> |
|---|
| 1178 | The mathematical text has been typeset with <a href="http://www.nisus-soft.com/" target="_top">Nisus |
|---|
| 1179 | Writer</a>. Jens Maurer has helped with portability and standard adherence, |
|---|
| 1180 | and was the Review Manager for this library. More acknowledgements in the |
|---|
| 1181 | History section. Thank you to all who contributed to the discussion about |
|---|
| 1182 | this library. |
|---|
| 1183 | </p> |
|---|
| 1184 | </div> |
|---|
| 1185 | <div class="section" lang="en"> |
|---|
| 1186 | <div class="titlepage"><div><div><h3 class="title"> |
|---|
| 1187 | <a name="boost_math.octonions.history"></a>History</h3></div></div></div> |
|---|
| 1188 | <div class="itemizedlist"><ul type="disc"> |
|---|
| 1189 | <li> |
|---|
| 1190 | 1.5.8 - 17/12/2005: Converted documentation to Quickbook Format. |
|---|
| 1191 | </li> |
|---|
| 1192 | <li> |
|---|
| 1193 | 1.5.7 - 25/02/2003: transitionned to the unit test framework; <boost/config.hpp> |
|---|
| 1194 | now included by the library header (rather than the test files), via <boost/math/quaternion.hpp>. |
|---|
| 1195 | </li> |
|---|
| 1196 | <li> |
|---|
| 1197 | 1.5.6 - 15/10/2002: Gcc2.95.x and stlport on linux compatibility by Alkis |
|---|
| 1198 | Evlogimenos (alkis@routescience.com). |
|---|
| 1199 | </li> |
|---|
| 1200 | <li> |
|---|
| 1201 | 1.5.5 - 27/09/2002: Microsoft VCPP 7 compatibility, by Michael Stevens |
|---|
| 1202 | (michael@acfr.usyd.edu.au); requires the /Za compiler option. |
|---|
| 1203 | </li> |
|---|
| 1204 | <li> |
|---|
| 1205 | 1.5.4 - 19/09/2002: fixed problem with multiple inclusion (in different |
|---|
| 1206 | translation units); attempt at an improved compatibility with Microsoft |
|---|
| 1207 | compilers, by Michael Stevens (michael@acfr.usyd.edu.au) and Fredrik Blomqvist; |
|---|
| 1208 | other compatibility fixes. |
|---|
| 1209 | </li> |
|---|
| 1210 | <li> |
|---|
| 1211 | 1.5.3 - 01/02/2002: bugfix and Gcc 2.95.3 compatibility by Douglas Gregor |
|---|
| 1212 | (gregod@cs.rpi.edu). |
|---|
| 1213 | </li> |
|---|
| 1214 | <li> |
|---|
| 1215 | 1.5.2 - 07/07/2001: introduced namespace math. |
|---|
| 1216 | </li> |
|---|
| 1217 | <li> |
|---|
| 1218 | 1.5.1 - 07/06/2001: (end of Boost review) now includes <boost/math/special_functions/sinc.hpp> |
|---|
| 1219 | and <boost/math/special_functions/sinhc.hpp> instead of <boost/special_functions.hpp>; |
|---|
| 1220 | corrected bug in sin (Daryle Walker); removed check for self-assignment |
|---|
| 1221 | (Gary Powel); made converting functions explicit (Gary Powel); added overflow |
|---|
| 1222 | guards for division operators and abs (Peter Schmitteckert); added sup |
|---|
| 1223 | and l1; used Vesa Karvonen's CPP metaprograming technique to simplify code. |
|---|
| 1224 | </li> |
|---|
| 1225 | <li> |
|---|
| 1226 | 1.5.0 - 23/03/2001: boostification, inlining of all operators except input, |
|---|
| 1227 | output and pow, fixed exception safety of some members (template version). |
|---|
| 1228 | </li> |
|---|
| 1229 | <li> |
|---|
| 1230 | 1.4.0 - 09/01/2001: added tan and tanh. |
|---|
| 1231 | </li> |
|---|
| 1232 | <li> |
|---|
| 1233 | 1.3.1 - 08/01/2001: cosmetic fixes. |
|---|
| 1234 | </li> |
|---|
| 1235 | <li> |
|---|
| 1236 | 1.3.0 - 12/07/2000: pow now uses Maarten Hilferink's (mhilferink@tip.nl) |
|---|
| 1237 | algorithm. |
|---|
| 1238 | </li> |
|---|
| 1239 | <li> |
|---|
| 1240 | 1.2.0 - 25/05/2000: fixed the division operators and output; changed many |
|---|
| 1241 | signatures. |
|---|
| 1242 | </li> |
|---|
| 1243 | <li> |
|---|
| 1244 | 1.1.0 - 23/05/2000: changed sinc into sinc_pi; added sin, cos, sinh, cosh. |
|---|
| 1245 | </li> |
|---|
| 1246 | <li> |
|---|
| 1247 | 1.0.0 - 10/08/1999: first public version. |
|---|
| 1248 | </li> |
|---|
| 1249 | </ul></div> |
|---|
| 1250 | </div> |
|---|
| 1251 | <div class="section" lang="en"> |
|---|
| 1252 | <div class="titlepage"><div><div><h3 class="title"> |
|---|
| 1253 | <a name="boost_math.octonions.to_do"></a>To Do</h3></div></div></div> |
|---|
| 1254 | <div class="itemizedlist"><ul type="disc"> |
|---|
| 1255 | <li> |
|---|
| 1256 | Improve testing. |
|---|
| 1257 | </li> |
|---|
| 1258 | <li> |
|---|
| 1259 | Rewrite input operatore using Spirit (creates a dependency). |
|---|
| 1260 | </li> |
|---|
| 1261 | <li> |
|---|
| 1262 | Put in place an Expression Template mechanism (perhaps borrowing from uBlas). |
|---|
| 1263 | </li> |
|---|
| 1264 | </ul></div> |
|---|
| 1265 | </div> |
|---|
| 1266 | </div> |
|---|
| 1267 | <table width="100%"><tr> |
|---|
| 1268 | <td align="left"></td> |
|---|
| 1269 | <td align="right"><small>Copyright © 2001 -2002 Daryle Walker, 2001-2003 Hubert Holin, 2005 |
|---|
| 1270 | John Maddock</small></td> |
|---|
| 1271 | </tr></table> |
|---|
| 1272 | <hr> |
|---|
| 1273 | <div class="spirit-nav"> |
|---|
| 1274 | <a accesskey="p" href="quaternions.html"><img src="../images/prev.png" alt="Prev"></a><a accesskey="u" href="../boost_math.html"><img src="../images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../images/home.png" alt="Home"></a><a accesskey="n" href="background_information_and_white_papers.html"><img src="../images/next.png" alt="Next"></a> |
|---|
| 1275 | </div> |
|---|
| 1276 | </body> |
|---|
| 1277 | </html> |
|---|
