docs/CAS/Op.html
<!DOCTYPE html>
<html>
<head>
<meta charset="UTF-8">
<title>class CAS::Op - RDoc Documentation</title>
<script type="text/javascript">
var rdoc_rel_prefix = "../";
</script>
<script src="../js/jquery.js"></script>
<script src="../js/darkfish.js"></script>
<link href="../css/fonts.css" rel="stylesheet">
<link href="../css/rdoc.css" rel="stylesheet">
<body id="top" role="document" class="class">
<nav role="navigation">
<div id="project-navigation">
<div id="home-section" role="region" title="Quick navigation" class="nav-section">
<h2>
<a href="../index.html" rel="home">Home</a>
</h2>
<div id="table-of-contents-navigation">
<a href="../table_of_contents.html#pages">Pages</a>
<a href="../table_of_contents.html#classes">Classes</a>
<a href="../table_of_contents.html#methods">Methods</a>
</div>
</div>
<div id="search-section" role="search" class="project-section initially-hidden">
<form action="#" method="get" accept-charset="utf-8">
<div id="search-field-wrapper">
<input id="search-field" role="combobox" aria-label="Search"
aria-autocomplete="list" aria-controls="search-results"
type="text" name="search" placeholder="Search" spellcheck="false"
title="Type to search, Up and Down to navigate, Enter to load">
</div>
<ul id="search-results" aria-label="Search Results"
aria-busy="false" aria-expanded="false"
aria-atomic="false" class="initially-hidden"></ul>
</form>
</div>
</div>
<div id="class-metadata">
<div id="parent-class-section" class="nav-section">
<h3>Parent</h3>
<p class="link">Object
</div>
<!-- Method Quickref -->
<div id="method-list-section" class="nav-section">
<h3>Methods</h3>
<ul class="link-list" role="directory">
<li ><a href="#method-c-init_simplify_dict">::init_simplify_dict</a>
<li ><a href="#method-c-new">::new</a>
<li ><a href="#method-c-numeric_to_const">::numeric_to_const</a>
<li ><a href="#method-c-simplify_dict">::simplify_dict</a>
<li ><a href="#method-i-21-3D">#!=</a>
<li ><a href="#method-i-2A">#*</a>
<li ><a href="#method-i-2A-2A">#**</a>
<li ><a href="#method-i-2B">#+</a>
<li ><a href="#method-i-2D">#-</a>
<li ><a href="#method-i-2D-40">#-@</a>
<li ><a href="#method-i-2F">#/</a>
<li ><a href="#method-i-3D-3D">#==</a>
<li ><a href="#method-i-args">#args</a>
<li ><a href="#method-i-as_proc">#as_proc</a>
<li ><a href="#method-i-call">#call</a>
<li ><a href="#method-i-depend-3F">#depend?</a>
<li ><a href="#method-i-diff">#diff</a>
<li ><a href="#method-i-dot_graph">#dot_graph</a>
<li ><a href="#method-i-equal">#equal</a>
<li ><a href="#method-i-greater">#greater</a>
<li ><a href="#method-i-greater_equal">#greater_equal</a>
<li ><a href="#method-i-inspect">#inspect</a>
<li ><a href="#method-i-limit">#limit</a>
<li ><a href="#method-i-simplify">#simplify</a>
<li ><a href="#method-i-simplify_dictionary">#simplify_dictionary</a>
<li ><a href="#method-i-smaller">#smaller</a>
<li ><a href="#method-i-smaller_equal">#smaller_equal</a>
<li ><a href="#method-i-subs">#subs</a>
<li ><a href="#method-i-to_c_lib">#to_c_lib</a>
<li ><a href="#method-i-to_code">#to_code</a>
<li ><a href="#method-i-to_s">#to_s</a>
</ul>
</div>
</div>
</nav>
<main role="main" aria-labelledby="class-CAS::Op">
<h1 id="class-CAS::Op" class="class">
class CAS::Op
</h1>
<section class="description">
<p><em>_ _ _ / <strong>|</strong> _ | | __ ()</em> _ <strong>_ _ _ _ | (/ _ \
' \ <em>/ ` | | ' / -) '</em>(<em>-<
__/</em>||<em>_</em>_<em>,</em>|<em>|</em>||<em>_|</em>| /</strong>/</p>
<p><strong>_ / _ \ _ <em>_ | (</em>) | '_ \ _</strong>/| ._<em>/
|</em>|</p>
</section>
<section id="5Buntitled-5D" class="documentation-section">
<section class="attribute-method-details" class="method-section">
<header>
<h3>Attributes</h3>
</header>
<div id="attribute-i-x" class="method-detail">
<div class="method-heading attribute-method-heading">
<span class="method-name">x</span><span
class="attribute-access-type">[R]</span>
</div>
<div class="method-description">
<p>Argument of the operation</p>
</div>
</div>
</section>
<section id="public-class-5Buntitled-5D-method-details" class="method-section">
<header>
<h3>Public Class Methods</h3>
</header>
<div id="method-c-init_simplify_dict" class="method-detail ">
<div class="method-heading">
<span class="method-name">init_simplify_dict</span><span
class="method-args">()</span>
<span class="method-click-advice">click to toggle source</span>
</div>
<div class="method-description">
<p>Initializes the simplification dictionary (one for each class)</p>
<ul><li>
<p><strong>returns</strong>: <code>Hash</code> with simplification dictionary</p>
</li></ul>
<div class="method-source-code" id="init_simplify_dict-source">
<pre><span class="ruby-comment"># File lib/operators/op.rb, line 234</span>
<span class="ruby-keyword">def</span> <span class="ruby-keyword">self</span>.<span class="ruby-identifier">init_simplify_dict</span>
<span class="ruby-ivar">@simplify_dict</span> = { }
<span class="ruby-keyword">end</span></pre>
</div>
</div>
</div>
<div id="method-c-new" class="method-detail ">
<div class="method-heading">
<span class="method-name">new</span><span
class="method-args">(x)</span>
<span class="method-click-advice">click to toggle source</span>
</div>
<div class="method-description">
<p>Initialize a new empty operation container. This is a virtual class and the
other must inherit from this basic container. Some methods raise a
<code>CAS::CASError</code> if called. The input element is a Numric, to
create a constant. <code>CAS::Op</code> specifies operations with a single
variable</p>
<ul><li>
<p><strong>argument</strong>: <code>Numeric</code> to be converted in
<code>CAS::Constant</code> or <code>CAS::Op</code> child operation</p>
</li><li>
<p><strong>returns</strong>: <code>CAS::Op</code> instance</p>
</li></ul>
<div class="method-source-code" id="new-source">
<pre><span class="ruby-comment"># File lib/operators/op.rb, line 46</span>
<span class="ruby-keyword">def</span> <span class="ruby-identifier">initialize</span>(<span class="ruby-identifier">x</span>)
<span class="ruby-keyword">if</span> <span class="ruby-identifier">x</span>.<span class="ruby-identifier">is_a?</span> <span class="ruby-constant">Numeric</span>
<span class="ruby-identifier">x</span> = <span class="ruby-constant">Op</span>.<span class="ruby-identifier">numeric_to_const</span> <span class="ruby-identifier">x</span>
<span class="ruby-keyword">end</span>
<span class="ruby-constant">CAS</span><span class="ruby-operator">::</span><span class="ruby-constant">Help</span>.<span class="ruby-identifier">assert</span>(<span class="ruby-identifier">x</span>, <span class="ruby-constant">CAS</span><span class="ruby-operator">::</span><span class="ruby-constant">Op</span>)
<span class="ruby-ivar">@x</span> = <span class="ruby-identifier">x</span>
<span class="ruby-keyword">end</span></pre>
</div>
</div>
</div>
<div id="method-c-numeric_to_const" class="method-detail ">
<div class="method-heading">
<span class="method-name">numeric_to_const</span><span
class="method-args">(x)</span>
<span class="method-click-advice">click to toggle source</span>
</div>
<div class="method-description">
<div class="method-source-code" id="numeric_to_const-source">
<pre><span class="ruby-comment"># File lib/operators/op.rb, line 55</span>
<span class="ruby-keyword">def</span> <span class="ruby-keyword">self</span>.<span class="ruby-identifier">numeric_to_const</span>(<span class="ruby-identifier">x</span>)
<span class="ruby-keyword">if</span> <span class="ruby-constant">CAS</span><span class="ruby-operator">::</span><span class="ruby-constant">NumericToConst</span>[<span class="ruby-identifier">x</span>]
<span class="ruby-keyword">return</span> <span class="ruby-constant">CAS</span><span class="ruby-operator">::</span><span class="ruby-constant">NumericToConst</span>[<span class="ruby-identifier">x</span>]
<span class="ruby-keyword">else</span>
<span class="ruby-keyword">return</span> <span class="ruby-constant">CAS</span><span class="ruby-operator">::</span><span class="ruby-identifier">const</span> <span class="ruby-identifier">x</span>
<span class="ruby-keyword">end</span>
<span class="ruby-keyword">end</span></pre>
</div>
</div>
</div>
<div id="method-c-simplify_dict" class="method-detail ">
<div class="method-heading">
<span class="method-name">simplify_dict</span><span
class="method-args">(k)</span>
<span class="method-click-advice">click to toggle source</span>
</div>
<div class="method-description">
<p>Returns an element of a</p>
<div class="method-source-code" id="simplify_dict-source">
<pre><span class="ruby-comment"># File lib/operators/op.rb, line 239</span>
<span class="ruby-keyword">def</span> <span class="ruby-keyword">self</span>.<span class="ruby-identifier">simplify_dict</span>(<span class="ruby-identifier">k</span>)
<span class="ruby-ivar">@simplify_dict</span>.<span class="ruby-identifier">keys</span>.<span class="ruby-identifier">each</span> <span class="ruby-keyword">do</span> <span class="ruby-operator">|</span><span class="ruby-identifier">op</span><span class="ruby-operator">|</span>
<span class="ruby-keyword">return</span> <span class="ruby-ivar">@simplify_dict</span>[<span class="ruby-identifier">op</span>] <span class="ruby-keyword">if</span> <span class="ruby-identifier">op</span>.<span class="ruby-identifier">simplify</span> <span class="ruby-operator">==</span> <span class="ruby-identifier">k</span>.<span class="ruby-identifier">simplify</span>
<span class="ruby-keyword">end</span>
<span class="ruby-keyword">return</span> <span class="ruby-keyword">nil</span>
<span class="ruby-keyword">end</span></pre>
</div>
</div>
</div>
</section>
<section id="public-instance-5Buntitled-5D-method-details" class="method-section">
<header>
<h3>Public Instance Methods</h3>
</header>
<div id="method-i-21-3D" class="method-detail ">
<div class="method-heading">
<span class="method-name">!=</span><span
class="method-args">(op)</span>
<span class="method-click-advice">click to toggle source</span>
</div>
<div class="method-description">
<p>Disequality operator, the standard operator is overloaded :warning: this
operates on the graph, not on the math See <code>CAS::equal</code>, etc.</p>
<ul><li>
<p><strong>argument</strong>: <code>CAS::Op</code> to be tested against</p>
</li><li>
<p><strong>returns</strong>: <code>FalseClass</code> if equal,
<code>TrueClass</code> if differs</p>
</li></ul>
<div class="method-source-code" id="21-3D-source">
<pre><span class="ruby-comment"># File lib/operators/op.rb, line 274</span>
<span class="ruby-keyword">def</span> <span class="ruby-operator">!=</span>(<span class="ruby-identifier">op</span>)
<span class="ruby-keyword">not</span> <span class="ruby-keyword">self</span>.<span class="ruby-operator">==</span>(<span class="ruby-identifier">op</span>)
<span class="ruby-keyword">end</span></pre>
</div>
</div>
</div>
<div id="method-i-2A" class="method-detail ">
<div class="method-heading">
<span class="method-name">*</span><span
class="method-args">(op)</span>
<span class="method-click-advice">click to toggle source</span>
</div>
<div class="method-description">
<p>Returns a product of two <code>CAS::Op</code>s</p>
<ul><li>
<p><strong>argument</strong>: <code>CAS::Op</code> tree</p>
</li><li>
<p><strong>returns</strong>: <code>CAS::Op</code> new object</p>
</li></ul>
<div class="method-source-code" id="2A-source">
<pre><span class="ruby-comment"># File lib/operators/op.rb, line 182</span>
<span class="ruby-keyword">def</span> <span class="ruby-operator">*</span>(<span class="ruby-identifier">op</span>)
<span class="ruby-constant">CAS</span><span class="ruby-operator">::</span><span class="ruby-constant">Prod</span>.<span class="ruby-identifier">new</span> [<span class="ruby-keyword">self</span>, <span class="ruby-identifier">op</span>]
<span class="ruby-keyword">end</span></pre>
</div>
</div>
</div>
<div id="method-i-2A-2A" class="method-detail ">
<div class="method-heading">
<span class="method-name">**</span><span
class="method-args">(op)</span>
<span class="method-click-advice">click to toggle source</span>
</div>
<div class="method-description">
<p>Returns the power of two <code>CAS::Op</code>s</p>
<ul><li>
<p><strong>argument</strong>: <code>CAS::Op</code> tree</p>
</li><li>
<p><strong>returns</strong>: <code>CAS::Op</code> new object</p>
</li></ul>
<div class="method-source-code" id="2A-2A-source">
<pre><span class="ruby-comment"># File lib/operators/op.rb, line 198</span>
<span class="ruby-keyword">def</span> <span class="ruby-operator">**</span>(<span class="ruby-identifier">op</span>)
<span class="ruby-constant">CAS</span>.<span class="ruby-identifier">pow</span>(<span class="ruby-keyword">self</span>, <span class="ruby-identifier">op</span>)
<span class="ruby-keyword">end</span></pre>
</div>
</div>
</div>
<div id="method-i-2B" class="method-detail ">
<div class="method-heading">
<span class="method-name">+</span><span
class="method-args">(op)</span>
<span class="method-click-advice">click to toggle source</span>
</div>
<div class="method-description">
<p>Returns a sum of two <code>CAS::Op</code>s</p>
<ul><li>
<p><strong>argument</strong>: <code>CAS::Op</code> tree</p>
</li><li>
<p><strong>returns</strong>: <code>CAS::Op</code> new object</p>
</li></ul>
<div class="method-source-code" id="2B-source">
<pre><span class="ruby-comment"># File lib/operators/op.rb, line 166</span>
<span class="ruby-keyword">def</span> <span class="ruby-operator">+</span>(<span class="ruby-identifier">op</span>)
<span class="ruby-constant">CAS</span><span class="ruby-operator">::</span><span class="ruby-constant">Sum</span>.<span class="ruby-identifier">new</span> [<span class="ruby-keyword">self</span>, <span class="ruby-identifier">op</span>]
<span class="ruby-keyword">end</span></pre>
</div>
</div>
</div>
<div id="method-i-2D" class="method-detail ">
<div class="method-heading">
<span class="method-name">-</span><span
class="method-args">(op)</span>
<span class="method-click-advice">click to toggle source</span>
</div>
<div class="method-description">
<p>Returns a difference of two <code>CAS::Op</code>s</p>
<ul><li>
<p><strong>argument</strong>: <code>CAS::Op</code> tree</p>
</li><li>
<p><strong>returns</strong>: <code>CAS::Op</code> new object</p>
</li></ul>
<div class="method-source-code" id="2D-source">
<pre><span class="ruby-comment"># File lib/operators/op.rb, line 174</span>
<span class="ruby-keyword">def</span> <span class="ruby-operator">-</span>(<span class="ruby-identifier">op</span>)
<span class="ruby-constant">CAS</span><span class="ruby-operator">::</span><span class="ruby-constant">Diff</span>.<span class="ruby-identifier">new</span> <span class="ruby-keyword">self</span>, <span class="ruby-identifier">op</span>
<span class="ruby-keyword">end</span></pre>
</div>
</div>
</div>
<div id="method-i-2D-40" class="method-detail ">
<div class="method-heading">
<span class="method-name">-@</span><span
class="method-args">()</span>
<span class="method-click-advice">click to toggle source</span>
</div>
<div class="method-description">
<p>Unary operator for inversion of a <code>CAS::Op</code></p>
<ul><li>
<p><strong>returns</strong>: <code>CAS::Op</code> new object</p>
</li></ul>
<div class="method-source-code" id="2D-40-source">
<pre><span class="ruby-comment"># File lib/operators/op.rb, line 205</span>
<span class="ruby-keyword">def</span> <span class="ruby-operator">-@</span>
<span class="ruby-constant">CAS</span>.<span class="ruby-identifier">invert</span>(<span class="ruby-keyword">self</span>)
<span class="ruby-keyword">end</span></pre>
</div>
</div>
</div>
<div id="method-i-2F" class="method-detail ">
<div class="method-heading">
<span class="method-name">/</span><span
class="method-args">(op)</span>
<span class="method-click-advice">click to toggle source</span>
</div>
<div class="method-description">
<p>Returns a division of two <code>CAS::Op</code>s</p>
<ul><li>
<p><strong>argument</strong>: <code>CAS::Op</code> tree</p>
</li><li>
<p><strong>returns</strong>: <code>CAS::Op</code> new object</p>
</li></ul>
<div class="method-source-code" id="2F-source">
<pre><span class="ruby-comment"># File lib/operators/op.rb, line 190</span>
<span class="ruby-keyword">def</span> <span class="ruby-operator">/</span>(<span class="ruby-identifier">op</span>)
<span class="ruby-constant">CAS</span><span class="ruby-operator">::</span><span class="ruby-constant">Div</span>.<span class="ruby-identifier">new</span> <span class="ruby-keyword">self</span>, <span class="ruby-identifier">op</span>
<span class="ruby-keyword">end</span></pre>
</div>
</div>
</div>
<div id="method-i-3D-3D" class="method-detail ">
<div class="method-heading">
<span class="method-name">==</span><span
class="method-args">(op)</span>
<span class="method-click-advice">click to toggle source</span>
</div>
<div class="method-description">
<p>Equality operator, the standard operator is overloaded :warning: this
operates on the graph, not on the math See <code>CAS::equal</code>, etc.</p>
<ul><li>
<p><strong>argument</strong>: <code>CAS::Op</code> to be tested against</p>
</li><li>
<p><strong>returns</strong>: <code>TrueClass</code> if equal,
<code>FalseClass</code> if differs</p>
</li></ul>
<div class="method-source-code" id="3D-3D-source">
<pre><span class="ruby-comment"># File lib/operators/op.rb, line 259</span>
<span class="ruby-keyword">def</span> <span class="ruby-operator">==</span>(<span class="ruby-identifier">op</span>)
<span class="ruby-comment"># CAS::Help.assert(op, CAS::Op)</span>
<span class="ruby-keyword">if</span> <span class="ruby-identifier">op</span>.<span class="ruby-identifier">is_a?</span> <span class="ruby-constant">CAS</span><span class="ruby-operator">::</span><span class="ruby-constant">Op</span>
<span class="ruby-keyword">return</span> <span class="ruby-keyword">false</span> <span class="ruby-keyword">if</span> <span class="ruby-identifier">op</span>.<span class="ruby-identifier">is_a?</span> <span class="ruby-constant">CAS</span><span class="ruby-operator">::</span><span class="ruby-constant">BinaryOp</span>
<span class="ruby-keyword">return</span> (<span class="ruby-keyword">self</span>.<span class="ruby-identifier">class</span> <span class="ruby-operator">==</span> <span class="ruby-identifier">op</span>.<span class="ruby-identifier">class</span> <span class="ruby-keyword">and</span> <span class="ruby-ivar">@x</span> <span class="ruby-operator">==</span> <span class="ruby-identifier">op</span>.<span class="ruby-identifier">x</span>)
<span class="ruby-keyword">end</span>
<span class="ruby-keyword">false</span>
<span class="ruby-keyword">end</span></pre>
</div>
</div>
</div>
<div id="method-i-args" class="method-detail ">
<div class="method-heading">
<span class="method-name">args</span><span
class="method-args">()</span>
<span class="method-click-advice">click to toggle source</span>
</div>
<div class="method-description">
<p>Returns a list of all <code>CAS::Variable</code>s of the current tree</p>
<ul><li>
<p><strong>returns</strong>: <code>Array</code> of <code>CAS::Variable</code>s</p>
</li></ul>
<div class="method-source-code" id="args-source">
<pre><span class="ruby-comment"># File lib/operators/op.rb, line 303</span>
<span class="ruby-keyword">def</span> <span class="ruby-identifier">args</span>
<span class="ruby-ivar">@x</span>.<span class="ruby-identifier">args</span>.<span class="ruby-identifier">uniq</span>
<span class="ruby-keyword">end</span></pre>
</div>
</div>
</div>
<div id="method-i-as_proc" class="method-detail ">
<div class="method-heading">
<span class="method-name">as_proc</span><span
class="method-args">(bind=nil)</span>
<span class="method-click-advice">click to toggle source</span>
</div>
<div class="method-description">
<p>Evaluates the proc against a given context. It is like having a snapshot of
the tree transformed in a callable object. Obviously <strong>if the tree
changes, the generated proc does notchanges</strong>. The proc takes as
input a feed dictionary in which each variable is identified through the
<code>CAS::Variable#name</code> key.</p>
<p>The proc is evaluated in the context devined by the input
<code>Binding</code> object If <code>nil</code> is passed, the
<code>eval</code> will run in this local context</p>
<ul><li>
<p><strong>argument</strong>: <code>Binding</code> or <code>NilClass</code>
that is the context of the Ruby VM</p>
</li><li>
<p><strong>returns</strong>: <code>Proc</code> object with a single argument
as an <code>Hash</code></p>
</li></ul>
<div class="method-source-code" id="as_proc-source">
<pre><span class="ruby-comment"># File lib/operators/op.rb, line 289</span>
<span class="ruby-keyword">def</span> <span class="ruby-identifier">as_proc</span>(<span class="ruby-identifier">bind</span>=<span class="ruby-keyword">nil</span>)
<span class="ruby-identifier">args_ext</span> = <span class="ruby-keyword">self</span>.<span class="ruby-identifier">args</span>.<span class="ruby-identifier">map</span> { <span class="ruby-operator">|</span><span class="ruby-identifier">e</span><span class="ruby-operator">|</span> <span class="ruby-node">"#{e} = fd[\"#{e}\"];"</span> }
<span class="ruby-identifier">code</span> = <span class="ruby-node">"Proc.new do |fd|; #{args_ext.join " "} #{self.to_code}; end"</span>
<span class="ruby-keyword">if</span> <span class="ruby-identifier">bind</span> <span class="ruby-comment"># All objects have eval value, we bind when not nil</span>
<span class="ruby-comment"># CAS::Help.assert(bind, Binding)</span>
<span class="ruby-identifier">bind</span>.<span class="ruby-identifier">eval</span>(<span class="ruby-identifier">code</span>)
<span class="ruby-keyword">else</span>
<span class="ruby-identifier">eval</span>(<span class="ruby-identifier">code</span>)
<span class="ruby-keyword">end</span>
<span class="ruby-keyword">end</span></pre>
</div>
</div>
</div>
<div id="method-i-call" class="method-detail ">
<div class="method-heading">
<span class="method-name">call</span><span
class="method-args">(f)</span>
<span class="method-click-advice">click to toggle source</span>
</div>
<div class="method-description">
<p>Call resolves the operation tree in a <code>Numeric</code> (if
<code>Fixnum</code>) or <code>Float</code> (depends upon promotions). As
input, it requires an hash with <code>CAS::Variable</code> or
<code>CAS::Variable#name</code> as keys, and a <code>Numeric</code> as a
value</p>
<pre class="ruby"><span class="ruby-identifier">x</span>, <span class="ruby-identifier">y</span> = <span class="ruby-constant">CAS</span><span class="ruby-operator">::</span><span class="ruby-identifier">vars</span> :<span class="ruby-identifier">x</span>, :<span class="ruby-identifier">y</span>
<span class="ruby-identifier">f</span> = (<span class="ruby-identifier">x</span> <span class="ruby-operator">**</span> <span class="ruby-value">2</span>) <span class="ruby-operator">+</span> (<span class="ruby-identifier">y</span> <span class="ruby-operator">**</span> <span class="ruby-value">2</span>)
<span class="ruby-identifier">f</span>.<span class="ruby-identifier">call</span>({<span class="ruby-identifier">x</span> =<span class="ruby-operator">></span> <span class="ruby-value">1</span>, <span class="ruby-identifier">y</span> =<span class="ruby-operator">></span> <span class="ruby-value">2</span>})
<span class="ruby-comment"># => 2</span>
</pre>
<ul><li>
<p><strong>argument</strong>: <code>Hash</code> with feed dictionary</p>
</li><li>
<p><strong>returns</strong>: <code>Numeric</code></p>
</li></ul>
<div class="method-source-code" id="call-source">
<pre><span class="ruby-comment"># File lib/operators/op.rb, line 112</span>
<span class="ruby-keyword">def</span> <span class="ruby-identifier">call</span>(<span class="ruby-identifier">f</span>)
<span class="ruby-constant">CAS</span><span class="ruby-operator">::</span><span class="ruby-constant">Help</span>.<span class="ruby-identifier">assert</span>(<span class="ruby-identifier">f</span>, <span class="ruby-constant">Hash</span>)
<span class="ruby-ivar">@x</span>.<span class="ruby-identifier">call</span>(<span class="ruby-identifier">f</span>)
<span class="ruby-keyword">end</span></pre>
</div>
</div>
</div>
<div id="method-i-depend-3F" class="method-detail ">
<div class="method-heading">
<span class="method-name">depend?</span><span
class="method-args">(v)</span>
<span class="method-click-advice">click to toggle source</span>
</div>
<div class="method-description">
<p>Return the dependencies of the operation. Requires a
<code>CAS::Variable</code> and it is one of the recursve method (implicit
tree resolution)</p>
<ul><li>
<p><strong>argument</strong>: <code>CAS::Variable</code> instance</p>
</li><li>
<p><strong>returns</strong>: <code>TrueClass</code> if depends,
<code>FalseClass</code> if not</p>
</li></ul>
<div class="method-source-code" id="depend-3F-source">
<pre><span class="ruby-comment"># File lib/operators/op.rb, line 68</span>
<span class="ruby-keyword">def</span> <span class="ruby-identifier">depend?</span>(<span class="ruby-identifier">v</span>)
<span class="ruby-constant">CAS</span><span class="ruby-operator">::</span><span class="ruby-constant">Help</span>.<span class="ruby-identifier">assert</span>(<span class="ruby-identifier">v</span>, <span class="ruby-constant">CAS</span><span class="ruby-operator">::</span><span class="ruby-constant">Op</span>)
<span class="ruby-ivar">@x</span>.<span class="ruby-identifier">depend?</span> <span class="ruby-identifier">v</span>
<span class="ruby-keyword">end</span></pre>
</div>
</div>
</div>
<div id="method-i-diff" class="method-detail ">
<div class="method-heading">
<span class="method-name">diff</span><span
class="method-args">(v)</span>
<span class="method-click-advice">click to toggle source</span>
</div>
<div class="method-description">
<p>Return the derivative of the operation using the chain rule The input is a
<code>CAS::Op</code> because it can handle derivatives with respect to
functions. E.g.:</p>
<pre>f(x) = (ln(x))**2
g(x) = ln(x)
d f(x)
------ = 2 ln(x)
d g(x)</pre>
<ul><li>
<p><strong>argument</strong>: <code>CAS::Op</code> object of the derivative</p>
</li><li>
<p><strong>returns</strong>: <code>CAS::Op</code> a derivated object, or
<code>CAS::Zero</code> for constants</p>
</li></ul>
<div class="method-source-code" id="diff-source">
<pre><span class="ruby-comment"># File lib/operators/op.rb, line 89</span>
<span class="ruby-keyword">def</span> <span class="ruby-identifier">diff</span>(<span class="ruby-identifier">v</span>)
<span class="ruby-constant">CAS</span><span class="ruby-operator">::</span><span class="ruby-constant">Help</span>.<span class="ruby-identifier">assert</span>(<span class="ruby-identifier">v</span>, <span class="ruby-constant">CAS</span><span class="ruby-operator">::</span><span class="ruby-constant">Op</span>)
<span class="ruby-keyword">if</span> <span class="ruby-ivar">@x</span>.<span class="ruby-identifier">depend?</span> <span class="ruby-identifier">v</span>
<span class="ruby-keyword">return</span> <span class="ruby-ivar">@x</span>.<span class="ruby-identifier">diff</span>(<span class="ruby-identifier">v</span>)
<span class="ruby-keyword">end</span>
<span class="ruby-constant">CAS</span><span class="ruby-operator">::</span><span class="ruby-constant">Zero</span>
<span class="ruby-keyword">end</span></pre>
</div>
</div>
</div>
<div id="method-i-dot_graph" class="method-detail ">
<div class="method-heading">
<span class="method-name">dot_graph</span><span
class="method-args">()</span>
<span class="method-click-advice">click to toggle source</span>
</div>
<div class="method-description">
<p>Return the local Graphviz node of the tree</p>
<ul><li>
<p><strong>returns</strong>: <code>String</code> of local Graphiz node</p>
</li></ul>
<div class="method-source-code" id="dot_graph-source">
<pre><span class="ruby-comment"># File lib/Mr.CAS/graphviz.rb, line 42</span>
<span class="ruby-keyword">def</span> <span class="ruby-identifier">dot_graph</span>
<span class="ruby-identifier">cls</span> = <span class="ruby-node">"#{self.class.to_s.gsub("CAS::", "")}_#{self.object_id}"</span>
<span class="ruby-node">"#{cls} -> #{@x.dot_graph}\n"</span>
<span class="ruby-keyword">end</span></pre>
</div>
</div>
</div>
<div id="method-i-equal" class="method-detail ">
<div class="method-heading">
<span class="method-name">equal</span><span
class="method-args">(v)</span>
<span class="method-click-advice">click to toggle source</span>
</div>
<div class="method-description">
<p>Shortcut for creating equality condition.</p>
<ul><li>
<p><strong>argument</strong>: <code>CAS::Op</code> ther element of the
condition</p>
</li><li>
<p><strong>returns</strong>: <code>CAS::Equal</code> new instance</p>
</li></ul>
<div class="method-source-code" id="equal-source">
<pre><span class="ruby-comment"># File lib/functions/fnc-conditions.rb, line 344</span>
<span class="ruby-keyword">def</span> <span class="ruby-identifier">equal</span>(<span class="ruby-identifier">v</span>)
<span class="ruby-constant">CAS</span>.<span class="ruby-identifier">equal</span>(<span class="ruby-keyword">self</span>, <span class="ruby-identifier">v</span>)
<span class="ruby-keyword">end</span></pre>
</div>
</div>
</div>
<div id="method-i-greater" class="method-detail ">
<div class="method-heading">
<span class="method-name">greater</span><span
class="method-args">(v)</span>
<span class="method-click-advice">click to toggle source</span>
</div>
<div class="method-description">
<p>Shortcut for creating greater kind condition.</p>
<ul><li>
<p><strong>argument</strong>: <code>CAS::Op</code> ther element of the
condition</p>
</li><li>
<p><strong>returns</strong>: <code>CAS::Greater</code> new instance</p>
</li></ul>
<div class="method-source-code" id="greater-source">
<pre><span class="ruby-comment"># File lib/functions/fnc-conditions.rb, line 352</span>
<span class="ruby-keyword">def</span> <span class="ruby-identifier">greater</span>(<span class="ruby-identifier">v</span>)
<span class="ruby-constant">CAS</span>.<span class="ruby-identifier">greater</span>(<span class="ruby-keyword">self</span>, <span class="ruby-identifier">v</span>)
<span class="ruby-keyword">end</span></pre>
</div>
</div>
</div>
<div id="method-i-greater_equal" class="method-detail ">
<div class="method-heading">
<span class="method-name">greater_equal</span><span
class="method-args">(v)</span>
<span class="method-click-advice">click to toggle source</span>
</div>
<div class="method-description">
<p>Shortcut for creating a greater equal kind condition.</p>
<ul><li>
<p><strong>argument</strong>: <code>CAS::Op</code> ther element of the
condition</p>
</li><li>
<p><strong>returns</strong>: <code>CAS::GreaterEqual</code> new instance</p>
</li></ul>
<div class="method-source-code" id="greater_equal-source">
<pre><span class="ruby-comment"># File lib/functions/fnc-conditions.rb, line 368</span>
<span class="ruby-keyword">def</span> <span class="ruby-identifier">greater_equal</span>(<span class="ruby-identifier">v</span>)
<span class="ruby-constant">CAS</span>.<span class="ruby-identifier">greater_equal</span>(<span class="ruby-keyword">self</span>, <span class="ruby-identifier">v</span>)
<span class="ruby-keyword">end</span></pre>
</div>
</div>
</div>
<div id="method-i-inspect" class="method-detail ">
<div class="method-heading">
<span class="method-name">inspect</span><span
class="method-args">()</span>
<span class="method-click-advice">click to toggle source</span>
</div>
<div class="method-description">
<p>Inspector for the current object</p>
<ul><li>
<p><strong>returns</strong>: <code>String</code></p>
</li></ul>
<div class="method-source-code" id="inspect-source">
<pre><span class="ruby-comment"># File lib/operators/op.rb, line 249</span>
<span class="ruby-keyword">def</span> <span class="ruby-identifier">inspect</span>
<span class="ruby-node">"#{self.class}(#{@x.inspect})"</span>
<span class="ruby-keyword">end</span></pre>
</div>
</div>
</div>
<div id="method-i-limit" class="method-detail ">
<div class="method-heading">
<span class="method-name">limit</span><span
class="method-args">(a, b, type=:closed)</span>
<span class="method-click-advice">click to toggle source</span>
</div>
<div class="method-description">
<p>Shortcut for creating a new box condition. It requires limits and type:</p>
<ul><li>
<p><strong>argument</strong>: <code>CAS::Constant</code> lower limit</p>
</li><li>
<p><strong>argument</strong>: <code>CAs::Constant</code> upper limit</p>
</li><li>
<p><strong>argument</strong>: <code>Symbol</code> of condition type it can be:</p>
<ul><li>
<p><code>:closed</code> for <code>CAs::BoxConditionClosed</code></p>
</li><li>
<p><code>:open</code> for <code>CAs::BoxConditionOpen</code></p>
</li><li>
<p><code>:upper_closed</code> for <code>CAs::BoxConditionUpperClosed</code></p>
</li><li>
<p><code>:lower_closed</code> for <code>CAs::BoxConditionLowerClosed</code></p>
</li></ul>
</li><li>
<p><strong>returns</strong>: <code>CAS::BoxCondition</code> new instance</p>
</li></ul>
<div class="method-source-code" id="limit-source">
<pre><span class="ruby-comment"># File lib/functions/fnc-box-conditions.rb, line 338</span>
<span class="ruby-keyword">def</span> <span class="ruby-identifier">limit</span>(<span class="ruby-identifier">a</span>, <span class="ruby-identifier">b</span>, <span class="ruby-identifier">type</span>=<span class="ruby-value">:closed</span>)
<span class="ruby-keyword">return</span> <span class="ruby-constant">CAS</span><span class="ruby-operator">::</span><span class="ruby-identifier">box</span>(<span class="ruby-keyword">self</span>, <span class="ruby-identifier">a</span>, <span class="ruby-identifier">b</span>, <span class="ruby-identifier">type</span>)
<span class="ruby-keyword">end</span></pre>
</div>
</div>
</div>
<div id="method-i-simplify" class="method-detail ">
<div class="method-heading">
<span class="method-name">simplify</span><span
class="method-args">()</span>
<span class="method-click-advice">click to toggle source</span>
</div>
<div class="method-description">
<p>Simplification callback. It simplify the subgraph of each node until all
possible simplification are performed (thus the execution time is not
deterministic).</p>
<ul><li>
<p><strong>returns</strong>: <code>CAS::Op</code> simplified version</p>
</li></ul>
<div class="method-source-code" id="simplify-source">
<pre><span class="ruby-comment"># File lib/operators/op.rb, line 214</span>
<span class="ruby-keyword">def</span> <span class="ruby-identifier">simplify</span>
<span class="ruby-identifier">hash</span> = <span class="ruby-ivar">@x</span>.<span class="ruby-identifier">to_s</span>
<span class="ruby-ivar">@x</span> = <span class="ruby-ivar">@x</span>.<span class="ruby-identifier">simplify</span>
<span class="ruby-keyword">while</span> <span class="ruby-ivar">@x</span>.<span class="ruby-identifier">to_s</span> <span class="ruby-operator">!=</span> <span class="ruby-identifier">hash</span>
<span class="ruby-identifier">hash</span> = <span class="ruby-ivar">@x</span>.<span class="ruby-identifier">to_s</span>
<span class="ruby-ivar">@x</span> = <span class="ruby-ivar">@x</span>.<span class="ruby-identifier">simplify</span>
<span class="ruby-keyword">end</span>
<span class="ruby-keyword">end</span></pre>
</div>
</div>
</div>
<div id="method-i-simplify_dictionary" class="method-detail ">
<div class="method-heading">
<span class="method-name">simplify_dictionary</span><span
class="method-args">()</span>
<span class="method-click-advice">click to toggle source</span>
</div>
<div class="method-description">
<p>Simplify dictionary performs a dictionary simplification that is the class
variable <code>@simplify_dict</code></p>
<ul><li>
<p><strong>returns</strong>: <code>CAS::Op</code> self</p>
</li></ul>
<div class="method-source-code" id="simplify_dictionary-source">
<pre><span class="ruby-comment"># File lib/operators/op.rb, line 227</span>
<span class="ruby-keyword">def</span> <span class="ruby-identifier">simplify_dictionary</span>
<span class="ruby-keyword">self</span>.<span class="ruby-identifier">class</span>.<span class="ruby-identifier">simplify_dict</span>(<span class="ruby-ivar">@x</span>) <span class="ruby-operator">||</span> <span class="ruby-keyword">self</span>
<span class="ruby-keyword">end</span></pre>
</div>
</div>
</div>
<div id="method-i-smaller" class="method-detail ">
<div class="method-heading">
<span class="method-name">smaller</span><span
class="method-args">(v)</span>
<span class="method-click-advice">click to toggle source</span>
</div>
<div class="method-description">
<p>Shortcut for creating a smaller kind condition.</p>
<ul><li>
<p><strong>argument</strong>: <code>CAS::Op</code> ther element of the
condition</p>
</li><li>
<p><strong>returns</strong>: <code>CAS::Smaller</code> new instance</p>
</li></ul>
<div class="method-source-code" id="smaller-source">
<pre><span class="ruby-comment"># File lib/functions/fnc-conditions.rb, line 360</span>
<span class="ruby-keyword">def</span> <span class="ruby-identifier">smaller</span>(<span class="ruby-identifier">v</span>)
<span class="ruby-constant">CAS</span>.<span class="ruby-identifier">smaller</span>(<span class="ruby-keyword">self</span>, <span class="ruby-identifier">v</span>)
<span class="ruby-keyword">end</span></pre>
</div>
</div>
</div>
<div id="method-i-smaller_equal" class="method-detail ">
<div class="method-heading">
<span class="method-name">smaller_equal</span><span
class="method-args">(v)</span>
<span class="method-click-advice">click to toggle source</span>
</div>
<div class="method-description">
<p>Shortcut for creating a smaller equal kind condition.</p>
<ul><li>
<p><strong>argument</strong>: <code>CAS::Op</code> ther element of the
condition</p>
</li><li>
<p><strong>returns</strong>: <code>CAS::SmallerEqual</code> new instance</p>
</li></ul>
<div class="method-source-code" id="smaller_equal-source">
<pre><span class="ruby-comment"># File lib/functions/fnc-conditions.rb, line 376</span>
<span class="ruby-keyword">def</span> <span class="ruby-identifier">smaller_equal</span>(<span class="ruby-identifier">v</span>)
<span class="ruby-constant">CAS</span>.<span class="ruby-identifier">smaller_equal</span>(<span class="ruby-keyword">self</span>, <span class="ruby-identifier">v</span>)
<span class="ruby-keyword">end</span></pre>
</div>
</div>
</div>
<div id="method-i-subs" class="method-detail ">
<div class="method-heading">
<span class="method-name">subs</span><span
class="method-args">(dt)</span>
<span class="method-click-advice">click to toggle source</span>
</div>
<div class="method-description">
<p>Perform substitution of a part of the graph using a data table:</p>
<pre class="ruby"><span class="ruby-identifier">x</span>, <span class="ruby-identifier">y</span> = <span class="ruby-constant">CAS</span><span class="ruby-operator">::</span><span class="ruby-identifier">vars</span> :<span class="ruby-identifier">x</span>, :<span class="ruby-identifier">y</span>
<span class="ruby-identifier">f</span> = (<span class="ruby-identifier">x</span> <span class="ruby-operator">**</span> <span class="ruby-value">2</span>) <span class="ruby-operator">+</span> (<span class="ruby-identifier">y</span> <span class="ruby-operator">**</span> <span class="ruby-value">2</span>)
<span class="ruby-identifier">puts</span> <span class="ruby-identifier">f</span>
<span class="ruby-comment"># => (x^2) + (y^2)</span>
<span class="ruby-identifier">puts</span> <span class="ruby-identifier">f</span>.<span class="ruby-identifier">subs</span>({<span class="ruby-identifier">x</span> =<span class="ruby-operator">></span> <span class="ruby-constant">CAS</span><span class="ruby-operator">::</span><span class="ruby-identifier">ln</span>(<span class="ruby-identifier">y</span>)})
<span class="ruby-comment"># => (ln(y)^2) + (y^2)</span>
</pre>
<ul><li>
<p><strong>argument</strong>: <code>Hash</code> with substitution table</p>
</li><li>
<p><strong>returns</strong>: <code>CAS::Op</code> (<code>self</code>) with
substitution performed</p>
</li></ul>
<div class="method-source-code" id="subs-source">
<pre><span class="ruby-comment"># File lib/operators/op.rb, line 131</span>
<span class="ruby-keyword">def</span> <span class="ruby-identifier">subs</span>(<span class="ruby-identifier">dt</span>)
<span class="ruby-constant">CAS</span><span class="ruby-operator">::</span><span class="ruby-constant">Help</span>.<span class="ruby-identifier">assert</span>(<span class="ruby-identifier">dt</span>, <span class="ruby-constant">Hash</span>)
<span class="ruby-identifier">sub</span> = <span class="ruby-identifier">dt</span>.<span class="ruby-identifier">keys</span>.<span class="ruby-identifier">select</span> { <span class="ruby-operator">|</span><span class="ruby-identifier">e</span><span class="ruby-operator">|</span> <span class="ruby-identifier">e</span> <span class="ruby-operator">==</span> <span class="ruby-ivar">@x</span> }[<span class="ruby-value">0</span>]
<span class="ruby-keyword">if</span> <span class="ruby-identifier">sub</span>
<span class="ruby-keyword">if</span> <span class="ruby-identifier">dt</span>[<span class="ruby-identifier">sub</span>].<span class="ruby-identifier">is_a?</span> <span class="ruby-constant">CAS</span><span class="ruby-operator">::</span><span class="ruby-constant">Op</span>
<span class="ruby-ivar">@x</span> = <span class="ruby-identifier">dt</span>[<span class="ruby-identifier">sub</span>]
<span class="ruby-keyword">elsif</span> <span class="ruby-identifier">dt</span>[<span class="ruby-identifier">sub</span>].<span class="ruby-identifier">is_a?</span> <span class="ruby-constant">Numeric</span>
<span class="ruby-ivar">@x</span> = <span class="ruby-constant">CAS</span><span class="ruby-operator">::</span><span class="ruby-identifier">const</span> <span class="ruby-identifier">dt</span>[<span class="ruby-identifier">sub</span>]
<span class="ruby-keyword">else</span>
<span class="ruby-identifier">raise</span> <span class="ruby-constant">CAS</span><span class="ruby-operator">::</span><span class="ruby-constant">CASError</span>, <span class="ruby-node">"Impossible subs. Received a #{dt[@x].class} = #{dt[@x]}"</span>
<span class="ruby-keyword">end</span>
<span class="ruby-keyword">else</span>
<span class="ruby-ivar">@x</span>.<span class="ruby-identifier">subs</span>(<span class="ruby-identifier">dt</span>)
<span class="ruby-keyword">end</span>
<span class="ruby-keyword">return</span> <span class="ruby-keyword">self</span>
<span class="ruby-keyword">end</span></pre>
</div>
</div>
</div>
<div id="method-i-to_c_lib" class="method-detail ">
<div class="method-heading">
<span class="method-name">to_c_lib</span><span
class="method-args">(name)</span>
<span class="method-click-advice">click to toggle source</span>
</div>
<div class="method-description">
<div class="method-source-code" id="to_c_lib-source">
<pre><span class="ruby-comment"># File lib/Mr.CAS/c-opt.rb, line 229</span>
<span class="ruby-keyword">def</span> <span class="ruby-identifier">to_c_lib</span>(<span class="ruby-identifier">name</span>)
<span class="ruby-constant">CAS</span><span class="ruby-operator">::</span><span class="ruby-constant">Help</span>.<span class="ruby-identifier">assert</span>(<span class="ruby-identifier">name</span>, <span class="ruby-constant">String</span>)
[<span class="ruby-constant">CAS</span><span class="ruby-operator">::</span><span class="ruby-constant">C_PLUGIN</span>.<span class="ruby-identifier">write_header</span>(<span class="ruby-keyword">self</span>, <span class="ruby-identifier">name</span>), <span class="ruby-constant">CAS</span><span class="ruby-operator">::</span><span class="ruby-constant">C_PLUGIN</span>.<span class="ruby-identifier">write_source</span>(<span class="ruby-keyword">self</span>, <span class="ruby-identifier">name</span>)]
<span class="ruby-keyword">end</span></pre>
</div>
</div>
</div>
<div id="method-i-to_code" class="method-detail ">
<div class="method-heading">
<span class="method-name">to_code</span><span
class="method-args">()</span>
<span class="method-click-advice">click to toggle source</span>
</div>
<div class="method-description">
<p>Convert expression to code (internal, for <code>CAS::Op#to_proc</code>
method)</p>
<ul><li>
<p><strong>returns</strong>: <code>String</code> that represent Ruby code to
be parsed in <code>CAS::Op#to_proc</code></p>
</li></ul>
<div class="method-source-code" id="to_code-source">
<pre><span class="ruby-comment"># File lib/operators/op.rb, line 158</span>
<span class="ruby-keyword">def</span> <span class="ruby-identifier">to_code</span>
<span class="ruby-node">"#{@x}"</span>
<span class="ruby-keyword">end</span></pre>
</div>
</div>
</div>
<div id="method-i-to_s" class="method-detail ">
<div class="method-heading">
<span class="method-name">to_s</span><span
class="method-args">()</span>
<span class="method-click-advice">click to toggle source</span>
</div>
<div class="method-description">
<p>Convert expression to string</p>
<ul><li>
<p><strong>returns</strong>: <code>String</code> to print on screen</p>
</li></ul>
<div class="method-source-code" id="to_s-source">
<pre><span class="ruby-comment"># File lib/operators/op.rb, line 151</span>
<span class="ruby-keyword">def</span> <span class="ruby-identifier">to_s</span>
<span class="ruby-node">"#{@x}"</span>
<span class="ruby-keyword">end</span></pre>
</div>
</div>
</div>
</section>
</section>
</main>
<footer id="validator-badges" role="contentinfo">
<p><a href="http://validator.w3.org/check/referer">Validate</a>
<p>Generated by <a href="http://docs.seattlerb.org/rdoc/">RDoc</a> 4.2.1.
<p>Based on <a href="http://deveiate.org/projects/Darkfish-RDoc/">Darkfish</a> by <a href="http://deveiate.org">Michael Granger</a>.
</footer>