docs/CAS/Div.html
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<h3>Parent</h3>
<p class="link"><a href="BinaryOp.html">CAS::BinaryOp</a>
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<!-- Method Quickref -->
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<h3>Methods</h3>
<ul class="link-list" role="directory">
<li ><a href="#method-i-call">#call</a>
<li class="calls-super" ><a href="#method-i-diff">#diff</a>
<li class="calls-super" ><a href="#method-i-simplify">#simplify</a>
<li ><a href="#method-i-to_code">#to_code</a>
<li ><a href="#method-i-to_s">#to_s</a>
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<h1 id="class-CAS::Div" class="class">
class CAS::Div
</h1>
<section class="description">
<p>Division between two functions. A function divided by zero it is considered
as an Infinity.</p>
</section>
<section id="5Buntitled-5D" class="documentation-section">
<section id="public-instance-5Buntitled-5D-method-details" class="method-section">
<header>
<h3>Public Instance Methods</h3>
</header>
<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. In this case it will call the <code>Fixnum#overloaded_plus</code>,
that is the old plus function.</p>
<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/functions/fnc-base.rb, line 235</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-identifier">overloaded_div</span>(<span class="ruby-ivar">@y</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-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>Performs the division between two <code>CAS::Op</code></p>
<pre>d
---- (f(x) / g(x)) = (f'(x) * g(x) - f(x) * g'(x))/(g(x)^2)
dx</pre>
<ul><li>
<p><strong>argument</strong>: <code>CAS::Op</code> argument of derivative</p>
</li><li>
<p><strong>returns</strong>: <code>CAS::Op</code> derivative</p>
</li></ul>
<div class="method-calls-super">
Calls superclass method
<a href="BinaryOp.html#method-i-diff">CAS::BinaryOp#diff</a>
</div>
<div class="method-source-code" id="diff-source">
<pre><span class="ruby-comment"># File lib/functions/fnc-base.rb, line 216</span>
<span class="ruby-keyword">def</span> <span class="ruby-identifier">diff</span>(<span class="ruby-identifier">v</span>)
<span class="ruby-identifier">diff_x</span>, <span class="ruby-identifier">diff_y</span> = <span class="ruby-keyword">super</span> <span class="ruby-identifier">v</span>
<span class="ruby-keyword">if</span> <span class="ruby-identifier">diff_y</span> <span class="ruby-operator">==</span> <span class="ruby-constant">CAS</span><span class="ruby-operator">::</span><span class="ruby-constant">Zero</span>
<span class="ruby-keyword">return</span> (<span class="ruby-identifier">diff_x</span><span class="ruby-operator">/</span><span class="ruby-ivar">@y</span>)
<span class="ruby-keyword">elsif</span> <span class="ruby-identifier">diff_x</span> <span class="ruby-operator">==</span> <span class="ruby-constant">CAS</span><span class="ruby-operator">::</span><span class="ruby-constant">Zero</span>
<span class="ruby-keyword">return</span> <span class="ruby-constant">CAS</span>.<span class="ruby-identifier">invert</span>(<span class="ruby-ivar">@x</span> <span class="ruby-operator">*</span> <span class="ruby-identifier">diff_y</span> <span class="ruby-operator">/</span> <span class="ruby-constant">CAS</span>.<span class="ruby-identifier">pow</span>(<span class="ruby-ivar">@y</span>, <span class="ruby-constant">CAS</span>.<span class="ruby-identifier">const</span>(<span class="ruby-value">2.0</span>)))
<span class="ruby-keyword">else</span>
<span class="ruby-keyword">return</span> ((<span class="ruby-identifier">diff_x</span> <span class="ruby-operator">*</span> <span class="ruby-ivar">@y</span>) <span class="ruby-operator">-</span> (<span class="ruby-identifier">diff_y</span> <span class="ruby-operator">*</span> <span class="ruby-ivar">@x</span>))<span class="ruby-operator">/</span><span class="ruby-constant">CAS</span>.<span class="ruby-identifier">pow</span>(<span class="ruby-ivar">@y</span>, <span class="ruby-constant">CAS</span>.<span class="ruby-identifier">const</span>(<span class="ruby-value">2.0</span>))
<span class="ruby-keyword">end</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>Same as <code>CAS::Op</code></p>
<p>Simplifcation engine supports:</p>
<ul><li>
<p>0 / y = 0</p>
</li><li>
<p>x / 0 = Inf</p>
</li><li>
<p>x / 1 = x</p>
</li><li>
<p>x / Inf = 0</p>
</li><li>
<p>a / b = c (constants reduction)</p>
</li><li>
<p><strong>returns</strong>: <code>CAS::Op</code> simplified version</p>
</li></ul>
<div class="method-calls-super">
Calls superclass method
<a href="BinaryOp.html#method-i-simplify">CAS::BinaryOp#simplify</a>
</div>
<div class="method-source-code" id="simplify-source">
<pre><span class="ruby-comment"># File lib/functions/fnc-base.rb, line 259</span>
<span class="ruby-keyword">def</span> <span class="ruby-identifier">simplify</span>
<span class="ruby-keyword">super</span>
<span class="ruby-keyword">return</span> <span class="ruby-keyword">self</span> <span class="ruby-keyword">if</span> (<span class="ruby-ivar">@x</span> <span class="ruby-operator">==</span> <span class="ruby-constant">CAS</span><span class="ruby-operator">::</span><span class="ruby-constant">Zero</span> <span class="ruby-keyword">and</span> <span class="ruby-ivar">@y</span> <span class="ruby-operator">==</span> <span class="ruby-constant">CAS</span><span class="ruby-operator">::</span><span class="ruby-constant">Zero</span>)
<span class="ruby-keyword">return</span> <span class="ruby-keyword">self</span> <span class="ruby-keyword">if</span> (<span class="ruby-ivar">@x</span> <span class="ruby-operator">==</span> <span class="ruby-constant">CAS</span><span class="ruby-operator">::</span><span class="ruby-constant">Infinity</span> <span class="ruby-keyword">and</span> <span class="ruby-ivar">@y</span> <span class="ruby-operator">==</span> <span class="ruby-constant">CAS</span><span class="ruby-operator">::</span><span class="ruby-constant">Infinity</span>)
<span class="ruby-keyword">return</span> <span class="ruby-keyword">self</span> <span class="ruby-keyword">if</span> (<span class="ruby-ivar">@x</span> <span class="ruby-operator">==</span> <span class="ruby-constant">CAS</span><span class="ruby-operator">::</span><span class="ruby-constant">Infinity</span> <span class="ruby-keyword">and</span> <span class="ruby-ivar">@y</span> <span class="ruby-operator">==</span> <span class="ruby-constant">CAS</span><span class="ruby-operator">::</span><span class="ruby-constant">Zero</span>)
<span class="ruby-keyword">return</span> <span class="ruby-keyword">self</span> <span class="ruby-keyword">if</span> (<span class="ruby-ivar">@x</span> <span class="ruby-operator">==</span> <span class="ruby-constant">CAS</span><span class="ruby-operator">::</span><span class="ruby-constant">Zero</span> <span class="ruby-keyword">and</span> <span class="ruby-ivar">@y</span> <span class="ruby-operator">==</span> <span class="ruby-constant">CAS</span><span class="ruby-operator">::</span><span class="ruby-constant">Infinity</span>)
<span class="ruby-keyword">return</span> <span class="ruby-constant">CAS</span><span class="ruby-operator">::</span><span class="ruby-constant">Zero</span> <span class="ruby-keyword">if</span> <span class="ruby-ivar">@x</span> <span class="ruby-operator">==</span> <span class="ruby-constant">CAS</span><span class="ruby-operator">::</span><span class="ruby-constant">Zero</span>
<span class="ruby-keyword">return</span> <span class="ruby-constant">CAS</span><span class="ruby-operator">::</span><span class="ruby-constant">Infinity</span> <span class="ruby-keyword">if</span> <span class="ruby-ivar">@y</span> <span class="ruby-operator">==</span> <span class="ruby-constant">CAS</span><span class="ruby-operator">::</span><span class="ruby-constant">Zero</span>
<span class="ruby-keyword">return</span> <span class="ruby-ivar">@x</span> <span class="ruby-keyword">if</span> <span class="ruby-ivar">@y</span> <span class="ruby-operator">==</span> <span class="ruby-constant">CAS</span><span class="ruby-operator">::</span><span class="ruby-constant">One</span>
<span class="ruby-keyword">return</span> <span class="ruby-constant">CAS</span><span class="ruby-operator">::</span><span class="ruby-constant">Zero</span> <span class="ruby-keyword">if</span> <span class="ruby-ivar">@y</span> <span class="ruby-operator">==</span> <span class="ruby-constant">CAS</span><span class="ruby-operator">::</span><span class="ruby-constant">Infinity</span>
<span class="ruby-keyword">return</span> <span class="ruby-constant">CAS</span><span class="ruby-operator">::</span><span class="ruby-constant">One</span> <span class="ruby-keyword">if</span> <span class="ruby-ivar">@x</span> <span class="ruby-operator">==</span> <span class="ruby-ivar">@y</span>
<span class="ruby-keyword">return</span> <span class="ruby-constant">CAS</span>.<span class="ruby-identifier">const</span>(<span class="ruby-keyword">self</span>.<span class="ruby-identifier">call</span>({})) <span class="ruby-keyword">if</span> (<span class="ruby-ivar">@x</span>.<span class="ruby-identifier">is_a?</span> <span class="ruby-constant">CAS</span><span class="ruby-operator">::</span><span class="ruby-constant">Constant</span> <span class="ruby-keyword">and</span> <span class="ruby-ivar">@y</span>.<span class="ruby-identifier">is_a?</span> <span class="ruby-constant">CAS</span><span class="ruby-operator">::</span><span class="ruby-constant">Constant</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_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/functions/fnc-base.rb, line 278</span>
<span class="ruby-keyword">def</span> <span class="ruby-identifier">to_code</span>
<span class="ruby-node">"(#{@x.to_code} / #{@y.to_code})"</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/functions/fnc-base.rb, line 244</span>
<span class="ruby-keyword">def</span> <span class="ruby-identifier">to_s</span>
<span class="ruby-node">"(#{@x}) / (#{@y})"</span>
<span class="ruby-keyword">end</span></pre>
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