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<a href="Scientific-module.html">Package Scientific</a> ::
<a href="Scientific.Functions-module.html">Package Functions</a> ::
<a href="Scientific.Functions.Rational-module.html">Module Rational</a> ::
Class RationalFunction
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<!-- ==================== CLASS DESCRIPTION ==================== -->
<h1 class="epydoc">Class RationalFunction</h1><p class="nomargin-top"></p>
<p>Rational Function</p>
<p>Instances of this class represent rational functions in a single
variable. They can be evaluated like functions.</p>
<p>Rational functions support addition, subtraction, multiplication, and
division.</p>
<!-- ==================== INSTANCE METHODS ==================== -->
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<span class="summary-type"> </span>
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<td><span class="summary-sig"><a name="__add__"></a><span class="summary-sig-name">__add__</span>(<span class="summary-sig-arg">self</span>,
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<td><span class="summary-sig"><a name="__call__"></a><span class="summary-sig-name">__call__</span>(<span class="summary-sig-arg">self</span>,
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<span class="summary-type"> </span>
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<td><span class="summary-sig"><a name="__coerce__"></a><span class="summary-sig-name">__coerce__</span>(<span class="summary-sig-arg">self</span>,
<span class="summary-sig-arg">other</span>)</span></td>
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<span class="summary-type"> </span>
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<td><span class="summary-sig"><a name="__div__"></a><span class="summary-sig-name">__div__</span>(<span class="summary-sig-arg">self</span>,
<span class="summary-sig-arg">other</span>)</span></td>
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<span class="summary-type"> </span>
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<td><span class="summary-sig"><a href="Scientific.Functions.Rational.RationalFunction-class.html#__init__" class="summary-sig-name">__init__</a>(<span class="summary-sig-arg">self</span>,
<span class="summary-sig-arg">numerator</span>,
<span class="summary-sig-arg">denominator</span>=<span class="summary-sig-default"><code class="variable-group">[</code>1.0<code class="variable-group">]</code></span>)</span></td>
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<span class="summary-type"> </span>
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<td><span class="summary-sig"><a name="__mul__"></a><span class="summary-sig-name">__mul__</span>(<span class="summary-sig-arg">self</span>,
<span class="summary-sig-arg">other</span>)</span></td>
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</td>
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<span class="summary-type"> </span>
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<td><span class="summary-sig"><a name="__radd__"></a><span class="summary-sig-name">__radd__</span>(<span class="summary-sig-arg">self</span>,
<span class="summary-sig-arg">other</span>)</span></td>
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</td>
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<td width="15%" align="right" valign="top" class="summary">
<span class="summary-type"> </span>
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<td><span class="summary-sig"><a name="__rdiv__"></a><span class="summary-sig-name">__rdiv__</span>(<span class="summary-sig-arg">self</span>,
<span class="summary-sig-arg">other</span>)</span></td>
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</td>
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<span class="summary-type"> </span>
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<td><span class="summary-sig"><a name="__repr__"></a><span class="summary-sig-name">__repr__</span>(<span class="summary-sig-arg">self</span>)</span></td>
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<td width="15%" align="right" valign="top" class="summary">
<span class="summary-type"> </span>
</td><td class="summary">
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<td><span class="summary-sig"><a name="__rmul__"></a><span class="summary-sig-name">__rmul__</span>(<span class="summary-sig-arg">self</span>,
<span class="summary-sig-arg">other</span>)</span></td>
<td align="right" valign="top">
</td>
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</td>
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<td width="15%" align="right" valign="top" class="summary">
<span class="summary-type"> </span>
</td><td class="summary">
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<td><span class="summary-sig"><a name="__rsub__"></a><span class="summary-sig-name">__rsub__</span>(<span class="summary-sig-arg">self</span>,
<span class="summary-sig-arg">other</span>)</span></td>
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</td>
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<td width="15%" align="right" valign="top" class="summary">
<span class="summary-type"> </span>
</td><td class="summary">
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<td><span class="summary-sig"><a name="__sub__"></a><span class="summary-sig-name">__sub__</span>(<span class="summary-sig-arg">self</span>,
<span class="summary-sig-arg">other</span>)</span></td>
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</td>
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</td>
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<td width="15%" align="right" valign="top" class="summary">
<span class="summary-type">(<a href="Scientific.Functions.Polynomial.Polynomial-class.html"
class="link">Scientific.Functions.Polynomial.Polynomial</a>, <a
href="Scientific.Functions.Rational.RationalFunction-class.html"
class="link">RationalFunction</a>)</span>
</td><td class="summary">
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr>
<td><span class="summary-sig"><a href="Scientific.Functions.Rational.RationalFunction-class.html#divide" class="summary-sig-name">divide</a>(<span class="summary-sig-arg">self</span>,
<span class="summary-sig-arg">shift</span>=<span class="summary-sig-default">0</span>)</span><br />
Returns:
a polynomial and a rational function such that the sum of the two is
equal to the original rational function.</td>
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</td>
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</td>
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<td width="15%" align="right" valign="top" class="summary">
<span class="summary-type"><code>Numeric.array</code></span>
</td><td class="summary">
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<td><span class="summary-sig"><a href="Scientific.Functions.Rational.RationalFunction-class.html#poles" class="summary-sig-name">poles</a>(<span class="summary-sig-arg">self</span>)</span><br />
Find the <a name="index-poles"></a><i class="indexterm">poles</i>
(zeros of the denominator) by diagonalization of the associated
Frobenius matrix.</td>
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</td>
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<td width="15%" align="right" valign="top" class="summary">
<span class="summary-type"><code>Numeric.array</code></span>
</td><td class="summary">
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<td><span class="summary-sig"><a href="Scientific.Functions.Rational.RationalFunction-class.html#zeros" class="summary-sig-name">zeros</a>(<span class="summary-sig-arg">self</span>)</span><br />
Find the <a name="index-zeros"></a><i class="indexterm">zeros</i> (<a
name="index-roots"></a><i class="indexterm">roots</i>) of the
numerator by diagonalization of the associated Frobenius matrix.</td>
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</td>
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</table>
</td>
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<!-- ==================== CLASS VARIABLES ==================== -->
<a name="section-ClassVariables"></a>
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cellspacing="0" width="100%" bgcolor="white">
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<span class="table-header">Class Variables</span></td>
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<span class="summary-type"> </span>
</td><td class="summary">
<a name="is_rational_function"></a><span class="summary-name">is_rational_function</span> = <code title="1">1</code>
</td>
</tr>
</table>
<!-- ==================== METHOD DETAILS ==================== -->
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<span class="table-header">Method Details</span></td>
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<a name="__init__"></a>
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<h3 class="epydoc"><span class="sig"><span class="sig-name">__init__</span>(<span class="sig-arg">self</span>,
<span class="sig-arg">numerator</span>,
<span class="sig-arg">denominator</span>=<span class="sig-default"><code class="variable-group">[</code>1.0<code class="variable-group">]</code></span>)</span>
<br /><em class="fname">(Constructor)</em>
</h3>
</td><td align="right" valign="top"
>
</td>
</tr></table>
<dl class="fields">
<dt>Parameters:</dt>
<dd><ul class="nomargin-top">
<li><strong class="pname"><code>numerator</code></strong> (<a href="Scientific.Functions.Polynomial.Polynomial-class.html"
class="link">Scientific.Functions.Polynomial.Polynomial</a> or
<code>list</code> of numbers) - polynomial in one variable, or a list of polynomial coefficients</li>
<li><strong class="pname"><code>denominator</code></strong> (<a href="Scientific.Functions.Polynomial.Polynomial-class.html"
class="link">Scientific.Functions.Polynomial.Polynomial</a> or
<code>list</code> of numbers) - polynomial in one variable, or a list of polynomial coefficients</li>
</ul></dd>
</dl>
</td></tr></table>
</div>
<a name="divide"></a>
<div>
<table class="details" border="1" cellpadding="3"
cellspacing="0" width="100%" bgcolor="white">
<tr><td>
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr valign="top"><td>
<h3 class="epydoc"><span class="sig"><span class="sig-name">divide</span>(<span class="sig-arg">self</span>,
<span class="sig-arg">shift</span>=<span class="sig-default">0</span>)</span>
</h3>
</td><td align="right" valign="top"
>
</td>
</tr></table>
<dl class="fields">
<dt>Parameters:</dt>
<dd><ul class="nomargin-top">
<li><strong class="pname"><code>shift</code></strong> (<code>int</code> (non-negative)) - the power of the independent variable by which the numerator is
multiplied prior to division</li>
</ul></dd>
<dt>Returns: (<a href="Scientific.Functions.Polynomial.Polynomial-class.html"
class="link">Scientific.Functions.Polynomial.Polynomial</a>, <a
href="Scientific.Functions.Rational.RationalFunction-class.html"
class="link">RationalFunction</a>)</dt>
<dd>a polynomial and a rational function such that the sum of the two
is equal to the original rational function. The returned rational
function's numerator is of lower order than its denominator.</dd>
</dl>
</td></tr></table>
</div>
<a name="poles"></a>
<div>
<table class="details" border="1" cellpadding="3"
cellspacing="0" width="100%" bgcolor="white">
<tr><td>
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr valign="top"><td>
<h3 class="epydoc"><span class="sig"><span class="sig-name">poles</span>(<span class="sig-arg">self</span>)</span>
</h3>
</td><td align="right" valign="top"
>
</td>
</tr></table>
<p>Find the <a name="index-poles"></a><i class="indexterm">poles</i>
(zeros of the denominator) by diagonalization of the associated Frobenius
matrix.</p>
<dl class="fields">
<dt>Returns: <code>Numeric.array</code></dt>
<dd>an array containing the poles</dd>
</dl>
</td></tr></table>
</div>
<a name="zeros"></a>
<div>
<table class="details" border="1" cellpadding="3"
cellspacing="0" width="100%" bgcolor="white">
<tr><td>
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr valign="top"><td>
<h3 class="epydoc"><span class="sig"><span class="sig-name">zeros</span>(<span class="sig-arg">self</span>)</span>
</h3>
</td><td align="right" valign="top"
>
</td>
</tr></table>
<p>Find the <a name="index-zeros"></a><i class="indexterm">zeros</i> (<a
name="index-roots"></a><i class="indexterm">roots</i>) of the numerator
by diagonalization of the associated Frobenius matrix.</p>
<dl class="fields">
<dt>Returns: <code>Numeric.array</code></dt>
<dd>an array containing the zeros</dd>
</dl>
</td></tr></table>
</div>
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