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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.Polynomial-module.html">Module Polynomial</a> ::
Class Polynomial
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<!-- ==================== CLASS DESCRIPTION ==================== -->
<h1 class="epydoc">Class Polynomial</h1><p class="nomargin-top"></p>
<p><a name="index-Multivariate"></a><i class="indexterm">Multivariate</i>
<a name="index-polynomial"></a><i class="indexterm">polynomial</i></p>
<p>Instances of this class represent polynomials of any order and in any
number of variables. The coefficients and thus the values can be real or
complex. Polynomials can be evaluated like functions.</p>
<!-- ==================== INSTANCE METHODS ==================== -->
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<span class="table-header">Instance Methods</span></td>
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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>,
<span class="summary-sig-arg">other</span>)</span></td>
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<td width="15%" align="right" valign="top" class="summary">
<span class="summary-type">number</span>
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<td><span class="summary-sig"><a href="Scientific.Functions.Polynomial.Polynomial-class.html#__call__" class="summary-sig-name">__call__</a>(<span class="summary-sig-arg">self</span>,
<span class="summary-sig-arg">*args</span>)</span><br />
Returns:
the value of the polynomial at the given point</td>
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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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</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 href="Scientific.Functions.Polynomial.Polynomial-class.html#__init__" class="summary-sig-name">__init__</a>(<span class="summary-sig-arg">self</span>,
<span class="summary-sig-arg">coefficients</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="__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="__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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<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="__repr__"></a><span class="summary-sig-name">__repr__</span>(<span class="summary-sig-arg">self</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">Polynomial</a></span>
</td><td class="summary">
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<td><span class="summary-sig"><a href="Scientific.Functions.Polynomial.Polynomial-class.html#derivative" class="summary-sig-name">derivative</a>(<span class="summary-sig-arg">self</span>,
<span class="summary-sig-arg">variable</span>=<span class="summary-sig-default">0</span>)</span><br />
Returns:
a polynomial of reduced order in one variable</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">Polynomial</a></span>
</td><td class="summary">
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<tr>
<td><span class="summary-sig"><a href="Scientific.Functions.Polynomial.Polynomial-class.html#integral" class="summary-sig-name">integral</a>(<span class="summary-sig-arg">self</span>,
<span class="summary-sig-arg">variable</span>=<span class="summary-sig-default">0</span>)</span><br />
Returns:
a polynomial of higher order in one variable</td>
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</td>
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</td>
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<span class="summary-type"><code>Numeric.array</code></span>
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<td><span class="summary-sig"><a href="Scientific.Functions.Polynomial.Polynomial-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
polynomial by diagonalization of the associated Frobenius matrix.</td>
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<!-- ==================== CLASS VARIABLES ==================== -->
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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_polynomial"></a><span class="summary-name">is_polynomial</span> = <code title="1">1</code>
</td>
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<!-- ==================== METHOD DETAILS ==================== -->
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<span class="table-header">Method Details</span></td>
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<a name="__call__"></a>
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<h3 class="epydoc"><span class="sig"><span class="sig-name">__call__</span>(<span class="sig-arg">self</span>,
<span class="sig-arg">*args</span>)</span>
<br /><em class="fname">(Call operator)</em>
</h3>
</td><td align="right" valign="top"
>
</td>
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<dl class="fields">
<dt>Parameters:</dt>
<dd><ul class="nomargin-top">
<li><strong class="pname"><code>args</code></strong> (<code>tuple</code> of numbers) - tuple of values, one for each variable of the polynomial</li>
</ul></dd>
<dt>Returns: number</dt>
<dd>the value of the polynomial at the given point</dd>
<dt>Raises:</dt>
<dd><ul class="nomargin-top">
<li><code><strong class='fraise'>TypeError</strong></code> - if the number of arguments is not equal to the number of variable
of the polynomial</li>
</ul></dd>
</dl>
</td></tr></table>
</div>
<a name="__init__"></a>
<div>
<table class="details" border="1" cellpadding="3"
cellspacing="0" width="100%" bgcolor="white">
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<tr valign="top"><td>
<h3 class="epydoc"><span class="sig"><span class="sig-name">__init__</span>(<span class="sig-arg">self</span>,
<span class="sig-arg">coefficients</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>coefficients</code></strong> (<code>Numeric.array</code> or nested list of numbers) - an <i class="math">N</i>-dimnesional array for a polynomial in <i
class="math">N</i> variables. <code>coeffcients[i, j, ...]</code>
is the coefficient of <i class="math">x_1^i x_2^j ...</i></li>
</ul></dd>
</dl>
</td></tr></table>
</div>
<a name="derivative"></a>
<div>
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cellspacing="0" width="100%" bgcolor="white">
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<h3 class="epydoc"><span class="sig"><span class="sig-name">derivative</span>(<span class="sig-arg">self</span>,
<span class="sig-arg">variable</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>variable</code></strong> (<code>int</code>) - the index of the variable with respect to which the <a
name="index-derivative"></a><i class="indexterm">derivative</i>
is taken</li>
</ul></dd>
<dt>Returns: <a href="Scientific.Functions.Polynomial.Polynomial-class.html"
class="link">Polynomial</a></dt>
<dd>a polynomial of reduced order in one variable</dd>
</dl>
</td></tr></table>
</div>
<a name="integral"></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">integral</span>(<span class="sig-arg">self</span>,
<span class="sig-arg">variable</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>variable</code></strong> (<code>int</code>) - the index of the variable with respect to which the <a
name="index-integral"></a><i class="indexterm">integral</i> is
computed</li>
</ul></dd>
<dt>Returns: <a href="Scientific.Functions.Polynomial.Polynomial-class.html"
class="link">Polynomial</a></dt>
<dd>a polynomial of higher order in one variable</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 polynomial
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>
<dt>Raises:</dt>
<dd><ul class="nomargin-top">
<li><code><strong class='fraise'>ValueError</strong></code> - is the polynomial has more than one variable</li>
</ul></dd>
</dl>
<div class="fields"> <p><strong>Note:</strong>
this is defined only for polynomials in one variable
</p>
</div></td></tr></table>
</div>
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