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<a name="Miscellaneous-Functions"></a>
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<a name="Miscellaneous-Functions-1"></a>
<h3 class="section">28.6 Miscellaneous Functions</h3>
<a name="XREFpoly"></a><dl>
<dt><a name="index-poly"></a>Function File: <em></em> <strong>poly</strong> <em>(<var>A</var>)</em></dt>
<dt><a name="index-poly-1"></a>Function File: <em></em> <strong>poly</strong> <em>(<var>x</var>)</em></dt>
<dd><p>If <var>A</var> is a square <em>N</em>-by-<em>N</em> matrix, <code>poly (<var>A</var>)</code>
is the row vector of the coefficients of <code>det (z * eye (N) - A)</code>,
the characteristic polynomial of <var>A</var>.
</p>
<p>For example, the following code finds the eigenvalues of <var>A</var> which are
the roots of <code>poly (<var>A</var>)</code>.
</p>
<div class="example">
<pre class="example">roots (poly (eye (3)))
⇒ 1.00001 + 0.00001i
1.00001 - 0.00001i
0.99999 + 0.00000i
</pre></div>
<p>In fact, all three eigenvalues are exactly 1 which emphasizes that for
numerical performance the <code>eig</code> function should be used to compute
eigenvalues.
</p>
<p>If <var>x</var> is a vector, <code>poly (<var>x</var>)</code> is a vector of the
coefficients of the polynomial whose roots are the elements of <var>x</var>.
That is, if <var>c</var> is a polynomial, then the elements of
<code><var>d</var> = roots (poly (<var>c</var>))</code> are contained in <var>c</var>. The
vectors <var>c</var> and <var>d</var> are not identical, however, due to sorting and
numerical errors.
</p>
<p><strong>See also:</strong> <a href="Finding-Roots.html#XREFroots">roots</a>, <a href="Basic-Matrix-Functions.html#XREFeig">eig</a>.
</p></dd></dl>
<a name="XREFpolyout"></a><dl>
<dt><a name="index-polyout"></a>Function File: <em></em> <strong>polyout</strong> <em>(<var>c</var>)</em></dt>
<dt><a name="index-polyout-1"></a>Function File: <em></em> <strong>polyout</strong> <em>(<var>c</var>, <var>x</var>)</em></dt>
<dt><a name="index-polyout-2"></a>Function File: <em><var>str</var> =</em> <strong>polyout</strong> <em>(…)</em></dt>
<dd><p>Display a formatted version of the polynomial <var>c</var>.
</p>
<p>The formatted polynomial
</p>
<div class="example">
<pre class="example">c(x) = c(1) * x^n + … + c(n) x + c(n+1)
</pre></div>
<p>is returned as a string or written to the screen if <code>nargout</code> is zero.
</p>
<p>The second argument <var>x</var> specifies the variable name to use for each term
and defaults to the string <code>"s"</code>.
</p>
<p><strong>See also:</strong> <a href="#XREFpolyreduce">polyreduce</a>.
</p></dd></dl>
<a name="XREFpolyreduce"></a><dl>
<dt><a name="index-polyreduce"></a>Function File: <em></em> <strong>polyreduce</strong> <em>(<var>c</var>)</em></dt>
<dd><p>Reduce a polynomial coefficient vector to a minimum number of terms by
stripping off any leading zeros.
</p>
<p><strong>See also:</strong> <a href="#XREFpolyout">polyout</a>.
</p></dd></dl>
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