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<h3 class="section">28.6 Miscellaneous Functions</h3>
<!-- poly scripts/polynomial/poly.m -->
<p><a name="doc_002dpoly"></a>
<div class="defun">
— Function File: <b>poly</b> (<var>A</var>)<var><a name="index-poly-2741"></a></var><br>
— Function File: <b>poly</b> (<var>x</var>)<var><a name="index-poly-2742"></a></var><br>
<blockquote><p>If <var>A</var> is a square N-by-N matrix, <code>poly (</code><var>A</var><code>)</code>
is the row vector of the coefficients of <code>det (z * eye (N) - A)</code>,
the characteristic polynomial of <var>A</var>. For example,
the following code finds the eigenvalues of <var>A</var> which are the roots of
<code>poly (</code><var>A</var><code>)</code>.
<pre class="example"> roots (poly (eye (3)))
⇒ 1.00001 + 0.00001i
1.00001 - 0.00001i
0.99999 + 0.00000i
</pre>
<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>If <var>x</var> is a vector, <code>poly (</code><var>x</var><code>)</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 <var>d</var><code> =
roots (poly (</code><var>c</var><code>))</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.
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<p class="noindent"><strong>See also:</strong> <a href="doc_002droots.html#doc_002droots">roots</a>, <a href="doc_002deig.html#doc_002deig">eig</a>.
</p></blockquote></div>
<!-- polyout scripts/polynomial/polyout.m -->
<p><a name="doc_002dpolyout"></a>
<div class="defun">
— Function File: <b>polyout</b> (<var>c</var>)<var><a name="index-polyout-2743"></a></var><br>
— Function File: <b>polyout</b> (<var>c, x</var>)<var><a name="index-polyout-2744"></a></var><br>
— Function File: <var>str</var> = <b>polyout</b> (<var><small class="dots">...</small></var>)<var><a name="index-polyout-2745"></a></var><br>
<blockquote><p>Write formatted polynomial
<pre class="example"> c(x) = c(1) * x^n + ... + c(n) x + c(n+1)
</pre>
<p>and return it as a string or write it to the screen (if <var>nargout</var> is
zero). <var>x</var> defaults to the string <code>"s"</code>.
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<p class="noindent"><strong>See also:</strong> <a href="doc_002dpolyreduce.html#doc_002dpolyreduce">polyreduce</a>.
</p></blockquote></div>
<!-- polyreduce scripts/polynomial/polyreduce.m -->
<p><a name="doc_002dpolyreduce"></a>
<div class="defun">
— Function File: <b>polyreduce</b> (<var>c</var>)<var><a name="index-polyreduce-2746"></a></var><br>
<blockquote><p>Reduce a polynomial coefficient vector to a minimum number of terms by
stripping off any leading zeros.
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<p class="noindent"><strong>See also:</strong> <a href="doc_002dpolyout.html#doc_002dpolyout">polyout</a>.
</p></blockquote></div>
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