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<h3 class="section">28.4 Derivatives / Integrals / Transforms</h3>
<p>Octave comes with functions for computing the derivative and the integral
of a polynomial. The functions <code>polyder</code> and <code>polyint</code>
both return new polynomials describing the result. As an example we'll
compute the definite integral of p(x) = x^2 + 1 from 0 to 3.
<pre class="example"> c = [1, 0, 1];
integral = polyint(c);
area = polyval(integral, 3) - polyval(integral, 0)
⇒ 12
</pre>
<!-- polyder scripts/polynomial/polyder.m -->
<p><a name="doc_002dpolyder"></a>
<div class="defun">
— Function File: <b>polyder</b> (<var>p</var>)<var><a name="index-polyder-2723"></a></var><br>
— Function File: [<var>k</var>] = <b>polyder</b> (<var>a, b</var>)<var><a name="index-polyder-2724"></a></var><br>
— Function File: [<var>q</var>, <var>d</var>] = <b>polyder</b> (<var>b, a</var>)<var><a name="index-polyder-2725"></a></var><br>
<blockquote><p>Return the coefficients of the derivative of the polynomial whose
coefficients are given by the vector <var>p</var>. If a pair of polynomials
is given, return the derivative of the product <var>a</var>*<var>b</var>.
If two inputs and two outputs are given, return the derivative of the
polynomial quotient <var>b</var>/<var>a</var>. The quotient numerator is
in <var>q</var> and the denominator in <var>d</var>.
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<p class="noindent"><strong>See also:</strong> <a href="doc_002dpolyint.html#doc_002dpolyint">polyint</a>, <a href="doc_002dpolyval.html#doc_002dpolyval">polyval</a>, <a href="doc_002dpolyreduce.html#doc_002dpolyreduce">polyreduce</a>.
</p></blockquote></div>
<!-- polyint scripts/polynomial/polyint.m -->
<p><a name="doc_002dpolyint"></a>
<div class="defun">
— Function File: <b>polyint</b> (<var>p</var>)<var><a name="index-polyint-2726"></a></var><br>
— Function File: <b>polyint</b> (<var>p, k</var>)<var><a name="index-polyint-2727"></a></var><br>
<blockquote><p>Return the coefficients of the integral of the polynomial whose
coefficients are represented by the vector <var>p</var>. The variable
<var>k</var> is the constant of integration, which by default is set to zero.
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<p class="noindent"><strong>See also:</strong> <a href="doc_002dpolyder.html#doc_002dpolyder">polyder</a>, <a href="doc_002dpolyval.html#doc_002dpolyval">polyval</a>.
</p></blockquote></div>
<!-- polyaffine scripts/polynomial/polyaffine.m -->
<p><a name="doc_002dpolyaffine"></a>
<div class="defun">
— Function File: <b>polyaffine</b> (<var>f, mu</var>)<var><a name="index-polyaffine-2728"></a></var><br>
<blockquote><p>Return the coefficients of the polynomial vector <var>f</var> after an affine
transformation. If <var>f</var> is the vector representing the polynomial f(x),
then <var>g</var><code> = polyaffine (</code><var>f</var><code>, </code><var>mu</var><code>)</code> is the vector
representing:
<pre class="example"> g(x) = f( (x - <var>mu</var>(1)) / <var>mu</var>(2) )
</pre>
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<p class="noindent"><strong>See also:</strong> <a href="doc_002dpolyval.html#doc_002dpolyval">polyval</a>, <a href="doc_002dpolyfit.html#doc_002dpolyfit">polyfit</a>.
</p></blockquote></div>
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