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<h3 class="section" id="Derivatives-_002f-Integrals-_002f-Transforms-1"><span>28.4 Derivatives / Integrals / Transforms<a class="copiable-link" href="#Derivatives-_002f-Integrals-_002f-Transforms-1"> ¶</a></span></h3>
<p>Octave comes with functions for computing the derivative and the integral
of a polynomial. The functions <code class="code">polyder</code> and <code class="code">polyint</code>
both return new polynomials describing the result. As an example we’ll
compute the definite integral of <em class="math">p(x) = x^2 + 1</em> from 0 to 3.
</p>
<div class="example">
<div class="group"><pre class="example-preformatted">c = [1, 0, 1];
integral = polyint (c);
area = polyval (integral, 3) - polyval (integral, 0)
⇒ 12
</pre></div></div>
<a class="anchor" id="XREFpolyder"></a><span style="display:block; margin-top:-4.5ex;"> </span>
<dl class="first-deftypefn">
<dt class="deftypefn" id="index-polyder"><span><code class="def-type"><var class="var">k</var> =</code> <strong class="def-name">polyder</strong> <code class="def-code-arguments">(<var class="var">p</var>)</code><a class="copiable-link" href="#index-polyder"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-polyder-1"><span><code class="def-type"><var class="var">k</var> =</code> <strong class="def-name">polyder</strong> <code class="def-code-arguments">(<var class="var">a</var>, <var class="var">b</var>)</code><a class="copiable-link" href="#index-polyder-1"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-polyder-2"><span><code class="def-type">[<var class="var">q</var>, <var class="var">d</var>] =</code> <strong class="def-name">polyder</strong> <code class="def-code-arguments">(<var class="var">b</var>, <var class="var">a</var>)</code><a class="copiable-link" href="#index-polyder-2"> ¶</a></span></dt>
<dd><p>Return the coefficients of the derivative of the polynomial whose
coefficients are given by the vector <var class="var">p</var>.
</p>
<p>If a pair of polynomials is given, return the derivative of the product
<em class="math"><var class="var">a</var>*<var class="var">b</var></em>.
</p>
<p>If two inputs and two outputs are given, return the derivative of the
polynomial quotient <em class="math"><var class="var">b</var>/<var class="var">a</var></em>. The quotient numerator is
in <var class="var">q</var> and the denominator in <var class="var">d</var>.
</p>
<p><strong class="strong">See also:</strong> <a class="ref" href="#XREFpolyint">polyint</a>, <a class="ref" href="Evaluating-Polynomials.html#XREFpolyval">polyval</a>, <a class="ref" href="Miscellaneous-Functions.html#XREFpolyreduce">polyreduce</a>.
</p></dd></dl>
<a class="anchor" id="XREFpolyint"></a><span style="display:block; margin-top:-4.5ex;"> </span>
<dl class="first-deftypefn">
<dt class="deftypefn" id="index-polyint"><span><code class="def-type"><var class="var">q</var> =</code> <strong class="def-name">polyint</strong> <code class="def-code-arguments">(<var class="var">p</var>)</code><a class="copiable-link" href="#index-polyint"> ¶</a></span></dt>
<dt class="deftypefnx def-cmd-deftypefn" id="index-polyint-1"><span><code class="def-type"><var class="var">q</var> =</code> <strong class="def-name">polyint</strong> <code class="def-code-arguments">(<var class="var">p</var>, <var class="var">k</var>)</code><a class="copiable-link" href="#index-polyint-1"> ¶</a></span></dt>
<dd><p>Return the coefficients of the integral of the polynomial whose
coefficients are represented by the vector <var class="var">p</var>.
</p>
<p>The variable <var class="var">k</var> is the constant of integration, which by default is
set to zero.
</p>
<p><strong class="strong">See also:</strong> <a class="ref" href="#XREFpolyder">polyder</a>, <a class="ref" href="Evaluating-Polynomials.html#XREFpolyval">polyval</a>.
</p></dd></dl>
<a class="anchor" id="XREFpolyaffine"></a><span style="display:block; margin-top:-4.5ex;"> </span>
<dl class="first-deftypefn">
<dt class="deftypefn" id="index-polyaffine"><span><code class="def-type"><var class="var">g</var> =</code> <strong class="def-name">polyaffine</strong> <code class="def-code-arguments">(<var class="var">f</var>, <var class="var">mu</var>)</code><a class="copiable-link" href="#index-polyaffine"> ¶</a></span></dt>
<dd><p>Return the coefficients of the polynomial vector <var class="var">f</var> after an affine
transformation.
</p>
<p>If <var class="var">f</var> is the vector representing the polynomial f(x), then
<code class="code"><var class="var">g</var> = polyaffine (<var class="var">f</var>, <var class="var">mu</var>)</code> is the vector representing:
</p>
<div class="example">
<pre class="example-preformatted">g(x) = f( (x - <var class="var">mu</var>(1)) / <var class="var">mu</var>(2) )
</pre></div>
<p><strong class="strong">See also:</strong> <a class="ref" href="Evaluating-Polynomials.html#XREFpolyval">polyval</a>, <a class="ref" href="Polynomial-Interpolation.html#XREFpolyfit">polyfit</a>.
</p></dd></dl>
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