<html lang="en"> <head> <title>Derivatives / Integrals / Transforms - GNU Octave</title> <meta http-equiv="Content-Type" content="text/html"> <meta name="description" content="GNU Octave"> <meta name="generator" content="makeinfo 4.13"> <link title="Top" rel="start" href="index.html#Top"> <link rel="up" href="Polynomial-Manipulations.html#Polynomial-Manipulations" title="Polynomial Manipulations"> <link rel="prev" href="Products-of-Polynomials.html#Products-of-Polynomials" title="Products of Polynomials"> <link rel="next" href="Polynomial-Interpolation.html#Polynomial-Interpolation" title="Polynomial Interpolation"> <link href="http://www.gnu.org/software/texinfo/" rel="generator-home" title="Texinfo Homepage"> <meta http-equiv="Content-Style-Type" content="text/css"> <style type="text/css"><!-- pre.display { font-family:inherit } pre.format { font-family:inherit } pre.smalldisplay { font-family:inherit; font-size:smaller } pre.smallformat { font-family:inherit; font-size:smaller } pre.smallexample { font-size:smaller } pre.smalllisp { font-size:smaller } span.sc { font-variant:small-caps } span.roman { font-family:serif; font-weight:normal; } span.sansserif { font-family:sans-serif; font-weight:normal; } --></style> </head> <body> <div class="node"> <a name="Derivatives-%2f-Integrals-%2f-Transforms"></a> <a name="Derivatives-_002f-Integrals-_002f-Transforms"></a> <p> Next: <a rel="next" accesskey="n" href="Polynomial-Interpolation.html#Polynomial-Interpolation">Polynomial Interpolation</a>, Previous: <a rel="previous" accesskey="p" href="Products-of-Polynomials.html#Products-of-Polynomials">Products of Polynomials</a>, Up: <a rel="up" accesskey="u" href="Polynomial-Manipulations.html#Polynomial-Manipulations">Polynomial Manipulations</a> <hr> </div> <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>. <!-- Texinfo @sp should work but in practice produces ugly results for HTML. --> <!-- A simple blank line produces the correct behavior. --> <!-- @sp 1 --> <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. <!-- Texinfo @sp should work but in practice produces ugly results for HTML. --> <!-- A simple blank line produces the correct behavior. --> <!-- @sp 1 --> <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> <!-- Texinfo @sp should work but in practice produces ugly results for HTML. --> <!-- A simple blank line produces the correct behavior. --> <!-- @sp 1 --> <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> </body></html>