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17     <refnamediv>
18         <refname>derivat</refname>
19         <refpurpose>Rational matrix derivative</refpurpose>
20     </refnamediv>
21     <refsynopsisdiv>
22         <title>Syntax</title>
23         <synopsis>pd=derivat(p)</synopsis>
24     </refsynopsisdiv>
25     <refsection>
26         <title>Arguments</title>
27         <variablelist>
28             <varlistentry>
29                 <term>p</term>
30                 <listitem>
31                     <para>polynomial or rational matrix</para>
32                 </listitem>
33             </varlistentry>
34         </variablelist>
35     </refsection>
36     <refsection>
37         <title>Description</title>
38         <para>
39             The derivat() function works with expressions like
40             <latex>p(z) = \sum \limits_{i = -\infty}^{\infty} A_{i} z^{i}</latex>
41             which consists of functions of linear combinations with integer exponents of one variable (in the example denoted by z).
42         </para>
43         <para>
44             The function derivat() implements the analytical derivation of p(z), giving the following result.
45             <latex>\dfrac{d(p(z))}{d z} = \sum \limits_{i = -\infty}^{\infty} i A_{i} z^{i - 1}</latex>
46         </para>
47     </refsection>
48     <refsection>
49         <title>Examples</title>
50         <programlisting role="example"><![CDATA[
51 s=poly(0,'s');
52 derivat(1/s)  // -1/s^2;
53  ]]></programlisting>
54         <programlisting role="example"><![CDATA[
55 p1 = poly([1 -2 1], 'x', 'coeff')
56 derivat(p1)
57  ]]></programlisting>
58         <programlisting role="example"><![CDATA[
59 p2 = poly([1 -4 2], 'y', 'coeff')
60 derivat(p2)
61  ]]></programlisting>
62         <programlisting role="example"><![CDATA[
63 p3 = poly(ones(1, 10), 'z', 'coeff')
64 derivat(p3)
65  ]]></programlisting>
66         <programlisting role="example"><![CDATA[
67 p4 = poly([-1 1], 't', 'roots')
68 derivat(p4)
69  ]]></programlisting>
70         <programlisting role="example"><![CDATA[
71 s = %s; p5 = s^{-1} + 2 + 3*s
72 derivat(p5)
73  ]]></programlisting>
74     </refsection>
75 </refentry>