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