Get ride of the useless pubdate tag.
[scilab.git] / scilab / modules / polynomials / help / en_US / poly.xml
1 <?xml version="1.0" encoding="UTF-8"?>
2 <refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" version="5.0-subset Scilab" xml:lang="en" xml:id="poly">
3   <refnamediv>
4     <refname>poly</refname>
5     <refpurpose>polynomial definition</refpurpose>
6   </refnamediv>
7   <refsynopsisdiv>
8     <title>Calling Sequence</title>
9     <synopsis>p=poly(a,vname, ["flag"])</synopsis>
10   </refsynopsisdiv>
11   <refsection>
12     <title>Arguments</title>
13     <variablelist>
14       <varlistentry>
15         <term>a</term>
16         <listitem>
17           <para>matrix or real number</para>
18         </listitem>
19       </varlistentry>
20       <varlistentry>
21         <term>vname</term>
22         <listitem>
23           <para>String, the symbolic variable name. If the string have more
24             than 4 characters only the first 4 are taken into account.
25           </para>
26         </listitem>
27       </varlistentry>
28       <varlistentry>
29         <term>"flag"  </term>
30         <listitem>
31           <para>
32             string ("roots", "coeff"), default value is <literal>"roots"</literal>.
33           </para>
34         </listitem>
35       </varlistentry>
36     </variablelist>
37   </refsection>
38   <refsection>
39     <title>Description</title>
40     <variablelist>
41       <varlistentry>
42         <term>
43           If <literal>a</literal> is a matrix,
44         </term>
45         <listitem>
46           <para>
47             <literal>p</literal> is the characteristic
48             polynomial i.e. <literal>determinant(x*eye()-a)</literal>, <literal>x</literal> being
49             the symbolic variable.
50           </para>
51         </listitem>
52       </varlistentry>
53       <varlistentry>
54         <term>If v is a vector,</term>
55         <listitem>
56           <itemizedlist>
57             <listitem>
58               <para>
59                 <literal>poly(v,"x",["roots"])</literal>  is the polynomial
60                 with <literal>roots</literal> the entries of <literal>v</literal> and
61                 <literal>"x"</literal> as formal variable. (In this case,
62                 <literal>roots</literal> and   <literal>poly</literal> are inverse functions). 
63                 Note that Infinite roots gives zero  highest degree coefficients. 
64               </para>
65             </listitem>
66             <listitem>
67               <para>
68                 <literal>poly(v,"x","coeff")</literal> creates the
69                 polynomial with symbol <literal>"x"</literal> and with coefficients
70                 the entries of <literal>v</literal> (<literal>v(1)</literal> is the constant term 
71                 of the polynomial). (Here <literal>poly</literal> and <literal>coeff</literal> are 
72                 inverse functions).
73               </para>
74             </listitem>
75           </itemizedlist>
76         </listitem>
77       </varlistentry>
78     </variablelist>
79     <para>
80       <literal>s=poly(0,"s")</literal> is the seed for defining
81       polynomials with symbol <literal>"s"</literal>.
82     </para>
83   </refsection>
84   <refsection>
85     <title>Examples</title>
86     <programlisting role="example"><![CDATA[ 
87 s=poly(0,"s");
88 p=1+s+2*s^2;
89 A=rand(2,2);
90 poly(A,"x")
91 //rational fractions
92 h=(1+2*%s)/poly(1:4,'s','c')
93  ]]></programlisting>
94   </refsection>
95   <refsection role="see also">
96     <title>See Also</title>
97     <simplelist type="inline">
98       <member>
99         <link linkend="coeff">coeff</link>
100       </member>
101       <member>
102         <link linkend="roots">roots</link>
103       </member>
104       <member>
105         <link linkend="varn">varn</link>
106       </member>
107       <member>
108         <link linkend="horner">horner</link>
109       </member>
110       <member>
111         <link linkend="derivat">derivat</link>
112       </member>
113       <member>
114         <link linkend="matrices">matrices</link>
115       </member>
116       <member>
117         <link linkend="rational">rational</link>
118       </member>
119     </simplelist>
120   </refsection>
121 </refentry>