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>