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