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<?xml version="1.0" encoding="UTF-8"?>
<!--
* Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
* Copyright (C) 2006-2008 - INRIA - Francois DELBECQUE
*
* This file must be used under the terms of the CeCILL.
* This source file is licensed as described in the file COPYING, which
* you should have received as part of this distribution. The terms
* are also available at
* http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt
*
-->
<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" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="determ">
<refnamediv>
<refname>determ</refname>
<refpurpose>determinant of polynomial matrix</refpurpose>
</refnamediv>
<refsynopsisdiv>
<title>Calling Sequence</title>
<synopsis>res=determ(W [,k])</synopsis>
</refsynopsisdiv>
<refsection>
<title>Arguments</title>
<variablelist>
<varlistentry>
<term>W</term>
<listitem>
<para>real square polynomial matrix</para>
</listitem>
</varlistentry>
<varlistentry>
<term>k</term>
<listitem>
<para>integer (upper bound for the degree of the determinant of W)</para>
</listitem>
</varlistentry>
</variablelist>
</refsection>
<refsection>
<title>Description</title>
<para>
returns the determinant of a real polynomial matrix
(computation made by FFT if W size is greater than 2*2).
</para>
<para>
<literal>res=determ(W [,k])</literal><literal>k</literal> is an integer larger than the actual degree of the determinant
of <literal>W</literal>.
</para>
<para>
The default value of <literal>k</literal> is the smallest power of 2 which is larger
than <literal>n*max(degree(W))</literal>.
</para>
<para>
Method (Only if W size is greater than 2*2) : evaluate the determinant of <literal>W</literal> for the Fourier frequencies
and apply inverse FFT to the coefficients of the determinant.
</para>
</refsection>
<refsection>
<title>Examples</title>
<programlisting role="example"><![CDATA[
s=poly(0,'s');
w=s*rand(10,10);
determ(w)
det(coeff(w,1))*s^10
]]></programlisting>
</refsection>
<refsection role="see also">
<title>See Also</title>
<simplelist type="inline">
<member>
<link linkend="det">det</link>
</member>
<member>
<link linkend="detr">detr</link>
</member>
<member>
<link linkend="coffg">coffg</link>
</member>
</simplelist>
</refsection>
</refentry>
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