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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
*
* 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="lcmdiag">
<refnamediv>
<refname>lcmdiag</refname>
<refpurpose>least common multiple diagonal factorization</refpurpose>
</refnamediv>
<refsynopsisdiv>
<title>Calling Sequence</title>
<synopsis>[N,D]=lcmdiag(H)
[N,D]=lcmdiag(H,flag)
</synopsis>
</refsynopsisdiv>
<refsection>
<title>Arguments</title>
<variablelist>
<varlistentry>
<term>H</term>
<listitem>
<para>rational matrix</para>
</listitem>
</varlistentry>
<varlistentry>
<term>N</term>
<listitem>
<para>polynomial matrix</para>
</listitem>
</varlistentry>
<varlistentry>
<term>D</term>
<listitem>
<para>diagonal polynomial matrix</para>
</listitem>
</varlistentry>
<varlistentry>
<term>flag</term>
<listitem>
<para>
character string: <literal>'row'</literal> or <literal>'col'</literal> (default)
</para>
</listitem>
</varlistentry>
</variablelist>
</refsection>
<refsection>
<title>Description</title>
<para>
<literal>[N,D]=lcmdiag(H,'row')</literal> computes a factorization <literal>D*H=N</literal>,
i.e. <literal>H=D^(-1)*N</literal> where D is a diagonal matrix with D(k,k)=lcm of
kth row of H('den').
</para>
<para>
<literal>[N,D]=lcmdiag(H)</literal> or <literal>[N,D]=lcmdiag(H,'col)</literal> returns
<literal>H=N*D^(-1)</literal> with diagonal D and D(k,k)=lcm of kth col of H('den')
</para>
</refsection>
<refsection>
<title>Examples</title>
<programlisting role="example"><![CDATA[
s=poly(0,'s');
H=[1/s,(s+2)/s/(s+1)^2;1/(s^2*(s+2)),2/(s+2)];
[N,D]=lcmdiag(H);
N/D-H
]]></programlisting>
</refsection>
<refsection role="see also">
<title>See Also</title>
<simplelist type="inline">
<member>
<link linkend="lcm">lcm</link>
</member>
<member>
<link linkend="gcd">gcd</link>
</member>
<member>
<link linkend="bezout">bezout</link>
</member>
</simplelist>
</refsection>
</refentry>
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