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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="simp">
<refnamediv>
<refname>simp</refname>
<refpurpose>rational simplification</refpurpose>
</refnamediv>
<refsynopsisdiv>
<title>Calling Sequence</title>
<synopsis>[N1,D1]=simp(N,D)
H1=simp(H)
</synopsis>
</refsynopsisdiv>
<refsection>
<title>Arguments</title>
<variablelist>
<varlistentry>
<term>N,D</term>
<listitem>
<para>real polynomials or real matrix polynomials</para>
</listitem>
</varlistentry>
<varlistentry>
<term>H</term>
<listitem>
<para>
rational matrix (i.e matrix with entries <literal>n/d</literal> ,<literal>n</literal> and <literal>d</literal> real polynomials)
</para>
</listitem>
</varlistentry>
</variablelist>
</refsection>
<refsection>
<title>Description</title>
<para>
<literal>[n1,d1]=simp(n,d)</literal> calculates two polynomials <literal>n1</literal> and <literal>d1</literal>
such that <literal>n1/d1 = n/d</literal>.
</para>
<para>
If <literal>N</literal> and <literal>D</literal> are polynomial matrices the calculation
is performed element-wise.
</para>
<para>
<literal>H1=simp(H)</literal> is also valid (each entry of <literal>H</literal> is
simplified in <literal>H1</literal>).
</para>
<para>
<warning>
Caution:
</warning>
</para>
<para>
-no threshold is given i.e. <literal>simp</literal> cannot forces a
simplification.
</para>
<para>
-For linear dynamic systems which include integrator(s) simplification
changes the static gain. (<literal>H(0)</literal> for continuous systems or <literal>H(1)</literal> for
discrete systems)
</para>
<para>
-for complex data, <literal>simp</literal> returns its input(s).
</para>
<para>
-rational simplification is called after nearly each operations on
rationals. It is possible to toggle simplification on or off using
<literal>simp_mode</literal> function.
</para>
</refsection>
<refsection>
<title>Examples</title>
<programlisting role="example"><![CDATA[
s=poly(0,'s');
[n,d]=simp((s+1)*(s+2),(s+1)*(s-2))
simp_mode(%F);hns=s/s
simp_mode(%T);hns=s/s
]]></programlisting>
</refsection>
<refsection role="see also">
<title>See Also</title>
<simplelist type="inline">
<member>
<link linkend="roots">roots</link>
</member>
<member>
<link linkend="trfmod">trfmod</link>
</member>
<member>
<link linkend="poly">poly</link>
</member>
<member>
<link linkend="clean">clean</link>
</member>
<member>
<link linkend="simp_mode">simp_mode</link>
</member>
</simplelist>
</refsection>
</refentry>
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