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Viewing changes to modules/polynomials/help/en_US/factors.xml

  • Committer: Package Import Robot
  • Author(s): Sylvestre Ledru
  • Date: 2012-08-30 14:42:38 UTC
  • mfrom: (1.4.7)
  • Revision ID: package-import@ubuntu.com-20120830144238-c1y2og7dbm7m9nig
Tags: 5.4.0-beta-3-1~exp1
* New upstream release
* Update the scirenderer dep
* Get ride of libjhdf5-java dependency

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modules/polynomials/help/en_US/factors.xml
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<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="factors">
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  <refnamediv>
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    <refname>factors</refname>
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    <refpurpose> numeric real factorization</refpurpose>
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  </refnamediv>
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  <refsynopsisdiv>
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    <title>Calling Sequence</title>
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    <synopsis>[lnum,g]=factors(pol [,'flag'])
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      [lnum,lden,g]=factors(rat [,'flag'])
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      rat=factors(rat,'flag')
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    </synopsis>
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  </refsynopsisdiv>
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  <refsection>
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    <title>Arguments</title>
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    <variablelist>
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      <varlistentry>
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        <term>pol</term>
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        <listitem>
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          <para>real polynomial</para>
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        </listitem>
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      </varlistentry>
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      <varlistentry>
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        <term>rat</term>
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        <listitem>
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          <para>
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            real rational polynomial (<literal>rat=pol1/pol2</literal>)
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          </para>
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        </listitem>
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      </varlistentry>
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      <varlistentry>
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        <term>lnum</term>
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        <listitem>
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          <para>list of polynomials (of degrees 1 or 2)</para>
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        </listitem>
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      </varlistentry>
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      <varlistentry>
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        <term>lden</term>
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        <listitem>
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          <para>list of polynomials (of degrees 1 or 2)</para>
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        </listitem>
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      </varlistentry>
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      <varlistentry>
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        <term>g</term>
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        <listitem>
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          <para>real number</para>
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        </listitem>
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      </varlistentry>
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      <varlistentry>
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        <term>flag</term>
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        <listitem>
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          <para>
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            character string <literal>'c'</literal> or <literal>'d'</literal>
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          </para>
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        </listitem>
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      </varlistentry>
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    </variablelist>
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  </refsection>
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  <refsection>
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    <title>Description</title>
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    <para>
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      returns the factors of polynomial <literal>pol</literal> in the list <literal>lnum</literal>
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      and the "gain" g.
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    </para>
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    <para>
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      One has pol= g times product of entries of the list <literal>lnum</literal>
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      (if <literal>flag</literal> is not given). If <literal>flag='c'</literal> is given, then
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      one has <literal>|pol(i omega)|</literal> = <literal>|g*prod(lnum_j(i omega)|</literal>.
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      If <literal>flag='d'</literal> is given, then
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      one has <literal>|pol(exp(i omega))|</literal> = <literal>|g*prod(lnum_i(exp(i omega))|</literal>.
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      If argument of <literal>factors</literal> is a 1x1 rational <literal>rat=pol1/pol2</literal>,
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      the factors of the numerator <literal>pol1</literal> and the denominator <literal>pol2</literal>
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      are returned in the lists <literal>lnum</literal> and <literal>lden</literal> respectively.
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    </para>
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    <para>
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      The "gain" is returned as <literal>g</literal>,i.e. one has:
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      rat= g times (product entries in lnum) / (product entries in lden).
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    </para>
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    <para>
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      If <literal>flag</literal> is <literal>'c'</literal> (resp. <literal>'d'</literal>), the roots of <literal>pol</literal>
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      are refected wrt the imaginary axis (resp. the unit circle), i.e.
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      the factors in <literal>lnum</literal> are stable polynomials.
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    </para>
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    <para>
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      Same thing if <literal>factors</literal> is invoked with a rational arguments:
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      the entries in <literal>lnum</literal> and <literal>lden</literal> are stable polynomials if
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      <literal>flag</literal> is given. <literal>R2=factors(R1,'c')</literal> or <literal>R2=factors(R1,'d')</literal>
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      with <literal>R1</literal> a rational function or SISO <literal>syslin</literal> list then the
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      output <literal>R2</literal> is a transfer with stable numerator and denominator and
101
 
      with same magnitude as <literal>R1</literal> along the imaginary axis (<literal>'c'</literal>)
102
 
      or unit circle (<literal>'d'</literal>).
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    </para>
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  </refsection>
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  <refsection>
106
 
    <title>Examples</title>
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    <programlisting role="example"><![CDATA[ 
 
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    <refnamediv>
 
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        <refname>factors</refname>
 
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        <refpurpose> numeric real factorization</refpurpose>
 
17
    </refnamediv>
 
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    <refsynopsisdiv>
 
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        <title>Calling Sequence</title>
 
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        <synopsis>[lnum,g]=factors(pol [,'flag'])
 
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            [lnum,lden,g]=factors(rat [,'flag'])
 
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            rat=factors(rat,'flag')
 
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        </synopsis>
 
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    </refsynopsisdiv>
 
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    <refsection>
 
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        <title>Arguments</title>
 
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        <variablelist>
 
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            <varlistentry>
 
29
                <term>pol</term>
 
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                <listitem>
 
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                    <para>real polynomial</para>
 
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                </listitem>
 
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            </varlistentry>
 
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            <varlistentry>
 
35
                <term>rat</term>
 
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                <listitem>
 
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                    <para>
 
38
                        real rational polynomial (<literal>rat=pol1/pol2</literal>)
 
39
                    </para>
 
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                </listitem>
 
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            </varlistentry>
 
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            <varlistentry>
 
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                <term>lnum</term>
 
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                <listitem>
 
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                    <para>list of polynomials (of degrees 1 or 2)</para>
 
46
                </listitem>
 
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            </varlistentry>
 
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            <varlistentry>
 
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                <term>lden</term>
 
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                <listitem>
 
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                    <para>list of polynomials (of degrees 1 or 2)</para>
 
52
                </listitem>
 
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            </varlistentry>
 
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            <varlistentry>
 
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                <term>g</term>
 
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                <listitem>
 
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                    <para>real number</para>
 
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                </listitem>
 
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            </varlistentry>
 
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            <varlistentry>
 
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                <term>flag</term>
 
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                <listitem>
 
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                    <para>
 
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                        character string <literal>'c'</literal> or <literal>'d'</literal>
 
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                    </para>
 
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                </listitem>
 
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            </varlistentry>
 
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        </variablelist>
 
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    </refsection>
 
70
    <refsection>
 
71
        <title>Description</title>
 
72
        <para>
 
73
            returns the factors of polynomial <literal>pol</literal> in the list <literal>lnum</literal>
 
74
            and the "gain" g.
 
75
        </para>
 
76
        <para>
 
77
            One has pol= g times product of entries of the list <literal>lnum</literal>
 
78
            (if <literal>flag</literal> is not given). If <literal>flag='c'</literal> is given, then
 
79
            one has <literal>|pol(i omega)|</literal> = <literal>|g*prod(lnum_j(i omega)|</literal>.
 
80
            If <literal>flag='d'</literal> is given, then
 
81
            one has <literal>|pol(exp(i omega))|</literal> = <literal>|g*prod(lnum_i(exp(i omega))|</literal>.
 
82
            If argument of <literal>factors</literal> is a 1x1 rational <literal>rat=pol1/pol2</literal>,
 
83
            the factors of the numerator <literal>pol1</literal> and the denominator <literal>pol2</literal>
 
84
            are returned in the lists <literal>lnum</literal> and <literal>lden</literal> respectively.
 
85
        </para>
 
86
        <para>
 
87
            The "gain" is returned as <literal>g</literal>,i.e. one has:
 
88
            rat= g times (product entries in lnum) / (product entries in lden).
 
89
        </para>
 
90
        <para>
 
91
            If <literal>flag</literal> is <literal>'c'</literal> (resp. <literal>'d'</literal>), the roots of <literal>pol</literal>
 
92
            are refected wrt the imaginary axis (resp. the unit circle), i.e.
 
93
            the factors in <literal>lnum</literal> are stable polynomials.
 
94
        </para>
 
95
        <para>
 
96
            Same thing if <literal>factors</literal> is invoked with a rational arguments:
 
97
            the entries in <literal>lnum</literal> and <literal>lden</literal> are stable polynomials if
 
98
            <literal>flag</literal> is given. <literal>R2=factors(R1,'c')</literal> or <literal>R2=factors(R1,'d')</literal>
 
99
            with <literal>R1</literal> a rational function or SISO <literal>syslin</literal> list then the
 
100
            output <literal>R2</literal> is a transfer with stable numerator and denominator and
 
101
            with same magnitude as <literal>R1</literal> along the imaginary axis (<literal>'c'</literal>)
 
102
            or unit circle (<literal>'d'</literal>).
 
103
        </para>
 
104
    </refsection>
 
105
    <refsection>
 
106
        <title>Examples</title>
 
107
        <programlisting role="example"><![CDATA[ 
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n=poly([0.2,2,5],'z');
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d=poly([0.1,0.3,7],'z');
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R=syslin('d',n,d);
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w=exp(2*%i*%pi*[0:0.1:1]);
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norm(abs(horner(R1,w))-abs(horner(R,w)))
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 ]]></programlisting>
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  </refsection>
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  <refsection role="see also">
119
 
    <title>See Also</title>
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    <simplelist type="inline">
121
 
      <member>
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        <link linkend="simp">simp</link>
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      </member>
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    </simplelist>
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  </refsection>
 
117
    </refsection>
 
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    <refsection role="see also">
 
119
        <title>See Also</title>
 
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        <simplelist type="inline">
 
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            <member>
 
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                <link linkend="simp">simp</link>
 
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            </member>
 
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        </simplelist>
 
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    </refsection>
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</refentry>