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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:ns4="http://www.w3.org/1999/xhtml"
            xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook"
            xmlns:scilab="http://www.scilab.org" xml:id="sylm" xml:lang="pt">
      <refnamediv>
          <refname>sylm</refname>
          <refpurpose>matriz de Sylvester</refpurpose>
      </refnamediv>
      <refsynopsisdiv>
          <title> Seqüência de Chamamento </title>
          <synopsis>S = sylm(a, b)</synopsis>
      </refsynopsisdiv>
      <refsection>
          <title>Parâmetros</title>
          <variablelist>
              <varlistentry>
                  <term>a, b</term>
                  <listitem>
                      <para>duas matrizes de polinômios </para>
                  </listitem>
              </varlistentry>
              <varlistentry>
                  <term>S</term>
                  <listitem>
                      <para>matriz</para>
                  </listitem>
              </varlistentry>
          </variablelist>
      </refsection>
      <refsection>
          <title>Descrição</title>
          <para>
              <literal>sylm(a,b)</literal> fornece a matriz de Sylvester associada
              aos polinômios <literal>a</literal> e <literal>b</literal>, i.e. a matriz
              <literal>S</literal> tal que:
          </para>
          <para>
              <literal>coeff( a*x + b*y )' = S * [coeff(x)';coeff(y)']</literal>.
          </para>
          <para>
              A dimensão de <literal>S</literal> é igual a <literal>degree(a)+degree(b)</literal>.
          </para>
          <para>
              Se <literal>a</literal> e <literal>b</literal> são polinômios primos entre si, então
          </para>
          <para>
              <literal>rank(sylm(a,b))=degree(a)+degree(b))</literal> e as instruções
              <screen><![CDATA[
  u = sylm(a,b) \ eye(na+nb,1)
  x = poly(u(1:nb),'z','coeff')
  y = poly(u(nb+1:na+nb),'z','coeff')
  ]]></screen>
          </para>
          <programlisting role=""><![CDATA[
  u = sylm(a,b) \ eye(na+nb,1)
  x = poly(u(1:nb),'z','coeff')
  y = poly(u(nb+1:na+nb),'z','coeff')
   ]]></programlisting>
          <para>
              computam os fatores de Bezout <literal>x</literal> e
              <literal>y</literal> de graus mínimos tais que <literal>a*x+b*y = 1</literal>
          </para>
      </refsection>
      <refsection>
          <title>Exemplos</title>
          <programlisting role="example"><![CDATA[
  x = poly(0,"x");
  y = poly ([1, 2, 3], "x", "coeff")
  sylm(x, y)
  ]]></programlisting>
      <screen><![CDATA[
  --> x = poly(0, "x");
  --> y = poly([1, 2, 3], "x","coeff")
   y  =
    1 +2x +3x²
  
  --> sylm(x, y)
   ans  =
     0.   0.   1.
     1.   0.   2.
     0.   1.   3.
  ]]></screen>
      </refsection>
      <refsection role="see also">
          <title>Ver também</title>
          <simplelist type="inline">
              <member>
                  <link linkend="bezout">bezout</link>
              </member>
              <member>
                  <link linkend="diophant">diophant</link>
              </member>
          </simplelist>
      </refsection>
  </refentry>
  