<?xml version="1.0" encoding="UTF-8"?>
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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>
