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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:ns5="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="asec" xml:lang="en">
    <refnamediv>
        <refname>asec</refname>
        <refpurpose>computes the element-wise inverse secant of the
            argument.
        </refpurpose>
    </refnamediv>
    <refsynopsisdiv>
        <title>Syntax</title>
        <synopsis>y = asec(x)</synopsis>
    </refsynopsisdiv>
    <refsection>
        <title>Arguments</title>
        <variablelist>
            <varlistentry>
                <term>x</term>
                <listitem>
                    <para>a real or complex array.</para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>y</term>
                <listitem>
                    <para>a real or complex array.</para>
                </listitem>
            </varlistentry>
        </variablelist>
    </refsection>
    <refsection>
        <title>Description</title>
        <para>Computes the element-wise inverse secant of the argument. For real
            argument with absolute value greater than 1 the result is real.
        </para>
        <para>
            The following equalities hold: <code>asec(z) == -acsc(-z) == asin(1/z) == %pi/2-asec(x) == %i*acsch(%i*z)</code>.
        </para>
    </refsection>
    <refsection>
        <title>Sample</title>
        <scilab:image>
            x=linspace(1,20,200);
            x=[-x($:-1:1) %nan x];
            plot(x,asec(x))
        </scilab:image>
    </refsection>
    <refsection>
        <title>Examples</title>
        <programlisting role="example"><![CDATA[
x=[1 2 -2 sqrt(2) -sqrt(2) 2/sqrt(3) -2/sqrt(3) -1];
asec(x)/%pi
 ]]></programlisting>
    </refsection>
    <refsection role="see also">
        <title>See also</title>
        <simplelist type="inline">
            <member>
                <link linkend="sec">sec</link>
            </member>
            <member>
                <link linkend="asecd">asecd</link>
            </member>
            <!--<member>
        <link linkend="csgn">csgn</link>
      </member>-->
        </simplelist>
    </refsection>
    <refsection>
        <title>References</title>
        <simplelist type="vert">
            <member>Kahan, W., "Branch cuts for complex elementary functions, or,
                Much ado about nothing's sign bit", Proceedings of the joing IMA/SIAM
                conference on The State of the Art in Numerical Analysis, University of
                Birmingham, A. Iserles and M.J.D. Powell, eds, Clarendon Press, Oxford,
                1987, 165-210.
            </member>
        </simplelist>
    </refsection>
</refentry>
