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<?xml version="1.0" encoding="UTF-8"?>
<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="poly">
<info>
<pubdate>$LastChangedDate$</pubdate>
</info>
<refnamediv>
<refname>poly</refname>
<refpurpose> polynomial definition</refpurpose>
</refnamediv>
<refsynopsisdiv>
<title>Calling Sequence</title>
<synopsis>p=poly(a,vname, ["flag"])</synopsis>
</refsynopsisdiv>
<refsection>
<title>Parameters</title>
<variablelist>
<varlistentry>
<term>a</term>
<listitem>
<para>matrix or real number</para>
</listitem>
</varlistentry>
<varlistentry>
<term>vname</term>
<listitem>
<para>String, the symbolic variable name. If the string have more
than 4 characters only the first 4 are taken into account.</para>
</listitem>
</varlistentry>
<varlistentry>
<term>"flag" </term>
<listitem>
<para>string ("roots", "coeff"), default value is
"roots".</para>
</listitem>
</varlistentry>
</variablelist>
</refsection>
<refsection>
<title>Description</title>
<variablelist>
<varlistentry>
<term>If a is a matrix,</term>
<listitem>
<para><literal>p</literal> is the characteristic
polynomial i.e. <literal>determinant(x*eye()-a)</literal>, <literal>x</literal> being
the symbolic variable.</para>
</listitem>
</varlistentry>
<varlistentry>
<term>If v is a vector,</term>
<listitem>
<itemizedlist>
<listitem>
<para><literal>poly(v,"x",["roots"])</literal> is the polynomial
with <literal>roots</literal> the entries of <literal>v</literal> and
<literal>"x"</literal> as formal variable. (In this case,
<literal>roots</literal> and <literal>poly</literal> are inverse functions). Note
that Infinite roots gives zero highest degree coefficients. </para>
</listitem>
<listitem>
<para><literal>poly(v,"x","coeff")</literal> creates the
polynomial with symbol <literal>"x"</literal> and with coefficients
the entries of <literal>v</literal> (v(1) is the constant term of the
polynomial). (Here <literal>poly</literal> and <literal>coeff</literal> are inverse
functions).</para>
</listitem>
</itemizedlist>
</listitem>
</varlistentry>
</variablelist>
<para><literal>s=poly(0,"s")</literal> is the seed for defining
polynomials with symbol <literal>"s"</literal>.</para>
</refsection>
<refsection>
<title>Examples</title>
<programlisting role="example"><![CDATA[
s=poly(0,"s");p=1+s+2*s^2;
A=rand(2,2);poly(A,"x")
//rational fractions
h=(1+2*%s)/poly(1:4,'s','c')
]]></programlisting>
</refsection>
<refsection>
<title>See Also</title>
<simplelist type="inline">
<member>
<link linkend="coeff">coeff</link>
</member>
<member>
<link linkend="roots">roots</link>
</member>
<member>
<link linkend="varn">varn</link>
</member>
<member>
<link linkend="horner">horner</link>
</member>
<member>
<link linkend="derivat">derivat</link>
</member>
<member>
<link linkend="matrices">matrices</link>
</member>
<member>
<link linkend="rational">rational</link>
</member>
</simplelist>
</refsection>
</refentry>
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