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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" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="poly">
<refnamediv>
<refname>poly</refname>
<refpurpose>polynomial definition</refpurpose>
</refnamediv>
<refsynopsisdiv>
<title>Calling Sequence</title>
<synopsis>p = poly(a, vname, ["flag"])</synopsis>
</refsynopsisdiv>
<refsection>
<title>Arguments</title>
<variablelist>
<varlistentry>
<term>a</term>
<listitem>
<para>a matrix or real number</para>
</listitem>
</varlistentry>
<varlistentry>
<term>vname</term>
<listitem>
<para>a string, the symbolic variable name. The string must be 4 characters max.
</para>
</listitem>
</varlistentry>
<varlistentry>
<term>"flag"</term>
<listitem>
<para>
string (<literal>"roots"</literal>, <literal>"coeff"</literal>),
default value is <literal>"roots"</literal>.
</para>
<para>
Shortcuts can be also used: <literal>"r"</literal> for <literal>"roots"</literal> and <literal>"c"</literal> for <literal>"coeff"</literal>.
</para>
</listitem>
</varlistentry>
</variablelist>
</refsection>
<refsection>
<title>Description</title>
<variablelist>
<varlistentry>
<term>
If <literal>a</literal> is a matrix,
</term>
<listitem>
<para>
<varname>p</varname> is the characteristic
polynomial i.e. <code>determinant(x*eye()-a)</code>, <literal>x</literal> being
the symbolic variable.
</para>
</listitem>
</varlistentry>
<varlistentry>
<term>
If <literal>v</literal> is a vector,
</term>
<listitem>
<itemizedlist>
<listitem>
<para>
<code>poly(v,"x",["roots"])</code> is the polynomial
with <literal>roots</literal> the entries of <varname>v</varname> and
<literal>"x"</literal> as formal variable. (In this case,
<function>roots</function> and <function>poly</function> are inverse functions).
<note>
Note that Infinite roots gives zero highest degree coefficients.
</note>
</para>
</listitem>
<listitem>
<para>
<code>poly(v,"x","coeff")</code> creates the
polynomial with symbol <literal>"x"</literal> and with coefficients
the entries of <varname>v</varname> (<code>v(1)</code> is the constant term
of the polynomial). (Here <function>poly</function> and <function>coeff</function> are inverse functions).
</para>
</listitem>
</itemizedlist>
</listitem>
</varlistentry>
</variablelist>
<para>
<code>s=poly(0,"s")</code> 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','coeff')
]]></programlisting>
</refsection>
<refsection role="see also">
<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>
<refsection>
<title>History</title>
<revhistory>
<revision>
<revnumber>5.5.0</revnumber>
<revremark>The only values allowed for the third argument are "roots", "coeff", "c" and "r".</revremark>
</revision>
</revhistory>
</refsection>
</refentry>
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