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<html><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><title>Chapter 9. Polynome in GEL</title><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot"><link rel="home" href="index.html" title="Genius-Handbuch"><link rel="up" href="index.html" title="Genius-Handbuch"><link rel="prev" href="ch08s03.html" title="Lineare Algebra"><link rel="next" href="ch10.html" title="Chapter 10. Mengenlehre in GEL"></head><body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">Chapter 9. Polynome in GEL</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="ch08s03.html">Prev</a> </td><th width="60%" align="center"> </th><td width="20%" align="right"> <a accesskey="n" href="ch10.html">Next</a></td></tr></table><hr></div><div class="chapter"><div class="titlepage"><div><div><h1 class="title"><a name="genius-gel-polynomials"></a>Chapter 9. Polynome in GEL</h1></div></div></div><div class="toc"><p><b>Table of Contents</b></p><dl class="toc"><dt><span class="sect1"><a href="ch09.html#genius-gel-polynomials-using">Verwendung von Polynomen</a></span></dt></dl></div><p lang="en">
Currently Genius can handle polynomials of one variable written out
as vectors, and do some basic operations with these. It is planned to
expand this support further.
</p><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a name="genius-gel-polynomials-using"></a>Verwendung von Polynomen</h2></div></div></div><p lang="en">
Currently
polynomials in one variable are just horizontal vectors with value only nodes.
The power of the term is the position in the vector, with the first position
being 0. So,
</p><pre lang="en" class="programlisting">[1,2,3]
</pre><p lang="en">
translates to a polynomial of
</p><pre lang="en" class="programlisting">1 + 2*x + 3*x^2
</pre><p lang="en">
</p><p lang="en">
You can add, subtract and multiply polynomials using the
<a class="link" href="ch11s15.html#gel-function-AddPoly"><code class="function">AddPoly</code></a>,
<a class="link" href="ch11s15.html#gel-function-SubtractPoly"><code class="function">SubtractPoly</code></a>, and
<a class="link" href="ch11s15.html#gel-function-MultiplyPoly"><code class="function">MultiplyPoly</code></a> functions respectively.
You can print a polynomial using the
<a class="link" href="ch11s15.html#gel-function-PolyToString"><code class="function">PolyToString</code></a>
function.
For example,
</p><pre lang="en" class="programlisting">PolyToString([1,2,3],"y")
</pre><p lang="en">
gives
</p><pre lang="en" class="programlisting">3*y^2 + 2*y + 1
</pre><p lang="en">
You can also get a function representation of the polynomial so that you can
evaluate it. This is done by using
<a class="link" href="ch11s15.html#gel-function-PolyToFunction"><code class="function">PolyToFunction</code></a>,
which
returns an anonymous function.
</p><pre lang="en" class="programlisting">f = PolyToFunction([0,1,1])
f(2)
</pre><p lang="en">
</p><p lang="en">
It is also possible to find roots of polynomials of degrees 1 through 4 by using the
function
<a class="link" href="ch11s13.html#gel-function-PolynomialRoots"><code class="function">PolynomialRoots</code></a>,
which calls the appropriate formula function. Higher degree polynomials must be converted to
functions and solved
numerically using a function such as
<a class="link" href="ch11s13.html#gel-function-FindRootBisection"><code class="function">FindRootBisection</code></a>,
<a class="link" href="ch11s13.html#gel-function-FindRootFalsePosition"><code class="function">FindRootFalsePosition</code></a>,
<a class="link" href="ch11s13.html#gel-function-FindRootMullersMethod"><code class="function">FindRootMullersMethod</code></a>, or
<a class="link" href="ch11s13.html#gel-function-FindRootSecant"><code class="function">FindRootSecant</code></a>.
</p><p lang="en">
See <a class="xref" href="ch11s15.html" title="Polynomials">the section called “Polynomials”</a> in the function list
for the rest of functions acting on polynomials.
</p></div></div><div class="navfooter"><hr><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="ch08s03.html">Prev</a> </td><td width="20%" align="center"> </td><td width="40%" align="right"> <a accesskey="n" href="ch10.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">Lineare Algebra </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> Chapter 10. Mengenlehre in GEL</td></tr></table></div></body></html>
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