1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
|
<html><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><title>Chapter 9. Polynômes en GEL</title><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot"><link rel="home" href="index.html" title="Manuel de Genius"><link rel="up" href="index.html" title="Manuel de Genius"><link rel="prev" href="ch08s03.html" title="Algèbre linéaire"><link rel="next" href="ch10.html" title="Chapter 10. Théorie des ensembles en 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. Polynômes en 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. Polynômes en 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">Utilisation des polynômes</a></span></dt></dl></div><p>Actuellement Genius peut prendre en charge des polynômes à une variable écrits sous la forme de vecteurs et réaliser des opérations élémentaires avec eux. Il est prévu d'étendre cette prise en charge.</p><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a name="genius-gel-polynomials-using"></a>Utilisation des polynômes</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>Il est aussi possible de trouver les racines des polynômes de degré 1 à 4 en utilisant la fonction <a class="link" href="ch11s13.html#gel-function-PolynomialRoots"><code class="function">PolynomialRoots</code></a> qui appelle la formule appropriée. Les polynômes de degré supérieur doit être convertis en fonctions et résolus numériquement en utilisant une fonction telle que <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> ou <a class="link" href="ch11s13.html#gel-function-FindRootSecant"><code class="function">FindRootSecant</code></a>.</p><p>Consultez <a class="xref" href="ch11s15.html" title="Polynômes">the section called “Polynômes”</a> dans la liste des fonctions pour le reste des fonctions agissant sur les polynômes.</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">Algèbre linéaire </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> Chapter 10. Théorie des ensembles en GEL</td></tr></table></div></body></html>
|
