File: xcasfr.html

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giac 1.9.0.93%2Bdfsg2-3
links: PTS, VCS
area: main
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size: 117,732 kB
sloc: cpp: 404,272; ansic: 205,462; python: 30,548; javascript: 28,788; makefile: 17,997; yacc: 2,690; lex: 2,464; sh: 705; perl: 314; lisp: 216; asm: 62; java: 41; xml: 36; sed: 16; csh: 7; pascal: 6
file content (4223 lines) | stat: -rw-r--r-- 407,293 bytes
<!DOCTYPE HTML>
<html id="fulldocument" lang="fr">
  <head>
  <meta charset="utf-8">
  <meta name=viewport content="width=device-width, initial-scale=1">
  <meta http-equiv="Content-Type" content="text/html; charset=utf-8">
  <meta name="keywords" content="xcas, firefox, navigateur, calcul, formel, en, ligne, programmation, algorithmique">
  <title>
    Xcas web
  </title>
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    .micropy {
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      border-color: orange;
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      border-color: cyan;
    }
    .xcas {
      border-color: magenta;
    }
  </style>
  <script>
      // Redirect to HTTPS page if not testing locally
      if (location.protocol === 'http:' && location.hostname !== 'localhost' && location.hostname !== '127.0.0.1') {
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</head>
<body>
<!-- https://developer.mozilla.org/fr/docs/Web/API/Service_Worker_API/Using_Service_Workers
    pour le moment, on utilise manifest="xcas.appcache" en en-tete et
      on modifie xcas.appcache...
    xcasfr.html
      Ok &#x2705;
      Annul. &#x274C;
    xcas.js
      Forum &#x282A;
      >X< &#x274C;
      Ok &#x2705;
    -->
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    KEY_K = 75;
    KEY_L = 76;
    KEY_M = 77;
    KEY_N = 78;
    KEY_O = 79;
    KEY_P = 80;
    KEY_Q = 81;
    KEY_R = 82;
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        if (intShiftKey && intKeyCode == KEY_ENTER) {
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        // raccourcis avec Alt
        // F1 aide, c cmdline, m menu,
        //console.log(intAltKey,intKeyCode);
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            if (intKeyCode == KEY_G || intKeyCode == KEY_LEFT) {
                UI.move_focus(UI.focused, -1);
                done = true;
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                done = true;
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            if (intKeyCode == KEY_T) {
                $id('progbuttons').style.display = 'block';
                $id('boutons_tortue').style.display = 'block';
                UI.hide_show_xcas('boutons_tortue_xcas');
                done = true;
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<div id="startup2" style="display:none">
  <button onclick="if (UI.usecm){ $id('config').usecm.checked=false;  UI.set_config(false);} cmentree.focus();">Version accessible
  </button>
  pour deficients visuels,
  <a href="xcasen.html#lang=en" target="_blank">English version</a>.
</div>
<div id="startup1">
  Bienvenue dans Xcas pour Firefox ou navigateur compatible
  (c) 2020, B. Parisse et R. De Graeve, Institut Fourier,
  Universit&eacute; de Grenoble.<br>
  Depuis Xcas, taper python ou js dans une ligne de commande pour
  changer d'interpr&eacute;teur vers <a target="_blank" href="https://micropython.org/">MicroPython</a> (Damien P. George et
  al) ou vers <a target="_blank" href="https://bellard.org/quickjs/">QuickJS</a> de
  Fabrice Bellard et Charlie Gordon.
</div>
<div id="startup">
  Si Xcas ne fonctionne pas, <a
    href="https://fr.wikipedia.org/wiki/Aide:Purge_du_cache_du_navigateur"
    target="_blank">effacez
  le cache du navigateur</a> et rechargez.
  <span id="startup_restore" style="display:none">
            <br>
            Restaurer la session pr&eacute;c&eacute;dente
            <button title="Charge la session pr&eacute;c&eacute;dente" onclick="var s=UI.readCookie('xcas_session');UI.restoresession(s,$id('mathoutput'),false,true);">evalu&eacute;e</button> ou
            <button title="Charge la session pr&eacute;c&eacute;dente sans l'&eacute;valuer" onclick="var s=UI.readCookie('xcas_session');UI.restoresession(s,$id('mathoutput'),false,false);">non</button>
            </span>
  <hr>
</div>
<form id="config" style="display:none" onsubmit="setTimeout(function(){
            UI.set_config(true);
            }); return false">
  <h3>Configuration</h3>
  <table>
    <tr>
      <td>
        E-mail personnel <input class="bouton" type="text" name="from"
                                title="Indiquez ici votre adresse e-mail" value="">
        correspondant <input class="bouton" type="text" name="to"
                             title="Indiquez ici l'adresse de la personne &agrave; qui vous envoyez habituellement des sessions, par exemple celle de l'enseignant pour un &eacute;l&egrave;ve" value="">,
        <br> langue de l'aide
        <input type="radio" name="lang" value="radio" title="Francais" checked>fr
        <input type="radio" name="lang" value="radio" title="English">en
        <input type="radio" name="lang" value="radio" title="Spanish">sp
        <input type="radio" name="lang" value="radio" title="Greek">el
        <input type="radio" name="lang" value="radio" title="Deutsch">de
	<br> Export vers
        <input type="radio" name="calc" value="radio" title="Casio" checked>Casio 35eii&90
        <input type="radio" name="calc" value="radio" title="Numworks">Numworks
        <input type="radio" name="calc" value="radio" title="Nspire">TI Nspire CX
	
      </td>
    </tr>
    <tr>
      <td>
        Chiffres:<input class="bouton" type="number" name="digits_mode" title="Nombre de chiffres significatifs (si &gt; 14 multipr&eacute;cision, calculs plus lents)" value=12>
        Autosimplification: <input class="bouton"
                                   type="number" name="autosimp_level"
                                   title="0: pas d'autosimplification, 1: minimum, 2: maximum" value=1
                                   max=2 min=0>
        Syntaxe <input class="bouton" type="button" value="Python"
                       onclick="python_mode.checked=!python_mode.checked; if (python_mode.checked) js_mode.checked=false;"> <input
          class="bouton" type="checkbox" name="python_mode"
	title="Cocher pour utiliser la syntaxe compatible Python">,
	<input class="bouton" type="button" value="MicroPython"
                       onclick="python_xor.checked=!python_xor.checked; if (python_xor.checked){ js_mode.checked=false;python_mode.checked=true;}"> <input class="bouton" type="checkbox" name="python_xor"
	title="Si coche, utilise l'interpreteur Micropython">,
	<input class="bouton" type="button" value="JS"
                       onclick="js_mode.checked=!js_mode.checked;if (js_mode.checked) python_mode.checked=python_xor.checked=false;"> <input class="bouton" type="checkbox" name="js_mode"
	title="Si coche, utilise l'interpreteur Javascript">,
        <input class="bouton" type="button" title="Afficher les alertes Python" value="warnings" onclick="warnpy_mode.checked=!warnpy_mode.checked">
        <input class="bouton" type="checkbox" name="warnpy_mode"
               title="Cocher pour afficher les alertes Python" checked>
      </td>
    </tr>
    <tr>
      <td>
        <input class="bouton" type="button" title="Bascule unit&eacute; d'angles radians/degr&eacute;s" value="Radians" onclick="angle_mode.checked=!angle_mode.checked;"> <input class="bouton" type="checkbox" name="angle_mode" title="Cocher pour utiliser les radians, d&eacute;cocher pour utiliser les degr&eacute;s" checked>,
        <input class="bouton" type="button" title="Bascule mode complexe/r&eacute;el" value="Complexe" onclick="complex_mode.checked=!complex_mode.checked"> <input class="bouton" type="checkbox" name="complex_mode" title="Cocher pour travailler par d&eacute;faut sur les complexes">,
        <input class="bouton" type="button" title="Bascule pour toujours factoriser les polynomes de degr&eacute; 2" value=" √ " onclick="sqrt_mode.checked=!sqrt_mode.checked"> <input class="bouton" type="checkbox" name="sqrt_mode" title="Cocher pour toujours factoriser les polynomes de degr&eacute; 2">,
        <input class="bouton" type="button" title="Bascule pour montrer les &eacute;tapes de certains calculs" value="step" onclick="step_mode.checked=!step_mode.checked"> <input class="bouton" type="checkbox" name="step_mode" title="Cocher pour montrer les &eacute;tapes de certains calculs">,
        <input class="bouton" type="button" title="Bascule pour executer les calculs par un webworker" value="worker" onclick="worker_mode.checked=!worker_mode.checked"> <input class="bouton" type="checkbox" name="worker_mode" title="Cocher pour executer les calculs par un webworker">
        <input class="bouton" type="button" title="Utiliser web-assembly si possible" value="wasm" onclick="wasm_mode.checked=!wasm_mode.checked"> <input class="bouton" type="checkbox" name="wasm_mode" title="Cocher pour executer les calculs en web-assembly">
      </td>
    </tr>
    <tr>
      <td>
        <input class="bouton" type="button" title="Bascule pour affichage 2d" value="2d" onclick="prettyprint.checked=!prettyprint.checked"> <input class="bouton" type="checkbox" name="prettyprint"
                                                                                                                                                    title="Cocher pour affichage 2d" checked>,
        <input class="bouton" type="button" title="Bascule pour avoir commandes et reponses sur le meme niveau" value="Q/R sur 1 ligne" onclick="qa.checked=!qa.checked"> <input class="bouton" type="checkbox" name="qa"
                                                                                                                                                                                 title="Cocher pour avoir commandes et reponses sur le meme niveau">,
        <input class="bouton" type="button" title="Coloration syntaxique si on edite un niveau existant" value="Coloration syntaxique" onclick="usecm.checked=!usecm.checked"> <input class="bouton" type="checkbox" name="usecm"
                                                                                                                                                                                      title="Coloration syntaxique si on edite un niveau existant">
        <input class="bouton" type="button" title="Boutons de deplacement et del persistants" value="Del fixe" onclick="fixeddel.checked=!fixeddel.checked"> <input class="bouton" type="checkbox" name="fixeddel"
                                                                                                                                                                    title="Les boutons de deplacement et del sont toujours affich&eacute;s" checked>
      </td>
    </tr>
    <tr>
      <td>
        Tortue <input class="bouton" type="number" name="canvas_w" value=400
                      title="Largeur des graphiques tortue">
        par <input class="bouton" type="number" name="canvas_h" value=300
                   title="Hauteur des graphiques tortue">
        Sortie <input class="bouton" type="number" name="outdiv_width" value=410
                      title="Largeur maximale d'un champ r&eacute;ponse">
        par <input class="bouton" type="number" name="outdiv_height" value=190
                   title="Hauteur maximale d'un champ r&eacute;ponse">
      </td>
    </tr>
    <tr>
      <td>
        Taille maximale de l'assistant matrice
        <input class="bouton" type="number" name="matr_cfg_rows" id="matr_cfg_rows"
               title="Nombre de lignes" value=40 min=1 max=1000>,
        <input class="bouton" type="number" name="matr_cfg_cols" id="matr_cfg_cols"
               title="Nombre de colonnes" value=6 min=1 max=100>
        <input class="bouton" type="checkbox" name="matr_textarea"
               onclick="UI.assistant_matr_textarea=checked; UI.assistant_matr_setmatrix(UI.assistant_matr_maxrows,UI.assistant_matr_maxcols); UI.assistant_matr_setdisplay();"
               id="matr_textarea" title="Cocher pour avoir des cellules dont on peut changer la taille">d&eacute;formable
      </td>
    </tr>
    <tr>
      <td>
        Documentation <input class="bouton" type="checkbox" name="online_doc"
                             title="Cocher si Xcas n'est pas install&eacute; (utilise la documentation en ligne)" checked>online
        <input class="bouton" type="text" name="doc_path" size="60"
               value="/usr/share/giac/doc/fr/cascmd_fr/"
               title="Chemin de la documentation hors-ligne (pr&eacute;rempli pour une installation Xcas sous linux, sous mac ajouter /Applications)">
      </td>
    </tr>
  </table>
  <input class="bouton" type="submit" title="ok" value="Ok">
  <input class="bouton" type="button" title="Annule les changements de configuration" value="Annul." onclick="form.style.display='none';  UI.focused.focus();">
  <hr>
</form>
<button id="settings" class="bouton" onclick="UI.show_config()" title="Permet de modifier la configuration">
  <img WIDTH="28" HEIGHT="28" SRC="config.png" alt="Configuration" align="center">
  <span id='curcfg'></span>
</button>
<span id='thelink'></span>
<span id='themailto'></span>
<textarea id='theforumlink' style="display:none"></textarea>
<textarea id='locallink' style="display:none"></textarea>
<span id="history1" style="display:none">
        <button class="bouton" title="Cliquer ici pour sauvegarder l'historique avec le nom de fichier du champ texte qui suit" onclick="if ($id('loadbutton_file').style.display=='none') UI.savesession(2); else UI.savesession(0);">&#x1f4be;</button>
        <textarea cols="7" id="outputfilename" class="filenamecss" style="font-size:large" title="Nom de sauvegarde du fichier. Avec Firefox, pour pouvoir faire plusieurs sauvegardes sous le meme nom, cocher Toujours demander... dans Pr&eacute;f&eacute;rences, G&eacute;n&eacute;ral, T&eacute;l&eacute;chargements.">session</textarea>
        <button id="exportbutton" class="bouton" title="Cliquer ici pour exporter pour calculatrices (Casio Graph 35eii&90, Numworks ou TI Nspire CX, &agrave; configurer dans les pr&eacute;f&eacute;rences) avec le nom de fichier du champ texte qui pr&eacute;c&egrave;de. Utilisez .py comme extension pour concatener tous les niveaux en un unique script." onclick='UI.savesession(1);'>Export</button>
  </span>
<span id="historyload" style="display:none">
  <button id="numworks_load" class="bouton" title="Cliquer ici pour charger un script depuis une calculatrice Numworks" onclick="UI.numworks_load()">Numworks→</button>
<button id="loadbutton_cookie" class="bouton" title="Cliquer ici pour charger une session sauvegard&eacute;e" onclick="$id('loadfile_cookie').innerHTML=UI.listCookies();">Charge</button>
</span>
  <span id="loadfile_cookie"></span>
<form id="loadbutton_file" style="display:none">
  <label for="loadfileinput">Charger</label>
  <input id="loadfileinput" accept=".xw" type="file" title="Cliquer ici pour charger une session sauvegard&eacute;e (s&eacute;lectionner un fichier terminant par .xw.tns pour les TI Nspire CX ou _xw.py pour les Numworks)" onchange="UI.loadfile(this.files);this.value=''">
</form>
<span id="help" style="display:none">
        <ul>
            <li style="display:inline">
                <button class="bouton"
                        onclick="$id('help').style.display='none';">
                <em>Masquer la documentation</em></button>
            </li>
            <li style="display:inline">
                <button class="bouton"
                        onclick="var tmp=$id('tutointro'); if (tmp.style.display=='none') tmp.style.display='block'; else tmp.style.display='none';">
                <strong>Introduction</strong></button>
                <div id="tutointro" style="display:none">
                    Tapez votre calcul ou programme dans la ligne de commande en bas de la page
		  (attention, tapez <tt>1.2</tt> pour 1 virgule
		  2). Pour apprendre &agrave; utiliser Xcas, vous
		  pouvez lire ce
		  <a href="https://www-fourier.univ-grenoble-alpes.fr/~parisse/giac/doc/fr/tutoriel/index.html" target="_blank">tutoriel</a>
		 
		  <br>
                    Cliquez sur l'icone de <tt>Xcas</tt> ou le bouton
                    <tt>Prog</tt> pour afficher des assistants
                    math&eacute;matiques ou algorithmiques, ou sur
                    <tt>123</tt> pour le clavier scientifique.
                    Validez par la touche Entr&eacute;e ou le bouton Ok en vert.
                    <br>
                    Pour obtenir de l'aide sur une commande, tapez le d&eacute;but de son nom
                    puis tapez <tt>F1</tt> ou cliquez sur le bouton <tt>?</tt>.
                    Pour trouver des noms de commandes, utilisez les assistants Maths et
                    Prog ou cliquez sur un des th&egrave;mes
                    ci-dessous ou consultez le
                    <a
                        href="http://www-fourier.univ-grenoble-alpes.fr/~parisse/giac/doc/fr/cascmd_fr"
                        target="_blank">guide de Xcas</a>
		  <br>
		  Vous pouvez choisir l'interpr&eacute;teur depuis la
    configuration (bouton en haut &agrave; gauche avec la roue
    dent&eacute;e) parmi Xcas, <a target="_blank" href="https://micropython.org/">MicroPython</a> ou
    Javascript. L'interpr&eacute;teur Javascript par d&eacute;faut est
    <a target="_blank" href="https://bellard.org/quickjs/">QuickJS</a> en mode math&eacute;matique sauf si votre ligne de
    commande commence par <tt>@</tt> (QuickJS sans le mode math) ou
		  <tt>@@</tt> (interpr&eacute;teur du navigateur).
		  
                </div>
            <li style="display:inline">
                <button class="bouton"
                        onclick="var tmp=$id('tutonet'); if (tmp.style.display=='none') tmp.style.display='block'; else tmp.style.display='none';">
                <strong>Partages</strong></button>
                <div id="tutonet" style="display:none">
                    Vous pouvez partager publiquement une session en cliquant sur le
                    bouton F.
                    Vous pouvez &eacute;changer des sessions de calculs Xcas entre
                    plusieurs personnes par email. Renseignez une fois pour toutes
                    les champs e-mail de la
                    configuration (bouton R&eacute;glages en haut &agrave; gauche)
                    et validez.
                    Vous pouvez alors envoyer votre session &agrave; votre
                    correspondant en cliquant
                    sur le lien &#x2709;, modifiez le destinataire si
                    n&eacute;cessaire (si vous utilisez un webmail
                    non reconnu, recopiez le contenu du lien x2 dans
                    un message ou configurez les param&egrave;tres de
                    votre navigateur pour l'utiliser, il peut &ecirc;tre n&eacute;cessaire de cloner
                    votre session avec le lien x2 avant de cliquer sur le lien &#x2709;).
                    Le destinataire
                    clique sur le lien du mail ce qui ouvrira un clone de votre
                    session dans son navigateur. Il peut alors modifier ou corriger
                    votre session, et si il clique sur le lien &#x2709;, il vous
                    renvoie votre session avec les corrections.
                    <br>
                    Lorsqu'une session est envoy&eacute;e par mail, le nom de la
                    session chez le destinataire est modifi&eacute; par ajout
                    pr&eacute;fix&eacute; de l'adresse e-mail de l'envoyeur, sauf si
                    le nom de session contient @. Si le nom de session commence par @,
                    le caract&egrave;re @ est supprim&eacute;.
                    <br>
                    Exemple: un enseignant envoie &agrave; ses &eacute;l&egrave;ves
                    une session &eacute;nonc&eacute;. Il choisit un nom de session commencant
                    par @, par exemple <tt>@exercice</tt>, il cr&eacute;e
                    la session puis il clique sur le lien &#x2709;
                    et met comme destinataire l'alias mail de la classe. S'il n'y
                    a pas d'alias mail pour la classe, l'enseignant clique
                    sur le lien &#x282A; et poste le sujet sur le forum.
                    Les &eacute;l&egrave;ves font le travail et le renvoient en
                    cliquant sur le lien &#x2709;, qui contient automatiquement
                    l'adresse mail de l'enseignant.
                    Le nom de session devient alors
                    <tt>mail_eleve@fournisseur_internet@exercice</tt> ce qui permet &agrave;
                    l'enseignant de savoir qui il corrige.
                    L'enseignant corrige la session et la renvoie, le nom de session
                    reste inchang&eacute;.
            </li>
            <li style="display:inline">
                <button class="bouton"
                        onclick="var tmp=$id('tutoinst'); if (tmp.style.display=='none') tmp.style.display='block'; else tmp.style.display='none';">
                <strong>Installer</strong></button>
                <div id="tutoinst" style="display:none">
                    Vous pouvez optionnellement installer
                    Xcas sur votre appareil, ce qui permet de l'utiliser
                    en mode avion.
                    <br>
                    Sur mobile, t&eacute;l&eacute;chargez
                    <a
                        href="http://www-fourier.univ-grenoble-alpes.fr/~parisse/giac/xcashtml.zip"
                        target="_blank">
                    xcashtml.zip</a>, d&eacute;zippez-le (par exemple avec Androzip sur Android),
                    cherchez le fichier <tt>xcasfr.html</tt> (sur Android depuis
                    <a href="file:///sdcard/">ici</a>) et ouvrez-le avec votre
                    navigateur.
                    Vous pouvez cr&eacute;er un raccourci sur votre &eacute;cran
                    d'accueil depuis le menu de votre navigateur.
                    <br>
                    Sur PC/Mac: si vous avez install&eacute; Xcas natif pour PC ou Mac
                    en version 1.4.9-57 ou
                    sup&eacute;rieure, Xcas pour Firefox est d&eacute;j&agrave;
                    install&eacute;, sinon faire comme sur mobile.
                    <ul>
                        <li> Windows: cherchez le fichier <tt>xcasfr.html</tt>
                            dans le sous-r&eacute;pertoire <tt>doc</tt> du
                            r&eacute;pertoire d'installation de Xcas, en principe <tt>c:\xcas</tt>.
                        <li> Mac:<a href="file:///Applications/usr/share/giac/doc/xcasfr.html"
                                    target="_blank"><tt>/Applications/usr/share/giac/doc/xcasfr.html</tt></a>,
                        <li> Linux: <a href="file:///usr/share/giac/doc/xcasfr.html"
                                       target="_blank"><tt>/usr/share/giac/doc/xcasfr.html</tt></a>,
		    </ul>
		    Si Xcas pour Firefox ne fonctionne pas avec Firefox en local,
		    il faut d&eacute;sactiver
		    <tt>security.fileuri.strict_origin_policy</tt>
		    dans <tt>about:config</tt>.
                </div>
            </li>
            <li style="display:inline">
                <button class="bouton"
                        onclick="var tmp=$id('tutonws'); if (tmp.style.display=='none') tmp.style.display='block'; else tmp.style.display='none';">
                <strong>Numworks</strong></button>
	    <div id="tutonws" style="display:none">
	      Sur les navigateurs qui impl&eacute;mentent webusb (par
	      exemple Chromium ou Chrome), vous pouvez
	      &eacute;changer facilement des scripts avec une
	      calculatrice Numworks. 
	      <br>
	      V&eacute;rifiez dans la configuration (bouton en haut
	      &agrave; gauche) que l'export est configur&eacute; vers la
	      calculatrice Numworks.
	      Pour r&eacute;cup&eacute;rer un script depuis la
	      calculatrice, cliquer sur le bouton Numworks→. Pour
	      renvoyer un script vers la Numworks, cliquer sur le
	      bouton →Numworks. Le nom du script apparait &agrave; gauche
	      du bouton →Numworks. S'il se termine par <tt>xw</tt>, il
	      d&eacute;signera une session KhiCAS Numworks, s'il se
	      termine par <tt>.py</tt> un script Python. Vous pouvez
	      ensuite facilement partager vos scripts par email ou sur
	      des forums (icone enveloppe ou bouton F)<br>
	      <a href="https://www-fourier.univ-grenoble-alpes.fr/~parisse/numworks/khicasnw.html" target="_blank">KhiCAS</a> est
	      une version pour Numworks de Xcas, qui
	      <a href="nws.html"
                    target="_blank">s'installe </a> sur les
	      Numworks N0110 qui ont une version du syst&egrave;me
	      inf&eacute;rieure ou &eacute;gale &agrave; 15.
	      Sur cette page vous pouvez certifier
	      qu'une calculatrice Numworks contient le firmware
	      KhiCAS d'origine, conforme &agrave; la
	      r&eacute;glementation
	      des examens en France.
	      <b>Attention, ne mettez pas &agrave; jour votre calculatrice
	      sur le site officiel de Numworks, les mises
	      &agrave; jour versions 16 ou plus sont
	      irr&eacute;versiblement incompatibles avec
	      Xcas</b>. <a
                    href="https://tiplanet.org/forum/viewtopic.php?f=97&t=24968"
	      target="_blank">Plus d'informations ici</a> et une
	      <a
                    href="https://www.change.org/freenumworks" target="_blank">p&eacute;tition</a>
                    en ligne pour protester contre cette volte-face de
                    Numworks.
	      <br>
	      Remerciements &agrave; Maxime Friess pour le script
	      <a
                    href="https://github.com/M4xi1m3/numworks.js/blob/master/README.md"
                    target="_blank">Numworks.js</a> (sous licence MIT).
	    </div>
            </li>
            <li style="display:inline">
                <button class="bouton"
                        onclick="var tmp=$id('tutoex'); if (tmp.style.display=='none') tmp.style.display='block'; else tmp.style.display='none';">
                <strong>Exemples lyc&eacute;e</strong></button>
                <div id="tutoex" style="display:none">
                    Ces sessions sont propos&eacute;es en syntaxe Xcas ou en syntaxe Python.
                    Les <em>programmes</em> des sessions
                    &eacute;crits en gras (<strong>Python</strong>)
                    fonctionnent avec un interpr&eacute;teur Python (apr&egrave;s avoir fait
                    <tt>from math import *</tt> dans certains cas), ceux &eacute;crits
                    en italiques (<em>Python</em>) fonctionnent partiellement
                    (<button onclick="$id('tutoprog').style.display='block';var tmp=$id('progpython');tmp.style.display='block';tmp.scrollIntoView()">plus de d&eacute;tails sur la compatibilit&eacute;</button>).
                    <ul>
                        <li>Variables,
                            types, affectation, test, boucle, fonction, syntaxe
                            <a
                                href="#python=0&exec&+///Utilisez%20le%20point%20(.)%20pour%20s%C3%A9parer%20partie%20enti%C3%A8re%20et%20d%C3%A9cimale,%20expliciter%20les%20multiplications,%20attention%20aux%20parenth%C3%A8ses&+1.2%3B%202*3%2B4%3B%202*(3%2B4)&+expand((x%2B1)%5E2)%3B%0Afactor(x%5E2%2B4x%2B4)%3B%0Asin(pi%2F3)&+///%20Variables,%20l'affectation%20se%20fait%20avec%20:=&+a%3A%3D2&+2*a%2B5&+a%3A%3D2%3B%20type(a)&+a%3A%3D2.3%3B%20type(a)&+a%3A%3D%22bonjour%22%3B%20type(a)&+///%20Un%20test&+a%3A%3D1%3B%20%0Asi%20a%3E0%20alors%20%22positif%22%3B%20%0Asinon%20%22negatif%22%3B%20fsi%3B&+///Une%20boucle%20d%C3%A9finie,%20l'affichage%20print%20se%20fait%20dans%20la%20console%20tout%20en%20bas&+pour%20j%20de%201%20jusque%2010%20faire%0A%20%20print(j%2B%22%20au%20carre%20vaut%20%22%2Bj%5E2)%3B%20%0Afpour%3B&+///%20Une%20boucle%20tantque,%20illustrant%20la%20pr%C3%A9cision%20des%20tests%20avec%20des%20nombres%20approch%C3%A9s.&+j%3A%3D1.0%3B%20%0Atantque%20j-1!%3Dj%20faire%20%0A%20%20j%3D2*j%3B%20%0Aftantque%3B&+///%20Cr%C3%A9ation%20d'une%20fonction%20simple,%20par%20exemple%20le%20milieu%20de%202%20points%20$A$%20et%20$B$.%20On%20construit%20d'abord%20le%20milieu%20de%20mani%C3%A8re%20interactive.&+A%3A%3Dpoint(1%2C2)%3B%20B%3A%3Dpoint(-2%2C-2)&+Ax%3A%3Dabscisse(A)%3B%20%0AAy%3A%3Dordonnee(A)%3B%0ABx%3A%3Dabscisse(B)%3B%20%0ABy%3A%3Dordonnee(B)&+///%20On%20calcule%20$M$%20et%20on%20fait%20la%20repr%C3%A9sentation%20graphique%20des%20trois%20points.&+M%3A%3Dpoint((Ax%2BBx)%2F2%2C(Ay%2BBy)%2F2)%3B%0AA%3B%0AB%3B&+///%20On%20regroupe%20maintenant%20ces%20instructions%20dans%20une%20fonction%20puis%20on%20teste%20la%20fonction.&+fonction%20Milieu(A%2CB)%0A%20%20var%20Ax%2CAy%2CBx%2CBy%3B%0A%20%20Ax%3A%3Dabscisse(A)%3B%20%0A%20%20Ay%3A%3Dordonnee(A)%3B%0A%20%20Bx%3A%3Dabscisse(B)%3B%20%0A%20%20By%3A%3Dordonnee(B)%3B%20%0A%20%20retourne%20point((Ax%2BBx)%2F2%2C(Ay%2BBy)%2F2)%3B%0Affonction%3A%3B&+A%3BB%3BM%3A%3DMilieu(A%2CB)&+///%3Ch1%3eExercice%3C/h1%3e%20%C3%A9crire%20une%20fonction%20%3Ctt%3eCercle(A,B,C)%3C/tt%3e%20qui%20renvoie%20le%20cercle%20circonscrit%20au%20triangle%20$ABC$,%20en%20utilisant%20les%20commandes%20%3Ctt%3emediatrice%3C/tt%3e,%20%3Ctt%3einter_unique%3C/tt%3e,%20%3Ctt%3edistance%3C/tt%3e%20et%20%3Ctt%3ecercle(centre,rayon)%3C/tt%3e&"
                                target="_blank">
                            Xcas</a> ou
                            <a
                                href="#exec&python=1&+///En%20ligne%20de%20commande,%20utiliser%20des%20points%20(.)%20pour%20s%C3%A9parer%20partie%20enti%C3%A8re%20et%20d%C3%A9cimale%20des%20nombres,%20expliciter%20les%20multiplications,%20attention%20aux%20parenth%C3%A8ses.%0aSi%20la%20commande%20est%20sur%20plusieurs%20lignes,%20utilisez%20Shift-Entr%C3%A9e%20pour%20passer%20%C3%A0%20la%20ligne.%0aDans%20Xcas,%20la%20syntaxe%20Python%20est%20activ%C3%A9e%20automatiquement%20lorsqu'on%20d%C3%A9finit%20une%20fonction%20ou%20si%20la%20commande%20commence%20par%20un%20commentaire%20Python%20(%3Ctt%3e#%3C/tt%3e)&+%23%20calcul%20avec%20des%20nombres%0A1.2%0A2*3%2B4%0A2*(3%2B4)&+%23%20calculs%20litteraux%0Adevelopper((x%2B1)%5E2)%0Afactoriser(x%5E2%2B4x%2B4)%0Asin(pi%2F3)&+///Variables,%20l'affectation%20se%20fait%20avec%20:=,%20ou%20=%20en%20mode%20Python.&+a%3D2&+2*a%2B5&+type(a)&+a%3D2.3&+type(a)&+%23%0Aa%3D%22bonjour%22%0Atype(a)&+///%20Un%20test&+%23%0Aa%3D1%0Aif%20a%3E0%3A%20%0A%20%20%20%20%22positif%22%0Aelse%3A%0A%20%20%20%20%22negatif%22&+///%20Une%20boucle%20d%C3%A9finie,%20l'affichage%20des%20print%20se%20fait%20dans%20la%20console%20tout%20en%20bas.&+for%20j%20in%20range(10)%3A%0A%20%20%20%20print(j%2B%22%20au%20carre%20vaut%20%22%2Bj%5E2)&+///Une%20boucle%20tantque,%20qui%20s'arr%C3%AAte%20lorsque%20la%20valeur%20approch%C3%A9e%20de%20%3Ctt%3ej%3C/tt%3e%20est%20consider%C3%A9e%20comme%20%C3%A9gale%20%C3%A0%20%3Ctt%3ej+1%3C/tt%3e&+%23%0Aj%3D1.0%0Awhile%20j-1!%3Dj%3A%0A%20%20%20%20j%3D2*j&+///D%C3%A9finition%20d'une%20fonction%20simple,%20la%20valeur%20absolue.&+def%20Abs(x)%3A%0A%20%20if%20x%3C0%3A%0A%20%20%20%20return%20-x%0A%20%20return%20x&+Abs(-3)%3B%20Abs(5)&+///%3Cem%3eAttention,%20ce%20qui%20pr%C3%A9c%C3%A8de%20fonctionne%20avec%20un%20interpr%C3%A9teur%20Python%20pur%20sauf%20les%20calculs%20litt%C3%A9raux,%20mais%20ce%20qui%20suit%20ne%20fonctionnera%20pas%20avec%20un%20interpr%C3%A9teur%20Python%20pur%3C/em%3e.%0aCr%C3%A9ation%20d'une%20fonction%20simple%20en%20g%C3%A9om%C3%A9trie.%20%0aCalcul%20du%20milieu%20de%202%20points%20:%20on%20construit%20d'abord%20le%20milieu%20de%20mani%C3%A8re%20interactive&+%23%20creation%20de%202%20points%0AA%3Dpoint(1%2C2)%20%0AB%3Dpoint(-2%2C-2)&+%23%20calcul%20des%20coordonnes%0AAx%3Dabscisse(A)%20%0AAy%3Dordonnee(A)%0ABx%3Dabscisse(B)%0ABy%3Dordonnee(B)&+%23%20calcul%20de%20M%20et%20representation%20graphique%0AM%3Dpoint((Ax%2BBx)%2F2%2C(Ay%2BBy)%2F2)%0AA%0AB&+///%20On%20regroupe%20ces%20instructions%20dans%20une%20fonction&+def%20Milieu(A%2CB)%3A%0A%20%20%20%20%23%20local%20Ax%2CAy%2CBx%2CBy%3B%0A%20%20%20%20Ax%3Dabscisse(A)%0A%20%20%20%20Ay%3Dordonnee(A)%0A%20%20%20%20Bx%3Dabscisse(B)%0A%20%20%20%20By%3Dordonnee(B)%0A%20%20%20%20return%20point((Ax%2BBx)%2F2%2C(Ay%2BBy)%2F2)&+%23%0AA%0AB%0AM%3DMilieu(A%2CB)&+///%3Ch1%3eExercice%3C/h1%3e%20%C3%A9crire%20une%20fonction%20%3Ctt%3eCercle(A,B,C)%3C/tt%3e%20qui%20renvoie%20le%20cercle%20circonscrit%20au%20triangle%20$ABC$,%20en%20utilisant%20les%20commandes%20%3Ctt%3emediatrice%3C/tt%3e,%20%3Ctt%3einter_unique%3C/tt%3e,%20%3Ctt%3edistance%3C/tt%3e%20et%20%3Ctt%3ecercle(centre,rayon)%3C/tt%3e&"
                                target="_blank"><em>Python</em></a>
                        </li>
                        <li> Seconde: tortue.
                            Cliquez sur le bouton     <button onclick="$id('tutotortue').style.display='block';$id('tutoprog').style.display='none' ">
                            <strong>Tortue</strong>
                            </button>pour voir des exemples.
                        </li>
                        <li> Seconde, longueur de courbe
                            <a
                                href="#exec&python=0&+///Longueur%20d'un%20arc%20de%20courbe%20en%20l'approchant%20par%20une%20ligne%20polygonale.%20Dans%20un%20premier%20temps,%20on%20peut%20faire%20tracer%20le%20graphe%20%C3%A0%20la%20main.%20On%20peut%20prolonger%20en%20remplacant%20$1/x$%20par%20une%20fonction%20$f$%20quelconque,%20par%20exemple%20$sqrt(1-x^2)$%20sur%20$[0,1]$.&+plot(1%2Fx%2Cx%2C1%2C4%2Ccolor%3Dred)%3B%20open_polygon(seq(point(x%2C1%2Fx)%2Cx%2C1%2C4))&+fonction%20Distance(xa%2Cxb)%0A%20%20local%20ya%2Cyb%3B%0A%20%20ya%3A%3D1%2Fxa%3B%0A%20%20yb%3A%3D1%2Fxb%3B%0A%20%20return%20sqrt((xb-xa)^2%2B(yb-ya)^2)%3B%0Affonction%3A%3B&+Distance(1%2C2)%2BDistance(2%2C3)%2BDistance(3%2C4)&+fonction%20Longueur(xa%2Cxb%2CN)%0A%20%20local%20h%2Cd%2Ck%3B%0A%20%20h%3A%3D(xb-xa)%2FN%3B%20%0A%20%20d%3A%3D0%3B%0A%20%20pour%20k%20de%200%20jusque%20N-1%20faire%0A%20%20%20%20d%3A%3Dd%2BDistance(xa%2Bk*h%2Cxa%2B(k%2B1)*h)%3B%0A%20%20fpour%3B%0A%20%20return%20d%3B%0Affonction%3A%3B&+l%3A%3DLongueur(1%2C4%2C10)&+arclen(1%2Fx%2C1.0%2C4)%3B&"
                                target="_blank">Xcas</a>,
                            <a href="#exec&python=1&+///Longueur%20d'un%20arc%20de%20courbe%20en%20l'approchant%20par%20une%20ligne%20polygonale.%20Dans%20un%20premier%20temps,%20on%20peut%20faire%20tracer%20le%20graphe%20%C3%A0%20la%20main.%20On%20peut%20prolonger%20en%20remplacant%20$1/x$%20par%20une%20fonction%20$f$%20quelconque,%20par%20exemple%20$sqrt(1-x^2)$%20sur%20$[0,1]$.&+plot(1%2Fx%2Cx%2C1%2C4%2Ccolor%3Dred)%3B%20open_polygon(seq(point(x%2C1%2Fx)%2Cx%2C1%2C4))&+def%20Distance(xa%2Cxb)%3A%0A%20%20%20%20%23%20local%20ya%2Cyb%0A%20%20%20%20ya%3D1%2Fxa%0A%20%20%20%20yb%3D1%2Fxb%0A%20%20%20%20return%20sqrt((xb-xa)**2%2B(yb-ya)**2)&+Distance(1%2C2)%2BDistance(2%2C3)%2BDistance(3%2C4)&+def%20Longueur(xa%2Cxb%2CN)%3A%0A%20%20%20%20%23%20local%20h%2Cd%2Ck%0A%20%20%20%20h%3D(xb-xa)%2F(N*1.0)%20%23%201.0%20pour%20Python%202%0A%20%20%20%20d%3D0%0A%20%20%20%20for%20k%20in%20range(N)%3A%0A%20%20%20%20%20%20%20%20d%3Dd%2BDistance(xa%2Bk*h%2Cxa%2B(k%2B1)*h)%0A%20%20%20%20return%20d&+l%3A%3DLongueur(1%2C4%2C10)&+arclen(1%2Fx%2C1.0%2C4)%3B&"
                               target="_blank"><strong>Python</strong></a>
                        </li>
                        <li> Seconde, recherche de minimum
                            <a
                                href="#exec&python=0&+///Recherche%20de%20minimum%20local.%0aPrincipe:%20automatiser%20ce%20qu'on%20ferait%20avec%20un%20tableau%20de%20valeurs,%20on%20cherche%20la%20plus%20petite%20valeur%20et%20on%20zoome%20le%20tableau%20%C3%A0%20proximit%C3%A9.%20Dans%20%3Ctt%3etabval%3C/tt%3e%20on%20peut%20faire%20changer%20le%20nombre%20de%20subdivisions%20par%20les%20%C3%A9l%C3%A8ves%20et%20leur%20faire%20observer%20qu'avec%20par%20exemple%20100%20ou%201000%20subdivisions,%20c'est%20trop%20difficile%20de%20trouver%20la%20plus%20petite%20valeur,%20d'o%C3%B9%20l'int%C3%A9r%C3%AAt%20de%20zoomer.%0aDans%20la%20fonction%20%3Ctt%3eposmin10%3C/tt%3e,%20on%20se%20donne%20un%20intervalle%20$[a,b]$%20et%20une%20fonction%20$f$,%20on%20coupe%20l'intervalle%20en%2010,%20on%20cherche%20la%20plus%20petite%20valeur.%0aDans%20la%20fonction%20%3Ctt%3eposmin%3C/tt%3e%20on%20recommence%20ensuite%20sur%20l'intervalle%20encadrant%20la%20plus%20petite%20valeur%20trouv%C3%A9e%20ce%20qui%20permet%20d'am%C3%A9liorer%20la%20pr%C3%A9cision.&+f(x)%3A%3Dx%5E4%2Bx%5E2%2Bx%2B1&+fonction%20tabval(f%2Ca%2Cb)%0A%20%20local%20x%2Cj%2Ch%2Cl%3B%0A%20%20h%3A%3D(b-a)%2F10.0%3B%0A%20%20l%3A%3D%5B%5D%3B%0A%20%20pour%20j%20de%200%20jusque%2010%20faire%0A%20%20%20%20x%3A%3Da%2Bj*h%3B%0A%20%20%20%20l.append(%5Bx%2Cf(x)%5D)%3B%0A%20%20fpour%3B%0A%20%20return%20l%3B%0Affonction%3A%3B&+l%3A%3Dtabval(f%2C-2%2C2)&+plotfunc(f(x)%2Cx%2C-2%2C2)%3B%0Acouleur(polygone_ouvert(l)%2C%0A%20%20rouge)&+///On%20voit%20que%20le%20minimum%20est%20entre%20-0.8%20et%200&+tabval(f%2C-0.8%2C0)&+fonction%20posmin10(f%2Ca%2Cb)%0A%20%20local%20j%2Cxcur%2Cxmin%2Cfxcur%2Cfxmin%2Ch%3B%0A%20%20h%3A%3D(b-a)%2F10.0%3B%0A%20%20xmin%3A%3Da%3B%0A%20%20fxmin%3A%3Df(xmin)%3B%0A%20%20pour%20j%20de%201%20jusque%2010%20faire%0A%20%20%20%20xcur%3A%3Da%2Bj*h%3B%0A%20%20%20%20fxcur%3A%3Df(xcur)%3B%0A%20%20%20%20si%20fxcur%3Cfxmin%20alors%0A%20%20%20%20%20%20xmin%3A%3Dxcur%3B%0A%20%20%20%20%20%20fxmin%3A%3Dfxcur%3B%0A%20%20%20%20fsi%3B%0A%20%20fpour%3B%0A%20%20return%20xmin%3B%0Affonction%3A%3B&+posmin10(f%2C-2%2C2)&+fonction%20posmin(f%2Ca%2Cb%2Ceps)%0A%20%20local%20x%2Ch%3B%0A%20%20x%3A%3Da%3B%0A%20%20tantque%20b-a%3Eeps%20faire%0A%20%20%20%20x%3A%3Dposmin10(f%2Ca%2Cb)%3B%0A%20%20%20%20h%3A%3D(b-a)%2F10.0%3B%0A%20%20%20%20si%20x!%3Da%20alors%20a%3A%3Dx-h%3B%20fsi%3B%0A%20%20%20%20si%20x!%3Db%20alors%20b%3A%3Dx%2Bh%3B%20fsi%3B%0A%20%20ftantque%3B%0A%20%20return%20x%3B%0Affonction%3A%3B&+posmin(f%2C-2%2C2%2C1e-4)&+///On%20peut%20prolonger%20l'exercice%20en%20premi%C3%A8re%20ou%20terminale.%0aLe%20minimum%20de%20$f$%20est%20un%20z%C3%A9ro%20de%20$f'$%20que%20l'on%20peut%20d%C3%A9terminer%20avec%20la%20commande%20%3Ctt%3efsolve%3C/tt%3e%20ou%20par%20dichotomie.&+fsolve(f'(x)%3D0%2Cx)&"
                                target="_blank">Xcas</a>,
                            <a
                                href="#exec&python=1&+///Recherche%20de%20minimum%20local.%0aOn%20se%20donne%20un%20intervalle%20$[a,b]$%20et%20une%20fonction%20$f$,%20on%20coupe%20l'intervalle%20en%2010,%20on%20cherche%20la%20plus%20petite%20valeur.%20On%20recommencera%20ensuite%20sur%20l'intervalle%20encadrant%20la%20plus%20petite%20valeur%20pour%20ameliorer%20la%20pr%C3%A9cision.&+def%20tabval(f%2Ca%2Cb)%3A%0A%20%20%20%20%23%20local%20x%2Cj%2Ch%2Cl%3B%0A%20%20%20%20h%3D(b-a)%2F10.0%0A%20%20%20%20l%3D%5B%5D%0A%20%20%20%20for%20j%20in%20range(11)%3A%0A%20%20%20%20%20%20%20%20x%3Da%2Bj*h%0A%20%20%20%20%20%20%20%20l.append(%5Bx%2Cf(x)%5D)%0A%20%20%20%20return%20l&+def%20f(x)%3A%0A%20%20%20%20return%20x**4%2Bx**2%2Bx%2B1&+l%3Dtabval(f%2C-2%2C2)&+plotfunc(f(x)%2Cx%2C-2%2C2)%3B%0Acouleur(polygone_ouvert(l)%2C%0A%20%20rouge)&+///Le%20minimum%20est%20entre%20-0.8%20et%200.%20On%20zoome.&+tabval(f%2C-0.8%2C0)&+///On%20automatise%20le%20zoom.&+def%20posmin10(f%2Ca%2Cb)%3A%0A%20%20%20%20%23%20local%20j%2Cxcur%2Cxmin%2Cfxcur%2Cfxmin%2Ch%0A%20%20%20%20h%3D(b-a)%2F10.0%0A%20%20%20%20xmin%3Da%0A%20%20%20%20fxmin%3Df(xmin)%0A%20%20%20%20for%20j%20in%20range(11)%3A%0A%20%20%20%20%20%20%20%20xcur%3Da%2Bj*h%0A%20%20%20%20%20%20%20%20fxcur%3Df(xcur)%0A%20%20%20%20%20%20%20%20if%20fxcur%3Cfxmin%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20xmin%3Dxcur%0A%20%20%20%20%20%20%20%20%20%20%20%20fxmin%3Dfxcur%0A%20%20%20%20return%20xmin&+posmin10(f%2C-3%2C0)&+def%20posmin(f%2Ca%2Cb%2Ceps)%3A%0A%20%20%20%20%23%20local%20x%2Ch%0A%20%20%20%20x%3Da%0A%20%20%20%20while%20b-a%3Eeps%3A%0A%20%20%20%20%20%20%20%20x%3Dposmin10(f%2Ca%2Cb)%0A%20%20%20%20%20%20%20%20h%3D(b-a)%2F10.0%0A%20%20%20%20%20%20%20%20if%20x!%3Da%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20a%3Dx-h%0A%20%20%20%20%20%20%20%20if%20x!%3Db%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20b%3Dx%2Bh%0A%20%20%20%20return%20x&+posmin(f%2C-2%2C1%2C1e-2)&"
                                target="_blank"><strong>Python</strong></a>
                        </li>
                        <li> Seconde: trac&eacute; de courbe, syntaxe
                            <a
                                href="#python=0&exec&+///Soit%20$f$%20la%20fonction%20d%C3%A9finie%20par%20$f(x)=-x^2-3$%20lorsque%20$x%3C0$%20et%20$f(x)=x^2+1$%20sinon&+f(x)%3A%3Dsi%20x%3C0%20alors%20-x%5E2-3%20%0A%20%20sinon%20x%5E2%2B1%20fsi%3B&+///%20On%20commence%20par%20faire%20un%20tableau%20de%20valeurs&+L%3A%3DNULL%3B%20%0Apour%20x%20de%20-3%20jusque%203%20pas%200.5%20faire%0A%20%20L%3A%3DL%2C%5Bx%2Cf(x)%5D%3B%0Afpour%3B&+polygone_ouvert(L)&+///Observer%20le%20saut%20%C3%A0%20la%20discontinuit%C3%A9.%20Il%20faudrait%20faire%202%20trac%C3%A9s,%20on%20a%20donc%20int%C3%A9ret%20%C3%A0%20faire%20une%20fonction%20et%20l'appeler%20deux%20fois.&+fonction%20tabval(f%2Cxmin%2Cxmax%2Cdx)%0A%20%20var%20x%2CL%3B%0A%20%20L%3A%3DNULL%3B%0A%20%20pour%20x%20de%20xmin%20jusque%20xmax%20pas%20dx%20faire%0A%20%20%20%20L%3A%3DL%2C%5Bx%2Cf(x)%5D%3B%0A%20%20fpour%3B%0A%20%20retourne%20L%3B%0Affonction%3A%3B&+polygone_ouvert(tabval(f%2C-3%2C-0.1%2C0.1))%3B%0Apolygone_ouvert(tabval(f%2C0.1%2C3%2C0.1))%3B&"
                                target="_blank">
                            Xcas</a> ou
                            <a
                                href="#exec&python=1&+///Soit%20$f$%20la%20fonction%20d%C3%A9finie%20par%20$f(x)=-x^2-3$%20lorsque%20$x%3C0$%20et%20$f(x)=x^2+1$%20sinon&+def%20f(x)%3A%0A%20%20%20%20if%20x%3C0%3A%0A%20%20%20%20%20%20%20%20return%20-x%5E2-3%20%0A%20%20%20%20else%3A%0A%20%20%20%20%20%20%20%20return%20x%5E2%2B1&+///%20On%20commence%20par%20faire%20un%20tableau%20de%20valeurs&+%23%0AL%3D%5B%5D%0Afor%20j%20in%20range(13)%3A%0A%20%20%20%20x%3D-3%2B0.5*j%0A%20%20%20%20L.append(%5Bx%2Cf(x)%5D)&+polygone_ouvert(L)&+///Observer%20le%20saut%20%C3%A0%20la%20discontinuit%C3%A9.%20Il%20faudrait%20faire%202%20trac%C3%A9s,%20on%20a%20donc%20int%C3%A9ret%20%C3%A0%20faire%20une%20fonction%20et%20l'appeler%20deux%20fois.&+def%20tabval(f%2Ca%2Cb%2Cdx)%3A%0A%20%20%20%20%23%20local%20x%2Cj%2CL%3B%0A%20%20%20%20L%3D%5B%5D%3B%0A%20%20%20%20for%20j%20in%20range((b-a)%2Fdx%2B1)%3A%0A%20%20%20%20%20%20%20%20x%3Da%2Bj*dx%0A%20%20%20%20%20%20%20%20L.append(%5Bx%2Cf(x)%5D)%0A%20%20%20%20return%20L%3B&+polygone_ouvert(tabval(f%2C-3%2C-0.1%2C0.1))%3B%0Apolygone_ouvert(tabval(f%2C0.1%2C3%2C0.1))%3B&"
                                target="_blank">Python</a>
                        </li>
                        <li> Seconde: &Eacute;quation  d'une droite
                            <a
                                href="#python=0&exec&+A%3A%3Dpoint(-2%2C3)%3B%20%0AB%3A%3Dpoint(1%2C-1)%3B%20%0AD%3A%3Ddroite(A%2CB)&+fonction%20eqdroite(A%2CB)%0A%20%20var%20Ax%2CAy%2CBx%2CBy%2Cm%3B%0A%20%20Ax%2CAy%3A%3Dcoordonnees(A)%3B%0A%20%20Bx%2CBy%3A%3Dcoordonnees(B)%3B%0A%20%20si%20Ax%3DBx%20alors%20return%20%22x%3D%22%2BAx%3B%20fsi%3B%0A%20%20m%3A%3D(By-Ay)%2F(Bx-Ax)%3B%0A%20%20%2F%2F%20m*Ax%2Bp%3DAy%0A%20%20retourne%20%22y%3D%22%2Bm%2B%22*x%2B%22%2B(Ay-m*Ax)%3B%0Affonction%3A%3B&+eqdroite(A%2CB)%3B%20equation(D)&"
                                target="_blank">Xcas</a>
                            ou
                            <a
                                href="#python=1&exec&+%23%20%0AA%3Dpoint(-2%2C3)%0AB%3A%3Dpoint(1%2C-1)%3B%20%0AD%3A%3Ddroite(A%2CB)&+def%20eqdroite(A%2CB)%3A%0A%20%20%20%20%23%20local%20Ax%2CAy%2CBx%2CBy%2Cm%3B%0A%20%20%20%20Ax%2CAy%3Dcoordonnees(A)%0A%20%20%20%20Bx%2CBy%3Dcoordonnees(B)%0A%20%20%20%20if%20Ax%3D%3DBx%3A%0A%20%20%20%20%20%20%20%20return%20%22x%3D%22%2BAx%0A%20%20%20%20m%3D(By-Ay)%2F(Bx-Ax)%0A%20%20%20%20%23%20m*Ax%2Bp%3DAy%0A%20%20%20%20return%20%22y%3D%22%2Bm%2B%22*x%2B%22%2B(Ay-m*Ax)&+eqdroite(A%2CB)%3B%20equation(D)&"
                                target="_blank">
                            Python</a>
                        </li>
                        <li> Seconde, fr&eacute;quence dans un &eacute;chantillon, syntaxe
                            <a
                                href="#python=0&exec&+///%20Algorithme%20de%20calcul%20de%20la%20fr%C3%A9quence%20de%20valeur%20dans%20echantillon&+fonction%20freq(echantillon%2Cvaleur)%0A%20%20var%20j%2Ctotal%3B%0A%20%20total%3A%3D0%3B%0A%20%20pour%20j%20de%201%20jusque%20dim(echantillon)%20faire%0A%20%20%20%20si%20echantillon(j)%3Dvaleur%20alors%20%0A%20%20%20%20%20%20total%3A%3Dtotal%2B1%3B%20%0A%20%20%20%20fsi%3B%0A%20%20fpour%3B%0A%20%20retourne%20total%2Fdim(echantillon)%3B%0Affonction%3A%3B&+echantillon%3A%3Dranv(100%2C2)&+freq(echantillon%2C1)%3B%20%0Afreq(echantillon%2C0)&+///%20Intervalle%20de%20fluctuation%20d%20une%20fr%C3%A9quence,%20ici%200.4.%20On%20tire%20100%20%C3%A9chantillons%20de%20N=200%20valeurs%20selon%20la%20loi%20binomiale%20et%20on%20renvoie%20la%20fr%C3%A9quence%20de%201.&+f%3A%3D0.4%3B%20N%3A%3D200&+echantillon%3A%3D%0Aranv(100%2Cbinomial%2CN%2Cf)%2FN&+count(x-%3E%0A%20%20abs(x-f)%3C1%2Fsqrt(N)%2Cechantillon)&+///%20Sans%20utiliser%20ranv,%20on%20peut%20simuler%20une%20frequence%20f%20avec%20rand()%20en%20comparant%20avec%20f&+rand()&+tirage(f)%3A%3Drand()%3Cf&+tirage(f)%3Btirage(f)%3Btirage(f)&+fonction%20simu(N%2Cf)%0A%20%20var%20j%2Cres%3B%0A%20%20res%3A%3D0%3B%0A%20%20pour%20j%20de%201%20jusque%20N%20faire%0A%20%20%20%20si%20tirage(f)%20alors%20res%3A%3Dres%2B1%3B%20fsi%3B%0A%20%20fpour%3B%0A%20%20return%20res%2FN%3B%0Affonction%3A%3B&+simu(200%2C.4)&+l%3A%3Dseq(simu(200%2C.4)%2C100)&+count(x-%3Eabs(x-f)%3C1%2Fsqrt(N)%2Cl)&"
                                target="_blank">
                            Xcas</a> ou
                            <a href="#exec&python=1&+///Algorithme%20de%20calcul%20de%20la%20fr%C3%A9quence%20de%20%3Ctt%3evaleur%3C/tt%3e%20dans%20%3Ctt%3eechantillon%3C/tt%3e&+def%20Freq(echantillon%2Cvaleur)%3A%0A%20%20%20%20%23%20local%20j%2Ctotal%3B%0A%20%20%20%20total%3D0%3B%0A%20%20%20%20for%20j%20in%20echantillon%3A%0A%20%20%20%20%20%20%20%20if%20j%3D%3Dvaleur%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20total%3Dtotal%2B1.0%0A%20%20%20%20return%20total%2Flen(echantillon)&+echantillon%3Dranv(100%2C2)&+///%3Ctt%3eranv%3C/tt%3e%20est%20une%20instruction%20Xcas%20qui%20cr%C3%A9e%20un%20vecteur%20al%C3%A9atoire%20ici%20de%20100%20entiers%20strictement%20inf%C3%A9rieurs%20%C3%A0%202.%20Voir%20plus%20bas%20comment%20faire%20la%20m%C3%AAme%20chose%20sans%20utiliser%20%3Ctt%3eranv%3C/tt%3e&+%23%0AFreq(echantillon%2C1)%0AFreq(echantillon%2C0)&+///%20Intervalle%20de%20fluctuation%20d%20une%20fr%C3%A9quence,%20ici%200.4.%20On%20tire%20100%20%C3%A9chantillons%20de%20N=200%20valeurs%20selon%20la%20loi%20binomiale%20et%20on%20renvoie%20la%20fr%C3%A9quence%20de%201.&+%23%0Af%3D0.4%0AN%3D200&+echantillon%3Devalf(ranv(100%2Cbinomial%2CN%2Cf)%2FN)&+def%20OK(echantillon%2Cf%2CN)%3A%0A%20%20%20%20%23%20local%20c%2Cx%0A%20%20%20%20c%3D0%0A%20%20%20%20for%20x%20in%20echantillon%3A%0A%20%20%20%20%20%20%20%20if%20abs(x-f)%3C1%2Fsqrt(N)%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20c%3Dc%2B1%0A%20%20%20%20return%20c&+OK(echantillon%2Cf%2CN)&+///%20Sans%20utiliser%20ranv,%20on%20peut%20simuler%20une%20frequence%20f%20avec%20random()%20en%20comparant%20avec%20f&+random()&+def%20Tirage(f)%3A%0A%20%20%20%20return%20random()%3Cf&+Tirage(f)%3BTirage(f)%3BTirage(f)&+def%20Simu(N%2Cf)%3A%0A%20%20%20%20%23%20local%20j%2Cres%0A%20%20%20%20res%3D0%0A%20%20%20%20for%20j%20in%20range(N)%3A%0A%20%20%20%20%20%20%20%20if%20Tirage(f)%3A%20%0A%20%20%20%20%20%20%20%20%20%20%20%20res%3Dres%2B1.0%0A%20%20%20%20return%20res%2FN&+Simu(200%2C.4)&+l%3D%5BSimu(200%2C.4)%20for%20j%20in%20range(100)%5D&+OK(l%2Cf%2CN)&"
                               target="_blank"><strong>Python</strong></a>
                        </li>
                        <li>
                            Lyc&eacute;e: d&eacute;composition d'un entier en facteurs premiers par division
                            <a href="#exec&python=0&+///Factorisation%20d'un%20entier%20par%20division%20naive%20(fonctionne%20pour%20$n%3C10000^2$)&+fonction%20tdiv(n)%0A%20%20local%20r%2Cj%3B%0A%20%20r%3A%3Dmakelist(0)%3B%0A%20%20pour%20j%20de%202%20jusque%2010000%20faire%0A%20%20%20%20si%20j*j%3En%20alors%20%0A%20%20%20%20%20%20%2F%2F%20ici%20n%20est%20premier%0A%20%20%20%20%20%20si%20n!%3D1%20alors%20r.append(n)%3B%20fsi%3B%0A%20%20%20%20%20%20return%20r%3B%20%0A%20%20%20%20fsi%3B%0A%20%20%20%20tantque%20irem(n%2Cj)%3D0%20faire%0A%20%20%20%20%20%20%2F%2F%20ici%20j%20divise%20n%0A%20%20%20%20%20%20n%3A%3Dn%2Fj%3B%0A%20%20%20%20%20%20r.append(j)%3B%0A%20%20%20%20ftantque%3B%0A%20%20%20%20si%20j%3E2%20alors%20j%2B%2B%3B%20fsi%3B%20%2F%2F%20saut%20de%202%20en%202%0A%20%20fpour%3B%0A%20%20return%20%22Trop%20grand%22%3B%0Affonction%3A%3B&+tdiv(1007)&"
                               target="_blank">Xcas</a>,
                            <a
                                href="#exec&python=1&+///Factorisation%20d'un%20entier%20par%20division%20naive%20(fonctionne%20pour%20$n%3C10000^2$)&+def%20tdiv(n)%3A%0A%20%20%20%20%23%20local%20r%2Cj%0A%20%20%20%20r%3D%5B%5D%0A%20%20%20%20for%20j%20in%20range(2%2C10000)%3A%0A%20%20%20%20%20%20%20%20if%20j*j%3En%20%3A%20%23%20ici%20n%20est%20premier%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20n%3C%3E1%20%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20r.append(n)%0A%20%20%20%20%20%20%20%20%20%20%20%20return(r)%0A%20%20%20%20%20%20%20%20while%20n%20%25j%20%3D%3D0%20%3A%20%23%20ici%20j%20divise%20n%20%20%20%20%20%20%20%20%20%20%20%0A%20%20%20%20%20%20%20%20%20%20%20%20n%3Dn%2F%2Fj%0A%20%20%20%20%20%20%20%20%20%20%20%20r.append(j)%0A%20%20%20%20%20%20%20%20if%20j%3E2%20%3A%20%23%20saut%20de%202%20en%202%0A%20%20%20%20%20%20%20%20%20%20%20%20j%2B%3D1%0A%20%20%20%20return(%22Trop%20grand%22)%0A&+tdiv(1007)&"
                                target="_blank"><strong>Python</strong></a>
                        </li>
                        <li>
                            Lyc&eacute;e: le paradoxe du duc de Toscane
                            <a
                                href="#exec&python=1&+///Le%20prince%20de%20Toscane%20avait%20remarqu%C3%A9%20que%2C%20bien%20qu'il%20y%20ait%20autant%20de%20fa%C3%A7ons%20d'%C3%A9crire%209%20et%2010%20comme%20somme%20de%203%20nombres%20compris%20entre%201%20et%206%2C%20on%20obtient%20plus%20souvent%20un%20total%20de%2010%20lorsqu'on%20lance%203%20d%C3%A9s.%0ACliquez%20sur%20Exec%20en%20bas%20pour%20relancer%20une%20simulation.&+fonction%20toscane(Nombre)%0A%20%20sommeA%20%3A%3D%20%5B0%5D*18%3B%0A%20%20pour%20j%20de%201%20jusque%20Nombre%20faire%0A%20%20%20%20s%20%3A%3D%20randint(1%2C6)%2Brandint(1%2C6)%2Brandint(1%2C6)%3B%0A%20%20%20%20sommeA%5Bs-1%5D%2B%2B%3B%0A%20%20fpour%3B%0A%20%20print(sommeA%5B9%5D%2B%20%22%20neufs%20et%20%22%2BsommeA%5B10%5D%2B%20%22%20dix%22)%3B%0A%20%20return%20sommeA%2FNombre%3B%0Affonction%3A%3B&+t%3Dtoscane(100000)&+barplot(t)&"
                                target="_blank">Xcas</a>,
                            <a
                                href="#exec&python=1&+///Le%20prince%20de%20Toscane%20avait%20remarqu%C3%A9%20que%2C%20bien%20qu'il%20y%20ait%20autant%20de%20fa%C3%A7ons%20d'%C3%A9crire%209%20et%2010%20comme%20somme%20de%203%20nombres%20compris%20entre%201%20et%206%2C%20on%20obtient%20plus%20souvent%20un%20total%20de%2010%20lorsqu'on%20lance%203%20d%C3%A9s.%0ACliquez%20sur%20Exec%20en%20bas%20pour%20relancer%20une%20simulation.&+def%20toscane(Nombre)%3A%0A%20%20%20%20sommeA%20%3D%20%5B0%20for%20j%20in%20range(18)%5D%0A%20%20%20%20for%20j%20in%20range(Nombre)%3A%0A%20%20%20%20%20%20%20%20s%3Drandint(1%2C6)%2Brandint(1%2C6)%2Brandint(1%2C6)%0A%20%20%20%20%20%20%20%20sommeA%5Bs-1%5D%2B%3D1%0A%20%20%20%20print(sommeA%5B9%5D%2B%20%22%20neufs%20et%20%22%2BsommeA%5B10%5D%2B%20%22%20dix%22)%0A%20%20%20%20sommeA%3D%5BsommeA%5Bj%5D%2FNombre%20for%20j%20in%20range(18)%5D%0A%20%20%20%20return%20sommeA&+t%3Dtoscane(100000)&+barplot(t)&"
                                target="_blank">
                            Python
                            </a>
                        </li>
                        <li> Premi&egrave;re, &eacute;quation du second degr&eacute;
                            <a
                                href="#python=0&exec&+fonction%20resolution2(a%2Cb%2Cc)%0A%20%20var%20delta%3B%0A%20%20delta%3A%3Db%5E2-4*a*c%3B%0A%20%20si%20delta%3C0%20alors%20retourne%20%22pas%20de%20racines%22%3B%20fsi%3B%0A%20%20si%20delta%3D0%20alors%20retourne%20-b%2F(2*a)%3B%20fsi%3B%0A%20%20delta%3A%3Dsqrt(delta)%3B%0A%20%20retourne%20(-b-delta)%2F(2*a)%2C(-b%2Bdelta)%2F(2*a)%3B%0Affonction%3A%3B&+resolution2(1%2C2%2C3)&+resolution2(1%2C2%2C1)&+resolution2(1%2C1%2C-1)&"
                                target="_blank">
                            Xcas</a>,
                            <a
                                href="#python=1&exec&+def%20resolution2(a%2Cb%2Cc)%3A%0A%20%20%20%20%23%20local%20delta%2Cs%0A%20%20%20%20delta%3Db**2-4*a*c%0A%20%20%20%20if%20delta%3C0%3A%0A%20%20%20%20%20%20%20%20return%20%22pas%20de%20racines%22%0A%20%20%20%20if%20delta%3D%3D0%3A%0A%20%20%20%20%20%20%20%20return%20-b%2F(2.0*a)%0A%20%20%20%20s%3Dsqrt(delta)%0A%20%20%20%20return%20%5B(-b-s)%2F(2.0*a)%2C(-b%2Bs)%2F(2.0*a)%5D&+resolution2(1%2C2%2C3)&+resolution2(1%2C2%2C1)&+resolution2(1%2C1%2C-1)&"
                                target="_blank"><strong>Python</strong></a>
                        </li>
                        <li> Premi&egrave;re, suites
                            <a
                                href="#exec&python=0&+///Calcul%20des%20premiers%20termes%20d'une%20suite%20donn%C3%A9e%20par%20une%20expression%20$u[n]=f(n)$&+u(n)%3A%3D1%2Fn&+s%3A%3Dseq(u(n)%2Cn%2C1%2C10)&+seq(point(n%2Cu(n))%2Cn%2C1%2C10)&+///Recherche%20du%20premier%20terme%20de%20la%20suite%20plus%20petit%20que%20eps.&+fonction%20N0(u%2Ceps)%0A%20%20local%20n%3B%0A%20%20n%3A%3D1%3B%0A%20%20tantque%20u(n)%3Eeps%20faire%0A%20%20%20%20n%3A%3Dn%2B1%3B%0A%20%20ftantque%3B%0A%20%20return%20n%3B%0Affonction%3A%3B%0A&+N0(u%2C0.01)&+///Calcul%20des%20premiers%20termes%20d'une%20suite%20r%C3%A9currente%20$u[n+1]=f(u[n])$&+fonction%20ntermes(f%2Cu0%2CN)%20%0A%20%20var%20n%2Cu%3B%0A%20%20u%3A%3D%5Bu0%5D%3B%0A%20%20pour%20n%20de%201%20jusque%20N%20faire%0A%20%20%20%20u%5Bn%5D%3A%3Df(u%5Bn-1%5D)%3B%0A%20%20fpour%3B%0A%20%20retourne%20u%3B%20%0A%20%20%2F%2F%20ou%20retourne%20u%5BN%5D%20pour%20le%20dernier%20terme%0Affonction%3A%3B&+f(x)%3A%3D1%2F2*(x%2B2%2Fx)&+ntermes(f%2C1.0%2C1)&+U%3A%3Dntermes(f%2C1.0%2C5)&+ntermes(f%2C1%2C5)&+seq(point(n%2CU%5Bn%5D)%2Cn%2C0%2Csize(U)-1)&"
                                target="_blank">Xcas
                            </a>,
                            <a
                                href="#exec&python=1&+///Calcul%20des%20premiers%20termes%20d'une%20suite%20donn%C3%A9e%20par%20une%20expression%20$u[n]=f(n)$&+def%20u(n)%3A%0A%20%20%20%20return%201.0%2Fn%0A&+s%3D%5Bu(n)%20for%20n%20in%20range(1%2C11)%5D&+%5Bpoint(n%2Cu(n))%20for%20n%20in%20range(1%2C11)%5D&+///Calcul%20du%20premier%20rang%20tel%20que%20$u[n]%3Ceps$&+def%20N0(u%2Ceps)%3A%0A%20%20%20%20%23%20local%20n%0A%20%20%20%20n%3D0%0A%20%20%20%20while%20u(n)%3Eeps%3A%0A%20%20%20%20%20%20%20%20n%3Dn%2B1%0A%20%20%20%20return%20n&+N0(u%2C0.01)&+///Calcul%20des%20premiers%20termes%20d'une%20suite%20r%C3%A9currente%20$f(u[n+1])=f(u[n])$&+def%20ntermes(f%2Cu0%2CN)%3A%0A%20%20%20%20%23%20local%20n%2Cu%0A%20%20%20%20u%3D%5Bu0%5D%3B%0A%20%20%20%20for%20n%20in%20range(N)%3A%0A%20%20%20%20%20%20%20%20u.append(f(u%5Bn%5D))%0A%20%20%20%20return%20u%20%0A%20%20%20%20%23%20ou%20retourne%20u%5BN%5D%20pour%20le%20dernier%20terme%0A&+def%20f(x)%3A%0A%20%20%20%20return%200.5*(x%2B2.0%2Fx)&+ntermes(f%2C1.0%2C10)&+U%3Dntermes(f%2C1.0%2C5)&+ntermes(f%2C1%2C5)&+%5Bpoint(n%2CU%5Bn%5D)%20for%20n%20in%20range(size(U))%5D%0A&"
                                target="_blank"><strong>Python</strong></a>
                        </li>
                        <li> Premi&egrave;re, Loi binomiale et loi g&eacute;om&eacute;trique tronqu&eacute;e
                            <a
                                href="#python=0&exec&+python_compat(0)&+///%20simulation%20de%20$n$%20tirages%20au%20hasard%20avec%20probabilit%C3%A9%20$p$%20de%20succ&egrave;s&+fonction%20Tirages(n%2Cp)%0A%20%20var%20total%2Cj%2Ch%3B%0A%20%20total%3A%3D0%3B%0A%20%20pour%20j%20de%201%20jusque%20n%20faire%0A%20%20%20%20h%3A%3Drand(0%2C1)%3B%0A%20%20%20%20si%20h%3C%3Dp%20alors%20total%3A%3Dtotal%2B1%3B%20fsi%3B%0A%20%20%20fpour%3B%0A%20%20retourne%20total%3B%0Affonction%3A%3B&+Tirages(10%2C0.4)&+///%20histogramme%20de%201000%20tirages%20et%20comparaison%20avec%20l'histogramme%20de%20la%20loi%20binomiale&+s%3A%3Dseq(Tirages(10%2C0.4)%2C1000)&+histogramme(s%2C-0.5%2C1%2Ccouleur%3Dred)%3B%20%0Ahistogramme(binomial%2C10%2C0.4)&+///%20calcul%20de%20l'intervalle%20de%20confiance%20centr%C3%A9%20pour%20la%20loi%20binomiale&+n%3A%3D100%3B%20p%3A%3D0.16%3B%20%0Axmin%3A%3Dbinomial_icdf(n%2Cp%2C0.025)%3B%0Axmax%3A%3Dbinomial_icdf(n%2Cp%2C0.975)&+gl_x%3D0..40%3B%20gl_y%3D0..0.15%3B%0Ahistogram(binomial%2Cn%2Cp)%3B%0Adroite(x%3Dxmin%2Ccolor%3Dred)%3B%0Adroite(x%3Dxmax%2Ccolor%3Dred)%3B&+///%20programme%20de%20calcul%20de%20l'intervalle%20de%20confiance%20%C3%A0%20partir%20de%20la%20loi%20binomiale&+fonction%20confiance(n%2Cp%2Cseuil)%0A%20%20var%20k%2Ctotal%3B%0A%20%20total%3A%3D0%3B%0A%20%20pour%20k%20de%200%20jusque%20n%20faire%0A%20%20%20%20total%3A%3Dtotal%2Bbinomial(n%2Cp%2Ck)%3B%0A%20%20%20%20si%20total%3E%3Dseuil%20alors%20retourne%20k%3B%20fsi%3B%0A%20%20fpour%3B%0Affonction%3A%3B&+confiance(100%2C.16%2C0.025)&+confiance(100%2C.16%2C0.975)&+///%20comparaison%20avec%20$[p-1/sqrt(n),p+1/sqrt(n)]$&+n%3A%3D30%3Bplotfunc(%0A%5Bbinomial_icdf(30%2Cp%2C0.025)%2Fn%2C%0Abinomial_icdf(30%2Cp%2C0.975)%2Fn%2C%0Ap-sqrt(1%2Fn)%2Cp%2Bsqrt(1%2Fn)%5D%2C%0Ap%3D0..1%2Ccolor%3D%5Bred%2Cred%2Cblack%2Cblack%5D)%3B&+///%20loi%20g%C3%A9om%C3%A9trique%20tronqu%C3%A9e%20(renvoie%20le%201er%20succ%C3%A8s%20ou%200)&+fonction%20geo(n%2Cp)%0A%20%20var%20k%2Ct%3B%0A%20%20pour%20k%20de%201%20jusque%20n%20faire%0A%20%20%20%20t%3A%3Dalea(0%2C1)%3B%0A%20%20%20%20si%20t%3C%3Dp%20alors%20retourne%20k%3B%20fsi%3B%0A%20%20fpour%3B%0A%20%20retourne%200%3B%0Affonction%3A%3B&+geo(10%2C.4)&+s%3A%3Dseq(geo(10%2C.4)%2C1000)&+histogramme(s%2C-0.5%2C1%2Ccouleur%3Dred)%3B%20%0Ahistogramme(geometric%2C0.4)&"
                                target="_blank">Xcas
                            </a>,
                            <a
                                href="#exec&python=1&+///%20simulation%20de%20$n$%20tirages%20au%20hasard%20avec%20probabilit%C3%A9%20$p$%20de%20succ%C3%A8s&+def%20Tirages(n%2Cp)%3A%0A%20%20%20%20%23%20local%20total%2Cj%2Ch%0A%20%20%20%20total%3D0%0A%20%20%20%20for%20j%20in%20range(n)%3A%0A%20%20%20%20%20%20%20%20h%3Drandom()%0A%20%20%20%20%20%20%20%20if%20h%3C%3Dp%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20total%3Dtotal%2B1%0A%20%20%20%20return%20total%0A&+Tirages(10%2C0.4)&+///%20histogramme%20de%201000%20tirages%20et%20comparaison%20avec%20l'histogramme%20de%20la%20loi%20binomiale&+s%3D%20%5BTirages(10%2C0.4)%20for%20j%20in%20range(1000)%5D&+histogramme(s%2C-0.5%2C1%2Ccouleur%3Dred)%3B%0Ahistogramme(binomial%2C10%2C0.4)&+///%20calcul%20de%20l'intervalle%20de%20confiance%20centr%C3%A9%20pour%20la%20loi%20binomiale&+%23%0An%3D100%0Ap%3D0.16%0Axmin%3Dbinomial_icdf(n%2Cp%2C0.025)%0Axmax%3Dbinomial_icdf(n%2Cp%2C0.975)&+%23%0Agl_x%3D0..40%0Agl_y%3D0..0.15%0Ahistogram(binomial%2Cn%2Cp)%0Acolor(droite(equal(x%2Cxmin))%2Cred)%0Acolor(droite(equal(x%2Cxmax))%2Cred)&+///%20programme%20de%20calcul%20de%20l'intervalle%20de%20confiance%20%C3%A0%20partir%20de%20la%20loi%20binomiale&+def%20confiance(n%2Cp%2Cseuil)%3A%0A%20%20%20%20%23%20local%20k%2Ctotal%0A%20%20%20%20total%3D0%0A%20%20%20%20for%20k%20in%20range(n%2B1)%3A%0A%20%20%20%20%20%20%20%20total%3Dtotal%2Bbinomial(n%2Cp%2Ck)%0A%20%20%20%20%20%20%20%20if%20total%3E%3Dseuil%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20return%20k%0A&+confiance(100%2C.16%2C0.025)&+confiance(100%2C.16%2C0.975)&+///%20comparaison%20avec%20$[p-1/sqrt(n),p+1/sqrt(n)]$&+%23%0An%3D30%0Aplotfunc(%5Bbinomial_icdf(30%2Cp%2C0.025)%2Fn%2Cbinomial_icdf(30%2Cp%2C0.975)%2Fn%2Cp-sqrt(1%2Fn)%2Cp%2Bsqrt(1%2Fn)%5D%2Cp%2C0%2C1)&+///%20loi%20g%C3%A9om%C3%A9trique%20tronqu%C3%A9e%20(renvoie%20le%201er%20succ%C3%A8s%20ou%200)&+def%20geo(n%2Cp)%3A%0A%20%20%20%20%23%20local%20k%2Ct%0A%20%20%20%20for%20k%20in%20range(n)%3A%0A%20%20%20%20%20%20%20%20t%3Drandom()%0A%20%20%20%20%20%20%20%20if%20t%3C%3Dp%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20return%20k%2B1%0A%20%20%20%20return%200%0A&+geo(10%2C.4)&+s%3D%5Bgeo(10%2C.4)%20for%20j%20in%20range(1000)%5D&+%23%0Acolor(histogramme(s%2C-0.5%2C1)%2Cred)%20%0Ahistogramme(geometric%2C0.4)&"
                                target="_blank">Python</a>
                        </li>
                        <li> Premi&egrave;re Triangle de Pascal
                            <a
                                href="#python=0&exec&+///%20Triangle%20de%20Pascal%20pour%20trouver%20les%20coefficients%20binomiaux&+fonction%20Pascal(n)%0A%20%20var%20tableau%2Cj%2Ck%3B%0A%20%20tableau%3A%3Dmatrix(n%2Cn)%3B%0A%20%20pour%20j%20de%200%20jusque%20n-1%20faire%0A%20%20%20%20tableau%5Bj%2C0%5D%3A%3D1%3B%0A%20%20%20%20pour%20k%20de%201%20jusque%20j%20faire%0A%20%20%20%20%20%20tableau%5Bj%2Ck%5D%3A%3Dtableau%5Bj-1%2Ck-1%5D%2Btableau%5Bj-1%2Ck%5D%3B%0A%20%20%20%20fpour%3B%0A%20%20fpour%3B%0A%20%20retourne%20tableau%3B%0Affonction%3A%3B&+Pascal(6)&"
                                target="_blank">
                            Xcas</a>,
                            <a href="#exec&python=1&+///Triangle%20de%20Pascal%20pour%20trouver%20les%20coefficients%20binomiaux.%0AOn%20calcule%20une%20ligne%20en%20fonction%20de%20la%20ligne%20pr%C3%A9c%C3%A9dente.&+def%20Pascal(n)%3A%0A%20%20%20%20%23%20local%20tableau%2Cligne%2Cj%2Ck%3B%0A%20%20%20%20tableau%3D%5B%5B1%5D%5D%0A%20%20%20%20for%20j%20in%20range(1%2Cn%2B1)%3A%0A%20%20%20%20%20%20%20%20ligne%3D%5B1%5D%0A%20%20%20%20%20%20%20%20for%20k%20in%20range(1%2Cj)%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20ligne.append(tableau%5Bj-1%5D%5Bk-1%5D%2Btableau%5Bj-1%5D%5Bk%5D)%0A%20%20%20%20%20%20%20%20ligne.append(1)%0A%20%20%20%20%20%20%20%20tableau.append(ligne)%3B%0A%20%20%20%20return%20tableau%0A&+Pascal(6)&"
                               target="_blank"><strong>Python</strong></a>
                        </li>
                        <li>
                            Terminale: Dichotomie
                            <a
                                href="#python=0&exec&+///Recherche%20d'une%20racine%20de%20$f$%20entre%20$a$%20et%20$b$%20par%20dichotomie,%20avec%20pr%C3%A9cision%20%3Ctt%3eeps%3C/tt%3e.%0aLa%20fonction%20%3Ctt%3edicho%3C/tt%3e%20commence%20par%20tester%20que%20le%20signe%20n'est%20pas%20identique%20en%20$a$%20et%20$b$.&+fonction%20dicho(f%2Ca%2Cb%2Ceps)%0A%20%20var%20c%2Cniter%3B%0A%20%20si%20f(a)*f(b)%3E%3D0%20alors%20retourne%20%22erreur%3A%20pas%20de%20changement%20de%20signe%22%3B%20fsi%3B%0A%20%20tantque%20abs(b-a)%3Eeps%20faire%0A%20%20%20%20c%3D(a%2Bb)%2F2%3B%0A%20%20%20%20si%20f(a)*f(c)%3E0%20alors%20a%3Dc%3B%20sinon%20b%3Dc%3B%20fsi%3B%0A%20%20ftantque%0A%20%20retourne%20c%3B%0Affonction%3A%3B&+f(x)%3A%3Dcos(x)-x%3B&+plot(f(x)%2Cx%2C0%2C2)&+dicho(f%2C0.0%2C1.0%2C1e-8)&"
                                target="_blank">
                            Xcas
                            </a>,
                            <a
                                href="#exec&python=1&+///Recherche%20d'une%20racine%20de%20$f$%20entre%20$a$%20et%20$b$%20par%20dichotomie,%20avec%20pr%C3%A9cision%20eps&+def%20dicho(f%2Ca%2Cb%2Ceps)%3A%0A%20%20%20%20%23%20local%20c%2Cniter%3B%0A%20%20%20%20if%20f(a)*f(b)%3E%3D0%3A%20%0A%20%20%20%20%20%20%20%20return%20%22erreur%3A%20f(a)*f(b)%3E%3D0%22%0A%20%20%20%20while%20b-a%3Eeps%3A%0A%20%20%20%20%20%20%20%20c%3D(a%2Bb)%2F2.0%0A%20%20%20%20%20%20%20%20if%20f(a)*f(c)%3E0%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20a%3Dc%0A%20%20%20%20%20%20%20%20else%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20b%3Dc%0A%20%20%20%20return%20c%0A&+def%20f(x)%3A%0A%20%20%20%20return%20cos(x)-x&+plot(f(x)%2Cx%2C0%2C2)&+dicho(f%2C0.0%2C1.0%2C1e-8)&"
                                target="_blank"><strong>Python</strong></a>
                        </li>
                        <li>
                            Terminale, Calcul approch&eacute; d'int&eacute;grales.
                            <a
                                href="#exec&python=0&+///Calcul%20approche%20d'int%C3%A9grale%20par%20la%20m%C3%A9thode%20des%20rectangles%20(%C3%A0%20droite),%20du%20point%20milieu%20et%20de%20Mont%C3%A9-Carlo.&+f(x)%3A%3Dsin(x)&+plot(f(x)%2Cx%2C0%2C1)%3B%20droite(y%3D0)%3B&+fonction%20Rect(f%2Ca%2Cb%2CN)%0A%20%20var%20S%3B%0A%20%20S%3A%3D0.0%3B%0A%20%20h%3A%3D(b-a)%2FN%3B%0A%20%20pour%20j%20de%201%20jusque%20N%20faire%0A%20%20%20%20S%3A%3DS%2Bf(a%2Bj*h)%3B%0A%20%20fpour%3B%0A%20%20retourne%20S*h%3B%0Affonction%3A%3B&+Rect(f%2C0%2C1%2C100)&+integrate(f(x)%2Cx%2C0%2C1.0)&+///Pour%20le%20point%20milieu%20on%20remplace%20%3Ctt%3ef(a+j*h)%3C/tt%3e%20par%20%3Ctt%3ef(a-h/2+j*h)%3C/tt%3e&+fonction%20pointmilieu(f%2Ca%2Cb%2CN)%0A%20%20var%20S%3B%0A%20%20S%3A%3D0.0%3B%0A%20%20h%3A%3D(b-a)%2FN%3B%0A%20%20pour%20j%20de%201%20jusque%20N%20faire%0A%20%20%20%20S%3A%3DS%2Bf(a-h%2F2%2Bj*h)%3B%0A%20%20fpour%3B%0A%20%20retourne%20S*h%3B%0Affonction%3A%3B&+pointmilieu(f%2C0%2C1%2C100)&+///%20Observer%20la%20pr%C3%A9cision%20bien%20meilleure,%20pour%20un%20cout%20de%20calcul%20quasi-identique.%20Intuitivement%20le%20rectangle%20correspondant%20approche%20mieux%20la%20fonction.&+plot(f(x)%2Cx%2C0%2C1)%3B%0Arectangle(0%2C1%2Cf(1)%2Ccolor%3Dred)%3B%20%0Arectangle(0%2C1%2Cf(1%2F2)%2Ccolor%3Dgreen)&+///Estimation%20par%20la%20m%C3%A9thode%20de%20Monte-Carlo.%20On%20fait%20plusieurs%20fois%20le%20calcul%20de%20la%20moyenne%20de%20$n$%20valeurs%20pour%20tracer%20l'histogramme%20des%20approximations%20obtenues%20et%20illustrer%20un%20%C3%A9cart%20en%20$1/sqrt(n)$.&+fonction%20Montecarlo(f%2Ca%2Cb%2Cn)%0A%20%20local%20k%2Cr%3B%0A%20%20r%3A%3D0%3B%0A%20%20pour%20k%20de%201%20jusque%20n%20faire%0A%20%20%20%20r%3A%3Dr%2Bf(alea(uniformd%2Ca%2Cb))%3B%0A%20%20fpour%3B%0A%20%20retourne%20r*(b-a)%2Fn%3B%0Affonction%3A%3B&+n%3A%3D100%3BMontecarlo(f%2C0%2C1%2Cn)&+N%3A%3D800%3B%0Al%3A%3Dseq(Montecarlo(f%2C0%2C1%2Cn)%2CN)%3B%0Ahistogram(l%2C0%2C0.005)%3B%0Am%3A%3D1-cos(1)%3B%0Adroite(x%3Dm%2Ccolor%3Dred)%3B%0Aplot(normald(m%2Cstddev(l)%2Cx)%2Cx%3D0.35..0.55)&"
                                target="_blank">Xcas
                            </a>,
                            <a
                                href="#exec&python=1&+///Calcul%20approch%C3%A9%20d'int%C3%A9grale%20par%20la%20m%C3%A9thode%20des%20rectangles%20(%C3%A0%20droite),%20puis%20par%20le%20point%20milieu.&+f%3Dsin&+plot(f(x)%2Cx%2C0%2C1)%3B%20droite(y%3D0)%3B&+def%20Rect(f%2Ca%2Cb%2CN)%3A%0A%20%20%20%20%23%20local%20S%2Ch%2Cj%0A%20%20%20%20S%3D0.0%0A%20%20%20%20h%3D(b-a)%2F(N*1.0)%0A%20%20%20%20for%20j%20in%20range(N)%3A%0A%20%20%20%20%20%20%20%20S%3DS%2Bf(a%2Bh%2Bj*h)%0A%20%20%20%20return%20S*h&+Rect(f%2C0%2C1%2C100)&+integrate(f(x)%2Cx%2C0%2C1.0)&+///Pour%20le%20point%20milieu,%20on%20remplace%20%3Ctt%3ef(a+j*h)%3C/tt%3e%20par%20%3Ctt%3ef(a-h/2+j*h)%3C/tt%3e&+def%20Pointmilieu(f%2Ca%2Cb%2CN)%3A%0A%20%20%20%20%23%20local%20S%2Ch%2Cj%0A%20%20%20%20S%3D0.0%0A%20%20%20%20h%3D(b-a)%2F(N*1.0)%0A%20%20%20%20for%20j%20in%20range(N)%3A%0A%20%20%20%20%20%20%20%20S%3DS%2Bf(a%2Bh%2F2%2Bj*h)%0A%20%20%20%20return%20S*h&+Pointmilieu(f%2C0%2C1%2C100)&+///%20Observer%20la%20pr%C3%A9cision%20bien%20meilleure,%20pour%20un%20cout%20de%20calcul%20quasi-identique.%20Intuitivement%20le%20rectangle%20correspondant%20approche%20mieux%20la%20fonction.&+plot(f(x)%2Cx%2C0%2C1)%3B%0Arectangle(0%2C1%2Cf(1)%2Ccolor%3Dred)%3B%20%0Arectangle(0%2C1%2Cf(1%2F2)%2Ccolor%3Dgreen)&+def%20Montecarlo(f%2Ca%2Cb%2Cn)%3A%0A%20%20%20%20%23%20local%20k%2Cr%2Cx%0A%20%20%20%20%23%20faire%20import%20random%20as%20random%20en%20Python%0A%20%20%20%20r%3D0%0A%20%20%20%20for%20k%20in%20range(n)%3A%0A%20%20%20%20%20%20%20%20r%3Dr%2Bf(random.uniform(a%2Cb))%0A%20%20%20%20return(r*(b-a)%2Fn)&+///M%C3%A9thode%20probabiliste%20de%20Mont%C3%A9-Carlo.%20On%20l'ex%C3%A9cute%20ensuite%20un%20grand%20nombre%20de%20fois%20($n$)%20et%20on%20trace%20l'histogramme%20des%20valeurs%20approch%C3%A9es%20obtenues%20pour%20mettre%20en%20%C3%A9vidence%20la%20pr%C3%A9cision%20en%20$1/sqrt(n)$%0aCliquez%20sur%20le%20bouton%20Exec%20pour%20refaire%20une%20simulation.&+%23%0An%3D100%0AMontecarlo(f%2C0%2C1%2Cn)&+%23%0AN%3D800%3B%0Al%3D%5BMontecarlo(f%2C0%2C1%2Cn)%20for%20j%20in%20range(N)%5D%0Ahistogram(l%2C0%2C0.01)%0Am%3D1-cos(1)%0Adroite(x%3D%3D%3Dm%2Ccolor%3D%3D%3Dred)%3B%0Aplot(normald(m%2Cstddev(l)%2Cx)%2Cx%3D%3D%3D0.35..0.55)&"
                                target="_blank"><strong>Python</strong></a>
                        </li>
                        <li>
                            Terminale: distribution cumul&eacute;e
                            <a
                                href="#exec&python=0&+///Illustration%20de%20la%20probabilit%C3%A9%20cumul%C3%A9e%20entre%202%20bornes%20$a$%20et%20$b$.%0aOn%20peut%20changer%20de%20loi,%20par%20exemple%20prendre%20exponentiald(1),%20il%20faut%20alors%20prendre%20garde%20aux%20valeurs%20de%20$a$%20et%20$b$%20et%20modifier%20x=-5..5%20par%20exemple%20en%20x=0..6&+loi%3A%3Dnormald(0%2C1)&*a,0,-5,5,0.125&*b,1.25,-5,5,0.125&+plotarea(loi(x)%2Cx%3Dmin(a%2Cb)..max(a%2Cb))%3B%0Aplotfunc(loi(x)%2Cx%3D-5..5)%3B%0A&+///Calcul%20d'intervalle%20de%20confiance%20bilat%C3%A9ral%20pour%20la%20loi%20au%20seuil%20alpha&+alpha%3A%3D0.05%3A%3B%0Aicdf(loi%2Calpha%2F2)%2Cicdf(loi%2C1-alpha%2F2)&"
                                target="_blank">loi normale</a>
                        </li>
                        <li>
                            <a
                                href="#exec&python=0&+n%3A%3D2%5E13%3B%0Al%3A%3Dseq(%0A%20%20%20%20sum(ranv(n%2Cuniformd%2C0%2C1))%2Fn-0.5%2C%0A%20%20%20%20400)&+sigma%3A%3Dstddev(uniformd%2C0%2C1)%3B%0Aevalf(sigma%2Fsqrt(n))%0A&+histogram(l%2C-0.01%2C0.001)%3B%0Aplot(normald(0%2Csigma%2Fsqrt(n)%2Cx)%2Cx%3D-0.01..0.01)&"
                                target="_blank">
                            Convergence d'une moyenne vers la loi normale.
                            </a>
                        </li>
                        <li> PGCD binaire:
                            <a
                                href="#exec&python=0&+///Le%20PGCD%20binaire%20calcule%20le%20PGCD%20de%202%20entiers%20%24a%24%20et%20%24b%24%20sans%20effectuer%20de%20division%2C%20sauf%20par%202%20(qui%20est%20un%20d%C3%A9calage%20pour%20un%20nombre%20%C3%A9crit%20en%20base%202).%0AOn%20commence%20par%20extraire%20%24n%24%2C%20la%20puissance%20de%202%20la%20plus%20grande%20possible%20de%20%24a%24%20et%20de%20%24b%24%2C%20%242%5En%24%20sera%20le%20facteur%20correspondant%20du%20PGCD.%20%0AOn%20est%20ramen%C3%A9%20%C3%A0%20%24a%24%20et%20%24b%24%20impairs%2C%20leur%20PGCD%20est%20celui%20de%20(%24a%24%20ou%20%24b%24)%20et%20%24a-b%24.%20Comme%20%24a-b%24%20est%20pair%20on%20divise%20par%202%20tant%20qu'on%20peut%20sans%20changer%20le%20PGCD%2C%20on%20est%20ramen%26eacute%3B%20au%20PGCD%20de%20%24min(a%2Cb)%24%20et%20%24abs(a-b)%2F2%5Ek%24%20avec%20%24k%3E%3D1%24%20le%20plus%20grand%20possible.&+///%3Cstrong%3EExercice%3A%3C%2Fstrong%3E%20%C3%A9crire%20cet%20algorithme%20avec%20une%20fonction%20r%C3%A9cursive.%0ACi-dessous%20une%20version%20it%C3%A9rative%20un%20peu%20plus%20longue.&+fonction%20pgcd(a%2Cb)%20%2F%2F%20pgcd%20binaire%0A%20%20local%20n%3B%0A%20%20a%3A%3Dabs(a)%3B%20b%3A%3Dabs(b)%3B%0A%20%20si%20a%3D0%20alors%20return%20b%3B%20fsi%3B%0A%20%20si%20b%3D0%20alors%20return%20a%3B%20fsi%3B%0A%20%20pour%20n%20de%200%20jusque%20a%20faire%20%0A%20%20%20%20si%20irem(a%2C2)%3D1%20alors%20%0A%20%20%20%20%20%20tantque%20irem(b%2C2)%3D0%20faire%20%0A%20%20%20%20%20%20%20%20b%3A%3Diquo(b%2C2)%3B%20%0A%20%20%20%20%20%20ftantque%3B%20break%3B%0A%20%20%20%20fsi%3B%0A%20%20%20%20si%20irem(b%2C2)%3D1%20alors%20%0A%20%20%20%20%20%20tantque%20irem(a%2C2)%3D0%20faire%20%0A%20%20%20%20%20%20%20%20a%3A%3Diquo(a%2C2)%3B%20%0A%20%20%20%20%20%20ftantque%3B%20break%3B%20%0A%20%20%20%20fsi%3B%0A%20%20%20%20a%3A%3Diquo(a%2C2)%3B%0A%20%20%20%20b%3A%3Diquo(b%2C2)%3B%0A%20%20fpour%3B%20%0A%20%20%2F%2F%20a%20et%20b%20sont%20impairs%20-%3E%20pgcd%3Dpgcd(min(a%2Cb)%2Cabs(a-b)%2F2%5Ek)%0A%20%20tantque%20vrai%20faire%0A%20%20%20%20si%20a%3Cb%20alors%20a%2Cb%3A%3Db%2Ca%3B%20fsi%3B%0A%20%20%20%20a%2Cb%3A%3Db%2Cabs(a-b)%2F2%3B%0A%20%20%20%20si%20b%3D0%20alors%20return%202%5En*a%3B%20fsi%3B%0A%20%20%20%20tantque%20irem(b%2C2)%3D0%20faire%20b%3A%3Diquo(b%2C2)%3B%20ftantque%3B%0A%20%20ftantque%3B%0Affonction%3A%3B&+pgcd(15%2C25)&+pgcd(15%2C50)&+pgcd(30%2C50)&"
                                target="_blank">Xcas</a>
                        </li>
                        <li>
                            <a
                                href="#exec&python=0&+def%20bezout(a%2Cb)%3A%0A%20%20%20%20%23%20local%20l1%2Cl2%2Cq%0A%20%20%20%20l1%3D%5B1%2C0%2Ca%5D%0A%20%20%20%20l2%3D%5B0%2C1%2Cb%5D%0A%20%20%20%20while%20l2%5B2%5D!%3D0%3A%0A%20%20%20%20%20%20%20%20q%3Dl1%5B2%5D%2F%2Fl2%5B2%5D%0A%20%20%20%20%20%20%20%20l1%2Cl2%3Dl2%2C%5Bl1%5B0%5D-q*l2%5B0%5D%2Cl1%5B1%5D-q*l2%5B1%5D%2Cl1%5B2%5D-q*l2%5B2%5D%5D%0A%20%20%20%20return%20l1&+bezout(15%2C25)&+fonction%20bezout(a%2Cb)%0A%20%20local%20l1%2Cl2%2Cq%3B%0A%20%20l1%3A%3D%5B1%2C0%2Ca%5D%3B%0A%20%20l2%3A%3D%5B0%2C1%2Cb%5D%3B%0A%20%20tantque%20l2%5B2%5D!%3D0%20faire%0A%20%20%20%20q%3A%3Diquo(l1%5B2%5D%2Cl2%5B2%5D)%3B%0A%20%20%20%20l1%2Cl2%3A%3Dl2%2Cl1-q*l2%3B%0A%20%20ftantque%3B%0A%20%20return%20l1%3B%0Affonction%3A%3B&+bezout(15%2C25)&"
                                target="_blank">
                            <strong>Identit&eacute; de B&eacute;zout.</strong></a>
                        </li>
                        <li>
                            <a href="#exec&python=1&+//Trois%20enfants%20A%2C%20B%2C%20C%20jouent%20%C3%A0%20la%20balle.%20Lorsque%20A%20a%20la%20balle%2C%20il%20l'envoie%20avec%20probabilit%C3%A9%203%2F4%20vers%20B%20et%201%2F4%20vers%20C%2C%20lorsque%20B%20a%20la%20balle%2C%20il%20l'envoie%20vers%20A%20avec%20probabilit%C3%A9%203%2F4%20et%20vers%20C%20avec%20probabilit%C3%A9%201%2F4%2C%20lorsque%20A%20a%20la%20balle%20il%20l'envoie%20vers%20B.&+m%3A%3D%5B%5B0%2C3%2F4%2C1%2F4%5D%2C%5B3%2F4%2C0%2C1%2F4%5D%2C%5B0%2C1%2C0%5D%5D&+axes%3D0%3B%20plotproba(m%2C%5B%22A%22%2C%22B%22%2C%22C%22%5D)&+p%3A%3Dmarkov(m)&+//La%20probabilit%C3%A9%20invariante%20est%20donc%20(12%2F35%2C16%2F35%2C1%2F5)&+p%5B1%5D*m%3B%20evalf(p%5B1%5D)&+//Simulation%20de%20lancers%20et%20comparaison%20du%20nombre%20de%20fois%20que%20le%20ballon%20est%20en%20A%2C%20B%20ou%20C%20avec%20la%20probabilit%C3%A9%20invariante.&+s%3A%3Drandmarkov(m%2C1%2C1000)&+count_eq(0%2Cs)%3B%20count_eq(1%2Cs)%3B%20count_eq(2%2Cs)&"
                               target="_blank">
                            Marche al&eacute;atoire sur un graphe</a>
                        </li>
                        <li>
                            <a href="#exec&python=0&+///Algorithme%20de%20recherche%20du%20plus%20court%20chemin%20d'un%20sommet%20%3Ctt%3Esource%3C%2Ftt%3E%20aux%20autres%20sommets%20du%20graphe.&+fonction%20Dijkstra(G%2Csource)%0A%20%20%2F%2F%20G%20matrice%20carree%20symetrique%20de%20taille%20n%20donnant%20la%20longueur%20%0A%20%20%2F%2F%20du%20sommet%20i%20au%20sommet%20j%0A%20%20%2F%2F%20renvoie%20la%20plus%20courte%20longueur%20et%20le%20sommet%20pr%C3%A9c%C3%A9dent%0A%20%20local%20v%2Ctodo%2Ctodov%2Cj%2Cdist%2Cdistv%2Calt%2Cprev%2Cn%3B%0A%20%20n%3A%3Dsize(G)%3B%0A%20%20%2F%2F%20initialisation%0A%20%20todo%3A%3Dseq(j%2Cj%2C0%2Cn-1)%3B%20dist%3A%3D%5Binf%24n%5D%3B%20prev%3A%3D%5B-1%24n%5D%3B%20dist%5Bsource%5D%3D%3C0%3B%0A%20%20tantque%20size(todo)!%3D0%20faire%0A%20%20%20%20%2F%2F%20sommet%20realisant%20la%20longueur%20min%20parmi%20ceux%20restant%0A%20%20%20%20v%3A%3D0%3B%20%0A%20%20%20%20todov%3A%3Dtodo%5Bv%5D%3B%20%0A%20%20%20%20distv%3A%3Ddist%5Btodov%5D%3B%0A%20%20%20%20pour%20j%20de%200%20jusque%20size(todo)-1%20faire%20%0A%20%20%20%20%20%20si%20dist%5Btodo%5Bj%5D%5D%3Cdistv%20alors%20v%3A%3Dj%3B%20todov%3A%3Dtodo%5Bv%5D%3B%20distv%3A%3Ddist%5Btodo%5Bj%5D%5D%3B%20fsi%3B%20%0A%20%20%20%20fpour%3B%0A%20%20%20%20si%20distv%3D%3Dinf%20alors%20return%20dist%2Cprev%3B%20fsi%3B%20%2F%2F%20fin%20algo%20prematuree%0A%20%20%20%20todo%3A%3Dsuppress(todo%2Cv)%3B%20%2F%2F%20supprime%20todo%5Bv%5D%0A%20%20%20%20%2F%2F%20cherche%20les%20distances%20en%20passant%20par%20todo%5Bv%5D%0A%20%20%20%20for%20j%20in%20todo%20do%0A%20%20%20%20%20%20alt%3A%3Ddistv%2BG%5Btodov%2Cj%5D%3B%0A%20%20%20%20%20%20si%20alt%3Cdist%5Bj%5D%20alors%20dist%5Bj%5D%3A%3Dalt%3B%20prev%5Bj%5D%3A%3Dtodov%3B%20fsi%3B%0A%20%20%20%20od%3B%0A%20%20ftantque%3B%0A%20%20return%20dist%2Cprev%3B%0Affonction%3A%3B&+///On%20g%C3%A9n%C3%A8re%20une%20matrice%20%24G%24%20sym%C3%A9trique%20de%20mani%C3%A8re%20al%C3%A9atoire%20%C3%A0%20coefficients%20positifs%2C%20on%20met%20%C3%A0%200%20la%20diagonale.&+G0%3A%3Drandmatrix(5%2C5%2Calea(50)%2B1)%3B%0AG%3A%3DG0%2Btran(G0)%3B%20%0Apour%20j%20de%200%20jusque%204%20faire%20G%5Bj%2Cj%5D%3A%3D0%20fpour&+Dijkstra(G%2C0)&+Dijkstra(G%2C1)&"
                               target="_blank">
                            algorithme de Dijkstra
                            </a>
                        </li>
                        <li>
                            Jour de la semaine:
                            <a
                                href="#exec&python=0&+fonction%20jour_semaine0(j%2Cm%2Ca)%0A%20%20local%20J%2CL%2CSL%2Ca1%2Cb%2Cbi%3B%0A%20%20J%3A%3D%5B%22Dimanche%22%2C%22Lundi%22%2C%22Mardi%22%2C%22Mercredi%22%2C%22Jeudi%22%2C%22Vendredi%22%2C%22Samedi%22%5D%3B%0A%20%20a1%3A%3Da-1%3Bbi%3A%3D0%3B%0A%20%20si%20(irem(a%2C4)%3D%3D0%20and%20irem(a%2C100)!%3D0)%20or%20irem(a%2C400)%3D%3D0%20alors%0A%20%20%20%20bi%3A%3D1%3B%0A%20%20fsi%3B%0A%20%20si%20(m%3D%3D1)%20ou%20(m%3D%3D2)%20alors%0A%20%20%20%20b%3A%3Da1%2Biquo(a1%2C4)%2Biquo(a1%2C400)-iquo(a1%2C100)%2B(iquo(23*m%2C9)%2B5)%2Bj%3B%0A%20%20%20%20sinon%0A%20%20%20%20b%3A%3Da1%2Bbi%2Biquo(a1%2C4)%2Biquo(a1%2C400)-iquo(a1%2C100)%2B(iquo(23*m%2C9)%2B3)%2Bj%3B%0A%20%20fsi%3B%0A%20%20return%20J%5Birem(b%2C7)%5D%3B%0Affonction%3A%3B%0A%0Afonction%20jour_semaine(j%2Cm%2Ca)%0A%20%20local%20J%2CL%2CSL%2Ca1%2Cb%3B%0A%20%20a1%3A%3Da-1%3B%0A%20%20L%3A%3D%5B0%2C31%2C28%2C31%2C30%2C31%2C30%2C31%2C31%2C30%2C31%2C30%5D%3B%0A%20%20J%3A%3D%5B%22Dimanche%22%2C%22Lundi%22%2C%22Mardi%22%2C%22Mercredi%22%2C%22Jeudi%22%2C%22Vendredi%22%2C%22Samedi%22%5D%3B%0A%20%20si%20(irem(a%2C4)%3D%3D0%20and%20irem(a%2C100)!%3D0)%20or%20irem(a%2C400)%3D%3D0%20alors%0A%20%20%20%20L%5B2%5D%3A%3D29%3B%0A%20%20fsi%3B%0A%20%20SL%3A%3Direm(cumSum(L)%2C7)%3B%0A%20%20b%3A%3Da1%2Biquo(a1%2C4)%2Biquo(a1%2C400)-iquo(a1%2C100)%2BSL%5Bm-1%5D%2Bj%3B%0A%20%20return%20J%5Birem(b%2C7)%5D%3B%0Affonction%3A%3B&+jour_semaine0(5%2C4%2C2018)&+jour_semaine(5%2C4%2C2018)&"
                                target="_blank">Xcas</a>
			</li>
			<li>
			<a
			href="#exec&python=0&+///%3Ca%20href%3D%22http%3A%2F%2Fwww.les-mathematiques.net%2Fphorum%2Ffile.php%3F6%2Cfile%3D78088%2Cfilename%3Dfre2.pdf%22%20target%3D%22_blank%22%3EProbl%C3%A8me%206%20olympiades%20maths.%3C%2Fa%3E%0AOn%20d%C3%A9finit%20une%20fonction%20qui%20calcule%20la%20tangente%20d'un%20angle%2C%20det%20permet%20de%20calculer%20le%20d%C3%A9terminant%202x2%20pour%20trouver%20le%20sinus%2C%20*%20calcule%20le%20produit%20scalaire.&+def%20Tan(A%2CB%2CC)%3A%0A%20%20%23%20A%2CB%2CC%20listes%2C%20tangente%20angle%20issu%20de%20B%3Dsin%2Fcos%20%0A%20%20%23%20avec%20cos%3Dvecteur(B%2CA).vecteur(B%2CC)%20et%20sin%3Ddet(vecteur(B%2CA)%2Cvecteur(B%2CC))%0A%20%20BA%3DA-B%3B%0A%20%20BC%3DC-B%3B%0A%20%20return%20det(BA%2CBC)%2F(BA*BC)&+A%3A%3D%5B0%2C0%5D%3B%20B%3A%3D%5Bb%2C0%5D%3B%20%20%0AC%3A%3D%5Bc1%2Cc2%5D%3B%20D%3A%3D%5Bd1%2Cd2%5D%3B%0AX%3A%3D%5Bx1%2Cx2%5D%3B&+///Par%20invariance%20par%20translation%20on%20peut%20prendre%20%24A%24%20en%20l'origine%2C%20et%20par%20rotation%20%24B%24%20sur%20l'axe%20des%20%24x%24%20(on%20pourrait%20par%20dilatation%20prendre%20%24b%3D1%24).&+///eq1%2C%20eq2%2C%20eq3%20sont%20la%20mise%20en%20%C3%A9quation%20des%203%20contraintes.%20eq4%20est%20la%20relation%20cherch%C3%A9e.&+eq1%3A%3D((B-A)*(B-A))*((D-C)*(D-C))-%0A%20%20((C-B)*(C-B))*((D-A)*(D-A))&+eq2%3A%3DTan(X%2CA%2CB)-Tan(X%2CC%2CD)&+eq3%3A%3DTan(X%2CB%2CC)-Tan(X%2CD%2CA)&+eq4%3A%3DTan(B%2CX%2CA)%2BTan(D%2CX%2CC)&+v%3A%3D%5Bb%2Cc1%2Cc2%2Cd1%2Cd2%2Cx1%2Cx2%5D&+Eq2%3A%3Dnumer(eq2)%3A%3B%20Eq3%3A%3Dnumer(eq3)%3A%3B&+degree(Eq2%2Cv)%3Bdegree(Eq3%2Cv)&+%5BD1%5D%3A%3Dsolve(eq2%3D0%2Cd1)&+///On%20peut%20donc%20r%C3%A9soudre%20eq2%20en%20d1%20ou%20d2%2C%20ou%20eq3%20en%20c1%20ou%20c2%20(premier%20degr%C3%A9).&+Eq1_%3A%3Dnumer(eq1(d1%3DD1))%3A%3B%0Adegree(Eq1_%2Cv)%3B&+Eq3_%3A%3Dnumer(eq3(d1%3DD1))%3A%3B%0Adegree(Eq3_%2Cv)%3B&+///On%20obtient%20deux%20%C3%A9quations%20de%20degr%C3%A9%202%20en%20%24b%24%20ou%20en%20%24d2%24%2C%20en%20faisant%20la%20combinaison%20lin%C3%A9aire%20ad%C3%A9quate%20on%20se%20ram%C3%A8ne%20%C3%A0%20une%20%C3%A9quation%20de%20degr%C3%A9%201%20en%20%24d2%24%2C%20qu'on%20r%C3%A9soud.&+Eq_%3A%3DEq1_*coeff(Eq3_%2Cd2%2C2)-%0A%20%20Eq3_*coeff(Eq1_%2Cd2%2C2)%3B%0A%5BD2%5D%3A%3Dsolve(Eq_%3D0%2Cd2)&+///On%20subtitue%20la%20valeur%20de%20d1%20et%20de%20d2%20dans%20eq4%2C%20on%20trouve%20bien%200.&+normal(subst(eq4(d1%3DD1)%2Cd2%3DD2))&+///Malheureusement%2C%20la%20preuve%20n'est%20pas%20complete.%20Il%20faut%20en%20effet%20verifier%20que%20l'equation%20qu'on%20resoud%20en%20d2%20n'est%20pas%20identiquement%20nulle.%20Or%20ceci%20peut%20arriver%3A&+cnd%3A%3Dfactor(gcd(coeffs(Eq_%2Cd2))&+///%24x1%5E2%2Bx2%5E2%24%20est%20non%20nul%2C%20de%20meme%20que%20%24(c1-x1)%5E2%2B(c2-x2)%5E2%24%20(points%20distincts).%20%24c2*x1-c1*x2%24%20est%20nul%20si%20%24A%24%2C%20%24C%24%20et%20%24X%24%20sont%20alignes.%20En%20fait%20ces%203%20facteurs%20n'interviennent%20pas%20si%20on%20utilise%20les%20bases%20de%20Groebner%2C%20ci-dessous.&+///La%20solution%20automatiquement%20avec%20des%20bases%20de%20Groebner%20et%20un%20ordre%20d'%C3%A9limination.&+G%3A%3Dgbasis(%5Bnumer(eq1)%2C%0A%20%20numer(eq2)%2Cnumer(eq3)%5D%2C%0A%20%20%5Bd1%2Cd2%5D)&+size(G)&+seq(degree(G%5Bj%5D%2C%5Bd1%2Cd2%5D)%2C%0A%20%20j%2C0%2Csize(G)-1)&+///On%20peut%20resoudre%20G%5B35%5D%20en%20%24d2%24%20si%20le%20facteur%20commun%20de%20degre%20total%205%20en%20%24b%2Cc1%2Cc2%2Cx1%2Cx2%24%20est%20non%20nul.&+factor(G%5B35%5D)%3B&+%5BD2%5D%3A%3Dsimplify(solve(G%5B35%5D%3D0%2Cd2))&+///On%20ne%20peut%20pas%20eliminer%20ce%20facteur%20commun%3A&+factor(gcd(%0A%20%20gcd(coeffs(G%5B33%5D%2Cd1))%2C%0A%20%20gcd(coeffs(G%5B34%5D%2Cd1))%2C%0A%20%20gcd(coeffs(G%5B35%5D%2Cd1)%0A%20%20)))&+///Si%20ce%20facteur%20est%20non%20nul%2C%20alors%20on%20conclut%20comme%20avant%3A&+%5BD1%5D%3A%3Dsolve(G%5B32%5D%3D0%2Cd1)&+normal(%0A%20%20subst(%0A%20%20%20%20subst(eq4%2Cd1%3DD1)%2C%0A%20%20%20%20d2%3DD2)&+///En%20fait%20si%20on%20elimine%20d1%20et%20d2%20des%203%20equations%2C%20on%20obtient%20le%20produit%20de%203%20facteurs%2C%20le%20premier%20etant%20non%20nul%20(%24X!%3DA%24)%2C%20l'un%20des%20deux%20facteurs%20restants%20est%20nul%2C%20c'est%20la%20condition%20que%20doit%20verifier%20%24X%24%20pour%20que%20les%203%20contraintes%20soient%20satisfaites.%20Or%20quand%20le%20troisieme%20facteur%20(de%20degre%20total%205)%20est%20nul%2C%20l'equation%20qui%20nous%20a%20permis%20de%20determiner%20d2%20est%20identiquement%20nulle.&+G36%3A%3Dfactors(G%5B36%5D)%3B%20size(G36)&+G36%5B2%5D&+///Au%20passage%2C%20on%20observe%20que%20si%20le%20deuxieme%20facteur%20(de%20degre%20total%204)%20s'annule%2C%20alors%20les%203%20contraintes%20sont%20bien%20verifiees.&+factors(eq1__%3A%3Dnumer(Eq1_(d2%3DD2)))&+factors(eq3__%3A%3Dnumer(Eq3_(d2%3DD2))&+///On%20ajoute%20la%20condition%20G36%5B4%5D%20pour%20determiner%20x1%20et%20x2&+H%3A%3Dgbasis(%5Bnumer(eq1)%2C%0A%20%20numer(eq2)%2Cnumer(eq3)%2CG36%5B4%5D%5D%2C%0A%20%20%5Bx1%2Cx2%5D)&+seq(degree(H%5Bj%5D%2Cv)%2Cj%2C0%2Csize(H)-1)%3Bsize(H)&+%5BX2%5D%3A%3Dsolve(H%5B64%5D%3D0%2Cx2)&+v%3Bdegree(H%5B56%5D%2Cv)%0A&+H56%3A%3Dnumer(subst(H%5B56%5D%2Cx2%3DX2))&+gcd(coeffs(H%5B56%5D%2Cx1))%0A&+%5BX1%5D%3A%3Dsolve(H%5B56%5D%3D0%2Cx1)&+///On%20verifie%20que%20eq2%20et%20eq3%20sont%20ok&+g364%3A%3Dnumer(subst(G36%5B4%5D(x1%3DX1)%2Cx2%2CX2))&+rem(g364%2Ceq1%2Cb)&+eq22%3A%3Dnumer(subst(eq2(x1%3DX1)%2Cx2%2CX2))&+rem(eq22%2Ceq1%2Cb)&+eq33%3A%3Dnumer(subst(eq3(x1%3DX1)%2Cx2%2CX2)&+rem(eq33%2Ceq1%2Cb)&+///Resterait%20a%20verifier%20que%20x1%2Cx2%20n'est%20pas%20dans%20le%20quadrilatere%3F%0AOn%20peut%20aussi%20calculer%20x1%2C%20x2%20en%20fonction%20de%20A%2CB%2CC%2CD%20dans%20le%20cas%20%22normal%22%2C%20de%20la%20meme%20facon.&+K%3A%3Dgbasis(%5Bnumer(eq1)%2C%0A%20%20numer(eq2)%2Cnumer(eq3)%2CG36%5B2%5D%5D%2C%0A%20%20%5Bx1%2Cx2%5D)&+seq(degree(K%5Bj%5D%2Cv)%2Cj%2C0%2Csize(K)-1)%3Bsize(K)&+%5BX2%5D%3A%3Dsolve(K%5B106%5D%3D0%2Cx2)&+K56%3A%3Dnumer(subst(K%5B100%5D%2Cx2%3DX2))&+gcd(coeffs(K%5B100%5D%2Cx1))&+%5BX1%5D%3A%3Dsolve(K%5B100%5D%3D0%2Cx1)&+///Il%20y%20a%20donc%20pour%20tout%20quadrilatere%20verifiant%20AB*CD%3DAC*BD%2C%202%20points%20X%20verifiant%20les%202%20conditions%20d'angle.%20On%20a%20determine%20leurs%20coordonnees%20(qui%20dependent%20rationnellement%20des%20coordonnees%20de%20A%2C%20B%2C%20C%20et%20D)%2C%20et%20montre%20qu'un%20de%20ces%20deux%20points%20verifie%20la%20propriete%20de%20l'exercice.&"
target="_blank">Olympiades de maths 2018, probl&egrave;me 6</a>
			</li>
                    </ul>
                </div>
            <li style="display:inline">
                <button class="bouton"
                        onclick="var tmp=$id('tutoex2'); if (tmp.style.display=='none') tmp.style.display='block'; else tmp.style.display='none';">
                <strong>Exemples</strong></button>
                <div id="tutoex2" style="display:none">
                    <ul>
                        <li> Nombres flottants (Licence):
                            <a
                                href="#exec&python=0&+///%3Ch1%3eNombres%20flottants%3C/h1%3e&+1.0-0.9-0.1&+///On%20voit%20ci-dessus%20que%20Xcas%20ne%20calcule%20pas%20en%20base%2010.%0aVoici%20un%20programme%20qui%20d%C3%A9termine%20la%20base%20utilis%C3%A9e%20pour%20repr%C3%A9senter%20les%20flottants.&+function%20Base()%0A%20%20local%20A%2CB%3B%0A%20%20A%3A%3D1.0%3B%20B%3A%3D1.0%3B%0A%20%20while%20-1%2B((A%2B1.0)-A)%3D0.0%20do%20%20A%3A%3D2*A%3B%20od%3B%0A%20%20while%20-B%2B((A%2BB)-A)!%3D0%20do%20B%3A%3DB%2B1%3B%20od%3B%0A%20%20return%20B%3B%0Affunction%3A%3B%20Base()&+///Plus%20grand%20et%20plus%20petit%20r%C3%A9el%20positif%20non%20nul%20repr%C3%A9sentable%20en%20arithm%C3%A9tique%20double%20pr%C3%A9cision.&+MINREAL%3BMAXREAL&+///Pr%C3%A9cision%20dans%20Xcas%20en%20nombre%20de%20bits.%20Si%20%3Ctt%3eDigits%3C/tt%3e%20est%20sup%C3%A9rieur%20%C3%A0%2014,%20les%20calculs%20sont%20plus%20lents%20mais%20plus%20pr%C3%A9cis.&+epsilon%3A%3D0%3A%3B%20Digits%3A%3D14%3B%0Apour%20j%20de%201%20jusque%201000%20faire%20%0A%20%20si%20evalf(1)%2B2%5E(-j)%3D%3Devalf(1)%20alors%20break%3B%20fsi%3B%20%0Afpour%3A%3B%0Aj&+///Erreur%20relative,%20exemple%20avec%20le%20calcul%20num%C3%A9rique%20de%20d%C3%A9riv%C3%A9e%20selon%20deux%20formules.%20Observer%20la%20valeur%20optimale%20de%20$h$,%20qui%20d%C3%A9pend%20de%20la%20valeur%20de%20%3Ctt%3eDigits%3C/tt%3e&+der(f%2Cx%2Ch)%3A%3D(f(x%2Bh)-f(x))%2Fh&+Digits%3A%3D14&+seq(der(exp%2C0.0%2C10%5E(-j))-1%0A%20%20%2Cj%2C1%2C15))&+der2(f%2Cx%2Ch)%3A%3D(f(x%2Bh)-f(x-h))%2F2%2Fh&+seq(der2(exp%2C0.0%2C10%5E(-j))-1%0A%20%20%2Cj%2C1%2C15))&+///L'erreur%20relative%20sur%20$f(x)$%20est%20en%20gros%20$abs(x*f'(x)/f(x))$.%20Illustration%20avec%20l'arithm%C3%A9tique%20d'intervalle.&+x%3A%3Dconvert(pi%2Cinterval)&+err%3A%3D(right(x)-left(x))%2Fpi&+f(x)%3A%3Dexp(x)%3A%3By%3A%3Df(x)&+(right(y)-left(y))%2Fexp(pi)%3B%20%0Aerr*pi*f'(pi)%2Ff(pi)&+///Somme%20de%20$n$%20erreurs%20absolues%20ind%C3%A9pendantes.%20%0aL'estimation%20rigoureuse%20sur%20l'erreur%20de%20la%20somme%20(multipli%C3%A9e%20par%20$n$)%20est%20pessimiste,%20statistiquement%20l'erreur%20totale%20est%20de%20l'ordre%20de%20$sqrt(n)$.%0aExemple%20de%20simulation%20:%20on%20somme%20$n=400$%20nombres%20r%C3%A9partis%20sur%20[%E2%88%921,1]%20selon%20la%20loi%20uniforme%20(repr%C3%A9sentant%20des%20erreurs),%20on%20divise%20par%20$sqrt(n)=20$,%20on%20effectue%20plusieurs%20tirages,%20disons%201000.%20On%20trace%20l%E2%80%99histogramme%20des%20erreurs%20divis%C3%A9ees%20par%20$sqrt(n)$%20et%20on%20compare%20avec%20la%20loi%20normale%20de%20moyenne%20nulle%20(l%E2%80%99esp%C3%A9rance%20de%20la%20somme)%20et%20d%E2%80%99%C3%A9cart-type%20celui%20de%20la%20loi%20uniforme.&+n%3A%3D400%3B%0Am%3A%3Dranm(n%2C1000%2C-1..1)%3A%3B%0Agl_x%3D-2..2%3B%0Ahistogram(sum(m)%2Fsqrt(n)%2C-1%2C0.1)%3B%20%0Aplot(normald(0%2Cstddev(uniform%2C-1%2C1))%2C-2..2)&+///Correction%20d'erreurs%20d'arrondi%20de%20la%20somme%20des%20%C3%A9l%C3%A9ments%20d'une%20liste.%20On%20accumule%20dans%20$c$%20%C3%A0%20peu%20pr%C3%A8s%20l'oppos%C3%A9%20de%20la%20somme%20des%20erreurs%20d'arrondis%20du%20calcul%20de%20%3Ctt%3es+=x%3C/tt%3e&+fonction%20Somme(l)%0A%20%20local%20x%2Cs%2Cc%3B%0A%20%20s%3A%3D0.0%3B%0A%20%20c%3A%3D0.0%3B%0A%20%20pour%20x%20in%20l%20faire%0A%20%20%20%20c%20%2B%3D%20(x-((s%2Bx)-s))%3B%0A%20%20%20%20s%20%2B%3D%20x%3B%0A%20%20fpour%3B%0A%20%20print(c)%3B%0A%20%20return%20s%2Bc%3B%0Affonction%3A%3B&+n%3A%3D6000%3B%0Al%3A%3Dseq(1%2Fj%2Cj%2C1%2Cn)%3A%3B%0ASomme(l)%3B&+///Comparaison%20avec%20la%20valeur%20approch%C3%A9e%20du%20calcul%20exact%20de%20$S$%20et%20le%20calcul%20approch%C3%A9%20sans%20pr%C3%A9caution&+S%3A%3Dsum(1%2Fj%2Cj%2C1%2Cn)%3A%3B%20evalf(S)%3B%0Asum(1.%20%2Fj%2Cj%2C1%2Cn)%3B&"
                                target="_blank">Xcas</a>,
                            <a
                                href="#exec&python=0&+///%3Ch1%3eNombres%20flottants%3C/h1%3e&+1.0-0.9-0.1&+///On%20voit%20ci-dessus%20que%20Xcas%20ne%20calcule%20pas%20en%20base%2010.%0aVoici%20un%20programme%20qui%20d%C3%A9termine%20la%20base%20utilis%C3%A9e%20pour%20repr%C3%A9senter%20les%20flottants.&+def%20Base()%3A%0A%20%20%23%20local%20A%2CB%0A%20%20A%3D1.0%20%0A%20%20B%3D1.0%0A%20%20while%20-1%2B((A%2B1.0)-A)%3D%3D0.0%3A%20%20%0A%20%20%20%20A%3D2*A%0A%20%20while%20-B%2B((A%2BB)-A)!%3D0%3A%0A%20%20%20%20B%3DB%2B1%0A%20%20return%20B%0A&+Base()&+///Plus%20grand%20et%20plus%20petit%20r%C3%A9el%20positif%20non%20nul%20repr%C3%A9sentable%20en%20arithm%C3%A9tique%20double%20pr%C3%A9cision.&+MINREAL%3BMAXREAL&+///Pr%C3%A9cision%20dans%20Xcas%20en%20nombre%20de%20bits.%20Si%20%3Ctt%3eDigits%3C/tt%3e%20est%20sup%C3%A9rieur%20%C3%A0%2014,%20les%20calculs%20sont%20plus%20lents%20mais%20plus%20pr%C3%A9cis.&+%23%0Aepsilon%3D0%0ADigits%3D14%0Afor%20j%20in%20range(1000)%3A%0A%20%20if%201.0%2B2**(-j)%3D%3D1.0%3A%0A%20%20%20%20print(j)%3B%0A%20%20%20%20break%0Aj&+///Erreur%20relative,%20exemple%20avec%20le%20calcul%20num%C3%A9rique%20de%20d%C3%A9riv%C3%A9e%20selon%20deux%20formules.%20Observer%20la%20valeur%20optimale%20de%20$h$,%20qui%20d%C3%A9pend%20de%20la%20valeur%20de%20%3Ctt%3eDigits%3C/tt%3e&+def%20der(f%2Cx%2Ch)%3A%0A%20%20return%20(f(x%2Bh)-f(x))%2Fh&+%23%0ADigits%3D14&+%5Bder(exp%2C0.0%2C10%5E(-j))-1%20for%20j%20in%20range(1%2C15)%5D&+def%20der2(f%2Cx%2Ch)%3A%0A%20%20return%20(f(x%2Bh)-f(x-h))%2F2%2Fh&+%5Bder2(exp%2C0.0%2C10%5E(-j))-1%20for%20j%20in%20range(1%2C15)%5D&+///L'erreur%20relative%20sur%20$f(x)$%20est%20en%20gros%20$abs(x*f'(x)/f(x))$.%20Illustration%20avec%20l'arithm%C3%A9tique%20d'intervalle.&+x%3Dconvert(pi%2Cinterval)&+err%3D(right(x)-left(x))%2Fpi&+def%20f(x)%3A%0A%20%20return%20exp(x)&+%23%0Ay%3Df(x)%0A(right(y)-left(y))%2Fexp(pi)%20%0Aerr*pi*function_diff(f)(pi)%2Ff(pi)&+///Somme%20de%20$n$%20erreurs%20absolues%20ind%C3%A9pendantes.%20%0aL'estimation%20rigoureuse%20sur%20l'erreur%20de%20la%20somme%20(multipli%C3%A9e%20par%20$n$)%20est%20pessimiste,%20statistiquement%20l'erreur%20totale%20est%20de%20l'ordre%20de%20$sqrt(n)$.%0aExemple%20de%20simulation%20:%20on%20somme%20$n=400$%20nombres%20r%C3%A9partis%20sur%20[%E2%88%921,1]%20selon%20la%20loi%20uniforme%20(repr%C3%A9sentant%20des%20erreurs),%20on%20divise%20par%20$sqrt(n)=20$,%20on%20effectue%20plusieurs%20tirages,%20disons%201000.%20On%20trace%20l%E2%80%99histogramme%20des%20erreurs%20divis%C3%A9ees%20par%20$sqrt(n)$%20et%20on%20compare%20avec%20la%20loi%20normale%20de%20moyenne%20nulle%20(l%E2%80%99esp%C3%A9rance%20de%20la%20somme)%20et%20d%E2%80%99%C3%A9cart-type%20celui%20de%20la%20loi%20uniforme.&+%23%0An%3D400%0Am%3Dranm(n%2C1000%2C-1..1)%0Agl_x%3D-2..2%0Ahistogram(sum(m)%2Fsqrt(n)%2C-1%2C0.1)%20%0Aplot(normald(0%2Cstddev(uniform%2C-1%2C1))%2C-2..2)&+///Correction%20d'erreurs%20d'arrondi%20de%20la%20somme%20des%20%C3%A9l%C3%A9ments%20d'une%20liste.%20On%20accumule%20dans%20$c$%20%C3%A0%20peu%20pr%C3%A8s%20l'oppos%C3%A9%20de%20la%20somme%20des%20erreurs%20d'arrondis%20du%20calcul%20de%20%3Ctt%3es+=x%3C/tt%3e&+def%20Somme(l)%3A%0A%20%20%23%20local%20x%2Cs%2Cc%0A%20%20s%3D0.0%0A%20%20c%3D0.0%0A%20%20for%20x%20in%20l%3A%0A%20%20%20%20c%20%2B%3D%20(x-((s%2Bx)-s))%0A%20%20%20%20s%20%2B%3D%20x%0A%20%20print(c)%0A%20%20return%20s%2Bc&+%23%0An%3D6000%0Al%3D%5B1.0%2Fj%20for%20j%20in%20range(1%2Cn%2B1)%5D%3A%3B%0ASomme(l)&+///Comparaison%20avec%20la%20valeur%20approch%C3%A9e%20du%20calcul%20exact%20de%20$S$%20et%20le%20calcul%20approch%C3%A9%20sans%20pr%C3%A9caution&+%23%0AS%3Dsum(1%2Fj%2Cj%2C1%2Cn)%3A%3B%20%0Aevalf(S)%0Asum(1.%20%2Fj%2Cj%2C1%2Cn)&"
                                target="_blank"><strong>Python</strong></a>
                        </li>
                        <li> Licence
                            <a
                                href="#exec&python=0&+///Temps%20de%20calcul%20et%20pr%C3%A9cision%20d'une%20factorisation%20LU%20en%20fonction%20de%20la%20taille%20$n$%20de%20la%20matrice&+t%3A%3D%5B%5D%3A%3B%20err%3A%3D%5B%5D%3A%3B%0Apour%20n%20de%201%20jusque%208%20faire%0A%20%20m%3A%3Dranm(n*50%2Cn*50%2Cuniformd%2C-1%2C1)%3B%20%0A%20%20t.append(time(p%2Cl%2Cu%3A%3Dlu(m)))%3B%20%0A%20%20err.append(maxnorm(permu2mat(p)*m-l*u))%3B%0Afpour%3A%3B%0At%3Berr%3B&+N%3A%3Dseq(ln(n)%2Cn%2C2%2C8)%3B%0AT%3A%3Dln(t)%5B1..11%5D%3B%0Apolygonscatterplot(N%2CT)%3B%0Alinear_regression_plot(N%2CT%2Ccolor%3Dred)&+linear_regression(N%2CT)&+///On%20est%20en-dessous%20du%20$O(n^3)$%20attendu,%20il%20y%20a%20des%20gains%20d'efficacit%C3%A9%20lorsque%20la%20taille%20de%20la%20matrice%20augmente,%20%20Xcas%20utilise%20des%20algorithmes%20par%20blocs%20plus%20efficaces.%20Il%20peut%20aussi%20etre%20int%C3%A9ressant%20d'utiliser%20des%20algorithmes%20sp%C3%A9cifiques%20lorsque%20la%20matrice%20est%20creuse%20par%20exemple%20pour%20la%20matrice%20du%20laplacien%20discret%20%3Ctt%3elaplacian(n)%3C/tt%3e,%20ou%20lorsque%20la%20matrice%20est%20sym%C3%A9trique%20d%C3%A9finie%20positive%20(%3Ctt%3echolesky%3C/tt%3e).&+n%3A%3D7%3B%20a%3A%3Dlaplacian(n)%3B&+///Comparaison%20entre%20r%C3%A9solution%20par%20LU%20en%20$O(n^2)$%20ou%20directe.&+fonction%20f(n)%0A%20%20local%20t1%2Ct2%2Cp%2Cl%2Cu%2Ca%2Cb%2Cv%2Cw%3B%0A%20%20p%2Cl%2Cu%3A%3Dlu(a%3A%3Dranm(n%2Cn%2Cuniformd%2C-1%2C1))%3A%3B%20%0A%20%20b%3A%3Dranv(n%2Cuniformd%2C-1%2C1)%3A%3B%20%0A%20%20t1%3A%3Dtime(v%3A%3Dlinsolve(p%2Cl%2Cu%2Cb))%3B%0A%20%20t2%3A%3Dtime(w%3A%3Dlinsolve(a%2Cb))%3B%0A%20%20return%20t1%2Ct2%2Cmaxnorm(v-w)%3B%0Affonction%3A%3B&+f(600)&+///Conditionnement%20d'une%20matrice,%20exemple%20de%20r%C3%A9solution%20de%20syst%C3%A8me%20avec%202%20seconds%20membres%20proches,%20l'erreur%20relative%20sur%20la%20solution%20est%20fortement%20amplifi%C3%A9e.&+a%3A%3D%5B%5B10%2C7%2C8%2C7%5D%2C%0A%20%20%5B7%2C5%2C6%2C5%5D%2C%0A%20%20%5B8%2C6%2C10%2C9%5D%2C%0A%20%20%5B7%2C5%2C9%2C10%5D%5D&+b%3A%3D%5B32%2C23%2C33%2C31%5D&+v%3A%3Dlinsolve(a%2Cb)&+delta_b%3A%3D%5B1%2C-1%2C1%2C-1%5D%2F100&+w%3A%3Dlinsolve(a%2Cb%2Bdelta_b)&+err1%3A%3Dl2norm(evalf(delta_b))%2Fl2norm(b)%3B%0Aerr2%3A%3Dl2norm(evalf(w-v))%2Fl2norm(v)%3B&+cond(a%2C2)%3B%20err2%2Ferr1&"
                                target="_blank">Syst&egrave;mes lin&eacute;aires, LU, conditionnement</a>
                        </li>
                        <li> Licence
                            <a
                                href="#exec&python=0&+///D%C3%A9composition%20$Q*R$%20et%20moindre%20carr%C3%A9s.%0aExemple:%20r%C3%A9gression%20lin%C3%A9aire.&+///On%20se%20donne%20une%20suite%20de%20valeurs%20sur%20une%20droite%20modulo%20une%20petite%20erreur%20al%C3%A9toire,%20on%20cherche%20la%20meilleure%20droite%20$y=a*x+b$%20approchant%20les%20points%20correspondants%20au%20sens%20des%20moindres%20carr%C3%A9s%20en%20$y$.&+n%3A%3D30%3B%20b%3A%3Dseq(2*j%2B5*rand()%2Cj%2C1%2Cn)&+x%3A%3Dseq(j%2Cj%2C1%2Cn)%3B%20scatterplot(x%2Cb)%3B%0Alinear_regression_plot(x%2Cb)&+///%C3%89criture%20matricielle%20du%20probl%C3%A8me%20sous%20la%20forme%20$A*x=b$%20avec%20$x=[m,p]$&+A%3A%3Dtrn(%5Bx%2Cseq(1%2Cn)%5D)&+A*%5Bm%2Cp%5D%3Db&+///Le%20syst%C3%A8me%20est%20surd%C3%A9termin%C3%A9.%0aOn%20le%20r%C3%A9soud%20au%20sens%20des%20moindres%20carr%C3%A9s,%20on%20cherche%20$x$%20tel%20que%20$abs(A*x-b)$%20minimal%20soit%20$A^t*A*x=A^t*b$&+///On%20utilise%20la%20d%C3%A9composition%20QR%20de%20$A$.%20%0aIci%20sous%20la%20forme%20$A=Q_1*R_1$%20avec%20$R_1$%20triangulaire%20sup%C3%A9rieure%20inversible.%20Donc%20$R_1*x=Q_1^t*b$&+q%2Cr%3A%3Dqr(evalf(A))&+q1%3A%3Dq%5B%3A%2C0..1%5D&+r1%3A%3Dr%5B0..1%2C0..1%5D&+linsolve(r1%2Ctran(q1)*b)&+///V%C3%A9rification%20avec%20la%20fonction%20int%C3%A9gr%C3%A9e%20de%20Xcas&+linear_regression(x%2Cb)&+///Int%C3%A9r%C3%AAt%20par%20rapport%20%C3%A0%20r%C3%A9soudre%20$A^t*A*x=A^t*b$.%20On%20a%20un%20syst%C3%A8me%20mieux%20conditionn%C3%A9.&+cond(A%2C2)&+///%20On%20perd%20intrins%C3%A8quement%20environ%201.5%20chiffres%20significatifs%20au%20lieu%20de%203.&"
                                target="_blank">D&eacute;composition QR, moindres carr&eacute;s,
                            exemple r&eacute;gression lin&eacute;aire</a>
                        </li>
                        <li> M&eacute;thodes it&eacute;ratives: point fixe, Newton, puissance
                            <a
                                href="#exec&python=0&+///M%C3%A9thodes%20it%C3%A9ratives&+///M%C3%A9thode%20du%20%3Cstrong%3epoint%20fixe%3C/strong%3e.%0aOn%20consid%C3%A8re%20la%20suite%20$u[n+1]=f(u[n])$,%20si%20la%20fonction%20$f$%20est%20contractante%20sur%20un%20intervalle,%20alors%20$u[n]$%20converge%20vers%20$l$%20tel%20que%20$f(l)=l$.&+fonction%20fixe(f%2Cu0%2CN%2Ceps)%0A%20%20local%20j%2Cu1%3B%0A%20%20u0%3A%3Devalf(u0)%3B%20%0A%20%20pour%20j%20de%201%20jusque%20N%20faire%0A%20%20%20%20u1%3A%3Df(u0)%3B%0A%20%20%20%20si%20abs(u1-u0)%3Ceps*abs(u0)%20alors%20return%20u1%2Cj%3B%20fsi%3B%0A%20%20%20%20u0%3A%3Du1%3B%0A%20%20fpour%3B%0A%20%20return%20%22Pas%20de%20convergence%22%3B%0Affonction%3A%3B&+f(x)%3A%3Dcos(x)%3B%0Afixe(f%2C0%2C100%2C1e-6)%3B%0Afixe(f%2C0%2C100%2C1e-8)%3B%0Afixe(f%2C0%2C100%2C1e-10)&+///La%20convergence%20est%20lin%C3%A9aire,%20il%20faut%20%C3%A0%20peu%20pr%C3%A8s%20le%20m%C3%AAme%20nombre%20d'it%C3%A9rations%20pour%20gagner%20une%20d%C3%A9cimale.%0aLa%20m%C3%A9thode%20de%20%3Cstrong%3eNewton%3C/strong%3e%20permet%20de%20r%C3%A9soudre%20$f(x)=0$%20en%20doublant%20le%20nombre%20de%20d%C3%A9cimales%20%C3%A0%20chaque%20it%C3%A9ration%20%3Cstrong%3esi%3C/strong%3e%20on%20est%20assez%20proche%20de%20la%20solution.%0aOn%20utilise%20la%20suite%20r%C3%A9currente%20$u[n+1]=u[n]-f(u[n])/f'(u[n])$,%20g%C3%A9om%C3%A9triquement%20c'est%20l'abscisse%20du%20point%20o%C3%B9%20la%20tangente%20au%20graphe%20de%20$f$%20en%20$x=u[n]$%20rencontre%20l'axe%20des%20$x$.&+gl_x%3D-1..2%3B%0Agl_y%3D-1..1.5%3B%0Af(x)%3A%3Dcos(x)-x%3B%0AG%3A%3Dplot(f(x)%2Cx%2C-1%2C2%2C%0A%20%20display%3Depaisseur_ligne_2)%3B%0AI0%3A%3Dpoint(0)%3B%0Avecteur(0%2Cpoint(0%2Cf(0)))%3B%0AT0%3A%3Dtangent(G%2C0%2C%0A%20%20display%3Dred%2Bhidden_name)%3B%0AI1%3A%3Dinter_unique(T0%2Cdroite(y%3D0))%3B%0Au1%3A%3Dabscisse(I1)%3B%0Avecteur(I1%2Cpoint(u1%2Cf(u1)))%3B%0AT1%3A%3Dtangent(G%2Cu1%2C%0A%20%20display%3Dmagenta%2Bhidden_name)%3B%0AI2%3A%3Dinter_unique(T1%2Cdroite(y%3D0))%3B%0A%2F%2Fu2%3A%3Dabscisse(I0)%3B%0A&+fonction%20Newton(f%2Cu0%2CN%2Ceps)%0A%20%20local%20j%2Cu1%2Cx%3B%0A%20%20purge(x)%3B%0A%20%20u0%3A%3Devalf(u0)%3B%0A%20%20pour%20j%20de%201%20jusque%20N%20faire%0A%20%20%20%20u1%3A%3Du0-f(u0)%2Ff'(u0)%3B%0A%20%20%20%20si%20abs(u1-u0)%3Ceps*abs(u0)%20alors%20return%20u1%2Cj%3B%20fsi%3B%0A%20%20%20%20u0%3A%3Du1%3B%0A%20%20fpour%3B%0A%20%20return%20%22Pas%20de%20convergence%22%3B%0Affonction%3A%3B&+f(x)%3A%3Dcos(x)-x%3B%0ANewton(f%2C0%2C100%2C1e-3)%3B%0ANewton(f%2C0%2C100%2C1e-6)%3B%0ANewton(f%2C0%2C100%2C1e-12)&+///Remarques:%20%0a*%20on%20observe%20le%20doublement%20du%20nombre%20de%20d%C3%A9cimales%20%C3%A0%20chaque%20it%C3%A9ration.%20%0a*%20il%20faudrait%20stocker%20la%20d%C3%A9riv%C3%A9e%20de%20$f$%20dans%20une%20variable%20locale%20pour%20ne%20pas%20la%20recalculer%20%C3%A0%20chaque%20it%C3%A9ration%0a*%20on%20peut%20d%C3%A9finir%20Newton%20en%20utilisant%20la%20fonction%20fixe%20ci-dessus%0a*%20il%20existe%20d'autres%20m%C3%A9thodes%20it%C3%A9ratives,%20par%20exemple%20la%20m%C3%A9thode%20de%20la%20s%C3%A9cante&+Newton(f%2Cu0%2CN%2Ceps)%3A%3D%0Afixe(id-f%2Ff'%2Cu0%2CN%2Ceps)&+///%3Cstrong%3eM%C3%A9thode%20de%20la%20puissance%3C/strong%3e%0aElle%20permet%20de%20trouver%20la%20plus%20grande%20valeur%20propre%20en%20module%20d'une%20matrice.%20L'id%C3%A9e%20est%20d'it%C3%A9rer%20$v[n+1]=A*v[n]$%20avec%20un%20vecteur%20$v[0]$%20al%C3%A9atoire,%20dans%20la%20base%20propre%20de%20$A$%20les%20coordonn%C3%A9es%20sont%20des%20suites%20g%C3%A9om%C3%A9triques%20de%20raisons%20les%20valeurs%20propres,%20donc%20la%20coordonn%C3%A9e%20correspondant%20%C3%A0%20la%20valeur%20propre%20de%20module%20maximal%20va%20dominer.&+fonction%20pui(A%2CN%2Ceps)%0A%20%20local%20v0%2Cv1%2Cl%2Cj%2Cn%3B%0A%20%20n%3A%3Dsize(A)%3B%0A%20%20v0%3A%3Dranv(n%2Cuniformd%2C-1%2C1)%3B%0A%20%20v0%3A%3Dnormalize(v0)%3B%0A%20%20pour%20j%20de%201%20jusque%20N%20faire%0A%20%20%20%20v1%3A%3DA*v0%3B%0A%20%20%20%20l%3A%3Ddot(v0%2Cv1)%3B%0A%20%20%20%20si%20l2norm(v1-l*v0)%3Ceps%20alors%20return(v0%2Cl%2Cj)%3B%20fsi%3B%0A%20%20%20%20v0%3A%3Dnormalize(v1)%3B%0A%20%20fpour%3B%0A%20%20return%20%22Pas%20de%20convergence%2C%20essayez%20avec%20A%2Bi*identity(A)%22%0Affonction%3A%3B&+a%3A%3Dranm(3%2C3)%3B%0AA%3A%3Da%2Btran(a)%3B%0A&+pui(A%2C1000%2C1e-6)%3B%0Apui(A%2C1000%2C1e-8)%3B%0Apui(A%2C1000%2C1e-10)%0A&+///La%20convergence%20est%20lin%C3%A9aire.%0aSi%20on%20a%20un%20couple%20de%20valeurs%20propres%20conjugu%C3%A9s%20de%20module%20maximal,%20il%20faut%20briser%20la%20sym%C3%A9trie%20par%20exemple%20en%20translatant%20de%20$i$%20dans%20la%20complexe.&+a%3A%3D%5B%5B-11%2C-69%2C-60%5D%2C%0A%20%20%5B84%2C-71%2C-88%5D%2C%0A%20%20%5B33%2C72%2C1%5D%5D%2F100.%3B%0A&+pui(a%2C1000%2C1e-6)%3B%0Apui(a%2Bi%2C1000%2C1e-6)&+///Si%20on%20connait%20une%20valeur%20approch%C3%A9e%20$lambda$%20d'une%20valeur%20propre,%20on%20peut%20acc%C3%A9l%C3%A9rer%20la%20convergence%20en%20it%C3%A9rant%20sur%20$(A-lambda*I)^(-1)$%20(on%20peut%20%C3%A9viter%20le%20calcul%20explicite%20de%20l'inverse%20en%20utilisant%20la%20d%C3%A9composition%20LU).&+pui((a%2B0.27)%5E-1%2C1000%2C1e-6)&"
                                target="_blank">
                            Xcas
                            </a>,
                            <a
                                href="#exec&python=0&+///M%C3%A9thodes%20it%C3%A9ratives&+///M%C3%A9thode%20du%20%3Cstrong%3epoint%20fixe%3C/strong%3e.%0aOn%20consid%C3%A8re%20la%20suite%20$u[n+1]=f(u[n])$,%20si%20la%20fonction%20$f$%20est%20contractante%20sur%20un%20intervalle,%20alors%20$u[n]$%20converge%20vers%20$l$%20tel%20que%20$f(l)=l$.&+def%20fixe(f%2Cu0%2CN%2Ceps)%3A%0A%20%20%23%20local%20j%2Cu1%0A%20%20u0%3Du0*1.0%20%0A%20%20for%20j%20in%20range(N)%3A%0A%20%20%20%20u1%3Df(u0)%0A%20%20%20%20if%20abs(u1-u0)%3Ceps*abs(u0)%3A%0A%20%20%20%20%20%20return%20u1%2Cj%0A%20%20%20%20u0%3Du1%0A%20%20return%20%22Pas%20de%20convergence%22&+fixe(cos%2C0%2C100%2C1e-6)%3B%0Afixe(cos%2C0%2C100%2C1e-8)%3B%0Afixe(cos%2C0%2C100%2C1e-10)&+///La%20convergence%20est%20lin%C3%A9aire,%20il%20faut%20%C3%A0%20peu%20pr%C3%A8s%20le%20m%C3%AAme%20nombre%20d'it%C3%A9rations%20pour%20gagner%20une%20d%C3%A9cimale.%0aLa%20m%C3%A9thode%20de%20%3Cstrong%3eNewton%3C/strong%3e%20permet%20de%20r%C3%A9soudre%20$f(x)=0$%20en%20doublant%20le%20nombre%20de%20d%C3%A9cimales%20%C3%A0%20chaque%20it%C3%A9ration%20%3Cstrong%3esi%3C/strong%3e%20on%20est%20assez%20proche%20de%20la%20solution.%0aOn%20utilise%20la%20suite%20r%C3%A9currente%20$u[n+1]=u[n]-f(u[n])/f'(u[n])$,%20g%C3%A9om%C3%A9triquement%20c'est%20l'abscisse%20du%20point%20o%C3%B9%20la%20tangente%20au%20graphe%20de%20$f$%20en%20$x=u[n]$%20rencontre%20l'axe%20des%20$x$.&+gl_x%3D-1..2%3B%0Agl_y%3D-1..1.5%3B%0Af(x)%3A%3Dcos(x)-x%3B%0AG%3A%3Dplot(f(x)%2Cx%2C-1%2C2%2C%0A%20%20display%3Depaisseur_ligne_2)%3B%0AI0%3A%3Dpoint(0)%3B%0Avecteur(0%2Cpoint(0%2Cf(0)))%3B%0AT0%3A%3Dtangent(G%2C0%2C%0A%20%20display%3Dred%2Bhidden_name)%3B%0AI1%3A%3Dinter_unique(T0%2Cdroite(y%3D0))%3B%0Au1%3A%3Dabscisse(I1)%3B%0Avecteur(I1%2Cpoint(u1%2Cf(u1)))%3B%0AT1%3A%3Dtangent(G%2Cu1%2C%0A%20%20display%3Dmagenta%2Bhidden_name)%3B%0AI2%3A%3Dinter_unique(T1%2Cdroite(y%3D0))%3B%0A%2F%2Fu2%3A%3Dabscisse(I0)%3B%0A&+def%20Newton(f%2Cu0%2CN%2Ceps)%3A%0A%20%20%23%20local%20j%2Cu1%2Cx%0A%20%20%23%20en%20Python%20pur%2C%0A%20%20%23%20il%20faudrait%20utiliser%20%0A%20%20%23%20une%20valeur%20approchee%20de%20la%20d%C3%A9riv%C3%A9e%0A%20%20purge(x)%0A%20%20u0%3Du0*1.0%0A%20%20for%20j%20in%20range(N)%3A%0A%20%20%20%20u1%3Du0-f(u0)%2Ffunction_diff(f)(u0)%0A%20%20%20%20if%20abs(u1-u0)%3Ceps*abs(u0)%3A%0A%20%20%20%20%20%20return%20u1%2Cj%0A%20%20%20%20u0%3Du1%0A%20%20return%20%22Pas%20de%20convergence%22&+def%20f(x)%3A%0A%20%20return%20cos(x)-x&+Newton(f%2C0%2C100%2C1e-3)%3B%0ANewton(f%2C0%2C100%2C1e-6)%3B%0ANewton(f%2C0%2C100%2C1e-12)&+///Remarques:%20%0a*%20on%20observe%20le%20doublement%20du%20nombre%20de%20d%C3%A9cimales%20%C3%A0%20chaque%20it%C3%A9ration%0a*%20il%20faudrait%20stocker%20la%20d%C3%A9riv%C3%A9e%20de%20$f$%20dans%20une%20variable%20locale%20pour%20ne%20pas%20la%20recalculer%20%C3%A0%20chaque%20it%C3%A9ration%0a*%20on%20peut%20d%C3%A9finir%20Newton%20en%20utilisant%20la%20fonction%20fixe%20ci-dessus,%20voir%20ci-dessous%0a*%20il%20existe%20d'autres%20m%C3%A9thodes%20it%C3%A9ratives,%20par%20exemple%20la%20m%C3%A9thode%20de%20la%20s%C3%A9cante&+Newton(f%2Cu0%2CN%2Ceps)%3A%3D%0Afixe(id-f%2Ff'%2Cu0%2CN%2Ceps)&+///%3Cstrong%3eM%C3%A9thode%20de%20la%20puissance%3C/strong%3e%0aElle%20permet%20de%20trouver%20la%20plus%20grande%20valeur%20propre%20en%20module%20d'une%20matrice.%20L'id%C3%A9e%20est%20d'it%C3%A9rer%20$v[n+1]=A*v[n]$%20avec%20un%20vecteur%20$v[0]$%20al%C3%A9atoire,%20dans%20la%20base%20propre%20de%20$A$%20les%20coordonn%C3%A9es%20sont%20des%20suites%20g%C3%A9om%C3%A9triques%20de%20raisons%20les%20valeurs%20propres,%20donc%20la%20coordonn%C3%A9e%20correspondant%20%C3%A0%20la%20valeur%20propre%20de%20module%20maximal%20va%20dominer.&+def%20pui(A%2CN%2Ceps)%3A%0A%20%20%23%20local%20v0%2Cv1%2Cl%2Cj%2Cn%0A%20%20n%3Dsize(A)%0A%20%20v0%3Dranv(n%2Cuniformd%2C-1%2C1)%0A%20%20v0%3Dnormalize(v0)%0A%20%20for%20j%20in%20range(N)%3A%0A%20%20%20%20v1%3DA*v0%0A%20%20%20%20l%3Ddot(v0%2Cv1)%0A%20%20%20%20if%20l2norm(v1-l*v0)%3Ceps%3A%0A%20%20%20%20%20%20return(v0%2Cl%2Cj)%0A%20%20%20%20v0%3Dnormalize(v1)%0A%20%20return%20%22Pas%20de%20convergence%2C%20essayez%20avec%20A%2Bi*identity(A)%22&+a%3A%3Dranm(3%2C3)%3B%0AA%3A%3Da%2Btran(a)%3B%0A&+pui(A%2C1000%2C1e-6)%3B%0Apui(A%2C1000%2C1e-8)%3B%0Apui(A%2C1000%2C1e-10)%0A&+///La%20convergence%20est%20lin%C3%A9aire.%0aSi%20on%20a%20un%20couple%20de%20valeurs%20propres%20conjugu%C3%A9s%20de%20module%20maximal,%20il%20faut%20briser%20la%20sym%C3%A9trie%20par%20exemple%20en%20translatant%20de%20$i$%20dans%20la%20complexe.&+a%3A%3D%5B%5B-11%2C-69%2C-60%5D%2C%0A%20%20%5B84%2C-71%2C-88%5D%2C%0A%20%20%5B33%2C72%2C1%5D%5D%2F100.%3B%0A&+pui(a%2C1000%2C1e-6)%3B%0Apui(a%2Bi%2C1000%2C1e-6)&+///Si%20on%20connait%20une%20valeur%20approch%C3%A9e%20$lambda$%20d'une%20valeur%20propre,%20on%20peut%20acc%C3%A9l%C3%A9rer%20la%20convergence%20en%20it%C3%A9rant%20sur%20$(A-lambda*I)^(-1)$%20(on%20peut%20%C3%A9viter%20le%20calcul%20explicite%20de%20l'inverse%20en%20utilisant%20la%20d%C3%A9composition%20LU).&+pui((a%2B0.27)%5E-1%2C1000%2C1e-6)&"
                                target="_blank"><em>Python</em></a>
                        </li>
                        <li><a name="exemplescas"> Polyn&ocirc;me en une variable, Horner et Taylor</a>
                            <a href="#exec&python=0&+///M%C3%A9thode%20de%20Horner%20pour%20%C3%A9valuer%20un%20polyn%C3%B4me%20en%20un%20point&+fonction%20Horner(p%2Ca)%0A%20%20%2F%2F%20p%20liste%20des%20coefficients%20par%20ordre%20decroissant%0A%20%20%2F%2F%20renvoie%20p%20evalue%20en%20a%0A%20%20local%20c%2Cr%3B%0A%20%20r%3A%3D0%3B%0A%20%20pour%20c%20in%20p%20faire%0A%20%20%20%20r%3A%3Dr*a%2Bc%3B%0A%20%20fpour%3B%0A%20%20return%20r%3B%0Affonction%3A%3B&+Horner(%5B1%2C2%2C3%5D%2C4)%3B%20%0Ahorner(%5B1%2C2%2C3%5D%2C4)&+///On%20modifie%20le%20programme%20pr%C3%A9c%C3%A9dent%20pour%20renvoyer%20le%20quotient%20de%20$p$%20par%20$x-a$.%0aNotez%20que%20%3Ctt%3eq.append%3C/tt%3e%20modifie%20en%20place%20la%20liste%20$q$,%20il%20faut%20donc%20l'initialiser%20en%20faisant%20une%20copie%20de%20la%20liste%20vide.&+fonction%20Horner2(p%2Ca)%0A%20%20local%20c%2Cr%2Cq%3B%0A%20%20r%3A%3D0%3B%20q%3A%3Dcopy(%5B%5D)%3B%0A%20%20pour%20c%20in%20p%20faire%0A%20%20%20%20r%3A%3Dr*a%2Bc%3B%0A%20%20%20%20q.append(r)%3B%0A%20%20fpour%3B%0A%20%20q%3A%3Dq%5B0..-2%5D%3B%0A%20%20return%20q%2Cr%3B%0Affonction%3A%3B&+Horner2(%5B1%2C2%2C3%5D%2C4)&+///Et%20on%20l'appelle%20pour%20faire%20un%20changement%20d'origine,%20on%20exprime%20$P(X)$%20en%20fonction%20des%20$(X-a)^k$&+fonction%20Taylor(p%2Ca)%0A%20%20local%20q%2Cj%2Cn%3B%0A%20%20q%3A%3Dp%3B%0A%20%20n%3A%3Ddegree(p)%3B%0A%20%20pour%20j%20de%200%20jusque%20n%20faire%0A%20%20%20%20p%2Cq%5Bj%5D%3A%3DHorner2(p%2Ca)%3B%0A%20%20fpour%3B%0A%20%20return%20reverse(q)%3B%0Afpour%3A%3B&+Taylor(%5B1%2C2%2C3%5D%2C4)%3B%0Aptayl(%5B1%2C2%2C3%5D%2C4)&"
                               target="_blank">Xcas</a>,
                            <a
                                href="#exec&python=0&+///M%C3%A9thode%20de%20Horner%20pour%20%C3%A9valuer%20un%20polyn%C3%B4me%20en%20un%20point.%0aN.B.:%20Cette%20session%20fonctionne%20sans%20changement%20en%20Python%20pur.&+def%20Horner(p%2Ca)%3A%0A%20%20%23%20p%20liste%20des%20coefficients%20par%20ordre%20d%C3%A9croissant%0A%20%20%23%20renvoie%20p%20%C3%A9valu%C3%A9%20en%20a%0A%20%20%23%20local%20c%2Cr%0A%20%20r%3D0%0A%20%20for%20c%20in%20p%3A%0A%20%20%20%20r%3Dr*a%2Bc%0A%20%20return%20r&+Horner(%5B1%2C2%2C3%5D%2C4)%3B%20%0Ahorner(%5B1%2C2%2C3%5D%2C4)&+///On%20modifie%20le%20programme%20pr%C3%A9c%C3%A9dent%20pour%20renvoyer%20le%20quotient%20de%20$p$%20par%20$x-a$.%0aNotez%20que%20%3Ctt%3eq.append%3C/tt%3e%20modifie%20en%20place%20la%20liste%20$q$,%20il%20faut%20donc%20l'initialiser%20en%20faisant%20une%20copie%20de%20la%20liste%20vide.&+def%20Horner2(p%2Ca)%3A%0A%20%20%23%20local%20c%2Cr%2Cq%0A%20%20r%3D0%20%0A%20%20q%3D%5B%5D%0A%20%20for%20c%20in%20p%3A%0A%20%20%20%20r%3Dr*a%2Bc%0A%20%20%20%20q.append(r)%0A%20%20q%3Dq%5B0%3A-1%5D%0A%20%20return%20q%2Cr&+Horner2(%5B1%2C2%2C3%5D%2C4)&+///Et%20on%20l'appelle%20pour%20faire%20un%20changement%20d'origine,%20on%20exprime%20$P(X)$%20en%20fonction%20des%20$(X-a)^k$&+def%20Taylor(p%2Ca)%3A%0A%20%20%23%20local%20q%2Cj%2Cn%0A%20%20q%3Dp%0A%20%20n%3Dlen(p)%0A%20%20for%20j%20in%20range(n)%3A%0A%20%20%20%20p%2Cq%5Bj%5D%3DHorner2(p%2Ca)%0A%20%20q.reverse()%0A%20%20return%20q&+Taylor(%5B1%2C2%2C3%5D%2C4)%3B%0Aptayl(%5B1%2C2%2C3%5D%2C4)&"
                                target="_blank"><strong>Python</strong></a>
                        </li>
                        <li> Interpolation polynomiale
                            <a href="#exec&python=0&+///Interpolation%20de%20$ln(x^2+1)$%20en%2011%20points%20%C3%A9quidistribu%C3%A9s%20sur%20$[0,1]$.&+f(x)%3A%3Dln(x%5E2%2B1)%3B%20n%3A%3D10%3B%20%0AX%3A%3Devalf(seq(j%2Fn%2Cj%2C0%2Cn))%3B%20%0AY%3A%3Dmap(X%2Cf)%3B&+P%3A%3Dinterp(X%2CY)%3B%0A&+plot(%5Bf(x)%2CP%5D%2Cx%3D-1..2%2Ccolor%3D%5Bred%2Cblue%5D)&+plot(1e7*abs(f(x)-P)%2Cx%3D0..1)&+///Ph%C3%A9nom%C3%A8ne%20de%20Runge,%20ajouter%20des%20points%20%C3%A9quidistribu%C3%A9s%20peut%20s'av%C3%A9rer%20n%C3%A9faste.%0aIci%20on%20prend%20$n+1$%20points%20sur%20[-1,1]%20avec%20$n=20$.&+f(x)%3A%3D1%2F(1%2B25x%5E2)%3B%20n%3A%3D20%3B%20%0AX%3A%3Dseq(2*j%2Fn-1.0%2Cj%2C0%2Cn)%3A%3B&+gl_y%3D-2..2%3B%0Al%3A%3Dlagrange(X%2Cmap(X%2Cf))%3A%3B%20%0Aplot(%5Bl%2Cf(x)%5D%2Cx%3D-1..1)&+plot(l-f(x)%2Cx%3D-1..1)%0A&+///Ceci%20n'arrive%20pas%20avec%20les%20points%20de%20Tchebyshev.&+T%3A%3Dseq(cos((j%2B0.5)*pi%2F(n%2B1))%2C%0A%20%20j%2C0%2Cn)%3B&+apply(point%2CT)&+l%3A%3Dlagrange(T%2Cmap(T%2Cf))%3A%3B%20%0Aplot(%5Bl%2Cf(x)%5D%2Cx%3D-1..1)&+plot((l-f(x))%2Cx%3D-1..1)&"
                               target="_blank">ph&eacute;nom&egrave;ne de Runge, points de
                            Tchebyshev</a>
                        </li>
                        <li>Int&eacute;gration num&eacute;rique
                            <a
                                href="#exec&python=0&+///M%C3%A9thodes%20d'int%C3%A9grations%20num%C3%A9riques.%20Rectangle,%20trap%C3%A8zes.&+f(x)%3A%3D1%2F(1%2Bx%5E2)&+gl_y%3D0..1%3B%0Aplotarea(f(x)%2Cx%3D0..1%2C10%2C%0A%20%20rectangle_droit)&+Rect(f%2Ca%2Cb%2Cn)%3A%3D(b-a)%2Fn*%0Asum(f(a%2Bj*(b-a)%2Fn)%2Cj%2C1%2Cn)&+Rect(f%2C0%2C1%2C10)&+Rect(f%2C0%2C1.0%2C100)&+evalf(int(f(x)%2Cx%2C0%2C1))&+///On%20observe%20le%20r%C3%A9sultat%20attendu%20pour%20les%20rectangles,%20en%20multipliant%20par%2010%20le%20nombre%20de%20points%20d'%C3%A9valuation,%20on%20gagne%20une%20d%C3%A9cimale.&+plotarea(f(x)%2Cx%3D-1..1%2C4%2Ctrapezoid)&+trap(f%2Ca%2Cb%2Cn)%3A%3D(b-a)%2Fn*%0A(f(a)%2F2%2Bf(b)%2F2%2B%0A%20%20sum(f(a%2Bj*(b-a)%2Fn)%2Cj%2C1%2Cn-1))&+trap(f%2C0%2C1%2C10)&+trap(f%2C0%2C1.0%2C100)&+///Ici%20on%20gagne%202%20d%C3%A9cimales%20au%20lieu%20d'une%20si%20on%20multiplie%20par%2010%20le%20nombre%20de%20subdivisions&+///Les%20rectangles%20sont%20une%20approximation%20par%20un%20polynome%20de%20degr%C3%A9%200%20%C3%A0%20une%20extr%C3%A9mit%C3%A9,%20les%20trap%C3%A8zes%20par%20degr%C3%A9%201%20aux%20deux%20extr%C3%A9mit%C3%A9s,%20on%20peut%20essayer%20par%20degr%C3%A9%202%20aux%202%20extr%C3%A9mit%C3%A9s%20et%20au%20milieu%20d'une%20subdivision.&+///On%20recherche%20les%20coefficients%20de%20la%20formule%20d'int%C3%A9gration%20en%20remplacant%20la%20fonction%20par%20son%20polyn%C3%B4me%20d'interpolation%20(voir%20des%20autres%20m%C3%A9thodes%20plus%20bas).&+int(interp(%5B0%2C1%2F2%2C1%5D%2C%0A%20%20%5By0%2Cy1%2Cy2%5D)%2Cx%2C0%2C1)&+fonction%20Simpson(f%2Ca%2Cb%2Cn)%0A%20%20%2F%2F%20voir%20ci-dessous%20en%20syntaxe%20Python%0A%20%20local%20h%2Cres%2Cj%2Cx%3B%0A%20%20h%3A%3D(b-a)%2Fn%3B%0A%20%20res%3A%3D0%3B%0A%20%20pour%20j%20de%200%20jusque%20n-1%20faire%0A%20%20%20%20x%20%3A%3D%20a%2Bj*h%3B%0A%20%20%20%20res%20%3A%3D%20res%2Bf(x)%2B2*f(x%2Bh%2F2)%3B%0A%20%20fpour%3B%0A%20%20res%20%3A%3D%202*res%2Bf(b)-f(a)%3B%20%2F%2F%20ajuste%20les%20bornes%0A%20%20return%20res*h%2F6%3B%0Affonction%3A%3B&+def%20Simpson(f%2Ca%2Cb%2Cn)%3A%0A%20%20%23%20local%20h%2Cres%2Cj%2Cx%0A%20%20h%3D(b-a)%2Fn%0A%20%20res%3D0%0A%20%20for%20j%20in%20range(n)%3A%0A%20%20%20%20x%20%3D%20a%2Bj*h%0A%20%20%20%20res%20%3D%20res%2Bf(x)%2B2*f(x%2Bh%2F2)%0A%20%20res%20%3D%202*res%2Bf(b)-f(a)%20%23%20ajuste%20les%20bornes%0A%20%20return%20res*h%2F6&+Simpson(f%2C0%2C1%2C10)%3B%0A&+///Plus%20le%20degr%C3%A9%20du%20polyn%C3%B4me%20est%20grand,%20plus%20l'approximation%20semble%20bonne.%20En%20fait%20c'est%20l'ordre%20d'une%20m%C3%A9thode%20qui%20importe,%20c'est-%C3%A0-dire%20le%20monome%20de%20plus%20grand%20degr%C3%A9%20pour%20lequel%20la%20formule%20est%20exacte.%20Bien%20sur,%20l'ordre%20est%20sup%C3%A9rieur%20au%20degr%C3%A9%20si%20on%20interpole.&+trap(x-%3Ex%2C0%2C1%2C1)%0A-integrate(x%2Cx%2C0%2C1)&+trap(x-%3Ex%5E2%2C0%2C1%2C1)%0A-integrate(x%5E2%2Cx%2C0%2C1)&+Simpson(x-%3Ex%5E2%2C0%2C1%2C1)-integrate(x%5E2%2Cx%2C0%2C1)&+Simpson(x-%3Ex%5E3%2C0%2C1%2C1)-integrate(x%5E3%2Cx%2C0%2C1)&+Simpson(x-%3Ex%5E4%2C0%2C1%2C1)-integrate(x%5E4%2Cx%2C0%2C1)&+///Pour%20Simpson,%20on%20s'attendait%20%C3%A0%20un%20ordre%202%20mais%20en%20fait%20c'est%203%20pour%20des%20raisons%20de%20sym%C3%A9trie%20(on%20peut%20faire%20la%20m%C3%AAme%20observation%20pour%20le%20point%20milieu%20qui%20est%20d'ordre%201%20au%20lieu%20de%200).%20On%20gagnera%20donc%20environ%204%20d%C3%A9cimales%20en%20multipliant%20par%2010%20le%20nombre%20de%20subdivisions.&+Simpson(cos%2C0%2C1.0%2C10)-sin(1)%0A&+Simpson(cos%2C0%2C1.0%2C100)-sin(1)&+///Les%20quadratures%20de%20Gauss%20sont%20des%20m%C3%A9thodes%20qui%20optimisent%20la%20position%20des%20points%20d'interpolation%20sur%20une%20subdivision%20pour%20obtenir%20l'ordre%20le%20plus%20grand%20possible.%20On%20montre%20qu'avec%20$n$%20points,%20l'ordre%20optimal%20est%20$2n-1$,%20atteint%20pour%20les%20racines%20du%20$n$-i%C3%A8me%20polyn%C3%B4me%20de%20Legendre.&+n%3A%3D3%3B%20l%3A%3Dlegendre(n)%3B%20r%3A%3Dsolve(l)&+I(f)%3A%3Dsum(w%5Bj%5D*f(r%5Bj%5D)%2C%0A%20%20j%2C0%2Csize(r)-1)&+///On%20peut%20trouver%20les%20poids%20de%20deux%20mani%C3%A8res,%20en%20int%C3%A9grant%20le%20polyn%C3%B4me%20qui%20s'annule%20en%20toutes%20les%20noeuds%20sauf%20un,%20ou%20en%20r%C3%A9solvant%20un%20syst%C3%A8me%20lin%C3%A9aire.&+normal(int(product(%0A%20%20x-r%5Bj%5D%2Cj%2C1%2Csize(r)-1)%2Cx%2C-1%2C1)%2F%0A%20%20product(r%5B0%5D-r%5Bj%5D%2Cj%2C1%2Csize(r)-1))&+W%3A%3Dsolve(%0A%20%20%5BI(1)-int(1%2Cx%2C-1%2C1)%2C%0A%20%20I(x-%3Ex)-int(x%2Cx%2C-1%2C1)%2C%0A%20%20I(x-%3Ex%5E2)-int(x%5E2%2Cx%2C-1%2C1)%5D%2C%0A%5Bw%5B0%5D%2Cw%5B1%5D%2Cw%5B2%5D%5D)%0A&+normal(I(x-%3Ex%5E3)(w%3DW%5B0%5D))%0A-int(x%5E3%2Cx%2C-1%2C1)&+normal(I(x-%3Ex%5E4)(w%3DW%5B0%5D))%0A-int(x%5E4%2Cx%2C-1%2C1)&+normal(I(x-%3Ex%5E5)(w%3DW%5B0%5D))%0A-int(x%5E5%2Cx%2C-1%2C1)&+normal(I(x-%3Ex%5E6)(w%3DW%5B0%5D))%0A-int(x%5E6%2Cx%2C-1%2C1)&"
                                target="_blank">
                            <em>rectangles, trap&egrave;zes, Simpson, ordre, Mont&eacute;-Carlo</em></a>
                        </li>
                        <li>
                            R&eacute;solution approch&eacute;e d'&eacute;quations
                            diff&eacute;rentielles ordinaires:
                            <a
                                href="#exec&python=0&+///M%C3%A9thode%20d'Euler%20pour%20approcher%20la%20solution%20d'une%20%C3%A9quation%20diff%C3%A9rentielle%20$y'=f(t,y)$&+fonction%20Euler(f%2Ct0%2Ct1%2Cy0%2CN)%0A%20%20local%20j%2Ch%2Ct%2Cy%3B%0A%20%20h%3A%3D(t1-t0)%2FN%3B%0A%20%20y%3A%3Devalf(y0)%3B%0A%20%20pour%20j%20de%200%20jusque%20N-1%20faire%0A%20%20%20%20t%3A%3Dt0%2Bj*h%3B%0A%20%20%20%20y%20%2B%3D%20f(t%2Cy)*h%3B%0A%20%20fpour%3B%0A%20%20return%20y%3B%0Affonction%3A%3B&+f(t%2Cy)%3A%3Dy&+///On%20v%C3%A9rifie%20avec%20$y'=y$%20dont%20la%20solution%20est%20$y=C*exp(t)*&+Euler(f%2C0%2C1%2C1%2C10)&+Euler(f%2C0%2C1%2C1%2C100)&+///Passons%20%C3%A0%20une%20%C3%A9quation%20dont%20on%20ne%20connait%20pas%20la%20solution%20g%C3%A9n%C3%A9rale,%20$y'=sin(t*y)$&+f(t%2Cy)%3A%3Dsin(t*y)&+gl_x%3D-0.5..1.5%3B%0Agl_y%3D0..2%3B%0Aplotfield(f(t%2Cy)%2C%0A%20%20%5Bt%3D-0.5..1.5%2Cy%3D0..2%5D%2C%0A%20%20xstep%3D0.2%2Cystep%3D0.2)%3B%0Aplotode(f(t%2Cy)%2C%0A%20%20%5Bt%3D-0.5..1.5%2Cy%5D%2C%0A%20%20%5B0%2C1%5D%2Ccolor%3Dmagenta)&+Euler(f%2C0%2C1%2C1%2C10)&+Euler(f%2C0%2C1%2C1%2C100)&+///La%20m%C3%A9thode%20du%20point%20milieu%20est%20l'analogue%20de%20l'int%C3%A9gration%20par%20la%20m%C3%A9thode%20du%20point%20milieu,%20mais%20on%20ne%20connait%20pas%20le%20$y$%20du%20point%20milieu,%20on%20l'approche%20par%20Euler.&+fonction%20Milieu(f%2Ct0%2Ct1%2Cy0%2CN)%0A%20%20local%20j%2Ch%2Ct%2Cy%2Cym%3B%0A%20%20h%3A%3D(t1-t0)%2FN%3B%0A%20%20y%3A%3Devalf(y0)%3B%0A%20%20pour%20j%20de%200%20jusque%20N-1%20faire%0A%20%20%20%20t%3A%3Dt0%2Bj*h%3B%0A%20%20%20%20ym%20%3A%3D%20y%2Bf(t%2Cy)*h%2F2%3B%0A%20%20%20%20y%20%2B%3D%20f(t%2Bh%2F2%2Cym)*h%3B%0A%20%20fpour%3B%0A%20%20return%20y%3B%0Affonction%3A%3B&+Milieu(f%2C0%2C1%2C1%2C10)&+odesolve(f(t%2Cy)%2C%5Bt%2Cy%5D%2C%5B0%2C1%5D%2C1)&+///Les%20m%C3%A9thodes%20de%20Runge-Kutta%20g%C3%A9n%C3%A9ralisent%20cela.%20Par%20exemple%20RK4%20est%20l'analogue%20de%20la%20m%C3%A9thode%20de%20Simpson%20en%20int%C3%A9gration,%20et%20utilise%20deux%20m%C3%A9thodes%20pour%20approcher%20le%20point%20milieu.&+fonction%20RK4(f%2Ct0%2Ct1%2Cy0%2CN)%0A%20%20local%20j%2Ch%2Ct%2Cy%2Cy1%2Cy2%2Cy3%3B%0A%20%20h%3A%3D(t1-t0)%2FN%3B%0A%20%20y%3A%3Devalf(y0)%3B%0A%20%20pour%20j%20de%200%20jusque%20N-1%20faire%0A%20%20%20%20t%3A%3Dt0%2Bj*h%3B%0A%20%20%20%20y1%20%3A%3D%20y%2Bf(t%2Cy)*h%2F2%3B%20%2F%2F%201er%20point%20milieu%0A%20%20%20%20y2%20%3A%3D%20y%2Bf(t%2Bh%2F2%2Cy1)*h%2F2%3B%20%2F%2F%202eme%20point%20milieu%0A%20%20%20%20y3%20%3A%3D%20y%2Bh*f(t%2Bh%2F2%2Cy2)%3B%20%2F%2F%201ere%20approx.%20a%20droite%0A%20%20%20%20y%20%2B%3D%20h%2F6*(f(t%2Cy)%2B2*f(t%2Bh%2F2%2Cy1)%2B2*f(t%2Bh%2F2%2Cy2)%2Bf(t%2Bh%2Cy3))%3B%0A%20%20fpour%3B%0A%20%20return%20y%3B%0Affonction%3A%3B&+RK4(f%2C0%2C1%2C1%2C100)&+RK4((t%2Cy)-%3Ey%2C0%2C1%2C1%2C100)%3B%20%0Aexp(1.0)&"
                                target="_blank">Xcas
                            </a>,
                            <a
                                href="#exec&python=0&+///M%C3%A9thode%20d'Euler%20pour%20approcher%20la%20solution%20d'une%20%C3%A9quation%20diff%C3%A9rentielle%20$y'=f(t,y)$&+def%20Euler(f%2Ct0%2Ct1%2Cy0%2CN)%3A%0A%20%20%23%20local%20j%2Ch%2Ct%2Cy%0A%20%20h%3D(t1-t0)%2F(N*1.0)%0A%20%20y%3Dy0%0A%20%20for%20j%20in%20range(N)%3A%20%0A%20%20%20%20t%20%3D%20t0%2Bj*h%0A%20%20%20%20y%20%2B%3D%20f(t%2Cy)*h%0A%20%20return%20y&+def%20f(t%2Cy)%3A%0A%20%20return%20y&+///On%20v%C3%A9rifie%20avec%20$y'=y$%20dont%20la%20solution%20est%20$y=C*exp(t)*&+Euler(f%2C0%2C1%2C1%2C10)&+Euler(f%2C0%2C1%2C1%2C100)&+///Passons%20%C3%A0%20une%20%C3%A9quation%20dont%20on%20ne%20connait%20pas%20la%20solution%20g%C3%A9n%C3%A9rale,%20$y'=sin(t*y)$&+def%20f(t%2Cy)%3A%0A%20%20return%20sin(t*y)&+gl_x%3D-0.5..1.5%3B%0Agl_y%3D0..2%3B%0Aplotfield(f(t%2Cy)%2C%0A%20%20%5Bt%3D-0.5..1.5%2Cy%3D0..2%5D%2C%0A%20%20xstep%3D0.2%2Cystep%3D0.2)%3B%0Aplotode(f(t%2Cy)%2C%0A%20%20%5Bt%3D-0.5..1.5%2Cy%5D%2C%0A%20%20%5B0%2C1%5D%2Ccolor%3Dmagenta)&+Euler(f%2C0%2C1%2C1%2C10)&+Euler(f%2C0%2C1%2C1%2C100)&+///La%20m%C3%A9thode%20du%20point%20milieu%20est%20l'analogue%20de%20l'int%C3%A9gration%20par%20la%20m%C3%A9thode%20du%20point%20milieu,%20mais%20on%20ne%20connait%20pas%20le%20$y$%20du%20point%20milieu,%20on%20l'approche%20par%20Euler.&+def%20Milieu(f%2Ct0%2Ct1%2Cy0%2CN)%3A%0A%20%20%23%20local%20j%2Ch%2Ct%2Cy%2Cym%0A%20%20h%3D(t1-t0)%2F(N*1.0)%0A%20%20y%3Dy0%0A%20%20for%20j%20in%20range(N)%3A%20%0A%20%20%20%20t%20%3D%20t0%2Bj*h%0A%20%20%20%20ym%20%3D%20y%2Bf(t%2Cy)*h%2F2%0A%20%20%20%20y%20%2B%3D%20f(t%2Bh%2F2%2Cym)*h%0A%20%20return%20y&+Milieu(f%2C0%2C1%2C1%2C10)&+odesolve(f(t%2Cy)%2C%5Bt%2Cy%5D%2C%5B0%2C1%5D%2C1)&+///Les%20m%C3%A9thodes%20de%20Runge-Kutta%20g%C3%A9n%C3%A9ralisent%20cela.%20Par%20exemple%20RK4%20est%20l'analogue%20de%20la%20m%C3%A9thode%20de%20Simpson%20en%20int%C3%A9gration,%20et%20utilise%20deux%20m%C3%A9thodes%20pour%20approcher%20le%20point%20milieu.&+def%20RK4(f%2Ct0%2Ct1%2Cy0%2CN)%3A%0A%20%20%23%20local%20j%2Ch%2Ct%2Cy%2Cy1%2Cy2%2Cy3%0A%20%20h%3D(t1-t0)%2F(N*1.0)%0A%20%20y%3Dy0%0A%20%20for%20j%20in%20range(N)%3A%0A%20%20%20%20t%20%3D%20t0%2Bj*h%0A%20%20%20%20y1%20%3D%20y%2Bf(t%2Cy)*h%2F2%20%23%201er%20point%20milieu%0A%20%20%20%20y2%20%3D%20y%2Bf(t%2Bh%2F2%2Cy1)*h%2F2%20%23%202eme%20point%20milieu%0A%20%20%20%20y3%20%3D%20y%2Bh*f(t%2Bh%2F2%2Cy2)%20%23%201ere%20approx.%20a%20droite%0A%20%20%20%20y%20%2B%3D%20h%2F6*(f(t%2Cy)%2B2*f(t%2Bh%2F2%2Cy1)%2B2*f(t%2Bh%2F2%2Cy2)%2Bf(t%2Bh%2Cy3))%0A%20%20return%20y&+RK4(f%2C0%2C1%2C1%2C100)&+RK4(lambda%20t%2Cy%3Ay%2C0%2C1%2C1%2C100)%3B%20%0Aexp(1.0)&"
                                target="_blank"><strong>Python</strong>
                            </a>
                        </li>
                        <li> PGCD de polyn&ocirc;mes, d'Euclide au sous-r&eacute;sultant:
                            <a href="#exec&python=0&+///Le%20PGCD%20de%20polyn%C3%B4mes%20en%20une%20variable%20%C3%A0%20coefficients%20entiers&+a%3A%3D(x-1)%5E8*(x%5E2%2B2)%3B%0Ab%3A%3D(x-1)*(x%5E2%2B2)%5E4&+fonction%20Euclide(a%2Cb)%0A%20%20tantque%20b!%3D0%20faire%0A%20%20%20%20print(b)%3B%0A%20%20%20%20a%2Cb%3A%3Db%2Crem(a%2Cb)%3B%0A%20%20ftantque%3B%0A%20%20return%20a%3B%0Affunction%3A%3B&+Euclide(a%2Cb)&+///Les%20coefficients%20sont%20rationnels%20donc%20les%20calculs%20plus%20couteux%20d'autant%20plus%20que%20la%20taille%20des%20num%C3%A9rateurs%20et%20d%C3%A9nominateurs%20augmente%20rapidement%20dans%20l'algorithme%20d'Euclide.%0aOn%20peut%20travailler%20dans%20Z%20au%20lieu%20de%20Q%20avec%20la%20pseudo-division&+fonction%20Euclide1(a%2Cb)%0A%20%20si%20degree(a)%3Cdegree(b)%20alors%20return%20Euclide1(b%2Ca)%3B%20fsi%3B%0A%20%20tantque%20b!%3D0%20faire%0A%20%20%20%20print(b)%3B%0A%20%20%20%20a%2Cb%3A%3Db%2Crem(lcoeff(b)%5E(degree(a)-degree(b)%2B1)*a%2Cb)%3B%0A%20%20ftantque%3B%0A%20%20return%20a%3B%0Affunction%3A%3B&+Euclide1(a%2Cb)&+///Mais%20le%20probl%C3%A8me%20de%20la%20taille%20des%20coefficients%20demeure.%20%0aOn%20peut%20remplacer%20$b$%20par%20sa%20partie%20primitive.&+fonction%20Euclide2(a%2Cb)%0A%20%20si%20degree(a)%3Cdegree(b)%20alors%20return%20Euclide2(b%2Ca)%3B%20fsi%3B%0A%20%20tantque%20b!%3D0%20faire%0A%20%20%20%20b%3A%3Dprimpart(b)%3B%0A%20%20%20%20print(b)%3B%0A%20%20%20%20a%2Cb%3A%3Db%2Crem(lcoeff(b)%5E(degree(a)-degree(b)%2B1)*a%2Cb)%3B%0A%20%20ftantque%3B%0A%20%20return%20a%3B%0Affunction%3A%3B&+Euclide2(a%2Cb)&+///C'est%20mieux,%20mais%20calculer%20le%20PGCD%20des%20coefficients%20de%20$b$%20%C3%A0%20chaque%20%C3%A9tape%20est%20co%C3%BBteux.%0aL'algorithme%20du%20sous-r%C3%A9sultant%20calcule%20%C3%A0%20la%20place%20un%20diviseur%20%C3%A0%20priori.%20Ce%20coefficient%20n'est%20pas%20optimal,%20mais%20presque,%20et%20il%20se%20calcule%20facilement.&+fonction%20Euclide3(a%2Cb)%0A%20%20local%20g%2Ch%2Cq%3B%0A%20%20si%20degree(a)%3Cdegree(b)%20alors%20return%20Euclide3(b%2Ca)%3B%20fsi%3B%0A%20%20g%3A%3D1%3B%20h%3A%3D1%3B%20%0A%20%20tantque%20b!%3D0%20faire%0A%20%20%20%20d%3A%3Ddegree(a)-degree(b)%3B%0A%20%20%20%20q%3A%3Dlcoeff(b)%3B%0A%20%20%20%20a%2Cb%3A%3Db%2Crem(q%5E(d%2B1)*a%2Cb)%3B%0A%20%20%20%20b%3A%3Dquo(b%2Cg*h%5Ed)%3B%0A%20%20%20%20g%3A%3Dq%3B%20h%3A%3Dq%5Ed%2Fh%5E(d-1)%3B%0A%20%20ftantque%3B%0A%20%20return%20a%3B%0Affunction%3A%3B&+Euclide3(a%2Cb)&+///Les%20m%C3%A9thodes%20modulaires%20sont%20plus%20efficaces.%20Si%20les%20polyn%C3%B4mes%20sont%20premiers%20entre%20eux,%20ils%20le%20sont%20toujours%20modulo%20n'importe%20quel%20nombre%20premier%20ne%20divisant%20pas%20leur%20r%C3%A9sultant,%20on%20s'en%20rend%20vite%20compte.%0aSinon%20on%20reconstruit%20le%20PGCD%20modulo%20un%20ou%20plusieurs%20nombres%20premiers%20qui%20donnent%20le%20degr%C3%A9%20minimal%20et%20on%20teste%20la%20divisibilit%C3%A9%20par%20les%20polyn%C3%B4mes%20$a$%20et%20$b$.&+Euclide(a%20mod%2011%2Cb%2B1%20mod%2011)&+g%3A%3DEuclide(a%20mod%2011%2Cb%20mod%2011)&+normal(g%2Flcoeff(g))%20mod%200&"
                               target="_blank">Xcas</a>,
                            <a
                                href="#exec&python=1&+///Le%20PGCD%20de%20polyn%C3%B4mes%20en%20une%20variable%20%C3%A0%20coefficients%20entiers&+a%3A%3D(x-1)%5E8*(x%5E2%2B2)%3B%0Ab%3A%3D(x-1)*(x%5E2%2B2)%5E4&+def%20Euclide(a%2Cb)%3A%0A%20%20while%20b!%3D0%3A%0A%20%20%20%20print(b)%0A%20%20%20%20a%2Cb%3Db%2Crem(a%2Cb)%0A%20%20return%20a&+Euclide(a%2Cb)&+///Les%20coefficients%20sont%20rationnels%20donc%20les%20calculs%20plus%20couteux%20d'autant%20plus%20que%20la%20taille%20des%20num%C3%A9rateurs%20et%20d%C3%A9nominateurs%20augmente%20rapidement%20dans%20l'algorithme%20d'Euclide.%0aOn%20peut%20travailler%20dans%20Z%20au%20lieu%20de%20Q%20avec%20la%20pseudo-division&+def%20Euclide1(a%2Cb)%3A%0A%20%20if%20degree(a)%3Cdegree(b)%3A%0A%20%20%20%20return%20Euclide1(b%2Ca)%0A%20%20while%20b!%3D0%3A%0A%20%20%20%20print(b)%0A%20%20%20%20a%2Cb%3Db%2Crem(lcoeff(b)%5E(degree(a)-degree(b)%2B1)*a%2Cb)%0A%20%20return%20a&+Euclide1(a%2Cb)&+///Mais%20le%20probl%C3%A8me%20de%20la%20taille%20des%20coefficients%20reste.%20%0aOn%20peut%20remplacer%20$b$%20par%20sa%20partie%20primitive.&+def%20Euclide2(a%2Cb)%3A%0A%20%20if%20degree(a)%3Cdegree(b)%3A%0A%20%20%20%20return%20Euclide2(b%2Ca)%0A%20%20while%20b!%3D0%3A%0A%20%20%20%20b%3A%3Dprimpart(b)%0A%20%20%20%20print(b)%0A%20%20%20%20a%2Cb%3Db%2Crem(lcoeff(b)%5E(degree(a)-degree(b)%2B1)*a%2Cb)%0A%20%20return%20a&+Euclide2(a%2Cb)&+///C'est%20mieux,%20mais%20calculer%20le%20PGCD%20des%20coefficients%20de%20$b$%20%C3%A0%20chaque%20%C3%A9tape%20est%20co%C3%BBteux.%0aL'algorithme%20du%20sous-r%C3%A9sultant%20calcule%20%C3%A0%20la%20place%20un%20diviseur%20%C3%A0%20priori.%20Ce%20coefficient%20n'est%20pas%20optimal,%20mais%20presque,%20et%20il%20se%20calcule%20facilement.&+def%20Euclide3(a%2Cb)%3A%0A%20%20%23%20local%20g%2Ch%2Cq%0A%20%20if%20degree(a)%3Cdegree(b)%3A%0A%20%20%20%20return%20Euclide3(b%2Ca)%0A%20%20g%3D1%20%0A%20%20h%3D1%20%0A%20%20while%20b!%3D0%3A%0A%20%20%20%20d%3Ddegree(a)-degree(b)%0A%20%20%20%20q%3Dlcoeff(b)%0A%20%20%20%20a%2Cb%3Db%2Crem(q%5E(d%2B1)*a%2Cb)%0A%20%20%20%20b%3Dquo(b%2C(g*h%5Ed))%0A%20%20%20%20g%3Dq%20%0A%20%20%20%20h%3Dq%5Ed%2Fh%5E(d-1)%0A%20%20return%20a&+Euclide3(a%2Cb)&+///Les%20m%C3%A9thodes%20modulaires%20sont%20plus%20efficaces.%20Si%20les%20polyn%C3%B4mes%20sont%20premiers%20entre%20eux,%20ils%20le%20sont%20toujours%20modulo%20n'importe%20quel%20nombre%20premier%20ne%20divisant%20pas%20leur%20r%C3%A9sultant,%20on%20s'en%20rend%20vite%20compte.%0aSinon%20on%20reconstruit%20le%20PGCD%20modulo%20un%20ou%20plusieurs%20nombres%20premiers%20qui%20donnent%20le%20degr%C3%A9%20minimal%20et%20on%20teste%20la%20divisibilit%C3%A9%20par%20les%20polyn%C3%B4mes%20$a$%20et%20$b$.&+Euclide(a%20mod%2011%2Cb%2B1%20mod%2011)&+g%3A%3DEuclide(a%20mod%2011%2Cb%20mod%2011)&+normal(g%2Flcoeff(g))%20mod%200&"
                                target="_blank">
                            Python</a>
                        </li>
			<li>Agr&eacute;gation:
			<a
			href="#exec&python=0&+///Intersection%20de%20courbes%20alg%C3%A9briques%20et%20r%C3%A9sultant.%0A%3Cstrong%3EPremier%20exemple%3A%3C%2Fstrong%3E%20cercle%20inter%20ellipse.&+c%3A%3Dcircle(0%2C2)%3B%20a%3A%3Dequation(c)%3B%20%0Ab%3A%3D4x%5E2%2B3x*y%2By%5E2-8%3B%20E%3A%3Dimplicitplot(b)%3B%0A&+a%3A%3Dequal2diff(equation(c))%3B%20%0Ar%3A%3Dresultant(a%2Cb%2Cx)%3B%0Asy%3A%3Dsolve(r%2Cy)%3B%20sx%3A%3Dsy%3A%3B&+j%3A%3D0%3B%20Y%3A%3Dsy%5Bj%5D%3B%0A%5BX%5D%3A%3Dsolve(gcd(a(y%3DY)%2Cb(y%3DY)))%3B&+c%3BE%3BM%3A%3Dpoint(X%2CY)&+///%3Cstrong%3EDeuxi%C3%A8me%20exemple%3A%3C%2Fstrong%3E%20une%20hyperbole%20avec%20une%20cubique.%0AOn%20s'attend%20%C3%A0%20au%20plus%206%20points%20d'intersection%2C%20il%20y%20en%20a%20en%20fait%205%2C%20on%20va%20essayer%20de%20comprendre%20pourquoi.&+hyp%3A%3Dx*y-4%3B%20cub%3A%3Dy%5E2-(x-3)*(x%5E2-16)%3B%0Agl_x%3D-5..8%3B%20gl_y%3A%3D-10..10%3B%0AH%3A%3Dimplicitplot(hyp%2C%5Bx%2Cy%5D%2Ccolor%3Dred)%3B%20%0Ac%3A%3Dimplicitplot(cub%2C%5Bx%3D-5..8%2Cy%3D-10..10%5D)&+r%3A%3Dresultant(hyp%2Ccub)&+solve(r%3D0%2Cy)&+hypt%3A%3Dx*y-4*t%5E2%3B%20cubt%3A%3Dy%5E2*t-(x-3t)*(x%5E2-16t%5E2)&+resultant(hypt%2Ccubt%2Cx)&+///Le%20r%C3%A9sultant%20homog%C3%A9n%C3%A9is%C3%A9%20en%20%24x%24%20est%20bien%20de%20degr%C3%A9%206%2C%20mais%20il%20n'a%20pas%20de%20terme%20en%20%24y%5E6%24.%20Il%20y%20a%20donc%20un%20point%20d'intersection%20%C3%A0%20l'infini%2C%20de%20la%20forme%20%24(x%2Cy%2C0)%24.%20En%20remplacant%20%24t%24%20par%200%20dans%20les%20%C3%A9quations%20de%20d%C3%A9part%2C%20on%20a%20%24x*y%3D0%24%20et%20%24x%5E3%3D0%24%2C%20donc%20le%20point%20%C3%A0%20l'infini%20est%20%24(0%2Cy%2C0)%24.%20L'intersection%20se%20fait%20en%20quelque%20sorte%20entre%20l'asymptote%20verticale%20de%20l'hyperbole%20et%20la%20branche%20parabolique%20de%20direction%20asymptotique%20verticale%20de%20la%20cubique.%0ALe%20r%C3%A9sultant%20homog%C3%A9n%C3%A9is%C3%A9%20en%20%24y%24%20est%20de%20degr%C3%A9%205%2C%20car%20le%20degr%C3%A9%20partiel%20en%20%24y%24%20est%201%20de%20moins%20que%20le%20deg%C3%A9%20total%20pour%20les%202%20polynomes%20(alors%20qu'en%20%24x%24%20le%20degr%C3%A9%20partiel%20est%20%C3%A9gal%20au%20degr%C3%A9%20total%20pour%20la%20cubique).&+///%3Cstrong%3ETroisi%C3%A8me%20exemple%3C%2Fstrong%3E%20avec%20des%20points%20complexes%20et%20de%20la%20multiplicit%C3%A9&+cer%3A%3D(x-2)%5E2%2By%5E2-4%3B%20%0Agl_x%3D-10..16%3B%20gl_y%3A%3D-8..8%3B%20%0AC%3A%3Dimplicitplot(cer%2C%5Bx%2Cy%5D%2Ccolor%3Dred)%3B%20%0Ac%3A%3Dimplicitplot(cub%2C%5Bx%3D-5..8%2Cy%3D-10..10%5D)&+rx%3A%3Dfactor(resultant(cer%2Ccub%2Cx))&+ry%3A%3Dfactor(resultant(cer%2Ccub%2Cy))&+csolve(rx%3D0%2Cy)&+csolve(ry%3D0%2Cx)&+///Ici%2C%20on%20perd%20un%20point%20d'intersection%20parce%20que%20le%20cercle%20est%20tangent%20%C3%A0%20la%20cubique%20pour%20%24x%3D4%2Cy%3D0%24%20(point%20d'intersection%20de%20multiplicit%C3%A9%202).%0AOn%20perd%20deux%20autres%20points%20d'intersection%20dans%20le%20complexe.&"
target="_blank">R&eacute;sultant et intersections</a>
			<li>
                            Agr&eacute;gation:
                            <a
                                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                                target="_blank">
                            Localisation des racines d'un polyn&ocirc;me
                            </a>
                        </li>
                        <li> Alg&egrave;bre lin&eacute;aire sur un corps fini (Agr&eacute;gration)
                            <a
                                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                                target="_blank">Xcas
                            </a>,
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                                href="#exec&python=0&+///%3Ch1%3eAlg%C3%A8bre%20lin%C3%A9aire%20exacte%20sur%20un%20corps%20fini.%3C/h1%3e%0aD%C3%A9composition%20LU,%20application%20au%20calcul%20d'un%20inverse%20de%20matrice.&+n%3A%3D5%3B%20p%3A%3D17%3B%20a%3A%3Drandmatrix(n%2Cn%2C1%20mod%20p)&+p%2Cl%2Cu%3A%3Dlu(a)&+def%20moninv(a)%3A%0A%20%20%23%20local%20b%2Cc%2Cj%2Cp%2Cl%2Cu%0A%20%20n%3Dsize(a)%0A%20%20b%3Da%20%0A%20%20c%3Didentity(n)%0A%20%20p%2Cl%2Cu%3Dlu(a)%0A%20%20for%20j%20in%20range(n)%3A%20%0A%20%20%20%20b%5Bj%5D%3Dlinsolve(p%2Cl%2Cu%2Cc%5Bj%5D)%0A%20%20return%20tran(b)&+moninv(a)%3B%20inv(a)&+///Calcul%20du%20polynome%20caract%C3%A9ristique%20en%20$O(n^4)$%20par%20interpolation.%20Si%20le%20corps%20fini%20$ZZ$/$p*ZZ$%20n'a%20pas%20assez%20d'%C3%A9l%C3%A9ments%20pour%20interpoler,%20on%20construit%20une%20extension.&+def%20polcar(a)%3A%0A%20%20%23%20local%20j%2Cp%2Cn%2CI%2CN%2Cg%2Cgj%2CX%2CY%3B%0A%20%20if%20type(a%5B0%2C0%5D)!%3D15%3A%20%0A%20%20%20%20return%20%22il%20faut%20une%20matrice%20%C3%A0%20coefficients%20dans%20Z%2FpZ%22%20%0A%20%20p%3Da%5B0%2C0%2C2%5D%20%23%20caracteristique%20du%20corps%0A%20%20if%20!isprime(p)%3A%20%0A%20%20%20%20return%20p%2B%22%20n'est%20pas%20premier%22%20%0A%20%20n%3Dsize(a)%0A%20%20I%3Didentity(n)%0A%20%20X%3D%5B%5D%0A%20%20Y%3D%5B%5D%0A%20%20if%20n%3Cp%3A%0A%20%20%20%20for%20j%20in%20range(n%2B1)%3A%0A%20%20%20%20%20%20X%5Bj%5D%3Dj%0A%20%20%20%20%20%20Y%5Bj%5D%3Ddet(j*I-a)%0A%20%20%20%20return%20normal(interp(X%2CY))%0A%20%20%23%20construction%20d'une%20extension%20de%20Z%2FpZ%0A%20%20N%3Dceil(log(n%2B1)%2Flog(p))%0A%20%20purge(g)%0A%20%20GF(p%2CN%2Cg)%0A%20%20%23%20interpolation%20en%20les%20g%5Ej%0A%20%20gj%3D1%0A%20%20for%20j%20in%20range(n%2B1)%3A%0A%20%20%20%20X%5Bj%5D%3Dgj%0A%20%20%20%20Y%5Bj%5D%3Ddet(gj*I-a)%0A%20%20%20%20gj%3Dg*gj%0A%20%20return%20normal(interp(X%2CY))&+polcar(a)%3B%20charpoly(a%2Cx)&+a%3A%3Drandmatrix(8%2C8%2C1%20mod%205)&+polcar(a)%3B%20charpoly(a%2Cx)&+///Un%20autre%20algorithme%20en%20$O(n^4)$%20(Fadeev-Souriau-Leverrier),%20la%20caract%C3%A9ristique%20du%20corps%20doit%20%C3%AAtre%20plus%20grande%20que%20la%20taille%20de%20la%20matrice.%20Il%20calcule%20aussi%20la%20comatrice%20de%20$x*identity(n)-A$.&+def%20Faddeev(A)%3A%20%0A%20%20%23%20local%20Aj%2CAAj%2CId%2Ccoef%2Cn%2Cpcara%2Clmat%2Cj%0A%20%20%23%20renvoie%20la%20liste%20des%20matrices%20B%20et%20le%20polynome%20P%0A%20%20n%3Dncols(A)%0A%20%20Id%3Didn(n)%20%20%20%20%20%23%20matrice%20identite%0A%20%20Aj%3DId%0A%20%20lmat%3D%5B%5D%20%20%20%20%20%20%23%20B%20initialise%20a%20liste%20vide%0A%20%20pcara%3D%5B1%5D%20%20%20%20%23%20coefficient%20de%20plus%20grand%20degre%20de%20P%0A%20%20for%20j%20in%20range(1%2Cn%2B1)%3A%0A%20%20%20%20lmat.append(Aj)%20%20%23%20rajoute%20Aj%20a%20la%20liste%20de%20matrices%0A%20%20%20%20AAj%3DAj*A%0A%20%20%20%20coef%3D-trace(AAj)%2Fj%20%20%20%20%0A%20%20%20%20pcara.append(coef)%20%20%23%20rajoute%20coef%20au%20pol.%20caract.%0A%20%20%20%20Aj%3DAAj%2Bcoef*Id%0A%20%20return%20lmat%2Cpcara&+n%3A%3D4%3B%20p%3A%3D101%3B%20%0Aa%3A%3Drandmatrix(n%2Cn%2C1%20mod%20p)%3B%20%0AB%2CP%3A%3DFaddeev(a)%3B%0Acharpoly(a)&+///Xcas%20utilise%20l'algorithme%20de%20Danilevsky%20en%20$O(n^3)$%20(on%20se%20ram%C3%A8ne%20%C3%A0%20une%20matrice%20companion).%0aOn%20peut%20aussi%20calculer%20le%20polynome%20minimal%20par%20rapport%20%C3%A0%20un%20vecteur%20al%C3%A9atoire%20(recherche%20de%20relations%20entre%20$v$,%20$A*v$,%20...,%20$A^n*v$%20ou%20calcul%20de%20la%20matrice%20$P$%20de%20colonnes%20$v,A*v$,...,$A^(n-1)*v$,%20si%20elle%20est%20inversible%20alors%20$P^(-1)*A*P$%20est%20une%20matrice%20companion)%20ce%20qui%20donne%20g%C3%A9n%C3%A9riquement%20le%20polynome%20caract%C3%A9ristique.%20Ce%20calcul%20peut%20%C3%AAtre%20acc%C3%A9l%C3%A9r%C3%A9%20pour%20$n$%20grand,%20on%20calcule%20$v,Av$%20on%20multiplie%20par%20$A^2$%20(calcul%C3%A9%20avec%20Strassen%20par%20exemple),%20on%20a%20$v,Av,A^2*v,A^3*v$,%20on%20multiplie%20par%20$(A^2)^2$%20etc.,%20soit%20un%20cout%20en%20$O(n^(ln(7)/ln(2))*ln(n))$%0aOn%20peut%20enfin%20calculer%20les%20traces%20des%20puissances%20de%20$A$%20de%20mani%C3%A8re%20efficace%20et%20retrouver%20le%20polynome%20caract%C3%A9ristique%20par%20les%20identit%C3%A9s%20de%20Newton,%20mais%20l'algorithme%20de%20Faddeev%20calcule%20aussi%20la%20matrice%20$B$%20qui%20peut%20servir%20%C3%A0%20d%C3%A9terminer%20les%20vecteurs%20propres.&+normal((x*idn(a)-a)*horner(B%2Cx))&+l%3A%3Dsolve(charpoly(a%2Cx))&+///Si%20%3Ctt%3el%3C/tt%3e%20est%20non%20vide,%20on%20peut%20trouver%20la%20base%20propre%20avec%20$B$%20(sinon%20il%20faudrait%20construire%20une%20extension%20du%20corps%20fini).%0aAstuce:%20cliquez%20sur%20Exec%20en%20bas%20pour%20g%C3%A9n%C3%A9rer%20une%20autre%20matrice%20si%20%3Ctt%3el%3C/tt%3e%20est%20vide.&+horner(P%2Cl%5B0%5D)&+horner(B%2Cl%5B0%5D)%3B%0A(l%5B0%5D*identity(a)-a)*horner(B%2Cl%5B0%5D)&+///Si%20la%20valeur%20propre%20est%20simple,%20les%20vecteurs%20colonnes%20sont%20colin%C3%A9aires%20modulo%20101,%20l'espace%20propre%20est%20bien%20de%20dimension%201.&+///Conversion%20avec%20les%20identit%C3%A9s%20de%20Newton.%20On%20note%20$P[j]$%20la%20somme%20des%20$x[k]^j$%20et%20$(-1)^j*E[j]$%20le%20$j$-i%C3%A8me%20coefficient%20du%20polynome%20ayant%20les%20$x[k]$%20comme%20racines.%0a$E[1]=P[1]$%0a$2*E[2]=E[1]*P[1]-P[2]$%0a$3*E[3]=E[2]*P[1]-E[1]*P[2]+P[3]$%0a$4*E[4]=E[3]*P[1]-E[2]*P[2]+E[1]*P[3]-P[4]$&+def%20newton_E(P)%3A%0A%20%20%23%20local%20E%2Cn%2Cj%2Ck%2Cs%0A%20%20%23%20calcule%20les%20E%20en%20fonction%20des%20P%0A%20%20E%3DP%0A%20%20E%5B0%5D%3D1%0A%20%20n%3Dsize(P)-1%20%0A%20%20%23%20nombre%20de%20racines%0A%20%20for%20j%20in%20range(2%2Cn%2B1)%3A%0A%20%20%20%20s%3D0%0A%20%20%20%20for%20k%20in%20range(1%2Cj%2B1)%3A%0A%20%20%20%20%20%20s%20%2B%3D%20(-1)**(k-1)*P%5Bk%5D*E%5Bj-k%5D%0A%20%20%20%20E%5Bj%5D%3Ds%2Fj%0A%20%20return%20E&+///Exemple%20polynome%20ayant%20comme%20racines%201,%202,%20...,%20$n$.&+n%3A%3D4%3B%20P%3A%3Dseq(sum(j%5Ek%2Cj%2C1%2Cn)%2Ck%2C0%2Cn)&+E%3A%3Dnewton_E(P)&+pcoeff(seq(k%2Ck%2C1%2Cn))&+seq((-1)%5Ej*E%5Bj%5D%2Cj%2C0%2Csize(E)-1)&+///Calcul%20du%20polynome%20caract%C3%A9ristique%20avec%20les%20identit%C3%A9s%20de%20Newton&+P%3A%3Dseq(trace(a%5Ek)%2Ck%2C0%2Csize(a))&+newton_E(P)&+charpoly(a)&+def%20polnew(a)%3A%0A%20%20%23%20local%20n%0A%20%20n%3Dsize(a)%0A%20%20P%3D%5Bn%5D%0A%20%20aj%3Da%0A%20%20for%20j%20in%20range(n)%3A%0A%20%20%20%20P.append(trace(aj))%0A%20%20%20%20aj%3Daj*a%0A%20%20E%3Dnewton_E(P)%0A%20%20return%20seq((-1)**j*E%5Bj%5D%2Cj%2C0%2Csize(E)-1)&+polnew(a)&+a%3A%3Drandmatrix(6%2C6)%3A%3B%20%0Apolnew(a)%3B%20charpoly(a)&"
                                target="_blank">Python</a>
                        </li>
                        <li> Bases de Groebner
                            <a
                                href="#exec&python=0&+cyclic6%3A%3D%20%5B2*(x*y*z%2By*z*t%2Bz*t*u%2Bt*u*v%2Bu*v*x%2Bv*x*y)%2C%20%0Ax*y*z*t%2By*z*t*u%2Bz*t*u*v%2Bt*u*v*x%2Bu*v*x*y%2Bv*x*y*z%2C%20%0Ax*y*z*t*u*v-1%2C%20%0Ax%2By%2Bz%2Bt%2Bu%2Bv%2C%20%0Ax*y%2By*z%2Bz*t%2Bt*u%2Bu*v%2Bx*v%2C%20%0Ax*y*z*t*u%2By*z*t*u*v%2Bz*t*u*v*x%2Bt*u*v*x*y%2Bu*v*x*y*z%2Bv*x*y*z*t%5D%3B&+p%3A%3Dprevprime(2%5E24)%3B&+time(G%3A%3D%0A%20%20gbasis(cyclic6%20mod%20p%2C%0A%20%20%20%20indets(cyclic6)))&+size(G)&+G%5B20%5D&+time(H%3A%3D%0A%20%20gbasis(cyclic6%2C%0A%20%20%20%20indets(cyclic6)))&+H%5B20%5D&+normal(1%2F(lcoeff(H%5B20%5D%2Cv)%20mod%20p)%0A%20%20*H%5B20%5D)&+normal(1%2F(lcoeff(G%5B20%5D%2Cv)%20mod%20p)%0A%20%20*G%5B20%5D-1%2F(lcoeff(H%5B20%5D%2Cv)%20mod%20p)%0A%20%20*H%5B20%5D)&"
                                target="_blank">cyclic6</a>.
                            Pour des calculs plus intensifs, activez
			wasm dans les r&eacute;glages
                            et inspirez-vous de
                            <a
                                href="#exec&python=1&+cyclic7%3A%3D%5Bx1%2Bx2%2Bx3%2Bx4%2Bx5%2Bx6%2Bx7%2C%0A%20%20%20%20%20%20%20%20%20%20x1*x2%2Bx1*x7%2Bx2*x3%2Bx3*x4%2Bx4*x5%2Bx5*x6%2Bx6*x7%2C%0A%20%20%20%20%20%20%20%20%20%20x1*x2*x3%2Bx1*x2*x7%2Bx1*x6*x7%2Bx2*x3*x4%2Bx3*x4*x5%2Bx4*x5*x6%2Bx5*x6*x7%2C%0A%20%20%20%20%20%20%20%20%20%20x1*x2*x3*x4%2Bx1*x2*x3*x7%2Bx1*x2*x6*x7%2Bx1*x5*x6*x7%2Bx2*x3*x4*x5%2Bx3*x4*x5*x6%2Bx4*x5*x6*x7%2C%0A%20%20%20%20%20%20%20%20%20%20x1*x2*x3*x4*x5%2Bx1*x2*x3*x4*x7%2Bx1*x2*x3*x6*x7%2Bx1*x2*x5*x6*x7%2Bx1*x4*x5*x6*x7%2Bx2*x3*x4*x5*x6%2Bx3*x4*x5*x6*x7%2C%0A%20%20%20%20%20%20%20%20%20%20x1*x2*x3*x4*x5*x6%2Bx1*x2*x3*x4*x5*x7%2Bx1*x2*x3*x4*x6*x7%2Bx1*x2*x3*x5*x6*x7%2Bx1*x2*x4*x5*x6*x7%2Bx1*x3*x4*x5*x6*x7%2Bx2*x3*x4*x5*x6*x7%2C%0A%20%20%20%20%20%20%20%20%20%20x1*x2*x3*x4*x5*x6*x7-1%5D%3A%3B&+p%3A%3Dprevprime(2%5E24)&+time(G%3A%3Dgbasis(cyclic7%20mod%20p%2Clname(cyclic7)%2Crevlex))%3B&+size(G)&"
target="_blank">cyclic7 modulaire</a>.
Pour avoir des informations pendant le d&eacute;roulement des calculs, tapez la commande
<tt>debug_infolevel:=1</tt> (ou plus) et ouvrez la console du navigateur.
                            Pour des calculs vraiment intensifs, utilisez la version native de Xcas.
                        </li>
                        <li> Produit, quotient de polyn&ocirc;mes &agrave; plusieurs variables
                            (pour navigateur compatible avec web-assembly, par exemple Firefox &geq; 58)
                            <a
                                href="#exec&python=0&+n%3A%3D20%3B&+f%20%3A%3D%20symb2poly((1%20%2B%20x%20%2B%20y%20%2B%20z%2Bt)%5En%2C%5Bx%2Cy%2Cz%2Ct%5D)%3A%3B%0Aq%3A%3Dsymb2poly(x%5E(n-3)%2C%5Bx%2Cy%2Cz%2Ct%5D)%3A%3B%0Asize(f)%3B&+time(p%3A%3Df*(f%2B1))%3B%0Asize(p)%3B&+time(h%3A%3Dquo(p%2Cf%2C2))%3B%0Ah-f%3B&+time(h%2Cr%3A%3Dquorem(p%2Bq%2Cf%2C-1))%3B%0Ah-f%3Bpoly2symb(r%2C%5Bx%2Cy%2Cz%2Ct%5D)%3B&"
                                target="_blank">benchmark de Fateman n=20</a>
                        </li>
                        <li>
                            <a
                                href="#filename=parisseb%40orange.fr%40%20%20session&from=parisseb%40orange.fr&python=0&+///Approx%20linear%20algebra&+n%3A%3D500%3B%20%0Am%3A%3Dranm(n%2Cn%2Cuniformd%2C-1%2C1)%3A%3B%0Atime(q%2Cr%3A%3Dqr(m%2C-1))%3B%0Amaxnorm(m-q*r)%3B&+time(p%2Cq%3A%3Dschur(m))%3B%0Amaxnorm(p*q*trn(p)-m)%0A&+time(p%2Cl%2Cu%3A%3Dlu(m))%3B%0Amaxnorm(l*u-permu2mat(p)*m)&"
                                target="_blank">
                            Approx benchmarks
                            </a>
                        </li>
                        <li>
                            <a
                                href="#exec&python=0&+///Series%20expansion%20benchmark.&+n%3A%3D200%3Bseries(%22t%22)%3B%20%0Au%20%3A%3D%20t%20%2B%20O(t%5En)%3B%20%0Atime(r%3A%3D(u%2F(exp(u)-1))*exp(x*u))%3B&+///Expand%20power%20of%20polynomial%20with%20coefficient%20in%20an%20extension%20of%20$QQ$.&+x%3A%3Drootof(cyclotomic(20))%3B%0Af%3A%3D(3x%5E7%20%2B%20x%5E4%20-%203x%20%2B%201)*y%5E3%20%2B%20(2x%5E6-x%5E5%2B4x%5E4-x%5E3%2Bx%5E2-1)*y%20%2B(-3x%5E7%2B2x%5E6-x%5E5%2B3x%5E3-2x%5E2%2Bx)%3A%3B%0Ap%3A%3Dsymb2poly(f%2Cy%2C%5B%5D)%3A%3B%20time(s%3A%3Dp%5E400)%3B&+///Determinant%20of%20a%20matrix%20of%20size%20$n$%20with%20random%20coefficients%20in%20an%20extension%20of%20$QQ$.&+purge(x)%3Bn%3A%3D40%3B%0Aa%3A%3Drootof(x%5E3%2B3x%2B1)%3B%20%0Am%3A%3Dranm(n%2Cn%2Ca)%3A%3B%20%0Atime(d%3A%3Ddet(m))%3B&+///Determinant%20of%20a%20matrix%20with%20polynomial%20coefficients%20over%20$ZZ$/$p*ZZ$&+p%20%3A%3D%202003*1009%3B%20n%3A%3D40%3B%20%0Af(j%2Ck)%3A%3D%7B%20k%3A%3Drand(6)%3B%20return%20randpoly(x%2Ck)%20mod%20p%3B%20%7D%3B%20%0Am%3A%3Dmatrix(n%2Cn%2Cf)%3A%3B%20%0Atime(det(m))%3B&+///Characteristic%20polynomial%20of%20a%20matrix%20with%20integer%20coefficients.&+n%3A%3D70%3B%20%0Am%3A%3Dranm(n%2Cn%2C-21)%3A%3B%20%0Atime(charpoly(m))%3B&"
                                target="_blank">
                            Exact benchmarks
                            </a>
                        <li>
                            Des programmes graphiques
                            <ul>
                                <li>
                                    Fractale de Mandelbrot
                                    <a
                                        href="#python=0&exec&+///Fractale%20de%20Mandelbrot,%20programme%20qui%20n'utilise%20pas%20la%20sym%C3%A9trie&+fonction%20fra(X%2CY%2CNmax)%0A%20%20local%20x%2Cy%2Cz%2Cc%2Cj%2Cw%2Ch%2Cres1%2Cres2%3B%0A%20%20w%3A%3D2.7%2FX%3B%0A%20%20h%3A%3D-1.87%2FY%3B%0A%20%20res1%3A%3D%5B%5D%3B%20%0A%20%20Y%3A%3DY-1%3B%0A%20%20pour%20y%20de%200%20jusque%20Y%20faire%0A%20%20%20%20c%3A%3D-2.1%2Bi*(h*y%2B0.935)%3B%0A%20%20%20%20pour%20x%20de%200%20jusque%20X-1%20faire%0A%20%20%20%20%20%20z%3A%3D0%3B%0A%20%20%20%20%20%20pour%20j%20de%200%20jusque%20Nmax-1%20faire%0A%20%20%20%20%20%20%20%20if%20abs(z%3A%3Dz%5E2%2Bc)%3E2%20then%20break%3B%20fi%3B%0A%20%20%20%20%20%20fpour%3B%0A%20%20%20%20%20%20res1.append(pixon(x%2Cy%2C126*j%2B2079))%3B%0A%20%20%20%20%20%20c%3A%3Dc%2Bw%3B%0A%20%20%20%20fpour%3B%0A%20%20fpour%3B%0A%20%20return%20res1%3B%0Affonction%3A%3B&+///%20Fractale%20de%20Mandelbrot%20plus%20rapide,%20en%20utilisant%20la%20sym%C3%A9trie&+fonction%20fra1(X%2CY%2CNmax)%0A%20%20local%20x%2Cy%2Cz%2Cc%2Cj%2Cw%2Ch%2Cres1%2Cres2%3B%0A%20%20w%3A%3D2.7%2FX%3B%0A%20%20h%3A%3D-1.87%2FY%3B%0A%20%20res1%3A%3Dmakelist(-ceil(X*Y%2F2)-1)%3B%20%0A%20%20res2%3A%3Dcopy(res1)%3B%0A%20%20Y%3A%3DY-1%3B%0A%20%20pour%20y%20de%200%20jusque%20Y%2F2%20faire%0A%20%20%20%20c%3A%3D-2.1%2Bi*(h*y%2B0.935)%3B%0A%20%20%20%20pour%20x%20de%200%20jusque%20X-1%20faire%0A%20%20%20%20%20%20z%3A%3D0%3B%0A%20%20%20%20%20%20pour%20j%20de%200%20jusque%20Nmax-1%20faire%0A%20%20%20%20%20%20%20%20if%20abs(z%3A%3Dz%5E2%2Bc)%3E2%20then%20break%3B%20fi%3B%0A%20%20%20%20%20%20fpour%3B%0A%20%20%20%20%20%20res1.append(pixon(x%2Cy%2C126*j%2B2079))%3B%0A%20%20%20%20%20%20res2.append(pixon(x%2CY-y%2C126*j%2B2079))%3B%0A%20%20%20%20%20%20c%3A%3Dc%2Bw%3B%0A%20%20%20%20fpour%3B%0A%20%20fpour%3B%0A%20%20return%20res1%2Cres2%3B%0Affonction%3A%3B&+pixon(1)&+fra1(260%2C222%2C10)&"
                                        target="_blank">Xcas</a>,
                                    <a href="#python=1&exec&+///Fractale%20de%20Mandelbrot%20sans%20utiliser%20la%20sym%C3%A9trie&+def%20fra(X%2CY%2CNmax)%3A%0A%20%20local%20x%2Cy%2Cz%2Cc%2Cj%2Cw%2Ch%2Cres1%0A%20%20w%3D2.7%2FX%0A%20%20h%3D-1.87%2FY%0A%20%20res1%3D%5B%5D%0A%20%20res2%3D%5B%5D%0A%20%20for%20y%20in%20range(Y)%3A%0A%20%20%20%20c%20%3D%20-2.1%2Bi*(h*y%2B0.935)%0A%20%20%20%20for%20x%20in%20range(X)%3A%0A%20%20%20%20%20%20z%20%3D%200%0A%20%20%20%20%20%20for%20j%20in%20range(Nmax)%3A%0A%20%20%20%20%20%20%20%20if%20abs(z%3A%3Dz**2%2Bc)%3E2%3A%0A%20%20%20%20%20%20%20%20%20%20%20break%0A%20%20%20%20%20%20res1.append(pixon(x%2Cy%2C126*j%2B2079))%0A%20%20%20%20%20%20c%20%3D%20c%2Bw%3B%0A%20%20return%20res1&+///%20Fractale%20de%20Mandelbrot%20plus%20rapide,%20en%20utilisant%20la%20sym%C3%A9trie&+def%20fra1(X%2CY%2CNmax)%3A%0A%20%20local%20x%2Cy%2Cz%2Cc%2Cj%2Cw%2Ch%2Cres1%2Cres2%0A%20%20w%3D2.7%2FX%0A%20%20h%3D-1.87%2FY%0A%20%20res1%3Dmakelist(-ceil(X*Y%2F2)-1)%0A%20%20res2%3Dcopy(res1)%0A%20%20Y%3DY-1%0A%20%20for%20y%20in%20range(ceil(Y%2F2)%2B1)%3A%0A%20%20%20%20c%20%3D%20-2.1%2Bi*(h*y%2B0.935)%0A%20%20%20%20for%20x%20in%20range(X)%3A%0A%20%20%20%20%20%20z%20%3D%200%0A%20%20%20%20%20%20for%20j%20in%20range(Nmax)%3A%0A%20%20%20%20%20%20%20%20if%20abs(z%3A%3Dz**2%2Bc)%3E2%3A%0A%20%20%20%20%20%20%20%20%20%20%20break%0A%20%20%20%20%20%20res1.append(pixon(x%2Cy%2C126*j%2B2079))%0A%20%20%20%20%20%20res2.append(pixon(x%2CY-y%2C126*j%2B2079))%0A%20%20%20%20%20%20c%20%3D%20c%2Bw%3B%0A%20%20return%20res1%2Cres2&+pixon(1)&+fra1(260%2C222%2C10)&"
                                       target="_blank">Python</a>,
                                </li>
                                <li>Julia
                                    <a href="#exec&python=1&+def%20julia(c%2CN%2Cxmin%2Cxmax%2Cymin%2Cymax)%3A%0A%20%20%20%20%23%20local%20x%2Cy%2Cj%2Cz%2Czy%2Cres%2Chx%2Chy%0A%20%20%20%20res%3Dmakelist(-320*222-1)%0A%20%20%20%20hx%3D(xmax-xmin)%2F320.0%0A%20%20%20%20hy%3D(ymax-ymin)%2F222.0%0A%20%20%20%20for%20y%20in%20range(222)%3A%0A%20%20%20%20%20%20%20%20zy%3Dxmin%2Bi*(ymax-y*hy)%0A%20%20%20%20%20%20%20%20for%20x%20in%20range(320)%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20z%3Dzy%0A%20%20%20%20%20%20%20%20%20%20%20%20for%20j%20in%20range(N)%3A%20%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20if%20(abs(z%3A%3Dz*z%2Bc)%3E2)%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20break%0A%20%20%20%20%20%20%20%20%20%20%20%20res.append(pixon(x%2Cy%2C126*j%2B2079))%0A%20%20%20%20%20%20%20%20%20%20%20%20zy%2B%3Dhx%0A%20%20%20%20res&+pixon(1)%3B%0Ajulia(.3%2B.5*i%2C20%2C-1%2C1%2C-1%2C1)&"
                                       target="_blank">Python
                                    </a>
                                </li>
                                <li>
                                    Fractale de Newton ou bassins d'attraction des racines d'un polynome
                                    <a href="#python=0&exec&+///Bassins%20d'attraction%20des%20racines%20du%20polynome%20$P$On%20it%C3%A8re%20la%20m%C3%A9thode%20de%20Newton%20$z[n+1]=z[n]-P(z[n])/P'(z[n])$%20et%20on%20regarde%20si%20on%20converge%20vers%20une%20des%20racines%20de%20$P$,%20on%20colorie%20$z[0]$%20en%20fonction%20de%20la%20racine%20et%20de%20la%20vitesse%20de%20convergence.On%20pr%C3%A9sente%20deux%20versions,%20la%20premi%C3%A8re%20utilise%20la%20conjugaison%20complexe%20pour%20acc%C3%A9l%C3%A9rer%20les%20calculs.&+fonction%20f(P%2Cxmin%2Cxmax%2Cymin%2Cymax%2CN%2Cmaxiter)%0A%20%20local%20z0%2Cz%2Czp%2Chx%2Chy%2Cj%2Ck%2Cl%2Cn%2Cr%2Crs%2Cres%3B%0A%20%20P%3A%3Dsymb2poly(P)%3B%0A%20%20res%3A%3Dmakelist(-(N%2B1)%5E2)%3B%0A%20%20r%3A%3Dproot(P)%3B0%3B%20%2F%2F%20f(x%5E5-1%2C-1.3%2C1.3%2C-1.3%2C1.3%2C134%2C10)%0A%20%20rs%3A%3Dsize(r)-1%3B%0A%20%20hx%3A%3Devalf(xmax-xmin)%2FN%3B%20%0A%20%20hy%3A%3Devalf(ymax-ymin)%2FN%3B%0A%20%20for%20k%20from%200%20to%20N%20do%0A%20%20%20%20z0%3A%3Dxmin%2Bi*(ymin%2Bk*hy)%3B%0A%20%20%20%20for%20j%20from%200%20to%20N%20do%0A%20%20%20%20%20%20z%3A%3Dz0%3B%0A%20%20%20%20%20%20for%20l%20from%200%20to%20maxiter%20do%0A%20%20%20%20%20%20%20%20si%20distance((z%3A%3Dhorner(P%2C(zp%3A%3Dhorner(P%2Cz%2Cnewton))%2Cnewton))%2Czp)%3C1e-4%20ou%20abs(z)%3E1e20%20alors%20break%3B%20fsi%3B%0A%20%20%20%20%20%20od%3B%0A%20%20%20%20%20%20si%20z%3D%3Dundef%20alors%20continue%3B%20fsi%3B%0A%20%20%20%20%20%20for%20n%20from%200%20to%20rs%20do%0A%20%20%20%20%20%20%20%20si%20distance(z%2Cr%5Bn%5D)%3C1e-4%20alors%20break%3B%20fsi%3B%0A%20%20%20%20%20%20od%3B%0A%20%20%20%20%20%20res.append(pixon(j%2Ck%2C256%2B25*n%2Bl))%3B%0A%20%20%20%20%20%20z0%3A%3Dz0%2Bhx%3B%0A%20%20%20%20od%3B%0A%20%20od%3B%0A%20%20return%20res%3B%0Affonction%3A%3B&+fonction%20fsym(P%2Cxmin%2Cxmax%2Cymin%2CN%2Cmaxiter)%0A%20%20local%20z0%2Cz%2Czp%2Chx%2Chy%2Cj%2Ck%2Cl%2Cn%2Cr%2Crs%2Crimag%2Cres1%2Cres2%3B%0A%20%20P%3A%3Dsymb2poly(P)%3B%0A%20%20si%20size(im(P))!%3D0%20alors%20return%20%22Le%20polynome%20doit%20etre%20a%20coefficients%20reels%22%3B%20fsi%3B%0A%20%20r%3A%3Dproot(P)%3B%0A%20%20%2F%2F%20extrait%20les%20racines%20de%20partie%20imaginaire%20%3E%3D0%2C%20place%20les%20reelles%20en%20fin%0A%20%20res1%3A%3Dselect(x-%3Eim(x)%3E0%2Cr)%3B%0A%20%20rimag%3A%3D2*size(res1)%3B%0A%20%20res2%3A%3Dselect(x-%3Eim(x)%3D%3D0%2Cr)%3B%0A%20%20r%3A%3Dconcat(res1%2Creverse(conj(res1))%2Cres2)%3B%0A%20%20rs%3A%3Dsize(r)-1%3B%0A%20%20res1%3A%3Dmakelist(-ceil((N%2B1)%5E2%2F2))%3B%20%0A%20%20res2%3A%3Dmakelist(-ceil((N%2B1)%5E2%2F2))%3B%0A%20%20hx%3A%3Devalf(xmax-xmin)%2FN%3B%20%0A%20%20hy%3A%3Devalf(-2*ymin)%2FN%3B%0A%20%20for%20k%20from%200%20to%20N%2F2%20do%0A%20%20%20%20z0%3A%3Dxmin%2Bi*(ymin%2Bk*hy)%3B%0A%20%20%20%20for%20j%20from%200%20to%20N%20do%0A%20%20%20%20%20%20z%3A%3Dz0%3B%0A%20%20%20%20%20%20for%20l%20from%200%20to%20maxiter%20do%0A%20%20%20%20%20%20%20%20si%20distance((z%3A%3Dhorner(P%2C(zp%3A%3Dhorner(P%2Cz%2Cnewton))%2Cnewton))%2Czp)%3C1e-4%20ou%20abs(z)%3E1e20%20alors%20break%3B%20fsi%3B%0A%20%20%20%20%20%20od%3B%0A%20%20%20%20%20%20si%20z%3D%3Dundef%20alors%20continue%3B%20fsi%3B%0A%20%20%20%20%20%20for%20n%20from%200%20to%20rs%20do%0A%20%20%20%20%20%20%20%20si%20distance(z%2Cr%5Bn%5D)%3C1e-4%20alors%20break%3B%20fsi%3B%0A%20%20%20%20%20%20od%3B%0A%20%20%20%20%20%20res1.append(pixon(j%2Ck%2C256%2B25*n%2Bl))%3B%0A%20%20%20%20%20%20res2.append(pixon(j%2CN-k%2C256%2B25*quand(n%3E%3Drimag%2Cn%2Crimag-n-1)%2Bl))%3B%0A%20%20%20%20%20%20z0%3A%3Dz0%2Bhx%3B%0A%20%20%20%20od%3B%0A%20%20od%3B%0A%20%20return%20res1%2Cres2%3B%0Affonction%3A%3B&+pixon(1)&+fsym(x%5E5-1%2C-1.3%2C1.3%0A%2C-1.3%2C150%2C10)&+0%3B%20%2F%2F%20f(x%5E5-1%2C-1.3%2C1.3%2C-1.3%2C1.3%2C134%2C10)&"
                                       target="_blank">Xcas</a>,
                                    <a href="#python=1&exec&+///%3Ch1%3eBassins%20d'attractions%3C/h1%3e%20On%20se%20donne%20un%20polynome%20$P$%20et%20on%20cherche%20en%20partant%20d'un%20point%20$u_0$%20du%20plan%20complexe%20si%20la%20m%C3%A9thode%20de%20Newton$u[n+1]=u_n-P(u_n)/P'(u_n)$converge%20vers%20une%20des%20racines%20complexes%20de%20$P(z)=0$.%20On%20colorie%20le%20point%20en%20fonction%20de%20la%20racine%20et%20de%20la%20vitesse%20de%20convergence.Deux%20fonctions%20sont%20donn%C3%A9es,%20la%20deuxi%C3%A8me%20utilise%20la%20conjugaison%20complexe%20pour%20acc%C3%A9l%C3%A9rer%20les%20calculs.&+def%20f(P%2Cxmin%2Cxmax%2Cymin%2Cymax%2CN%2Cmaxiter)%3A%0A%20%20%20%20%23%20local%20z%2Cz0%2Czp%2Chx%2Chy%2Cj%2Ck%2Cl%2Cn%2Cr%2Crs%2Cres%0A%20%20%20%20P%3Dsymb2poly(P)%0A%20%20%20%20res%3D%5B%5D%0A%20%20%20%20r%3Dproot(P)%0A%20%20%20%20rs%3Dsize(r)%0A%20%20%20%20hx%3Devalf(xmax-xmin)%2FN%0A%20%20%20%20hy%3Devalf(ymax-ymin)%2FN%0A%20%20%20%20for%20k%20in%20range(N%2B1)%3A%0A%20%20%20%20%20%20%20%20z0%3Dxmin%2Bi*(ymin%2Bk*hy)%0A%20%20%20%20%20%20%20%20for%20j%20in%20range(N%2B1)%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20z%3Dz0%0A%20%20%20%20%20%20%20%20%20%20%20%20for%20l%20in%20range(maxiter)%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20if%20distance((z%3A%3Dhorner(P%2C(zp%3A%3Dhorner(P%2Cz%2Cnewton))%2Cnewton))%2Czp)%3C1e-4%20or%20abs(z)%3E1e20%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20break%3B%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20z%3D%3Dundef%3A%20%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20continue%0A%20%20%20%20%20%20%20%20%20%20%20%20for%20n%20in%20range(rs)%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20if%20distance(z%2Cr%5Bn%5D)%3C1e-4%3A%20%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20break%0A%20%20%20%20%20%20%20%20%20%20%20%20res.append(pixon(j%2Ck%2C256%2B25*n%2Bl))%0A%20%20%20%20%20%20%20%20%20%20%20%20z0%3Dz0%2Bhx%0A%20%20%20%20return%20res&+def%20fsym(P%2Cxmin%2Cxmax%2Cymin%2CN%2Cmaxiter)%3A%0A%20%20%20%20%23%20local%20z0%2Cz%2Czp%2Chx%2Chy%2Cj%2Ck%2Cl%2Cn%2Cr%2Crs%2Crimag%2Cres1%2Cres2%0A%20%20%20%20P%3Dsymb2poly(P)%0A%20%20%20%20if%20size(im(P))%3C%3E0%20%3A%0A%20%20%20%20%20%20%20%20return(%22Le%20polynome%20doit%20etre%20a%20coefficients%20reels%22)%0A%20%20%20%20r%3Dproot(P)%0A%20%20%20%20res1%3Dselect(lambda%20x%3Aim(x)%3E0%2Cr)%0A%20%20%20%20rimag%3D2*size(res1)%0A%20%20%20%20res2%3Dselect(lambda%20x%3Aim(x)%3D%3D0%2Cr)%0A%20%20%20%20r%3Dconcat(res1%2Creverse(conj(res1))%2Cres2)%0A%20%20%20%20rs%3Dsize(r)%0A%20%20%20%20res1%3D%5B%5D%0A%20%20%20%20res2%3D%5B%5D%0A%20%20%20%20hx%3Devalf(xmax-xmin)%2FN%0A%20%20%20%20hy%3Devalf(-2*ymin)%2FN%0A%20%20%20%20for%20k%20in%20range(ceil((N%2B1)%2F2))%3A%0A%20%20%20%20%20%20%20%20z0%3Dxmin%2Bi*(ymin%2Bk*hy)%0A%20%20%20%20%20%20%20%20for%20j%20in%20range(0%2CN%2B1)%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20z%3Dz0%0A%20%20%20%20%20%20%20%20%20%20%20%20for%20l%20in%20range(maxiter)%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20if%20distance((z%3A%3Dhorner(P%2C(zp%3A%3Dhorner(P%2Cz%2Cnewton))%2Cnewton))%2Czp)%3C0.0001%20or%20abs(z)%3E1e%2B20%20%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20break%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20(z%3D%3Dundef)%20%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20continue%0A%20%20%20%20%20%20%20%20%20%20%20%20for%20n%20in%20range(rs)%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20if%20(distance(z%2Cr%5Bn%5D))%3C0.0001%20%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20break%0A%20%20%20%20%20%20%20%20%20%20%20%20res1.append(pixon(j%2Ck%2C256%2B25*n%2Bl))%0A%20%20%20%20%20%20%20%20%20%20%20%20res2.append(pixon(j%2CN-k%2C256%2B25*when(n%3E%3Drimag%2Cn%2Crimag-n-1)%2Bl))%0A%20%20%20%20%20%20%20%20%20%20%20%20z0%3Dz0%2Bhx%0A%20%20%20%20return(res1%2Cres2)&+pixon(1)&+fsym(x%5E5-1%2C-1.3%2C1.3%2C-1.3%2C150%2C10)&+0%3B%20%2F%2F%20f(x%5E5-1%2C-1.3%2C1.3%2C-1.3%2C1.3%2C134%2C10)&"
                                       target="_blank">Python</a>
                                </li>
                                <li> Foug&egrave;re et choux-fleur
                                    <a
                                        href="#exec&python=1&+def%20fougere(nb)%3A%0A%20%20%20%20w%3D%5B%5D%3Bb%3D%5B%5D%3Bp%3D%5B%5D%0A%20%20%20%20m%3D11%0A%20%20%20%20w.append(%5B%5B0%2C0%5D%2C%5B0%2C.16%5D%5D)%3B%20b.append(%5B0%2C0%5D)%3B%20p.append(.01)%0A%20%20%20%20w.append(%5B%5B.85%2C.04%5D%2C%5B-.04%2C.85%5D%5D)%3B%20b.append(%5B0%2C2%5D)%3B%20p.append(p%5B-1%5D%2B.85)%0A%20%20%20%20w.append(%5B%5B.2%2C-.26%5D%2C%5B.23%2C.22%5D%5D)%3B%20b.append(%5B0%2C1%5D)%3B%20p.append(p%5B-1%5D%2B(1-p%5B-1%5D)%2F2)%0A%20%20%20%20w.append(%5B%5B-.15%2C.28%5D%2C%5B.26%2C.24%5D%5D)%3B%20b.append(%5B0%2C.9%5D)%3B%20p.append(1)%0A%0A%20%20%20%20x%3D%5B0%2C0%5D%0A%20%20%20%20res%3D%5B%5D%0A%20%20%20%20for%20_%20in%20range(nb)%3A%0A%20%20%20%20%20%20%20%20h%3Drandom()%0A%20%20%20%20%20%20%20%20i%3D0%0A%20%20%20%20%20%20%20%20while%20True%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20h%3C%3Dp%5Bi%5D%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20x%3Db%5Bi%5D%2Bw%5Bi%5D*x%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20break%0A%20%20%20%20%20%20%20%20%20%20%20%20i%2B%3D1%0A%20%20%20%20%20%20%20%20%23print(x)%0A%20%20%20%20%20%20%20%20res.append(pixon(160%2Bint(m*x%5B0%5D)%2C140-int(m*x%5B1%5D)%2C5100))&+fougere(10000)%0A&+def%20arbre(nb)%3A%0A%20%20%20%20w%3D%5B%5D%3Bb%3D%5B%5D%3Bp%3D%5B%5D%0A%20%20%20%20%23%20Arbre%0A%20%20%20%20m%3D222%0A%20%20%20%20w.append(%5B%5B0%2C0%5D%2C%5B0%2C.5%5D%5D)%3B%20b.append(%5B0%2C0%5D)%3B%20p.append(.05)%0A%20%20%20%20w.append(%5B%5B.42%2C-.42%5D%2C%5B.42%2C.42%5D%5D)%3B%20b.append(%5B0%2C.2%5D)%3B%20p.append(p%5B-1%5D%2B.4)%0A%20%20%20%20w.append(%5B%5B.42%2C.42%5D%2C%5B-.42%2C.42%5D%5D)%3B%20b.append(%5B0%2C.2%5D)%3B%20p.append(p%5B-1%5D%2B.4)%0A%20%20%20%20w.append(%5B%5B.1%2C0%5D%2C%5B0%2C.1%5D%5D)%3B%20b.append(%5B0%2C.2%5D)%3B%20p.append(1)%0A%0A%20%20%20%20x%3D%5B0%2C0%5D%0A%20%20%20%20res%3D%5B%5D%0A%20%20%20%20for%20_%20in%20range(nb)%3A%0A%20%20%20%20%20%20%20%20h%3Drandom()%0A%20%20%20%20%20%20%20%20i%3D0%0A%20%20%20%20%20%20%20%20while%20True%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20h%3C%3Dp%5Bi%5D%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20x%3Db%5Bi%5D%2Bw%5Bi%5D*x%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20break%0A%20%20%20%20%20%20%20%20%20%20%20%20i%2B%3D1%0A%20%20%20%20%20%20%20%20%23print(x)%0A%20%20%20%20%20%20%20%20res.append(pixon(160%2Bint(m*x%5B0%5D)%2C140-int(m*x%5B1%5D)%2C5100))&+arbre(10000)&"
                                        target="_blank">
                                    Python
                                    </a>
                                </li>
                                <li> courbe de Hilbert
                                    <a
                                        href="#exec&python=1&+def%20Draw_line(x%2C%20y%2C%20dx%2C%20dy%2C%20c)%3A%0A%20%20if%20dx%20%3D%3D%200%3A%0A%20%20%20%20if%20dy%20%3E%200%3A%0A%20%20%20%20%20%20y1%2C%20y2%20%3D%20y%2C%20y%2Bdy%2B1%0A%20%20%20%20else%3A%0A%20%20%20%20%20%20y1%2C%20y2%20%3D%20y%2Bdy%2C%20y%2B1%0A%20%20%20%20for%20y0%20in%20range(y1%2C%20y2)%3A%0A%20%20%20%20%20%20set_pixel(x%2C%20y0%2C%20c)%0A%20%20%20%20y%20%2B%3D%20dy%0A%20%20else%3A%0A%20%20%20%20if%20dx%20%3E%200%3A%0A%20%20%20%20%20%20x1%2C%20x2%20%3D%20x%2C%20x%2Bdx%2B1%0A%20%20%20%20else%3A%0A%20%20%20%20%20%20x1%2C%20x2%20%3D%20x%2Bdx%2C%20x%2B1%0A%20%20%20%20for%20x0%20in%20range(x1%2C%20x2)%3A%0A%20%20%20%20%20%20set_pixel(x0%2C%20y%2C%20c)%0A%20%20%20%20x%20%2B%3D%20dx%0A%20%20return%20x%2C%20y%0A&+def%20Hilbert(n%3D5%2C%20dx%3D5%2C%20dy%3D0%2C%20x%3D5%2C%20y%3D5%2C%20a%3D90%2C%20c%3D1)%3A%0A%20%20if%20n%20%3D%3D%200%3A%0A%20%20%20%20return%20x%2C%20y%2C%20dx%2C%20dy%0A%20%20elif%20a%20%3D%3D%2090%3A%0A%20%20%20%20dx%2C%20dy%20%3D%20-dy%2C%20dx%0A%20%20%20%20x%2C%20y%2C%20dx%2C%20dy%20%3D%20Hilbert(n-1%2C%20dx%2C%20dy%2C%20x%2C%20y%2C%20-90%2C%20c)%0A%20%20%20%20x%2C%20y%20%3D%20Draw_line(x%2C%20y%2C%20dx%2C%20dy%2C%20c)%0A%20%20%20%20dx%2C%20dy%20%3D%20dy%2C%20-dx%0A%20%20%20%20x%2C%20y%2C%20dx%2C%20dy%20%3D%20Hilbert(n-1%2C%20dx%2C%20dy%2C%20x%2C%20y%2C%2090%2C%20c)%0A%20%20%20%20x%2C%20y%20%3D%20Draw_line(x%2C%20y%2C%20dx%2C%20dy%2C%20c)%0A%20%20%20%20x%2C%20y%2C%20dx%2C%20dy%20%3D%20Hilbert(n-1%2C%20dx%2C%20dy%2C%20x%2C%20y%2C%2090%2C%20c)%0A%20%20%20%20dx%2C%20dy%20%3D%20dy%2C%20-dx%0A%20%20%20%20x%2C%20y%20%3D%20Draw_line(x%2C%20y%2C%20dx%2C%20dy%2C%20c)%0A%20%20%20%20x%2C%20y%2C%20dx%2C%20dy%20%3D%20Hilbert(n-1%2C%20dx%2C%20dy%2C%20x%2C%20y%2C%20-90%2C%20c)%0A%20%20%20%20dx%2C%20dy%20%3D%20-dy%2C%20dx%0A%20%20else%3A%0A%20%20%20%20dx%2C%20dy%20%3D%20dy%2C%20-dx%0A%20%20%20%20x%2C%20y%2C%20dx%2C%20dy%20%3D%20Hilbert(n-1%2C%20dx%2C%20dy%2C%20x%2C%20y%2C%2090%2C%20c)%0A%20%20%20%20x%2C%20y%20%3D%20Draw_line(x%2C%20y%2C%20dx%2C%20dy%2C%20c)%0A%20%20%20%20dx%2C%20dy%20%3D%20-dy%2C%20dx%0A%20%20%20%20x%2C%20y%2C%20dx%2C%20dy%20%3D%20Hilbert(n-1%2C%20dx%2C%20dy%2C%20x%2C%20y%2C%20-90%2C%20c)%0A%20%20%20%20x%2C%20y%20%3D%20Draw_line(x%2C%20y%2C%20dx%2C%20dy%2C%20c)%0A%20%20%20%20x%2C%20y%2C%20dx%2C%20dy%20%3D%20Hilbert(n-1%2C%20dx%2C%20dy%2C%20x%2C%20y%2C%20-90%2C%20c)%0A%20%20%20%20dx%2C%20dy%20%3D%20-dy%2C%20dx%0A%20%20%20%20x%2C%20y%20%3D%20Draw_line(x%2C%20y%2C%20dx%2C%20dy%2C%20c)%0A%20%20%20%20x%2C%20y%2C%20dx%2C%20dy%20%3D%20Hilbert(n-1%2C%20dx%2C%20dy%2C%20x%2C%20y%2C%2090%2C%20c)%0A%20%20%20%20dx%2C%20dy%20%3D%20dy%2C%20-dx%0A%20%20return%20x%2C%20y%2C%20dx%2C%20dy&+set_pixel(0)%3B%20Hilbert()%3B%20set_pixel()&"
                                        target="_blank">Python
                                    </a>
                                </li>
                                <li>
                                    <a
                                        href="#exec&python=0&+etoilo(z0%2Cr%2Ca)%3A%3D%7B%0A%20%20local%20j%2Cl%2Csomet%2Cp%2CL%2Cpa%3B%0A%20%20z0%3A%3Devalf(z0)%3B%0A%20%20r%3A%3Devalf(r)%3B%0A%20%20a%3A%3Devalf(a)%3B%0A%20%20l%3A%3Devalf(r*(3-sqrt(7))%2F2)%3B%0A%20%20somet%3A%3D%5Bz0%2Bl*exp(i*a)%2Cz0%2Br*exp(i*(a%2Bevalf(pi%2F7)))%5D%3B%0A%20%20L%3A%3Dsomet%3B%0A%20%20for%20(j%3A%3D1%3Bj%3C7%3Bj%2B%2B)%7B%0A%20%20%20%20L%3A%3Dconcat(L%2Crotation(z0%2C2*j*evalf(pi%2F7)%2Csomet))%3B%0A%20%20%7D%0A%20%20p%3A%3Dpolygone(L)%3B%0A%20%20return%20p%3B%0A%7D%3A%3B%0A%20%20%0Aetoilog(z0%2Cr%2Ca)%3A%3D%7B%0A%20%20return%20affichage(etoilo(z0%2Cr%2Ca)%2Crempli)%3B%0A%7D%3A%3B%0A%0Alogox(z0%2Cr%2Ca%2Cc)%3A%3D%7B%0A%20%20local%20j%2Ck%2CR%2CL%2Cnr%2Cnz0%3B%0A%20%20L%3A%3D%5Baffichage(etoilo(z0%2Cr%2Ca)%2Cc%2Brempli)%5D%3B%0A%20%20R%3A%3Dr%3B%0A%20%20for%20(j%3A%3D0%3Bj%3C7%3Bj%2B%2B)%7B%0A%20%20%20%20nr%3A%3D2*R%2F(1%2Bsqrt(7))%3B%0A%20%20%20%20nz0%3A%3Dz0%2BR*exp(2*i*j*pi%2F7%2Bi*a)%3B%0A%20%20%20%20for%20(k%3A%3D1%3Bk%3C7%3Bk%2B%2B)%7B%0A%20%20%20%20%20%20L%3A%3Dappend(L%2Caffichage(etoilo(evalf(nz0)%2Cnr%2Ca)%2Cc%2B(j%2B1)*k%2Brempli))%3B%0A%20%20%20%20%20%20r%3A%3Dnr%3B%0A%20%20%20%20%20%20nr%3A%3D2*r%2F(1%2Bsqrt(7))%3B%0A%20%20%20%20%20%20nz0%3A%3Dnz0%2Br*exp(2*i*j*pi%2F7%2Bi*a)%3B%0A%20%20%20%20%7D%0A%20%20%7D%0A%20%20return%20L%3B%0A%7D%3A%3B%0A%0Alx(z0%2Cr)%3A%3D%7B%0A%20%20return(segment(z0%2Br*(-1-i)%2Cz0%2Br*(1%2Bi))%2Csegment(z0%2Br*(1-i)%2Cz0%2Br*(-1%2Bi)))%3B%0A%7D%3A%3B%0A%0Alc(z0%2Cr)%3A%3D%7B%0A%20%20return%20(cercle(z0%2Cr%2Cpi%2F4%2C7*pi%2F4))%3B%0A%7D%3A%3B%0A%0Ala(z0%2Cr)%3A%3D%7B%0A%20%20return(segment(z0%2Br*(-1-i)%2Cz0%2Br*i)%2C%0A%20%20%20%20segment(z0%2Br*(1-i)%2Cz0%2Br*i)%2C%0A%20%20%20%20segment(z0%2Br*-0.5%2C%2Bz0%2Br*0.5))%3B%0A%7D%3A%3B%0A%0Als(z0%2Cr)%3A%3D%7B%0A%20%20return%20(segment(z0%2Br*(-1%2F2-i)%2Cz0-r*i)%2C%0A%20%20%20%20segment(z0%2Br*(1%2F2%2Bi)%2Cz0%2Br*i)%2C%0A%20%20%20%20cercle(z0%2Br*i%2F2%2Cr%2F2%2C%2Bpi%2F2%2C3*pi%2F2)%2C%0A%20%20%20%20cercle(z0-r*i%2F2%2Cr%2F2%2C-pi%2F2%2Cpi%2F2))%3B%0A%7D%3A%3B%0A%0A%2F%2Fc%20represente%20la%20couleur%0Alogoxcas(z0%2Cr%2Ca%2Cc)%3A%3D%7B%0A%20%20return%20logox(z0%2Cr%2Ca%2Cc)%2C%0A%20%20affichage(lx(evalf(z0-2*r*exp(i*a)%2Cr*0.2))%2Cline_width_3%2Bc%2B4)%2C%0A%20%20affichage(lc(evalf(z0-2*r*exp(-2*i*pi%2F7%2Bi*a)%2C0.2*r))%2Cline_width_3%2Bc%2B3)%2C%0A%20%20affichage(la(evalf(z0-2*r*exp(-4*i*pi%2F7%2Bi*a)%2C0.2*r))%2Cline_width_3%2Bc%2B2)%2C%0A%20%20affichage(ls(evalf(z0-2*r*exp(-6*i*pi%2F7%2Bi*a)%2C0.2*r))%2Cline_width_3%2Bc%2B1)%3B%0A%7D%3A%3B%0A%0A&+axes%3D0%3Blogoxcas(0%2C1%2C0%2C264)&"
                                        target="_blank">logo Xcas</a>
                                </li>
                            </ul>
                        </li>
                    </ul>
                </div>
            <li style="display:inline">
                <button class="bouton"
                        onclick="var tmp=$id('tutointerface'); if (tmp.style.display=='none') tmp.style.display='block'; else tmp.style.display='none';">
                <strong>Interface</strong></button>
                <div id="tutointerface" style="display:none">
                    Cette feuille de calcul est compos&eacute;e du haut vers le bas de:
                    <ul>
                        <li>
                            Un panel de boutons permettant de restaurer/sauvegarder
                            une session, et des aides &agrave; la saisie de commandes
                            (Xcas/math, programmation, clavier scientifique, documentation) .
                            Au lancement de Xcas, le panel est
                            r&eacute;duit &agrave; insertion d'une session, consultation des
                            manuels, configuration et restauration de la session
                            pr&eacute;c&eacute;dente.
                            D&egrave;s que vous avez valid&eacute; une commande, il apparait
                            <ul>
                                <li> un lien x2 (respectivement local)
                                    qui permet de <strong>cloner</strong> une session existante
                                    (respectivement localement).
                                    A utiliser si le noyau de calcul formel a crash&eacute; ou
                                    pour copier-coller dans une page web, ou pour ex&eacute;cuter
                                    dans Xcas natif (s&eacute;lectionner un niveau en cliquant sur
                                    son num&eacute;ro de niveau puis faire Ctrl/Cmd-V)
                                <li> un lien &#x2709; qui permet de <strong>partager
                                    votre session</strong> par e-mail.
                                </li>
                            </ul>
                        </li>
                        <li> une zone d'<strong>aide</strong>, qui contient des courtes description des
                            commandes dont vous avez demand&eacute; la syntaxe. Vous pouvez
                            effacer l'aide avec le bouton d'effacement &agrave; droite du champ de recherche.
                        </li>
                        <li> un <strong>historique</strong> qui contient 0 ou plusieurs
                            niveaux (0 au d&eacute;but). Un niveau est une paire
                            ligne de commande (en noir)/r&eacute;sultats (en
                            bleu), les boutons ↑ et ↓ permettent de d&eacute;placer un niveau
                            dans l'historique. Vous pouvez modifier une ligne
                            de commande de l'historique et valider en cliquant sur le bouton Ok
                            ou sur Entree en d&eacute;but de champ. Vous
                            pouvez placer un niveau dans la corbeille avec le bouton
                            d'effacement &agrave; droite du niveau. Pour le restaurer,
                            cliquez sur le bouton Restaure, pour l'effacer
                            d&eacute;finitivement cliquez sur le bouton Vide. Le lien <tt>+</tt>
                            &agrave; droite du bouton Vide permet d'ouvrir un nouvel onglet
                            sur une session vide.
                        </li>
                        <li>
                            une <strong>ligne de commande</strong>, on y tape des commandes
                            ou des programmes Xcas, et on
                            valide en cliquant sur le bouton Ok ou en tapant Entree (si
                            votre commande est sur plusieurs lignes, tapez Ctrl-Entree ou Entree
                            sur une ligne vide). Pour
                            forcer un passage
                            &agrave; la ligne, tapez Shift-Entree au clavier
                            ou utilisez le bouton <tt>\n</tt>.
                            <br>
                            Par exemple, tapez un calcul simple comme <tt>1/2+1/3</tt>
                            ou <tt>sin(pi/4)</tt> ou <tt>sin(pi/4.0)</tt>.
                            <br>
                            Pour vous aider &agrave; remplir la ligne de commande,
                            vous pouvez cliquer sur le bouton 123 qui fait apparaitre
                            le <strong>clavier scientifique</strong> et sur l'icone de Xcas
                            qui contient des commandes
                            fr&eacute;quemment utili&eacute;es et des assistants
                            (d&eacute;placez la souris pr&egrave;s des boutons pour
                            une description de leur action).
                            <br>
                            Si vous connaissez le nom d'une commande,
                            vous pouvez taper (le d&eacute;but) du nom d'une commande
                            (par exemple <tt>factor</tt>) puis
                            la touche <button>F1</button>
                            ou cliquer sur le bouton <button>?</button>
                            pour obtenir une
                            <strong>aide courte</strong> sur la commande (si elle
                            est compl&egrave;te) ou des suggestions de noms de
                            commande (sinon).
                            <br>
                            Par exemple, cliquer sur le bouton <tt>math</tt> puis
                            <tt>reecr.</tt> puis
                            <tt>factor</tt> puis tapez sur <tt>?</tt>, observez l'aide
                            en haut, cliquez sur un des exemples ou completez avec
                            x^4-1 puis tapez Entree.
                            <br>
                            Sur mobile, vous pouvez
                            <strong>s&eacute;lectionner</strong> du texte en laissant le doigt appuy&eacute;
                            sur un mot, puis taper sur l'icone avec des ciseaux (pour couper) ou
                            avec deux feuilles (pour copier), pour coller le presse-papier,
                            laisser le doigt appuy&eacute; puis taper sur l'icone avec une
                            feuille. Vous pouvez aussi appuyer sur les boutons <tt>beg</tt>
                            et <tt>end</tt> pour marquer le d&eacute;but et la fin de la
                            s&eacute;lection, puis optionnellement sur <tt>del</tt> pour
                            effacer, puis sur <tt>cp</tt> pour coller ce que vous aviez
                            s&eacute;lectionn&eacute;.  <br>
                            Vous pouvez ajouter un <strong>commentaire</strong> en validant une ligne de commande
                            vide (ou en cliquant sur le bouton
                            <tt>math</tt> puis <tt>texte</tt>). Vous pouvez transformer une ligne
                            de commande en un commentaire (ou inversement un commentaire en ligne
                            de commande) en ajoutant <tt>///</tt> au d&eacute;but et en validant.
                            Vous pouvez commenter une ligne de
                            commande en cliquant sur le bouton repr&eacute;sentant un
                            crayon &agrave; gauche de la r&eacute;ponse.
                            Vous pouvez utiliser des commandes de
                            balisage HTML dans un commentaire, par exemple inclure un
                            graphique
                            <tt>
                            &lt;img WIDTH="32" HEIGHT="32" SRC="turtle.png" alt="Tortue"
                            align="center"&gt;
                            </tt>.
                            Lorsque vous &eacute;ditez un
                            commentaire, des boutons facilitent la saisie des commandes HTML pour
                            cr&eacute;er un titre, ou &eacute;crire en gras ou italique ou fonte
                            fixe. Vous pouvez taper des math&eacute;matiques de deux
                            mani&egrave;res mutuellement exclusives
                            <ul>
                                <li> en saisissant une ligne de commande
                                    valide entre deux signes dollar (<tt>$...$</tt>),
                                    ce morceau de ligne de commande sera interpr&eacute;t&eacute;
                                    par Xcas sans etre &eacute;valu&eacute; puis transform&eacute; en
                                    MathML pour affichage 2d, par exemple <tt>$x[n+1]^2$</tt> affichera x indice
                                    n+1 exposant 2, <tt>$A=[[1,2],[3,4]]$</tt> affichera une matrice (sans donner
                                    de valeur &agrave; A), <tt>$integrate(sin(x),x,0,pi)$</tt> affichera
                                    l'int&eacute;grale de sinus x entre 0 et pi sans la calculer,
                                    <tt>$vecteur(u), vecteur(A,B)$</tt> affichera une fl&egrave;che
                                    au-dessus de u ou de AB. Les
                                    symboles des ensembles tels que ℤ,ℕ s'obtiennent par <tt>$ZZ$, $NN$</tt>,
                                    ainsi pour saisir x∈ℚ on tape <tt>$x in QQ$</tt>. On peut aussi utiliser du
                                    code HTML comme <tt>&amp;in;</tt> pour &in;, <tt>&amp;forall;</tt> pour
                                    &forall;, <tt>&amp;exist;</tt>, <tt>&amp;oplus;</tt>, <tt>&amp;otimes;</tt>,
                                    <tt>&amp;notin;</tt>, <tt>&amp;empty;</tt>, <tt>&amp;part;</tt>
                                    etc. ou recopier directement un symbole par exemple depuis
                                    <a href="https://www.w3schools.com/charsets/ref_utf_math.asp">ici</a>.
                                <li> soit en saisissant un commentaire contenant au moins
                                    une paire de double-dollars (<tt>$$  ... $$</tt>).
                                    Dans ce cas, MathJax sera charg&eacute; pour afficher l'ensemble des
                                    commentaires en utilisant la syntaxe LaTeX
                                    (attention, cette m&eacute;thode ne fonctionne pas sans
                                    connexion Internet).
                            </ul>
                        </li>
                        <li>
                            une <strong>console</strong> qui affiche des messages du CAS :
                            erreurs de syntaxe mais aussi lors
                            d'un calcul en mode pas-&agrave;-pas, par exemple d'une
                            d&eacute;riv&eacute;e.
                            La console n'est pas visible si elle est vide.
                            Vous pouvez effacer la console ou ajuster sa taille verticale.
                        </li>
                        <li>
                            une zone affichant des <strong>graphes 3d</strong>
                            lorsqu'on ex&eacute;cute une commande
                            ayant une sortie graphique 3d. Cette zone n'est pas visible s'il n'y
                            a pas de graphique 3d.
                        </li>
                    </ul>
                    A tout moment, vous pouvez <strong>sauvegarder</strong> l'historique,
                    avec le nom de session affich&eacute; &agrave; droite du bouton
                    <tt>&#x1f4be;</tt>
                    (par d&eacute;faut <tt>session</tt>).
                    Une session sauvegard&eacute;e
                    s'ouvre ensuite avec le bouton Charger.
                    Sur mobile, les sauvegardes sont faites dans localStorage.
                    Vous pouvez aussi <strong>exporter</strong> la feuille de calcul (sauf
                    sur mobile), l'export occupe plus de place mais
                    permet de publier le fichier HTML comme une page autonome.
                    Vous pouvez sauvegarder les graphes 2d au format SVG avec le bouton
                    save &agrave; droite du graphe. Le fichier SVG cr&eacute;&eacute;
                    est au format 1.2 (il utilise la balise
                    <tt>vector-effect="non-scaling-stroke"</tt> qui n'est pas compris
                    par tous les visualisateurs ou convertisseurs).
                    <br>
                    Sous Firefox, pour pouvoir
                    choisir l'emplacement de sauvegarde et &eacute;craser
                    une version ant&eacute;rieure : cocher Toujours demander...
                    dans Pr&eacute;f&eacute;rences,
                    G&eacute;n&eacute;ral, T&eacute;l&eacute;chargements.
                    <br>
                    Vous pouvez ouvrir (partiellement) dans Xcas pour Firefox
                    une session existante Xcas natif en la clonant
                    (menu Fich, Clone du programme Xcas, ou en ligne de commande
                    <tt>xcas --online nom_fichier.xws</tt>)
                    <br>
                    Notez que Chrome (et plus g&eacute;n&eacute;ralement
                    le navigateur install&eacute; par d&eacute;faut sur votre appareil)
                    est beaucoup plus lent que Firefox pour
                    faire les calculs (5 fois plus lent environ), en particulier le
                    premier calcul dure une bonne dizaine de secondes. De plus, Chrome
                    n'a pas de support natif pour afficher les formules en 2d en mathml,
                    il faut alors charger MathJax ce qui n&eacute;cessite
                    un acc&egrave;s r&eacute;seau.
                    <br>
                    <strong>Il est donc recommend&eacute; de t&eacute;l&eacute;charger
                    Firefox et d'ex&eacute;cuter Xcas depuis Firefox</strong>
                    <br>
                    <button class="bouton"
                            onclick="$id('tutointerface').style.display='none';">Masquer
                    l'aide sur l'interface</button>
                </div>
            </li>
            <li style="display:inline">
                <button class="bouton"
                        onclick="var tmp=$id('tutokbd'); if (tmp.style.display=='none') tmp.style.display='block'; else tmp.style.display='none';">
                <strong>Clavier</strong></button>
                <div id="tutokbd" style="display:none">
                    Raccourcis clavier avec Alt (ou Ctrl si Alt ne marche pas car
                    d&eacute;j&agrave; utilis&eacute; par le navigateur ou le
                    syst&egrave;me d'exploitation).
                    <ul>
                        <li> D, curseur droit : d&eacute;place le focus d'un champ
                            vers la droite ou le bas
                        <li> G, curseur gauche : d&eacute;place le focus d'un champ
                            vers la gauche ou le haut
                        <li> curseur bas : d&eacute;place le focus de 2 champs
                            vers la droite ou le bas
                        <li> curseur bas : d&eacute;place le focus de 2 champs
                            vers la gauche ou le haut
                        <li> B: d&eacute;place le focus vers la ligne de commande
                        <li> C: copie le champ courant vers la ligne de commande
                        <li> A: d&eacute;place le focus vers l'aide
                        <li> TAB: affiche l'aide sur la commande &agrave; gauche du
                            curseur de la ligne de commande.
                        <li> M: affiche ou cache le menu Maths
                        <li> P: affiche ou cache le menu Programmation
                        <li> T: affiche ou cache le menu Tortue
                        <li> E ou F: ex&eacute;cute la session
                        <li> N: efface la console
                    </ul>
                </div>
            </li>
            <li style="display:inline">
                <button class="bouton"
                        onclick="var tmp=$id('tutocfg'); if (tmp.style.display=='none') tmp.style.display='block'; else tmp.style.display='none';">
                <strong>Configuration</strong></button>
                <div id="tutocfg" style="display:none">
		  Le bouton en haut &agrave; gauche de la feuille permet de changer
		  la configuration de Xcas pour Firefox. Vous pouvez par exemple
		  modifier le nombre de chiffres significatifs utilis&eacute;s par
		  d&eacute;faut,  l'unit&eacute; d'angle, le mode pas &agrave; pas,
		  etc. Si vous avez un navigateur compatible, par exemple Firefox&geq;58,
		  vous pouvez activer l'option <tt>wasm</tt> qui permet d'effectuer
		  la plupart des calculs plus rapidement et donne acc&egrave;s aux
		  commandes de PARI-GP (apr&egrave;s avoir &eacute;valu&eacute; la
		  commande <tt>pari()</tt>). Vous pouvez aussi
		  utiliser l'interpr&eacute;teur MicroPython &agrave;
		  la place de l'interpr&eacute;teur Xcas si la compatibilit&eacute;
		  Python de Xcas est insuffisante: il est fourni avec
		  des modules pour un usage scolaire (math, cmath,
		  random, turtle, matplotl, linalg, numpy, graphic, arit,
		  cas). Le passage d'un interpr&eacute;teur &agrave;
		  l'autre peut aussi s'effectuer avec les commandes
		  <tt>python</tt> ou <tt>xcas</tt>.
		  Pour visualiser la tortue en mode MicroPython, taper <tt>.</tt>
		  sur une ligne de commande vide, pour visualiser un
		  graphique de <tt>graphic</tt> taper <tt>;</tt>, pour
		  un graphique dans un rep&eacute;re, taper <tt>,</tt>.
                </div>
            </li>
            <li style="display:inline">
                <button class="bouton" onclick="var tmp=$id('manuels'); if (tmp.style.display=='none') tmp.style.display='block'; else tmp.style.display='none';">
                <strong>Manuels</strong>
                </button>
                <span id="manuels" style="display:none">
                    <strong>Manuels de Xcas</strong> <button class="bouton"
                                                             onclick="$id('manuels').style.display='none';">Masquer</button>
                    <br>
                    La version "disque dur" est accessible en local sous Linux si vous avez
                    install&eacute; <tt>giac</tt>, sinon s&eacute;lectionnez la version "Internet".
                    <ul>
                        <li> Algorithmes de calcul formel et num&eacute;rique:
                            PDF <a href="giac/doc/fr/algo.pdf"
                                   target="_blank">local</a>,
                            <a href="https://www-fourier.univ-grenoble-alpes.fr/~parisse/giac/doc/fr/algo.pdf"
                               target="_blank">Internet</a>,
                            HTML <a href="giac/doc/fr/algo.html"
                                    target="_blank">local</a>,
                            <a href="https://www-fourier.univ-grenoble-alpes.fr/~parisse/giac/doc/fr/algo.html"
                               target="_blank">Internet</a>,
                        </li>
                        <li> Programmation :
                            <a href="irem/algolycee.html" target="_blank">algorithmique lyc&eacute;e</a>,
                            <a href="giac/doc/fr/casrouge/index.html"
                               target="_blank">local</a>,
                            <a href="https://www-fourier.univ-grenoble-alpes.fr/~parisse/giac/doc/fr/casrouge/index.html"
                               target="_blank">Internet</a>,
                        </li>
                        <li> G&eacute;om&eacute;trie :
                            <a href="giac/doc/fr/casgeo/index.html"
                               target="_blank">local</a>,
                            <a href="https://www-fourier.univ-grenoble-alpes.fr/~parisse/giac/doc/fr/casgeo/index.html"
                               target="_blank">Internet</a>,
                        </li>
                        <li> Simulation :
                            <a href="giac/doc/fr/cassim/index.html"
                               target="_blank">local</a>,
                            <a href="https://www-fourier.univ-grenoble-alpes.fr/~parisse/giac/doc/fr/cassim/index.html"
                               target="_blank">Internet</a>,
                        </li>
                        <li> Tortue logo :
                            <a href="giac/doc/fr/castor/index.html"
                               target="_blank">local</a>,
                            <a href="https://www-fourier.univ-grenoble-alpes.fr/~parisse/giac/doc/fr/castor/index.html"
                               target="_blank">Internet</a>,
                        </li>
                        <li> Exercices :
                            <a href="giac/doc/fr/casexo/index.html"
                               target="_blank">local</a>,
                            <a href="http://www-fourier.univ-grenoble-alpes.fr/~parisse/giac/doc/fr/casexo/index.html"
                               target="_blank">Internet</a>,
                        </li>
                        <li> Amusement :
                            <a href="giac/doc/fr/cascas/index.html"
                               target="_blank">local</a>,
                            <a href="http://www-fourier.univ-grenoble-alpes.fr/~parisse/giac/doc/fr/cascas/index.html"
                               target="_blank">Internet</a>,
                        </li>
                    </ul>
                </span>
            </li>
            <li style="display:inline">
                <button class="bouton" onclick="var tmp=$id('apropos'); if (tmp.style.display=='none') tmp.style.display='block'; else tmp.style.display='none';">
                <strong>&Agrave; propos</strong>
                </button>
                <span id="apropos" style="display:none">
                Xcasfr.html est une interface javascript optimis&eacute;e pour Firefox
                du système de calcul formel
                <a
                    href="http://www-fourier.univ-grenoble-alpes.fr/~parisse/giac/emgiac.tgz">Giac/Xcas</a>
                compil&eacute; par emscripten (l'&eacute;diteur de
                programme de cette interface
                utilise <a href="http://codemirror.net">CodeMirror</a>).
                Il n'a pas besoin de serveur, il s'exécute localement
                (avec le moteur javascript de votre navigateur qui doit être récent,
                mettez-le &agrave; jour pour avoir de bonnes performances, il faut
                aussi avoir au moins 300M de RAM disponible)
                à partir du code du CAS qui est téléchargé
                une fois. Le prix à payer pour cette simplicité
                est la vitesse, le code est plus lent pour tous les
                calculs exacts.
                La plupart du temps, cela n'est pas vraiment
                genant, mais
                si vous devez exécuter un gros calcul, il
                vaut mieux installer
                <a href="http://www-fourier.univ-grenoble-alpes.fr/~parisse/giac_fr.html">Xcas</a>!
                <br>
                Giac/Xcas (c) 2018 B. Parisse, R. De Graeve, Institut Fourier, Université
                de Grenoble, sous licence GPL3, pour une licence commerciale nous
	        contacter.
	        <br>
	        Optimization, signalprocessing, graph theory code (c) Luka Marohnić.
                <br>
                Sortie mathml et SVG (c) code principalement
	    &eacute;crit par J.P. Branchard.
<br><a target="_blank" href="https://micropython.org/">MicroPython</a> (c) Damien P. George et al <br>
<a target="_blank" href="https://bellard.org/quickjs/">QuickJS</a> (c)
  Fabrice Bellard et Charlie Gordon.
                </span>
            </li>
            <br>
            <li style="display:inline">
                <button class="bouton"
                        onclick="var tmp=$id('tutosimplifier'); if (tmp.style.display=='none') tmp.style.display='block'; else tmp.style.display='none';">
                <strong>Simplifier</strong></button>
                <span id="tutosimplifier" style="display:none">
                    Il n'existe pas de mani&egrave;re universelle de simplifier une
                    expression, parfois il vaut mieux d&eacute;velopper, parfois factoriser,
                    parfois lin&eacute;ariser, etc., il est donc important de connaitre
                    quelques commandes de r&eacute;&eacute;criture, que l'on peut
                    retrouver depuis le menu Math, r&eacute;&eacute;cr.
                    <ul>
                        <li>
                            L'appui sur le bouton <tt>math</tt> puis <tt>r&eacute;ecr.</tt> puis <tt>simpl</tt>
                            ins&egrave;re
                            la commande
                            <button onclick="UI.insert_focused('simplify(')">simplify</button>,
                            tapez ensuite
                            l'expression que
                            vous voulez d&eacute;velopper et simplifier.<br>
                            <button onclick="UI.insert_focused('normal(')">normal</button>,
                            <button onclick="UI.insert_focused('reorder(')">reorder</button>,
                            <button onclick="UI.insert_focused('ratnormal(')">ratnormal</button>
                            sont des versions moins puissantes mais plus rapides que simplify
                            (normal ne recherche pas de relations entre fonctions
                            trigonom&eacute;triques et exponentielles, ratnormal n'effectue
                            que des simplifications rationnelles, reorder r&eacute;ordonne
                            selon une liste de variables).
                        </li>
                        <li>
                            <button onclick="UI.insert_focused('factor(')">factor</button>
                            factorise sur R,
                            <button onclick="UI.insert_focused('cfactor(')">cfactor</button>
                            sur C
                        </li>
                        <li>
                            <button onclick="UI.insert_focused('partfrac(')">partfrac</button>
                            d&eacute;compose en &eacute;l&eacute;ments simples sur R,
                            <button onclick="UI.insert_focused('cpartfrac(')">cpartfrac</button>
                            sur C.
                        </li>
                        <li>
                            <button onclick="UI.insert_focused('texpand(')">texpand</button>
                            d&eacute;veloppe les expressions trigonom&eacute;triques,
                            exponentielles et logarithmes,
                            <button onclick="UI.insert_focused('lin(')">lin</button>
                            lin&eacute;rise les exponentielles,
                            <button onclick="UI.insert_focused('tlin(')">tlin</button>
                            lin&eacute;rise les expressions trigonom&eacute;triques.
                        </li>
                        <li> <button onclick="UI.insert_focused('subst(')">subst</button>
                            permet de substituer une ou des variables par une ou des valeurs
                        </li>
                        <li> Conversions trigo: <button onclick="UI.insert_focused('trigcos(')">trigcos</button>,
                            <button onclick="UI.insert_focused('trigsin(')">trigsin</button>,
                            <button onclick="UI.insert_focused('trigtan(')">trigtan</button>,
                            <button onclick="UI.insert_focused('halftan(')">halftan</button>,
                            <button onclick="UI.insert_focused('tan2sincos(')">tan2sincos</button>
                        </li>
                        <li> Autres: <button onclick="UI.insert_focused('trig2exp(')">trig2exp</button>,
                            <button onclick="UI.insert_focused('exp2trig(')">exp2trig</button>
                            <button onclick="UI.insert_focused('pow2exp(')">pow2exp</button>,
                            <button onclick="UI.insert_focused('exp2pow(')">exp2pow</button>
                            <button onclick="UI.insert_focused('lncollect(')">lncollect</button>
                            <button onclick="UI.insert_focused('lnexpand(')">lnexpand</button>
                        </li>
                    </ul>
                </span>
            </li>
            <li style="display:inline">
                <button class="bouton"
                        onclick="var tmp=$id('tutolinalg'); if (tmp.style.display=='none') tmp.style.display='block'; else tmp.style.display='none';">
                <strong>Alg&egrave;bre lin&eacute;aire </strong>
                </button>
                <span id="tutolinalg" style="display:none">
                    <ul>
                        <li>  Pour cr&eacute;er un vecteur, tapez ses coordonn&eacute;es
                            s&eacute;par&eacute;es par des virgules entre 2 crochets [].
                            <button onclick="UI.insert_focused('dot(')">dot</button> produit
                            scalaire de deux vecteurs,   <button onclick="UI.insert_focused('cross(')">cross</button> produit
                            vectoriel en dimension 2 ou 3.
                        </li>
                        <li>
                            Pour cr&eacute;er une matrice, utilisez l'assistant <tt>matrix</tt>
                            du menu <tt>math</tt>. Vous pouvez d&eacute;finir les coefficients par
                            une formule en fonction de la ligne et de la colonne ou
                            &eacute;l&eacute;ment par &eacute;l&eacute;ment
                            (vous pouvez entrer plusieurs coefficients en les s&eacute;parant par
                            un espace et passer &agrave; la ligne suivante avec Entree). Pour
                            une matrice al&eacute;atoire, utilisez l'assistant <tt>alea</tt>.
                        </li>
                        <li>
                            Les indices de lignes et colonnes commencent &agrave; 0 avec une
                            seule paire de <tt>[]</tt> et &agrave; 1 avec une double-paire
                            <tt>[[]]</tt>, par
                            exemple
                            <button onclick="UI.insert_focused('A[0,1]')">A[0,1]</button>
                            ou <button onclick="UI.insert_focused('A[[1,2]]')">A[[1,2]]</button>.
                        <li>
                            Vous pouvez utiliser <tt>+,-,*</tt> et <button onclick="UI.insert_focused('matpow(')">matpow</button> pour
                            effectuer les op&eacute;rations usuelles sur les matrices.
                        </li>
                        <li>
                            <button onclick="UI.insert_focused('tran(')">tran</button>
                            transpos&eacute;e, <button onclick="UI.insert_focused('tran(')">trn</button>: transconjugu&eacute;e,
                            <button onclick="UI.insert_focused('idn(')">idn</button> identit&eacute;
                        </li>
                        <li>
                            <button onclick="UI.insert_focused('linsolve(')">linsolve</button>
                            syst&egrave;me lin&eacute;aire,
                            <button onclick="UI.insert_focused('rref(')">rref</button> :
                            pivot de Gauss,
                            <button onclick="UI.insert_focused('p,l,u:=lu(')">det</button>
                            : d&eacute;terminant,
                            <button onclick="UI.insert_focused('inv(')">inv</button>
                            : inverse,
                            <button onclick="UI.insert_focused('p,l,u:=lu(')">lu</button>
                            : d&eacute;composition LU et application &agrave;
                            <button onclick="UI.insert_focused('linsolve(p,l,u,')">linsolve</button>,
                        </li>
                        <li>
                            <button onclick="UI.insert_focused('charpoly(')">charpoly(</button>
                            polynome caract&eacute;ristique ou
                            <button onclick="UI.insert_focused('pmin(')">pmin(</button>
                            minimal,
                            <button onclick="UI.insert_focused('p,d:=jordan(')">p,d:=jordan(</button>
                            vecteurs et valeurs propres.
                        </li>
                        <li>
                            Factorisations
                            <button onclick="UI.insert_focused('lu(')">lu</button>,
                            <button onclick="UI.insert_focused('cholesky(')">cholesky</button>,
                            <button onclick="UI.insert_focused('qr(')">qr</button>,
                            <button onclick="UI.insert_focused('svd(')">svd</button>
                        </li>
                        <li> Normes
                            <button onclick="UI.insert_focused('l1norm(')">l1norm</button>,
                            <button onclick="UI.insert_focused('l2norm(')">l2norm</button>,
                            <button onclick="UI.insert_focused('maxnorm(')">maxnorm</button> :
                            <button onclick="UI.insert_focused('matrix_norm(')">matrix_norm</button>
                            de matrice subordonn&eacute;e
                        </li>
                    </ul>
            <li style="display:inline">
            <button class="bouton"
                    onclick="var tmp=$id('tutoarit'); if (tmp.style.display=='none') tmp.style.display='block'; else tmp.style.display='none';">
            <strong>Arithm&eacute;tique</strong>
            </button>
            <span id="tutoarit" style="display:none">
            Les commandes fr&eacute;quentes se trouvent dans le menu Math, bouton arit.
            Certaines commandes agissent indiff&eacute;ramment sur les entiers
            et sur les polyn&ocirc;mes, par exemple <tt>gcd</tt> ou <tt>lcm</tt>,
            d'autres commandes ont deux versions, celle qui agit sur des entiers
            a comme initiale <tt>i</tt>, par exemple <tt>irem</tt> est le reste
            euclidien pour des entiers, et <tt>rem</tt> pour des polyn&ocirc;mes.
            <ul>
            <li>
            <button onclick="UI.insert_focused('gcd(')">gcd</button>,
            <button onclick="UI.insert_focused('lcm(')">lcm</button> PGCD et PPCM
            </li>
            <li>
            <button onclick="UI.insert_focused('irem(')">irem</button>,
            <button onclick="UI.insert_focused('iquo(')">iquo</button>,
            <button onclick="UI.insert_focused('iquorem(')">iquorem</button>:
            reste et quotient de la division euclidienne sur les entiers
            </li>
            <li>
            <button onclick="UI.insert_focused('iegcd(')">iegcd</button> identit&eacute;
            de B&eacute;zout sur les entiers,
            <button onclick="UI.insert_focused('iabcuv(')">iabcuv</button> solutions
            de au+bv=c,
            <button onclick="UI.insert_focused('isprime(')">isprime</button> test de pseudo-primalit&eacute;,
            <button onclick="UI.insert_focused('nextprime(')">nextprime</button>
            prochain nombre premier,
            <button onclick="UI.insert_focused('ifactor(')">ifactor</button>
            factorisation d'entier, indicatrice d'<button onclick="UI.insert_focused('euler(')">Euler</button>,
            <button onclick="UI.insert_focused('powmod(')">powmod</button> puissance
            modulaire rapide.
            </li>
            <li>
            <button onclick="UI.insert_focused('rem(')">rem</button>,
            <button onclick="UI.insert_focused('quo(')">quo</button>,
            <button onclick="UI.insert_focused('quorem(')">quorem</button>:
            reste et quotient de la division euclidienne sur les polynomes. La
            variable par d&eacute;faut est <tt>x</tt>, sinon l'indiquer en
            3&egrave;me argument
            <li>
            <button onclick="UI.insert_focused('egcd(')">egcd</button> identit&eacute;
            de B&eacute;zout sur les polynomes,
            <button onclick="UI.insert_focused('abcuv(')">abcuv</button> solutions
            de au+bv=c,
            <button onclick="UI.insert_focused('horner(')">horner</button> valeur en
            un point par Horner,
            <button onclick="UI.insert_focused('interp(')">interp</button> interpolation
            polynomiale.
            </li>
            <li> Pour travailler dans ℤ/nℤ, utiliser le signe <tt>mod</tt>, par
            exemple <tt>x^3+5x-11 mod 17</tt> est un polynome a coefficients dans ℤ/17ℤ.
            Pour travailler sur un corps fini non premier, utiliser la
            commande
            <button onclick="UI.insert_focused('GF(')">GF</button>
            </li>
            </ul>
            </span>
            </li>
            <li style="display:inline">
            <button class="bouton"
                    onclick="var tmp=$id('tutosolve'); if (tmp.style.display=='none') tmp.style.display='block'; else tmp.style.display='none';">
            <strong>R&eacute;soudre</strong>
            </button>
            <span id="tutosolve" style="display:none">
            Depuis le bouton <tt>math</tt>
            <ul>
            <li> l'assistant <tt>solve</tt>
            vous guidera pour r&eacute;soudre une &eacute;quation ou un
            syst&egrave;me
            polynomial en mode exact ou approch&eacute; sur les r&eacute;els ou
            les complexes (fonctions
            <button onclick="UI.insert_focused('solve(')">solve</button>
            <button onclick="UI.insert_focused('csolve(')">csolve</button>
            <button onclick="UI.insert_focused('fsolve(')">fsolve</button>
            <button onclick="UI.insert_focused('cfsolve(')">cfsolve</button>)
            </li>
            <li>
            Pour r&eacute;soudre une &eacute;quation diff&eacute;rentielle,
            cliquez sur <tt>analyse</tt> du menu <tt>Math</tt>,
            <button onclick="UI.insert_focused('desolve(')">desolve</button> pour un
            calcul exact,
            <button onclick="UI.insert_focused('odesolve(')">odesolve</button>
            approch&eacute;, ou cliquez sur <tt>graphe</tt> puis
            <button onclick="UI.insert_focused('odeplot(')">ode</button>
            pour un graphe de solution approch&eacute;e.
            </li>
            <li>
            Pour calculer le terme g&eacute;n&eacute;ral d'une suite
            r&eacute;currente (ou d'un syst&egrave;me), cliquez sur <tt>u_n</tt>
            du menu <tt>Math</tt> (commande
            <button onclick="UI.insert_focused('rsolve(')">rsolve</button>).
            </li>
            </ul>
            </span>
            </li>
            <li style="display:inline">
            <button class="bouton"
                    onclick="var tmp=$id('tutoanalyse'); if (tmp.style.display=='none') tmp.style.display='block'; else tmp.style.display='none';">
            <strong>Analyse</strong>
            </button>
            <span id="tutoanalyse" style="display:none">
            Le <tt>math</tt> contient des assistants pour
            d&eacute;finir une fonction (bouton <tt>fonct</tt>),
            d&eacute;terminer le tableau de variations d'une expression
            (<tt>f(x)</tt>),
            travailler avec des suites (<tt>u_n</tt>),
            calculer une somme (<tt>∑</tt>), des limites (<tt>limit</tt>),
            des d&eacute;riv&eacute;es (<tt>∂</tt>),
            des primitives et valeurs d'int&eacute;grales (<tt>∫</tt>),
            des d&eacute;veloppement limit&eacute;s  (<tt>series</tt>).
            <br>
            Par exemple pour d&eacute;finir une fonction alg&eacute;brique
            <tt>f</tt> d'une variable, cliquer sur
            <tt>fonct</tt> de <tt>math</tt> puis
            mettre <tt>f</tt> comme nom de fonction,
            <tt>x</tt> comme liste des arguments et <tt>sin(x^2)</tt> comme
            valeur renvoy&eacute;ee :
            <button onclick="UI.insert_focused('f(x):=sin(x^2):;')"><tt>f(x):=sin(x^2)</tt></button>.
            On peut ensuite calcule la valeur
            de <tt>f</tt> ou de sa d&eacute;riv&eacute;e par
            <button onclick="UI.insert_focused('f(sqrt(pi)); f\'(2);f\'(y);')">
            <tt>f(sqrt(pi)); f'(2); f'(y) </tt></button>.
            <br>
            Une d&eacute;riv&eacute;e se calcule avec
            <button onclick="UI.insert_focused('diff(')">diff</button> ou <tt>'</tt>.
            Une primitive d'une
            expression se calcule avec <button onclick="UI.insert_focused('integrate(')">int</button>, par
            exemple <button onclick="UI.insert_focused('integrate(1/(x^4-1))')">int(1/(x^4-1));</button>,
            pour une int&eacute;grale entre deux bornes
            <button onclick="UI.insert_focused('int(1/(x^4+1),x,0,+infinity)')">
            int(1/(x^4+1)^4,x,0,+infinity);</button>.
            <br>
            Enfin  <button onclick="UI.insert_focused('limit(')">limit</button> et
            <button onclick="UI.insert_focused('series(')">series</button>
            permettent de calculer une limite ou un d&eacute;veloppement de
            Taylor, par exemple
            <button onclick="UI.insert_focused('limit(sin(x)/x,x=0); series(sin(x),x=0,5,polynom)')">
            limit(sin(x)/x,x=0); series(sin(x),x=0,5,polynom);</button>
            </span>
            </li>
            <li style="display:inline">
            <button class="bouton"
                    onclick="var tmp=$id('tutoproba'); if (tmp.style.display=='none') tmp.style.display='block'; else tmp.style.display='none';">
            <strong>Probabilit&eacute;s </strong></button>
            <span id="tutoproba" style="display:none">
            Utiliser l'assistant <tt>al&eacute;a</tt> de <tt>math</tt> pour
            g&eacute;n&eacute;rer des nombres pseudo-al&eacute;atoires.
            <br>
            Lois continues:
            <button onclick="UI.insert_focused('uniformd(')">uniformd</button>,
            <button onclick="UI.insert_focused('normald(')">normald</button>,
            <button onclick="UI.insert_focused('studentd(')">studentd</button>,
            <button onclick="UI.insert_focused('chisquared(')">chisquared</button>,
            <button onclick="UI.insert_focused('gammad(')">gammad</button>,
            <button onclick="UI.insert_focused('exponentiald(')">exponentiald</button>,
            <button onclick="UI.insert_focused('cauchyd(')">cauchyd</button>,
            <button onclick="UI.insert_focused('fisherd(')">fisherd</button>,
            <button onclick="UI.insert_focused('betad(')">betad</button>.
            <br>
            Lois discr&egrave;tes :
            <button onclick="UI.insert_focused('binomial(')">binomial</button>,
            <button onclick="UI.insert_focused('negbinomial(')">negbinomial</button>,
            <button onclick="UI.insert_focused('geometric(')">geometric</button>,
            <button onclick="UI.insert_focused('poisson(')">poisson</button>.
            <br>
            Les distributions cumul&eacute;es s'obtiennent en rajoutant le
            suffixe <tt>_cdf</tt> ou par la commande  <button onclick="UI.insert_focused('cdf(')">cdf</button>, et les
            inverses avec le suffixe  <tt>_icdf</tt> ou par la commande  <button onclick="UI.insert_focused('icdf(')">icdf</button>.
            <br>
            La commande    <button onclick="UI.insert_focused('histogram(')">histogram</button>
            permet de repr&eacute;senter un histogramme.
            <br>
            La commande    <button onclick="UI.insert_focused('markov(')">markov</button> permet
            de d&eacute;composer une matrice de transition.
            </span>
            </li>
            <li style="display:inline">
            <button class="bouton"
                    onclick="var tmp=$id('tutograph'); if (tmp.style.display=='none') tmp.style.display='block'; else tmp.style.display='none';">
            <strong>Graphes </strong>
            </button>
            <span id="tutograph" style="display:none">
            Utiliser les assistants du bouton <tt>math</tt> pour
            cr&eacute;er un graphe d'une fonction d'une ou deux variables
            (<tt>plot</tt>, voir aussi <tt>f(x)</tt> pour avoir un tableau
            de variations),
            une courbe ou surface param&eacute;trique (<tt>param</tt>), un champ de tangentes
            pour une &eacute;quation diff&eacute;rentielle (<tt>field</tt>).
            <br>
            Exemples
            <button onclick="UI.insert_focused('plot([sin(x),x-x^3/3!],x=-3..3,color=[red,blue])')">
            <tt>plot([sin(x),x-x^3/3!],x=-3..3,color=[red,blue])</tt>
            </button> affiche
            le graphe 2d des fonctions sin(x) et x-x^3/6, alors que
            <button onclick="UI.insert_focused('plotfunc(x^2-y^2,[x=-2..2,y=-2..2]);plan(z=0,color=cyan+filled);')">
            <tt>plotfunc(x^2-y^2,[x=-2..2,y=-2..2]);plan(z=0,color=cyan+filled);</tt>
            </button>
            affiche un graphe 3d avec un plan, vous pouvez changer de point de
            vue &agrave; la souris.
            <br>
            Vous pouvez aussi utiliser de nombreuses instructions
            g&eacute;om&eacute;triques:
            <button onclick="UI.insert_focused('point(')">point</button>,
            <button onclick="UI.insert_focused('milieu(')">milieu</button>,
            <button onclick="UI.insert_focused('droite(')">droite</button>,
            <button onclick="UI.insert_focused('bissectrice(')">bissectrice</button>,
            <button onclick="UI.insert_focused('mediatrice(')">mediatrice</button>,
            <button onclick="UI.insert_focused('segment(')">segment</button>,
            <button onclick="UI.insert_focused('triangle(')">triangle</button>,
            <button onclick="UI.insert_focused('cercle(')">cercle</button>,
            <button onclick="UI.insert_focused('ellipse(')">ellipse</button>,
            <button onclick="UI.insert_focused('hyperbole(')">hyperbole</button>,
            <button onclick="UI.insert_focused('parabole(')">parabole</button>, ...
            </span>
            </li>
            <li style="display:inline">
            <button class="bouton"
                    onclick="var tmp=$id('tutoprog'); if (tmp.style.display=='none') tmp.style.display='block'; else tmp.style.display='none';">
            <strong>Programmation</strong>
            </button>
            <span id="tutoprog" style="display:none">
            Si vous n'avez jamais programm&eacute;, vous pouvez apprendre
            &agrave; le faire avec la tortue, cliquez sur le tutoriel
            <tt>Tortue</tt>.
            <br>
            Le bouton <tt>Prog</tt> affiche des assistants
            pour cr&eacute;er les structures de programmation
            (test, boucle, fonction). Pour passer &agrave; la ligne dans un
            champ d'entr&eacute;e d&eacute;j&agrave; valid&eacute; que vous
            modifiez, tapez Entree. Dans
            la ligne de commande en bas de page, il faut
            taper simultan&eacute;ment sur Shift-Entree ou utiliser le
            bouton <tt>\n</tt>.
            Pour indenter, utilisez le bouton <tt>→|</tt>.
            Le bouton <tt>debug</tt>
            permet d'ex&eacute;cuter une fonction en mode pas &agrave; pas
            pour la mettre au point.
            <br>
            Plusieurs syntaxes sont accept&eacute;es,
            dont une syntaxe en francais tr&egrave;s proche du langage
            algorithmique et une syntaxe compatible avec
            <button onclick="var tmp=$id('progpython'); if (tmp.style.display=='none') tmp.style.display='block'; else tmp.style.display='none';">Python</button>
            Vous pouvez afficher un
            <button onclick="var tmp=$id('progex'); if (tmp.style.display=='none') tmp.style.display='block'; else tmp.style.display='none';">
            <strong>exemple de programme</strong>
            </button>, regarder les sessions exemples ou lire le
            <a href="irem/algolycee.html" target="_blank">manuel de
            programmation</a> lyc&eacute;e.
            <div id="progpython" style="display:none">
            La syntaxe Python dans Xcas permet aux utilisateurs du langage
            Python une prise en main plus rapide de Xcas.
            Il faut prendre quelques pr&eacute;cautions :
            <ul>
            <li> activez la compatibilit&eacute; de syntaxe Python dans la
            configuration (bouton en haut &agrave; gauche), afin que les
            assistants utilisent des structures de controle Python et que
            certaines commandes comme <tt>int</tt> aient le m&ecirc;me
            comportement qu'en Python.
            <li> la syntaxe Python est activ&eacute;e lorsqu'on
            commence une commande par un commentaire Python (<tt>#</tt>), ou
            une structure de controle Python (<tt>def ...:</tt>,
            <tt>if...:</tt>, ...).
            <li> la compatibilit&eacute; se limite &agrave; la
            programmation imp&eacute;rative courante: test, boucle,
            fonction, slices, liste en compr&eacute;hension simple.
            La programmation orient&eacute;e objet n'est pas
            support&eacute;e, <tt>yield</tt>, le <tt>else</tt> en fin de <tt>for/while</tt>
            ou les listes en compr&eacute;hension imbriqu&eacute;es non plus.
            <li> il est inutile de charger des modules avec <tt>import</tt>,
            toutes les instructions Xcas sont directement accessibles. Les
            instructions built-in Python fonctionnent en
            g&eacute;n&eacute;ral en Xcas (sauf pour les chaines) ainsi
            que le module <tt>random</tt> (et <tt>math/cmath</tt> bien sur).
            Par contre les modules comme <tt>matplotlib, scipy, numpy</tt>
            ne sont pas support&eacute;s, il faut utiliser des instructions
            natives Xcas &agrave; la place (utilisez l'assistant Maths pour
            trouver les plus courantes).
            R&eacute;ciproquement, une session Xcas &eacute;crite en syntaxe Python
            qui contient des objets CAS
            (expressions symboliques, flottants multi-pr&eacute;cisions, ...)
            ou certaines commandes int&eacute;gr&eacute;es de Xcas
            (par exemple commandes de trac&eacute;)
            ne fonctionnera pas en Python pur.
            <li> choisissez des noms de fonction commencant par une
            majuscule pour &eacute;viter les conflits avec des noms de
            commande de Xcas.
            Il est conseill&eacute; de d&eacute;clarer les
            variables locales dans une fonction avec un commentaire
            <tt># local nom_des_variables_locales</tt>
            <li> les d&eacute;limiteurs de chaines de caract&egrave;res sont
            <tt>"..."</tt>, en effet <tt>'...'</tt> sert en calcul formel
            &agrave; diff&eacute;rer l'&eacute;valuation d'une expression
            <li> la division de deux entiers renvoie un rationnel (ou un
            entier), et pas un nombre flottant
            <li> <tt>^</tt> est synonyme de <tt>**</tt>
            <li> <tt>liste1+liste2</tt> ne concat&egrave;ne pas deux listes mais les
            additionne comme des vecteurs, utilisez
            <tt>liste1.extend(liste2)</tt>  pour concat&eacute;ner,
            <tt>n*liste</tt> ne duplique pas une liste, utilisez <tt>liste*n</tt>.
            <li> <tt>=</tt> est traduit en <tt>:=</tt>. On peut bien sur
            utiliser <tt>:=</tt> pour l'affectation &agrave; la place de
            <tt>=</tt>, mais il n'est pas
            possible d'utiliser certaines facilit&eacute;s de notation Xcas
            comme par exemple <tt>P:=x^3-2x+1; P(x=x+1)</tt> (il faudrait utiliser
            ici <tt>subst(P,x,x+1)</tt>)
            <li> l'affectation dans une liste se fait par
            r&eacute;f&eacute;rence en Python, dans Xcas elle se fait par valeur
            si on utilise <tt>=</tt>, par r&eacute;f&eacute;rence avec <tt>=<</tt>.
            </ul>
            </div>
            <div id="progex" style="display:none">
            Voici un programme calculant
            la somme des carr&eacute;s de 1 &agrave; x &eacute;crit en syntaxe Xcas
            <br>
            <tt>fonction f(x)
            <br>
            &nbsp;&nbsp;local y,s;
            <br>
            &nbsp;&nbsp;si x &gt; 100000 alors retourne "Nombre trop grand"; fsi;
            <br>
            &nbsp;&nbsp;s:=0;
            <br>
            &nbsp;&nbsp;pour y de 1 jusque x faire
            <br>
            &nbsp;&nbsp;&nbsp;&nbsp;s:=s+y^2;
            <br>
            &nbsp;&nbsp;fpour
            <br>
            &nbsp;&nbsp;retourne s;
            <br>
            ffonction:;
            </tt><br>
            En syntaxe compatible Python<br>
            <tt>def f(x):<br>
            &nbsp;&nbsp;&nbsp;&nbsp;# local y,s<br>
            &nbsp;&nbsp;&nbsp;&nbsp;if x &gt; 100000:<br>
            &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;return "Nombre trop grand"<br>
            &nbsp;&nbsp;&nbsp;&nbsp;s=0<br>
            &nbsp;&nbsp;&nbsp;&nbsp;for y in range(x+1):<br>
            &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;s=s+y**2<br>
            &nbsp;&nbsp;&nbsp;&nbsp;return s<br>
            </tt>
            <button onclick="UI.insert_focused('fonction f(x)\n  local y,s;\n  si x &gt; 100 alors retourne &quot;Nombre trop grand&quot; fsi;\n  s:=0;\n  pour y de 1 jusque x faire\n    s:=s+y^2;\n  fpour\n  retourne s;\nffonction:; ')">Tester (Xcas)</button>
            <button onclick="UI.insert_focused('def f(x):\n    # local y,s\n    if x > 100000:\n        return &quot;Nombre trop grand&quot;\n    s=0\n    for y in range(x+1):\n        s=s+y**2\n    return s\n')">Tester (Python)</button>
            <br>
            <br>
            </div>
            </span>
            </li>
            <li style="display:inline">
            <button class="bouton"
                    onclick="var tmp=$id('tutotortue'); if (tmp.style.display=='none') tmp.style.display='block'; else tmp.style.display='none';">
            <strong>Tortue</strong>
            </button>
            <span id="tutotortue" style="display:none">
            La tortue est un module pour apprendre &agrave; programmer,
            utilisable d&egrave;s le primaire. Il s'agit d'un robot
            qui se d&eacute;place selon des commandes avec un crayon
            qui marque son passage, avec une couleur donn&eacute;e.
            <br>
            Tapez Ctrl-T ou cliquez sur le bouton Prog puis Tortue &agrave;
            droite pour faire apparaitre les commandes de la tortue.
            Cliquez sur le bouton <tt>nouveau</tt> de la premi&egrave;re ligne des
            commandes de la tortue pour cr&eacute;er un nouveau dessin tortue.
            <br>
            Deux champs d'entr&eacute;e
            sont cr&eacute;&eacute;s, le premier pour d&eacute;finir des fonctions,
            le second pour saisir en-dessous
            de la commande <tt>efface</tt>
            des commandes de d&eacute;placement de la tortue ou des
            appels &agrave; des fonctions (d&eacute;finies auparavant au-dessus),
            La barre de bouton &agrave; droite du bouton <tt>nouveau</tt>
            <tt>av rec td ...</tt>
            permet de saisir facilement les commandes de d&eacute;placement, comme
            <tt>avance</tt> (la tortue avance de 10 pas ou de la longueur
            indiqu&eacute;e en param&egrave;tre), <tt>recule</tt>, <tt>tourne_droite</tt>
            (la tortue tourne &agrave; droite, par d&eacute;faut de 90
            degr&eacute;s), etc.
            <br>
            Par exemple, si vous cliquez juste en-dessous de <tt>efface</tt>,
            puis sur le bouton <tt>av</tt> puis sur le bouton <tt>tg</tt> puis
            validez la ligne, la tortue se d&eacute;placera de 10 pixels vers
            la gauche puis s'orientera vers le haut.
            <br>
            Le premier champ d'entr&eacute;e sert &agrave; d&eacute;finir des
            fonctions regroupant plusieurs instructions de d&eacute;placement,
            il peut contenir des tests et des boucles. Vous pouvez vous aider
            des assistants <tt>test</tt>, <tt>boucle</tt> et <tt>fonct</tt>
            pour cr&eacute;er une nouvelle fonction.
            <br>
            Voici un exemple de construction
            de carr&eacute;s et polygones r&eacute;guliers
            <a
                href="#python=0&exec&+fonction%20Carre(l)%0A%20%20local%20k%3B%0A%20%20pour%20k%20de%201%20jusque%204%20faire%0A%20%20%20%20avance(l)%3B%0A%20%20%20%20tourne_gauche%3B%0A%20%20fpour%3B%0Affonction%3A%3B&+%23%0Aefface%0ACarre(40)%0Asaute%2080%0ACarre(40)&+fonction%20Polygone(l%2Cn)%0A%20%20local%20k%2Ct%3B%0A%20%20t%3A%3D360%2Fn%3B%0A%20%20pour%20k%20de%201%20jusque%20n%20faire%0A%20%20%20%20avance(l)%3B%0A%20%20%20%20tourne_gauche(t)%3B%0A%20%20fpour%3B%0Affonction%3A%3B&+%23%0Aefface%0APolygone(50%2C5)&"
                target="_blank">
            Xcas</a>,
            <a
                href="#python=1&exec&+def%20Carre(l)%3A%0A%20%20%20%20%23%20local%20k%0A%20%20%20%20for%20k%20in%20range(4)%3A%0A%20%20%20%20%20%20%20%20avance(l)%0A%20%20%20%20%20%20%20%20tourne_gauche&+%23%0Aefface%0ACarre(40)%0Asaute%2080%0ACarre(40)&+def%20Polygone(l%2Cn)%3A%0A%20%20%20%20%23%20local%20k%2Ct%0A%20%20%20%20t%3D360%2Fn%0A%20%20%20%20for%20k%20in%20range(n)%3A%0A%20%20%20%20%20%20%20%20avance(l)%0A%20%20%20%20%20%20%20%20tourne_gauche(t)&+%23%0Aefface%0APolygone(50%2C5)&"
                target="_blank">Python</a>, ou
            <a
                href="#python=0&exec&+sap(n)%3A%3D%7B%0A%20%20triangle_plein(5*n%2C5*n)%3B%0A%20%20tourne_gauche%20%3B%0A%20%20triangle_plein(5*n%2C5*n)%3B%0A%20%20saute%204*n%3B%0A%20%20triangle_plein(4*n%2C4*n)%3B%0A%20%20tourne_droite%20%3B%0A%20%20triangle_plein(4*n%2C4*n)%3B%0A%20%20pas_de_cote%20-4*n%3B%0A%7D%3A%3B&+sapins2(n)%3A%3D%7B%0A%20%20si%20n%3C%3D1%20alors%20crayon%20jaune%3B%20disque%2010%3B%20crayon%20vert%3B%20return%3B%20fsi%3B%0A%20%20crayon%20vert%3B%0A%20%20sap(n)%3B%0A%20%20tourne_gauche%2030%3B%0A%20%20saute%2010*n%3B%0A%20%20tourne_droite%2030%3B%0A%20%20sapins2(n-2)%3B%0A%20%20tourne_droite%2030%3B%0A%20%20saute%2010*n%3B%0A%20%20tourne_gauche%2030%3B%0A%20%20sap(n)%3B%0A%7D%3A%3B&+efface%3B%0Apas_de_cote%2050%3B%0Asaute%20-75%3B%0Asapins2(8)%3B%0Acrayon%20bleu%3B%0Asigne%20%22Joyeux%20Xcas%22&"
                target="_blank">
            Joyeux Xcas</a>,
            <a
                href="#python=1&exec&+def%20sap(n)%3A%0A%20%20%20%20triangle_plein(5*n%2C5*n)%0A%20%20%20%20tourne_gauche%0A%20%20%20%20triangle_plein(5*n%2C5*n)%0A%20%20%20%20saute%204*n%0A%20%20%20%20triangle_plein(4*n%2C4*n)%0A%20%20%20%20tourne_droite%0A%20%20%20%20triangle_plein(4*n%2C4*n)%0A%20%20%20%20pas_de_cote%20-4*n&+def%20sapins2(n)%3A%0A%20%20%20%20if%20n%3C%3D1%3A%0A%20%20%20%20%20%20%20%20crayon%20jaune%0A%20%20%20%20%20%20%20%20disque%2010%20%0A%20%20%20%20%20%20%20%20crayon%20vert%20%0A%20%20%20%20%20%20%20%20return%0A%20%20%20%20crayon%20vert%0A%20%20%20%20sap(n)%0A%20%20%20%20tourne_gauche%2030%0A%20%20%20%20saute%2010*n%0A%20%20%20%20tourne_droite%2030%0A%20%20%20%20sapins2(n-2)%0A%20%20%20%20tourne_droite%2030%0A%20%20%20%20saute%2010*n%0A%20%20%20%20tourne_gauche%2030%0A%20%20%20%20sap(n)&+%23%0Aefface%0Apas_de_cote%2050%0Asaute%20-75%0Asapins2(8)%0Acrayon%20bleu%0Asigne%20%22Joyeux%20Xcas%22&"
                target="_blank">Joyeux Xcas (version Python)</a>
            <br>
            Le <a
                href="https://www-fourier.univ-grenoble-alpes.fr/~parisse/giac/doc/fr/castor/index.html"
                target="_blank">manuel
            tortue</a> de Xcas explique ces commandes et contient de nombreux
            exemples d'activit&eacute;s d&egrave;s le primaire.
            </span>
            </li>
            <li style="display:inline">
            <button class="bouton"
                    onclick="var l=['tutocfg','tutonet','tutoinst','tutoex','tutoex2','tutointro','tutointerface','tutokbd','tutosimplifier','tutoarit','tutosolve','tutoanalyse','tutoproba','tutoprog','tutograph','tutolinalg','tutotortue','manuels','apropos']; var s=l.length; for (var i=0;i<s;++i) $id(l[i]).style.display='none';">
            <em>Replier tout</em>
            </button>
        </ul>
        </span>
<div id="divhelpoutput" style="max-height: 200px; overflow:auto">
  <table id="helpoutput" title="Aide" style="max-width:1000px "></table>
</div>
<div>
  <button id="bouton_math" class="bouton" onclick="UI.show_menu();"
          title="Montrer ou cacher les assistants math&eacute;matiques">
    <img WIDTH="28" HEIGHT="28" SRC="logo.png" alt="Maths" align="center">
    Math
  </button><button id="prog_key" class="bouton" title="Programmation" onclick="var tmp=$id('progbuttons'); if (tmp.style.display=='none'){ tmp.style.display='block';} else { tmp.style.display='none';}">Prog</button><button class="bouton" id="button_123" onmousedown="event.preventDefault()"
          onclick="if ($id('keyboard').style.display=='inline'){ $id('keyboard').style.display='none'; $id('alpha_keyboard').style.display='none';} else UI.kbdonfuncoff(); if (UI.focusaftereval){ UI.focused.focus(); }"
          title="Montrer ou cacher le clavier scientifique">123
  </button>
  <button class="bouton" style="vertical-align:bottom"
          onclick="if($id('help').style.display=='none')
                $id('help').style.display='block';
                else $id('help').style.display='none';"
          title="Montrer ou cacher la documentation">
    <strong>Doc</strong>
  </button><textarea cols="9" class="bouton" style="font-size:large;vertical-align:bottom" id="helptxt"
            title="Aide courte sur un nom de commande" rows=1 onclick="UI.focused=this;" onkeypress="if (event.keyCode!=13) return true;UI.addhelp('?',value); return false;"></textarea><button class="bouton" style="vertical-align:bottom" onmousedown="event.preventDefault()"
          title="Efface l'aide" onclick="var helptxt=$id('helptxt'); helpoutput.innerHTML='';helptxt.value='';$id('helptxt').focus();">&#x232b;
  </button>
</div>
<table border="0" align="center" summary="" id="keyboard"
       style="display:none" onmousedown="event.preventDefault()">
  <tr>
    <td>
      <input type="button" style="width:29px;height:35px;"
             name="add_newline" id="add_newline" value=" "
             onmousedown="event.preventDefault()" onClick="if (UI.kbdshift) UI.insert_focused(' \n') ; else UI.insert_focused(' ');">
      <input type="button" style="width:29px;height:35px;" name="add_sin" id="add_sin" value="sin" onmousedown="event.preventDefault()" onClick="UI.insert_focused(value+'(')" title="fonction sinus, taper asin pour arcinus">
      <input type="button" style="width:29px;height:35px;" name="add_cos"
             id="add_cos"
             value="cos" onmousedown="event.preventDefault()" onClick="UI.insert_focused(value+'(')" title="fonction cosinus, taper acos pour arccosinus">
      <input type="button" style="width:29px;height:35px;" name="add_tan"
             id="add_tan"
             value="tan" onmousedown="event.preventDefault()" onClick="UI.insert_focused(value+'(')" title="fonction tangente, taper atan pour arctangente">
      <input type="button" style="width:29px;height:35px;" name="add_ln"
             id="add_ln"
             value="exp" onmousedown="event.preventDefault()" onClick="UI.insert_focused(value+'(')" title="logarithme neperien et exponentielle.">
      <input type="button" style="width:29px;height:35px;" name="add_^" id="add_^" value="^" onmousedown="event.preventDefault()" onClick="UI.insert_focused('^')">
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      <input type="button" style="width:29px;height:35px;" name="add_/"
             id="add_/"
             value="/" onmousedown="event.preventDefault()" onClick="UI.insert_focused(value)" title="Division. // pour faire un commentaire, % pour travailler dans Z/nZ.">
    </td>
  </tr>
  <tr>
    <td>
      <input type="button" style="width:29px;height:35px;" name="add_left_par" id="add_left_par" value="(" onmousedown="event.preventDefault()" onClick="UI.insert_focused(value);">
      <input type="button" style="width:29px;height:35px;" name="add_right_par" id="add_right_par" value=")" onmousedown="event.preventDefault()" onClick="UI.insert_focused(value);">
      <input type="button" style="width:29px;height:35px;" name="add_xtn"
             id="add_xtn"
             value="x,t,n" onmousedown="event.preventDefault()" onClick="UI.insert_focused(UI.xtn)" title="Ins&egrave;re x ou t ou n">
      <input type="button" style="width:29px;height:35px;" name="add_pi" id="add_pi" value="π" onmousedown="event.preventDefault()" onClick="if (UI.kbdshift) UI.insert_focused('∞'); else UI.insert_focused('pi')">
      <input type="button" style="width:29px;height:35px;" name="add_i"
             id="add_i"
             value="i" onmousedown="event.preventDefault()" onClick="UI.insert_focused('i')" title="Nombre complexe racine carree de -1">
      <input type="button" style="width:29px;height:35px;" name="add_sqrt"
             id="add_sqrt"
             value="√" onmousedown="event.preventDefault()" onClick="if (UI.kbdshift) UI.insert_focused('^2'); else UI.insert_focused('sqrt(');" title="racine carree">
      <input type="button" style="width:29px;height:35px;" name="add_4" id="add_4" value="4" onmousedown="event.preventDefault()" onClick="UI.insert_focused('4')">
      <input type="button" style="width:29px;height:35px;" name="add_5" id="add_5" value="5" onmousedown="event.preventDefault()" onClick="UI.insert_focused('5')">
      <input type="button" style="width:29px;height:35px;" name="add_6" id="add_6" value="6" onmousedown="event.preventDefault()" onClick="UI.insert_focused('6')">
      <input type="button" style="width:29px;height:35px;" name="add_*" id="add_*" value="*" onmousedown="event.preventDefault()" onClick="UI.insert_focused('*')">
    </td>
  </tr>
  <tr>
    <td>
      <input type="button" style="width:29px;height:35px;"
             name="add_abc" id="add_abc" value="abc"
             onmousedown="event.preventDefault()" onClick="var tmp=$id('alpha_keyboard'); if (tmp.style.display=='none') tmp.style.display='inline'; else tmp.style.display='none'"
             title="clavier alphab&eacute;tique">
      <input type="button" style="width:29px;height:35px;" name="add-=" id="add-=" value="=" onmousedown="event.preventDefault()" onClick="UI.insert_focused(value)">
      <input type="button" style="width:29px;height:35px;" name="add_,"
             id="add_,"
             value="," onmousedown="event.preventDefault()" onClick="UI.insert_focused(value)" title="La virgule est utilisee comme separateur des composantes d'un vecteur. La quote sert &agrave; empecher l'&eacute;valuation.">
      <input type="button" id="add_infer" value="&lt;"
             title=""
             onmousedown="event.preventDefault()" onClick="UI.insert_focused(value);">
      <input type="button" style="display:none" name="curseur_up"
             id="curseur_up"
             value="↑" onmousedown="event.preventDefault()" onClick="UI.moveCaretUpDown(UI.focused,-1)" title="deplace le curseur vers le haut">
      <input type="button" style="width:29px;height:35px;" name="copy_button" id="copy_button" value="cp"
             onmousedown="event.preventDefault()" onClick="UI.insert_focused(UI.selection)" title="Copie la derni&egrave;re ligne de commande s&eacute;lectionn&eacute;e vers le focus.">
      <input type="button" style="width:29px;height:35px;" name="add_dosel"
             id="add_dosel"
             value="sel" onmousedown="event.preventDefault()" onClick="UI.selectionne()" title="Selectionne.">
      <input type="button" style="width:29px;height:35px;" name="add_1" id="add_1" value="1" onmousedown="event.preventDefault()" onClick="UI.insert_focused('1')">
      <input type="button" style="width:29px;height:35px;" name="add_2" id="add_2" value="2" onmousedown="event.preventDefault()" onClick="UI.insert_focused('2')">
      <input type="button" style="width:29px;height:35px;" name="add_3" id="add_3" value="3" onmousedown="event.preventDefault()" onClick="UI.insert_focused('3')">
      <input type="button" style="width:29px;height:35px;" name="add_-" id="add_-" value="-" onmousedown="event.preventDefault()" onClick="UI.insert_focused('-')">
    </td>
  </tr>
  <tr>
    <td>
      <input type="button" style="width:29px;height:35px" id="shift_key" value="alt" title="Touches compl&eacute;mentaires" onmousedown="event.preventDefault()" onClick="UI.toggleshift();">
      <input type="button" style="width:29px;height:35px;" name="add_:"
             id="add_:"
             value=":=" onmousedown="event.preventDefault()" onClick="UI.insert_focused(value)" title=":= effectue une affectation, par exemple a:=pi/2; sin(a). ! calcule une factorielle.">
      <input type="button" style="width:29px;height:35px;"
             name="add_semi" id="add_semi" value=";" onmousedown="event.preventDefault()" onClick="UI.insert_focused(value)"
             title="Le point virgule permet de separer plusieurs commandes pour les executer en une fois, par exemple dans un programme.">
      <input type="button" id="add_super" value="&gt;"
             title=""
             onmousedown="event.preventDefault()" onClick="UI.insert_focused(value);">
      <input type="button" style="display:none" name="curseur_down" id="curseur_down" value="↓" onmousedown="event.preventDefault()" onClick="UI.moveCaretUpDown(UI.focused,1)" title="deplace le curseur vers le bas">
      <input type="button" style="width:29px;height:35px;"
             id="add_beg"
             value="beg" onmousedown="event.preventDefault()"
             onClick="UI.setselbeg(UI.focused);" title="Debut selection">
      <input type="button" style="width:29px;height:35px;"
             id="add_end"
             value="end" onmousedown="event.preventDefault()"
             onClick="UI.setselend(UI.focused)" title="Fin selection">
      <input type="button" style="width:29px;height:35px;" name="add_e"
             id="add_e"
             value="e" onmousedown="event.preventDefault()" onClick="UI.insert_focused('e')" title="e est la base de l'exponentielle ou le separateur entre la mantisse et l'exposant d'un nombre approche ">
      <input type="button" style="width:29px;height:35px;" name="add_0" id="add_0" value="0" onmousedown="event.preventDefault()" onClick="UI.insert_focused('0')">
      <input type="button" style="width:29px;height:35px;" name="add_." id="add_." value="." onmousedown="event.preventDefault()" onClick="UI.insert_focused('.')">
      <input type="button" style="width:29px;height:35px;" name="add_+" id="add_+" value="+" onmousedown="event.preventDefault()" onClick="UI.insert_focused('+')">
    </td>
  </tr>
</table>
<table border="0" align="center" summary="" id="keyboardfunc"
       style="display:none" onmousedown="event.preventDefault()">
  <tr>
    <td>
      <input type="button" style="width:60px;height:35px"
             name="add_rewritetrig" id="add_rewritetrig" value="r&eacute;ecr."
             onmousedown="event.preventDefault()"
             onClick="$id('assistant_rewrite').style.display='block';UI.funcoff();"
             title="Commandes pour transformer des expressions">
      <input type="button" style="width:29px;height:35px" name="add_calculus"
             id="add_calculus"
             value="analyse" onClick="$id('assistant_calculus').style.display='block';UI.funcoff();"
             title="Calcul diff&eacute;rentiel et int&eacute;gral">
      <input type="button" style="width:60px;height:35px" name="add_solve"
             id="add_solve"
             value="solve" onmousedown="event.preventDefault()" onClick="UI.funcoff();UI.savefocused=UI.focused; $id('assistant_solve').style.display='block';UI.set_focus('solveeq') ;"
             title="Assistant pour r&eacute;soudre une &eacute;quation ou expression=0 par rapport &agrave; une ou plusieurs variables">
      <input type="button" style="width:60px;height:35px"
             name="add_graph" id="add_graph" value="graph"
             onmousedown="event.preventDefault()"
             onClick="$id('assistant_graph').style.display='block';UI.funcoff();"
             title="Commandes de trac&eacute; de graphes">
      <input type="button" style="width:29px;height:35px" name="add_geo"
             id="add_geo"
             value="g&eacute;om&eacute;trie" onClick="$id('assistant_geo').style.display='block';UI.funcoff();"
             title="Commandes de g&eacute;om&eacute;trie">
      <input type="button" style="width:60px;height:35px"
             name="add_arit" id="add_arit" value="arit"
             onmousedown="event.preventDefault()"
             onClick="$id('assistant_arit').style.display='block';UI.funcoff();"
             title="Commandes d'arithm&eacute;tique">
      <input type="button" style="width:60px;height:35px"
             name="add_linalg" id="add_linalg" value="linalg"
             onmousedown="event.preventDefault()"
             onClick="$id('assistant_linalg').style.display='block';UI.funcoff();"
             title="Commandes d'alg&egrave;bre lin&eacute;aire">
      <input type="button" style="width:29px;height:35px" name="add_mathcomment"
             id="add_mathcomment"
             value="texte" onmousedown="event.preventDefault()"
             onClick="UI.eval_cmdline1('///Tapez votre commentaire, vous pouvez vous aider du bouton math pour taper des expressions en syntaxe Xcas',true)" title="Cr&eacute;e une entr&eacute;e commentaire.">
    </td>
  </tr>
  <tr>
    <td>
      <input type="button" style="width:60px;height:35px" name="add_tabvar"
             id="add_tabvar"
             value="f(x)" onmousedown="event.preventDefault()" onClick="UI.funcoff();UI.savefocused=UI.focused;$id('assistant_tabvar').style.display='block';"
             title="Etude de graphe de fonction ou de courbe parametrique, par exemple tabvar(sin(x)) ou tabvar([cos(2t),sin(3t)])">
      <input type="button" style="width:60px;height:35px"
             name="add_rsolve" id="add_rsolve" value="u_n"
             onmousedown="event.preventDefault()" onClick="UI.funcoff();UI.savefocused=UI.focused;$id('assistant_suites').style.display='block';UI.xtn='n';" title="Recherche de l'expression du terme g&eacute;n&eacute;ral d'une suite r&eacute;currente, par exemple rsolve(u(n+2)===u(n+1)+u(n),u(n),[u(0)===1,u(1)==s=1])">
      <input type="button" style="width:50px;height:35px"
             name="add_seq" id="add_seq" value="list"
             onmousedown="event.preventDefault()"
             onClick="UI.funcoff();UI.savefocused=UI.focused;$id('assistant_seq').style.display='block';UI.set_focus('seqexpr')"
             title="assistant de cr&eacute;ation de liste ou tableau de valeurs, par exemple seq(j^2,j,1,n) cr&eacute;e la liste des carr&eacute;s des entiers de 1 &agrave; n ou seq(x^2,x,-2,2,0.1) cr&eacute;e la liste des carr&eacute;s des r&eacute;els de -2 &agrave; 2 par pas de 0.1">
      <input type="button" style="width:60px;height:35px"
             name="add_tableur" id="add_tableur" value="tabl."
             onmousedown="event.preventDefault()"
             onClick="UI.open_sheet(true);"
             title="Tableur">
      <input type="button" style="width:60px;height:35px"
             name="add_matr" id="add_matr" value="matrx"
             onmousedown="event.preventDefault()"
             onClick="UI.open_sheet(false);"
             title="assistant cr&eacute;ation de matrice">
      <input type="button" style="width:60px;height:35px"
             name="add_stats" id="add_stats" value="stats"
             title="Probabilit&eacute;s et statistiques"
             onmousedown="event.preventDefault()"
             onClick="UI.funcoff();UI.savefocused=UI.focused;var mat=$id('assistant_matr');mat.style.display='block';mat.matr_formule.checked=false;mat.matr_formuleshadow.checked=true;$id('matr_type_chooser').style.display='none';$id('matr_stat12').style.display='none';$id('matr_stats').style.display='block';UI.assistant_matr_setdisplay();$id('matr').style.display='none';$id('matr_matr').style.display='none';$id('matr_testhyp').style.display='none';$id('risque_alpha').style.display='none';"
      >
      <input type="button" style="width:60px;height:35px"
             name="add_rand" id="add_rand" value="al&eacute;a"
             onmousedown="event.preventDefault()"
             onClick="UI.savefocused=UI.focused;$id('assistant_rand').style.display='block';UI.assistant_rand_setdisplay();UI.funcoff();"
             title="g&eacute;n&eacute;rer un nombre, une liste ou une matrice al&eacute;atoirement">
      <input type="button" value="curseur" id="add_curseur" style="height:35px" onclick="UI.addcurseur(String.fromCharCode(UI.paramname),0,-5,5,0.125); UI.paramname++;" title="Ajoute un param&egrave;tre modifiable &agrave; la souris"/>
    </td>
  </tr>
</table>
<div id="progbuttons" style="display:none">
  <input type="button" style="width:29px;height:35px" name="add_//"
         id="add_//"
         value="//" onmousedown="event.preventDefault()" onClick="UI.insert_focused(UI.python_mode?'#':'//');UI.funcoff();" title="commentaire">
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             id="add_if"
             value="if" onmousedown="event.preventDefault()" onClick="UI.insert_focused('if :')" title="if condition: action "><input type="button" style="width:32px;height:35px;" name="add_else"
             id="add_else"
             value="else" onmousedown="event.preventDefault()" onClick="UI.insert_focused('else :')" title="if condition: action_vrai else: action_faux">
<input type="button"  name="add_for" style="width:29px;height:35px;"
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             value="for" onmousedown="event.preventDefault()" onClick="UI.insert_focused('for in range():')" title="boucle for "><input type="button"  name="add_while" style="width:40px;height:35px;"
             id="add_while"
             value="while" onmousedown="event.preventDefault()" onClick="UI.insert_focused('while :')" title="boucle tantque ">
      <input type="button" name="add_def"
             id="add_def" style="width:29px;height:35px;"
             value="def" onmousedown="event.preventDefault()" onClick="UI.insert_focused('def f():')" title="definition de fonction "><input type="button" name="add_return"
             id="add_return" style="width:40px;height:35px;"
             value="return" onmousedown="event.preventDefault()" onClick="UI.insert_focused('return ')" title="valeur renvoyée par la fonction ">
<br>
  <input type="button" style="width:29px;height:35px" name="add_test"
         id="add_test"
         value="test" onmousedown="event.preventDefault()" onClick="UI.savefocused=UI.focused;  $id('assistant_boucle').style.display='none'; $id('assistant_prog').style.display='none'; $id('assistant_test').style.display='block' ;UI.set_focus('sicond'); //UI.insert_focused('\nsi  alors  sinon  fsi; ');UI.moveCaret(UI.focused,-20);UI.funcoff();" title="Assistant de cr&eacute;ation de test">
  <input type="button" style="width:40px;height:35px"
         id="add_boucle" value="boucle" onclick="UI.savefocused=UI.focused; $id('assistant_boucle').style.display='block';$id('assistant_test').style.display='none';$id('assistant_prog').style.display='none'" title="Assistant de cr&eacute;ation de boucle">
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  <input type="button" style="width:46px;height:35px" name="add_debug"
         id="add_debug"
         value="debug" onmousedown="event.preventDefault()"
         onClick="UI.insert_focused('debug(')" title="Mettre au point (Xcas, ne fonctionne pas avec MicroPython), par exemple debug(f(2,3)) execute la fonction f avec arguments 2 et 3 en pas &agrave; pas">
  <input type="button" style="width:29px;height:35px" name="add_nlprog"
         id="add_nlprog"
         value="cmds" onmousedown="event.preventDefault()"
         onClick="UI.hide_show($id('list_cmds')); UI.hide_show_xcas('list_cmds_xcas'); UI.hide_show_python('python_mods');"
         title="Commandes">
  <input type="button" style="width:29px;height:35px" name="add_listechaine"
         id="add_listechaine"
         value='graph' onmousedown="event.preventDefault()"
         onClick="UI.hide_show($id('prog_graph_cmds'));"
         title="Commandes graphiques">
  <input type="button" style="width:29px;height:35px"
         id="add_tortue"
         value="Tortue" onmousedown="event.preventDefault()"
         onClick="UI.hide_show_xcas('boutons_tortue_xcas'); var f=$id('boutons_tortue'); if (f.style.display=='none'){ f.style.display='block'; } else { f.style.display='none'; }" title="Commandes de la tortue">
  <div id="list_cmds" style="display:none">
<button class="bouton" onclick="UI.insert_focused('pow(');">pow</button> <button class="bouton" onclick="UI.insert_focused('range(');">range</button><button class="bouton" onclick="UI.insert_focused('len(');">len</button><button class="bouton" onclick="UI.insert_focused('append(');">append</button><button class="bouton" onclick="UI.insert_focused('sorted(');">sorted</button>
    <div id="list_cmds_xcas">
    <button class="bouton" onclick="UI.insert_focused('seq(');">seq</button>
    <button class="bouton" onclick="UI.insert_focused('makelist(');">makelist</button>
    <button class="bouton" onclick="UI.insert_focused('concat(');">concat</button>
    <button class="bouton" onclick="UI.insert_focused('head(');">head</button>
    <button class="bouton" onclick="UI.insert_focused('tail(');">tail</button>
    <button class="bouton" onclick="UI.insert_focused('member(');">member</button>
    <button class="bouton" onclick="UI.insert_focused('revlist(');">revlist</button>
    <button class="bouton" onclick="UI.insert_focused('mid(');">mid</button>
    <button class="bouton" onclick="UI.insert_focused('suppress(');">suppress</button>
    <button class="bouton" onclick="UI.insert_focused('select(');">select</button>
    <button class="bouton" onclick="UI.insert_focused('count(');">count</button>
    <br>
    <button class="bouton" onclick="UI.insert_focused('set[');"><strong>set[]</strong></button>
    <button class="bouton" onclick="UI.insert_focused('intersect(');">intersect</button>
    <button class="bouton" onclick="UI.insert_focused('minus(');">minus</button>
    <button class="bouton" onclick="UI.insert_focused('union(');">union</button>
    <button class="bouton" onclick="UI.insert_focused('est_element(');">est_element</button>
    <button class="bouton" onclick="UI.insert_focused('est_inclus(');">est_inclus</button>
    <br>
    <button class="bouton" onclick="UI.insert_focused('&quote;');"><strong>""</strong></button>
    <button class="bouton" onclick="UI.insert_focused('asc(');">asc</button>
    <button class="bouton" onclick="UI.insert_focused('char(');">char</button>
    <button class="bouton" onclick="UI.insert_focused('inString(');">inString</button>
    <button class="bouton" onclick="UI.insert_focused('gauche(');">gauche</button>
    <button class="bouton" onclick="UI.insert_focused('ord(');">ord</button>
    <button class="bouton" onclick="UI.insert_focused('droit(');">droit</button>
    <button class="bouton" onclick="UI.insert_focused('string(');">string</button>
    </div>
    <div id="python_mods" style="display:none">
      <br>
    <button class="bouton" onclick="UI.insert_focused('from math import *');"><strong>math</strong></button><button class="bouton" onclick="UI.insert_focused('sqrt(');">racine</button><button class="bouton" onclick="UI.insert_focused('abs(');">abs</button><button class="bouton" onclick="UI.insert_focused('max(');">max</button><button class="bouton" onclick="UI.insert_focused('min(');">min</button><button class="bouton" onclick="UI.insert_focused('round(');">arrondi</button><button class="bouton" onclick="UI.insert_focused('floor(');">floor</button>
    <br>
<button class="bouton" onclick="UI.insert_focused('from cmath import *');"><strong>cmath</strong></button>
    <button class="bouton" onclick="UI.insert_focused('from random import *');"><strong>random</strong></button><button class="bouton" onclick="UI.insert_focused('random(');">random</button><button class="bouton" onclick="UI.insert_focused('randint(');">randint</button><button class="bouton" onclick="UI.insert_focused('choice(');">choice</button>
    <br>
    
    <button class="bouton" onclick="UI.insert_focused('from arit import *');"><strong>arit</strong></button><button class="bouton" onclick="UI.insert_focused('isprime(');">isprime</button><button class="bouton" onclick="UI.insert_focused('nextprime(');">nextp</button><button class="bouton" onclick="UI.insert_focused('ifactor(');">ifactor</button><button class="bouton" onclick="UI.insert_focused('gcd(');">gcd</button><button class="bouton" onclick="UI.insert_focused('lcm(');">lcm</button><button class="bouton" onclick="UI.insert_focused('iegcd(');">iegcd</button>
    <br>

    <button class="bouton" onclick="UI.insert_focused('from linalg import *');"><strong>linalg</strong></button><button class="bouton" onclick="UI.insert_focused('add(');">add</button><button class="bouton" onclick="UI.insert_focused('sub(');">sub</button><button class="bouton" onclick="UI.insert_focused('mul(');">mul</button><button class="bouton" onclick="UI.insert_focused('inv(');">inv</button><button class="bouton" onclick="UI.insert_focused('transpose(');">tran</button><button class="bouton" onclick="UI.insert_focused('rref(');">rref</button>
    <br>

    <button class="bouton" onclick="UI.insert_focused('from numpy import *');"><strong>numpy</strong></button><button class="bouton" onclick="UI.insert_focused('array(');">array</button><button class="bouton" onclick="UI.insert_focused('linspace(');">linspace</button><button class="bouton" onclick="UI.insert_focused('arange(');">arange</button><button class="bouton" onclick="UI.insert_focused('solve(');">solve</button><button class="bouton" onclick="UI.insert_focused('eig(');">eig</button><button class="bouton" onclick="UI.insert_focused('inv(');">inv</button>
    <br>
  </div>

  </div>
  <div id="prog_graph_cmds" style="display:none">
    <button class="bouton" title="Taper ; sur une ligne de commande vide pour voir le graphique." onclick="UI.insert_focused('from graphic import *');"><strong>graphic</strong></button><button class="bouton" onclick="UI.insert_focused('set_pixel(');">pixel</button><button class="bouton" onclick="UI.insert_focused('draw_line(');">line</button><button class="bouton" onclick="UI.insert_focused('draw_rectangle(');">rect</button><button class="bouton" onclick="UI.insert_focused('draw_circle(');">cercle</button><button class="bouton" onclick="UI.insert_focused('draw_string(');">string</button><button class="bouton" onclick="UI.insert_focused(';');">show</button>
    <br>
    <button class="bouton" onclick="UI.insert_focused('red');">rouge</button><button class="bouton" onclick="UI.insert_focused('green');">vert</button><button class="bouton" onclick="UI.insert_focused('blue');">bleu</button><button class="bouton" onclick="UI.insert_focused('yellow');">jaune</button><button class="bouton" onclick="UI.insert_focused('cyan');">cyan</button><button class="bouton" onclick="UI.insert_focused('magenta');">magenta</button>
    <br>
    
    <button class="bouton" title="En MicroPython, taper , sur une ligne de commande vide pour voir le graphique." onclick="UI.insert_focused('from matplotl import *');"><strong>matplotl</strong></button><button class="bouton" onclick="UI.insert_focused(UI.micropy?'bar(':'barplot(');">bar</button><button class="bouton" onclick="UI.insert_focused(UI.micropy?'scatter(':'scatterplot(');">scat.</button><button class="bouton" onclick="UI.insert_focused('arrow(');">arrow</button><button class="bouton" onclick="UI.insert_focused(UI.micropy?'plot(':'polygonplot(');">plot</button><button class="bouton" onclick="UI.insert_focused(UI.micropy?'text(':'legend(');">txt</button><button class="bouton" onclick="UI.insert_focused(',');">,</button><button class="bouton" onclick="UI.insert_focused('clf()');">clf</button>
    
  </div>
  <div id="boutons_tortue" style="display:none">
    <input type="button" style="width:46px;height:35px" name="add_efface"
           id="add_efface"
           value="nouveau" onmousedown="event.preventDefault()"
           onClick="if (UI.python_mode){ UI.eval_cmdline1('# fonctions du script\nfrom turtle import *\nreset()\n',true);UI.eval_cmdline1(UI.micropy?'.':'efface # Script de d&eacute;placement\n',true);} else {UI.eval_cmdline1('/* fonctions du script */\n',true); UI.eval_cmdline1('/* Script de d&eacute;placement*/\nefface;\n',true);}" title="cr&eacute; un &eacute;cran tortue. Taper . dans une ligne de commande vide pour voir la tortue.">
    <input type="button" style="width:46px;height:35px" name="add_avance"
           id="add_avance"
           value="av" onmousedown="event.preventDefault()"
           onClick="UI.insertsemi(UI.focused,UI.micropy?'forward(':'avance ');" title="la tortue avance de n pas (10 par d&eacute;faut)">
    <input type="button" style="width:46px;height:35px" name="add_recule"
           id="add_recule"
           value="rec" onmousedown="event.preventDefault()"
           onClick="UI.insertsemi(UI.focused,UI.micropy?'backward(':'recule ');" title="la tortue recule de n pas (10 par d&eacute;faut)">
    <input type="button" style="width:46px;height:35px" name="add_tourne_droite"
           id="add_tourne_droite"
           value="td" onmousedown="event.preventDefault()"
           onClick="UI.insertsemi(UI.focused,UI.micropy?'right(':'tourne_droite ');" title="la tortue tourne &agrave; droite de n degr&eacute;s (90 par d&eacute;faut)">
    <input type="button" style="width:46px;height:35px" name="add_tourne_gauche"
           id="add_tourne_gauche"
           value="tg" onmousedown="event.preventDefault()"
           onClick="UI.insertsemi(UI.focused,UI.micropy?'left(':'tourne_gauche ');" title="la tortue tourne &agrave; gauche de n degr&eacute;s (90 par d&eacute;faut)">
    <input type="button" style="width:46px;height:35px" name="add_crayon"
           id="add_crayon"
           value="crayon" onmousedown="event.preventDefault()"
           onClick="UI.insertsemi(UI.focused,UI.micropy?'pencolor(':'crayon ');" title="change la couleur du crayon de la tortue"> 
    <input type="button" style="width:46px;height:35px" name="add_rond"
           id="add_rond"
           value="rond" onmousedown="event.preventDefault()"
           onClick="UI.insertsemi(UI.focused,UI.micropy?'circle(':'rond ');" title="Arc de cercle">
    <input type="button" style="width:46px;height:35px" name="add_ecris"
           id="add_ecris"
           value="ecris" onmousedown="event.preventDefault()"
           onClick="UI.insertsemi(UI.focused,UI.micropy?'write(':'ecris ');" title="&Eacute;crire &agrave; la droite de la tortue"><br>
    <span id="boutons_tortue_xcas">
    <input type="button" style="width:46px;height:35px" name="add_pas_de_cote"
           id="add_pas_de_cote"
           value="pas_de_cote" onmousedown="event.preventDefault()"
           onClick="UI.insertsemi(UI.focused,'pas_de_cote ');" title="la tortue saute de n pas  vers la gauche (10 par d&eacute;faut)">
    <input type="button" style="width:46px;height:35px" name="add_saute"
           id="add_saute"
           value="saute" onmousedown="event.preventDefault()"
           onClick="UI.insertsemi(UI.focused,'saute ');" title="la tortue saute de n pas (10 par d&eacute;faut)">
    <input type="button" style="width:46px;height:35px" name="add_disque"
           id="add_disque"
           value="disque" onmousedown="event.preventDefault()"
           onClick="UI.insertsemi(UI.focused,'disque ');" title="Arc de cercle
                    rempli">
    <input type="button" style="width:46px;height:35px" name="add_rectangle_plein"
           id="add_rectangle_plein"
           value="rectangle_plein" onmousedown="event.preventDefault()"
           onClick="UI.insertsemi(UI.focused,'rectangle_plein ');" title="Rectangle plein">
    <input type="button" style="width:46px;height:35px" name="add_triangle_plein"
           id="add_triangle_plein"
           value="triangle_plein" onmousedown="event.preventDefault()"
           onClick="UI.insertsemi(UI.focused,'triangle_plein ');" title="Triangle plein">
    <input type="button" style="width:46px;height:35px" name="add_repete"
           id="add_repete"
           value="repete" onmousedown="event.preventDefault()"
           onClick="UI.insertsemi(UI.focused,'repete ');"
           title="R&eacute;p&eacute;ter plusieurs instructions">
    <input type="button" style="width:46px;height:35px" name="tortue_maillage"
           id="tortue_maillage"
           value="maillage" onmousedown="event.preventDefault()"
           onClick="UI.turtle_maillage=(UI.turtle_maillage+1)%3" title="Change de type de maillage (successivement quadrillage, triangulaire, rien)">
   </span>
   <input type="button" style="width:46px;height:35px" name="tortue_clear"
           id="tortue_clear"
           value="Annul." onmousedown="event.preventDefault()"
           onClick="$id('boutons_tortue').style.display='none'" title="Enleve les boutons de la tortue">
  </div>
</div>
<div id="assistant_rewrite" style="display:none">
  <button class="bouton" onclick="UI.insert_focused('simplify(')" title="Tentative de simplifier une expression, par exemple simplify(sin(3x)/sin(x)). Essayez une commande comme ratnormal, normal ou de reecriture si simplify echoue.">simpl.</button>
  <button class="bouton" onclick="UI.insert_focused('normal(')"
          title="D&eacute;veloppe et r&eacute;duit au meme d&eacute;nominateur">normal
  </button>
  <button class="bouton" onclick="UI.insert_focused('c')" title="Pr&eacute;fixe pour factoriser sur C">c</button>
  <button class="bouton" onclick="UI.insert_focused('factor(')" title="Factorisation, par exemple factor(x^4-1). Utiliser cfactor pour factoriser sur C">factor</button>
  <button class="bouton" onclick="UI.insert_focused('partfrac(')" title="D&eacute;composition en &eacute;l&eacute;ments simples. Utiliser cpartfrac pour d&eacute;composer sur C">partf</button>
  <button class="bouton" onclick="UI.insert_focused('subst(')" title="Substituer">subst</button>
  <button class="bouton" onclick="UI.insert_focused('reorder(')" title="Changer l'ordre des variables d'un polynome">reord</button>
  <br>
  <button class="bouton" onclick="UI.insert_focused('texpand(')"
          title="D&eacute;veloppe sin/cos/tan/exp/ln">texpand
  </button>
  <button class="bouton" onclick="UI.insert_focused('tlin(')"
          title="Lin&eacute;rise les expressions trigonom&eacute;triques">tlin
  </button>
  <button class="bouton" onclick="UI.insert_focused('tcollect(')"
          title="Rassemble les expressions trigonom&eacute;triques">tcoll.
  </button>
  <button class="bouton" onclick="UI.insert_focused('trigsin(')"
          title="R&eacute;ecrire avec des sinus">trigsin
  </button>
  <button class="bouton" onclick="UI.insert_focused('trigcos(')"
          title="R&eacute;ecrire avec des cos">cos
  </button>
  <button class="bouton" onclick="UI.insert_focused('trigtan(')"
          title="R&eacute;ecrire avec des tan">tan
  </button>
  <button class="bouton"
          onclick="UI.insert_focused('halftan(')"
          title="R&eacute;ecrire en fonction de tan de l'angle moiti&eacute;">halftan
  </button>
  <br>
  <button class="bouton" onclick="UI.insert_focused('trig2exp(')"
          title="sin/cos/tan en fonction de exp(i*.)">trig2exp
  </button>
  <button class="bouton" onclick="UI.insert_focused('exp2trig(')" title="exp(i*.)->cos(.)+i*sin(.)">exp2trig</button>
  <button class="bouton" onclick="UI.insert_focused('lin(')" title="Lin&eacute;arise les exponentielles">lin</button>
  <button class="bouton" onclick="UI.insert_focused('lncollect(')"
          title="Rassemble les logarithmes">lncoll.
  </button>
  <button class="bouton" onclick="UI.insert_focused('exp2pow(')" title="e^(a*ln(b))->b^a">exp2^</button>
  <button class="bouton" onclick="UI.insert_focused('pow2exp(')" title="b^a->e^(a*ln(b))">^2exp</button>
  <button class="bouton"
          onclick="$id('assistant_rewrite').style.display='none'">Annul.
  </button>
</div>
<div id="assistant_graph" style="display:none">
  <button class="bouton" onmousedown="event.preventDefault()" onClick="UI.funcoff();UI.savefocused=UI.focused;$id('assistant_plotfunc').style.display='block';UI.xtn='x';" title="Graphe d'une expression, par exemple plotfunc(sin(x),x===-5..5,xstep===0.1)">plot</button>
  <button class="bouton" onmousedown="event.preventDefault()" onClick="UI.funcoff();UI.savefocused=UI.focused; $id('assistant_plotimplicit').style.display='block';UI.set_focus('plotimplicitexprf') ;" title="Graphe d'une courbe implicite, par exemple plotimplicit(x^2+x*y+y^2=3)">implicit</button>
  <button class="bouton" onmousedown="event.preventDefault()" onClick="UI.funcoff();UI.savefocused=UI.focused;$id('assistant_plotparam').style.display='block';UI.xtn='t';" title="Graphe d'une courbe en parametriques, par exemple plotparam([cos(t),sin(t)],t=0..2*pi,tstep===0.1)">param</button>
  <button class="bouton" onmousedown="event.preventDefault()" onClick="UI.funcoff();UI.savefocused=UI.focused; $id('assistant_plotpolar').style.display='block';UI.xtn='t'; UI.set_focus('plotpolarexpr');"
          title="Graphe en polaires, par exemple plotpolar(sin(3*t),t)">polar
  </button>
  <button class="bouton" onmousedown="event.preventDefault()" onClick="UI.funcoff();UI.savefocused=UI.focused;$id('assistant_plotfield').style.display='block';UI.set_focus('plotfieldexprf');"
          title="Champ des tangentes, par exemple plotfield(sin(t*y),[t===-5..5,y===-3..3],xstep===0.5,ystep===0.5))">field
  </button>
  <button class="bouton" onclick="UI.insert_focused('plotode(')"
          title="Graphe d'une solution d'&eacute;quation diff&eacute;rentielle">ode
  </button>
  <br>
  <button class="bouton" onclick="UI.insert_focused('plotseq(')"
          title="Graphe en toile d'araign&eacute;e d'une suite r&eacute;currente">suite
  </button>
  <button class="bouton" onclick="UI.insert_focused('plotlist(')"
          title="Trac&eacute; des points (i,y_i) d'une liste [y_i]">liste
  </button>
  <button class="bouton" onclick="UI.insert_focused('moustache(')"
          title="Boite &agrave; moustaches">moustache
  </button>
  <button class="bouton" onclick="UI.insert_focused('histogram(')"
          title="Histogramme">histo.
  </button>
  <button class="bouton" onclick="UI.insert_focused('scatterplot(')"
          title="Nuage de points">nuage
  </button>
  <button class="bouton" onclick="UI.insert_focused('polygonplot(')"
          title="Ligne polygonale donn&eacute;e par une liste de points">polyg.
  </button>
  <button class="bouton" onclick="UI.insert_focused('linear_regression_plot(')"
          title="Droite de r&eacute;gression lin&eacute;aire">regr.
  </button>
  <button class="bouton" onclick="UI.insert_focused('bar_plot(')"
          title="Diagramme batons">baton
  </button>
  <button class="bouton" onclick="UI.insert_focused('plotcdf(')"
          title="Graphe d'une loi de r&eacute;partition cumul&eacute;e">cdf
  </button>
  <button class="bouton" onclick="UI.insert_focused('plotcontour(')"
          title="Courbes de niveau d'une fonction de 2 variables">niveau
  </button>
  <button class="bouton" onclick="UI.insert_focused('plotarea(')"
          title="Aire sous la courbe">aire
  </button>
  <button class="bouton" onclick="UI.insert_focused('bezier(')"
          title="Courbe de Bezier">bezier
  </button>
  <button class="bouton"
          onclick="$id('assistant_graph').style.display='none'">Annul.
  </button>
  <div id="assistant_plotfunc" style="display:none">
    Choisir un trac&eacute; de
    <button class="bouton" onclick="$id('assistant_plotfunc1var').style.display='block';$id('assistant_plotfunc2var').style.display='none';UI.set_focus('plotfuncexpr');">Courbe</button>
    ou
    <button class="bouton" onclick="$id('assistant_plotfunc1var').style.display='none';$id('assistant_plotfunc2var').style.display='block';UI.set_focus('plotfunc2expr');">Surface</button>
    <div id="assistant_plotfunc1var" style="display:none">
      Expression <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                           id="plotfuncexpr" title="Expression, par exemple x^2" rows=1></textarea><br>
      variable <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                         id="plotfuncvarname" title="Nom de variable, par exemple x" rows=1>x</textarea><br>
      xmin <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                     id="plotfuncvarmin" title="Valeur de d&eacute;part" rows=1>-4</textarea><br>
      xmax <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                     id="plotfuncvarmax" title="Valeur de fin" rows=1>4</textarea><br>
      xstep <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                      id="plotfuncvarstep" title="Pas entre 2 &eacute;valuations successives de l'expression" rows=1>0.0625</textarea>
      <br>
      <button class="bouton" onclick="UI.assistant_plotfunc1var_ok();">Ok</button>
      <button class="bouton"
              onclick="UI.focused=UI.savefocused;$id('assistant_plotfunc').style.display='none'">Annul.
      </button>
      <button class="bouton"
              onclick="$id('plotfuncexpr').value='';$id('plotfuncvarname').value='';$id('plotfuncvarmin').value='';$id('plotfuncvarmax').value='';$id('plotfuncvarstep').value='';">Effacer
      </button>
      <button class="bouton" onclick="$id('plotfuncexpr').value='x^2';$id('plotfuncvarname').value='x';$id('plotfuncvarmin').value='-4';$id('plotfuncvarmax').value='4';">Exemple</button>
    </div>
    <div id="assistant_plotfunc2var" style="display:none">
      Expression <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                           id="plotfunc2expr" title="Expression, par exemple x^2-y^2" rows=1></textarea><br>
      1&egrave;re variable <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                                     id="plotfunc2varx" title="Premi&egrave;re variable, par exemple x===-3..3" rows=1>x===-3..3</textarea><br>
      2&egrave;me variable <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                                     id="plotfunc2vary" title="Deuxi&egrave;me variable, par exemple y===-3..3" rows=1>y===-3..3</textarea><br>
      xstep <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                      id="plotfunc2varxstep" title="Pas entre 2 &eacute;valuations successives de l'expression" rows=1>0.25</textarea><br>
      ystep <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                      id="plotfunc2varystep" title="Pas entre 2 &eacute;valuations successives de l'expression" rows=1>0.25</textarea>
      <br>
      <button class="bouton" onclick="UI.assistant_plotfunc2var_ok();">Ok</button>
      <button class="bouton"
              onclick="UI.focused=UI.savefocused;$id('assistant_plotfunc').style.display='none'">Annul.
      </button>
      <button onclick="$id('plotfunc2expr').value='';$id('plotfunc2varx').value='x';$id('plotfunc2vary').value='y';$id('plotfunc2varxstep').value='';$id('plotfunc2varystep').value='';">Effacer
      </button>
      <button onclick="$id('plotfunc2expr').value='x^2-y^2';$id('plotfunc2varx').value='x===-3..3';$id('plotfunc2vary').value='y===-3..3';$id('plotfunc2varxstep').value='0.25';$id('plotfunc2varystep').value='0.25';">Exemple</button>
    </div>
  </div>
  <div id="assistant_plotparam" style="display:none">
    Choisir un trac&eacute; de
    <button class="bouton"
            onclick="$id('assistant_plotparam1var').style.display='block';$id('assistant_plotparam2var').style.display='none';UI.set_focus('plotparamexprx');">Courbe
    </button>
    ou
    <button class="bouton"
            onclick="$id('assistant_plotparam1var').style.display='none';$id('assistant_plotparam2var').style.display='block';UI.set_focus('plotparam2exprx');">Surface
    </button>
    param&eacute;trique.
    <button class="bouton"
            onclick="UI.focused=UI.savefocused;$id('assistant_plotparam').style.display='none'">Annul.
    </button>
    <br>
    <div id="assistant_plotparam1var" style="display:none">
      x(t)= <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                      id="plotparamexprx" title="Expression de x(t), par exemple 2*cos(t)" rows=1></textarea><br>
      y(t)= <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                      id="plotparamexpry" title="Expression de y(t), par exemple 3*sin(t)" rows=1></textarea><br>
      variable<textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                        id="plotparamvarname" title="Nom de variable, par exemple t" rows=1>t</textarea><br>
      tmin <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                     id="plotparamvarmin" title="Valeur de d&eacute;part" rows=1>-4</textarea><br>
      tmax <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                     id="plotparamvarmax" title="Valeur de fin" rows=1>4</textarea><br>
      tstep <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                      id="plotparamvarstep" title="Pas entre 2 &eacute;valuations successives" rows=1>0.0625</textarea>
      <br>
      <button class="bouton" onclick="UI.assistant_plotparam_ok();;">Ok</button>
      <button class="bouton"
              onclick="UI.focused=UI.savefocused;$id('assistant_plotparam').style.display='none'">Annul.
      </button>
      <button class="bouton"
              onclick="$id('plotparamexprx').value='';$id('plotparamexpry').value='';$id('plotparamvarname').value='';$id('plotparamvarmin').value='';$id('plotparamvarmax').value='';$id('plotparamvarstep').value='';">Effacer
      </button>
      <button class="bouton" onclick="$id('plotparamexprx').value='cos(2t)';$id('plotparamexprx').value='cos(2t)';$id('plotparamexpry').value='sin(3t)';$id('plotparamvarname').value='t';$id('plotparamvarmin').value='-pi';$id('plotparamvarmax').value='pi';">Exemple</button>
    </div>
    <div id="assistant_plotparam2var" style="display:none">
      x(u,v)= <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                        id="plotparam2exprx" title="Expression, par exemple v*cos(u)" rows=1></textarea><br>
      y(u,v)= <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                        id="plotparam2expry" title="Expression, par exemple v*sin(u)" rows=1></textarea><br>
      z(u,v)= <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                        id="plotparam2exprz" title="Expression, par exemple v" rows=1></textarea><br>
      1&egrave;re variable <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                                     id="plotparam2varx" title="Premi&egrave;re variable, par exemple u===-3..3" rows=1>u===-3..3</textarea><br>
      2&egrave;me variable <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                                     id="plotparam2vary" title="Deuxi&egrave;me variable, par exemple v===-3..3" rows=1>v===-3..3</textarea><br>
      ustep <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                      id="plotparam2varxstep" title="Pas entre 2 &eacute;valuations successives de l'expression" rows=1>0.25</textarea><br>
      vstep <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                      id="plotparam2varystep" title="Pas entre 2 &eacute;valuations successives de l'expression" rows=1>0.25</textarea>
      <br>
      <button class="bouton" onclick="UI.assistant_plotparam2var_ok();">Ok</button>
      <button class="bouton"
              onclick="UI.focused=UI.savefocused;$id('assistant_plotparam').style.display='none'">Annul.
      </button>
      <button class="bouton"
              onclick="$id('plotparam2exprx').value='';$id('plotparam2expry').value='';$id('plotparam2exprz').value='';$id('plotparam2varx').value='u';$id('plotparam2vary').value='v';$id('plotparam2varxstep').value='';$id('plotparam2varystep').value='';">Effacer
      </button>
      <button class="bouton" onclick="$id('plotparam2exprx').value='v*cos(u)';$id('plotparam2expry').value='v*sin(u)';$id('plotparam2exprz').value='v';$id('plotparam2varx').value='u===-pi..pi';$id('plotparam2vary').value='v===-3..3';$id('plotparam2varxstep').value='pi/32';$id('plotparam2varystep').value='0.25';">Exemple</button>
    </div>
  </div>
  <div id="assistant_plotimplicit" style="display:none">
    f(x,y)= <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                      id="plotimplicitexprf" title="Expression, par exemple x^3+x-y^2-1" rows=1></textarea><br>
    Variable x<textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                        id="plotimplicitvarx" title="Premi&egrave;re variable, par exemple x===-3..3" rows=1>x===-3..3</textarea><br>
    Variable y<textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                        id="plotimplicitvary" title="Deuxi&egrave;me variable, par exemple y===-3..3" rows=1>y===-3..3</textarea><br>
    xstep <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                    id="plotimplicitvarxstep" title="Pas entre 2 &eacute;valuations successives de l'expression" rows=1>0.25</textarea><br>
    ystep <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                    id="plotimplicitvarystep" title="Pas entre 2 &eacute;valuations successives de l'expression" rows=1>0.25</textarea><br>
    niveaux=<textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                      id="plotimplicitlevel" title="Niveaux &agrave; tracer: laisser vide pour 0 ou mettre une liste" rows=1></textarea>
    <br>
    <button class="bouton" onclick="UI.assistant_plotimplicit_ok();">Ok</button>
    <button class="bouton"
            onclick="UI.focused=UI.savefocused;$id('assistant_plotimplicit').style.display='none'">Annul.
    </button>
    <button class="bouton"
            onclick="$id('plotimplicitexprf').value='';$id('plotimplicitvarx').value='x';$id('plotimplicitvary').value='y';$id('plotimplicitvarxstep').value='';$id('plotimplicitvarystep').value='';$id('plotimplicitlevel').value=''">Effacer
    </button>
    <button class="bouton" onclick="$id('plotimplicitexprf').value='x^3-x-y^2-1';$id('plotimplicitvarx').value='x===-3..3';$id('plotimplicitvary').value='y===-3..3';$id('plotimplicitvarxstep').value='0.02';$id('plotimplicitvarystep').value='0.02';$id('plotimplicitlevel').value=''">Exemple 1</button>
    <button class="bouton" onclick="$id('plotimplicitexprf').value='x^2-y^2';$id('plotimplicitvarx').value='x===-3..3';$id('plotimplicitvary').value='y===-3..3';$id('plotimplicitvarxstep').value='0.02';$id('plotimplicitvarystep').value='0.02';$id('plotimplicitlevel').value='[-3,-2,-1,0,1,2,3]'">Exemple 2</button>
  </div>
  <div id="assistant_plotfield" style="display:none">
    Champ des tangentes pour une &eacute;quation dy/dt=f(t,y) ou un
    syst&egrave;me autonome 2-d d[x,y]/dt=f(x,y)<br>
    f=<textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                id="plotfieldexprf" title="Expression, par exemple x^3+x-y^2-1" rows=1></textarea><br>
    Variable t (ou x)<textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                               id="plotfieldvarx" title="Premi&egrave;re variable, par exemple t===-3..3" rows=1>t===-3..3</textarea><br>
    Variable y<textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                        id="plotfieldvary" title="Deuxi&egrave;me variable, par exemple y===-3..3" rows=1>y===-3..3</textarea><br>
    xstep <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                    id="plotfieldvarxstep" title="Pas entre 2 &eacute;valuations successives de l'expression" rows=1>0.25</textarea><br>
    ystep <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                    id="plotfieldvarystep" title="Pas entre 2 &eacute;valuations successives de l'expression" rows=1>0.25</textarea><br>
    init=<textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                   id="plotfieldinit" title="Liste de conditions initiales optionnelles" rows=1></textarea>
    <br>
    <button class="bouton" onclick="UI.assistant_plotfield_ok();">Ok</button>
    <button class="bouton"
            onclick="UI.focused=UI.savefocused;$id('assistant_plotfield').style.display='none'">Annul.
    </button>
    <button class="bouton"
            onclick="$id('plotfieldexprf').value='';$id('plotfieldvarx').value='x';$id('plotfieldvary').value='y';$id('plotfieldvarxstep').value='';$id('plotfieldvarystep').value='';$id('plotfieldinit').value=''">Effacer
    </button>
    <button class="bouton" onclick="$id('plotfieldexprf').value='sin(t*y)';$id('plotfieldvarx').value='t===-3..3';$id('plotfieldvary').value='y===-3..3';$id('plotfieldvarxstep').value='0.25';$id('plotfieldvarystep').value='0.25';$id('plotfieldinit').value='[[0,1],[0,2]]'">Exemple 1d</button>
    <button class="bouton" onclick="$id('plotfieldexprf').value='[[0.2,-1],[1,0.2]]*[x,y]';$id('plotfieldvarx').value='x===-3..3';$id('plotfieldvary').value='y===-3..3';$id('plotfieldvarxstep').value='0.25';$id('plotfieldvarystep').value='0.25';$id('plotfieldinit').value='seq([0,j],j,-3,3)'">Exemple a 2d</button>
    <button class="bouton" onclick="$id('plotfieldexprf').value='[[0.2,0.5],[0.5,0.2]]*[x,y]';$id('plotfieldvarx').value='x===-3..3';$id('plotfieldvary').value='y===-3..3';$id('plotfieldvarxstep').value='0.25';$id('plotfieldvarystep').value='0.25';$id('plotfieldinit').value='seq([0,j],j,-3,3)'">Exemple b 2d</button>
  </div>
  <div id="assistant_plotpolar" style="display:none">
    Courbe en polaire <br>
    expression <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                         id="plotpolarexpr" title="Expression, par exemple sin(3*t)" rows=1></textarea><br>
    variable θ <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                         id="plotpolarvarname" title="Nom de variable, par exemple t" rows=1>t</textarea><br>
    θmin <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                   id="plotpolarvarmin" title="Valeur de d&eacute;part" rows=1></textarea><br>
    θmax <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                   id="plotpolarvarmax" title="Valeur de fin" rows=1></textarea><br>
    θstep <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                    id="plotpolarvarstep" title="Pas entre deux &eacute;valuations" rows=1></textarea>
    <br>
    <button class="bouton" onclick="UI.assistant_plotpolar_ok();">Ok</button>
    <button class="bouton" onclick="UI.focused=UI.savefocused;$id('assistant_plotpolar').style.display='none'">Annul.</button>
    <button class="bouton"
            onclick="$id('plotpolarexpr').value='';$id('plotpolarvarname').value='';$id('plotpolarvarmin').value='';$id('plotpolarvarmax').value='';$id('plotpolarvarstep').value='';">Effacer
    </button>
    <button class="bouton" onclick="$id('plotpolarexpr').value='sin(3*t)';$id('plotpolarvarname').value='t';$id('plotpolarvarmin').value='0';$id('plotpolarvarmax').value='pi';$id('plotpolarvarstep').value='';">Exemple</button>
  </div>
</div>
<div id="assistant_calculus" style="display:none">
  <button class="bouton" onmousedown="event.preventDefault()" onClick="UI.funcoff();UI.savefocused=UI.focused; $id('assistant_limit').style.display='block';UI.set_focus('limitexpr') ;" title="limite d'une expression lorsqu'une variable tend vers une limite, par exemple limit(sin(x)/x,x,0). Utiliser un 4eme parametre egal a 1 ou -1 pour une limite a droite ou a gauche.">limit</button>
  <button class="bouton" onmousedown="event.preventDefault()" onClick="UI.funcoff();UI.savefocused=UI.focused;$id('assistant_diff').style.display='block';UI.set_focus('diffexpr') ;" title="Derivee d'une expression. Pour une fonction f, par exemple f(x):=sin(x^2), la derivee de f est f', par exemple g:=f' ou f'(2)">∂</button>
  <button class="bouton" onmousedown="event.preventDefault()" onClick="UI.funcoff();UI.savefocused=UI.focused; $id('assistant_series').style.display='block';UI.set_focus('seriesexpr') ;" title="series calcule le developpement de Taylor d'une expression lorsqu'une variable tend vers un point, par exemple series(sin(x),x=0,5,polynom). Si on omet polynom un terme de reste est renvoye. On peut specifier un developpement a droite ou a gauche en ajoutant 1 ou -1 avant polynom"> series</button>
  <button class="bouton" onmousedown="event.preventDefault()" onClick="UI.funcoff();UI.savefocused=UI.focused;$id('assistant_sum').style.display='block';UI.set_focus('sumexpr') ; " title="Somme d'une expression pour une variable entre deux bornes, par exemple ∑(k,k,1,n) ou ∑(1/n^2,n,1,inf)"> ∑</button>
  <button class="bouton" onmousedown="event.preventDefault()" onClick="UI.funcoff();UI.savefocused=UI.focused; $id('assistant_int').style.display='block';UI.set_focus('intexpr');"
          title="Calcul d'int&eacute;grales, par exemple ∫(x^2*sin(x)*exp(x),x) ou ∫(1/(x^4+1),x,0,inf)">∫
  </button>
  <button class="bouton"
          onmousedown="event.preventDefault()" onClick="UI.funcoff();UI.savefocused=UI.focused;$id('assistant_desolve').style.display='block';UI.set_focus('desolveeq');" title="Resolution d'une equation differentielle, par exemple desolve(y''+y=0), desolve(y'+y=0,y(0)=1)">desolve
  </button>
  <br>
  <button class="bouton" onclick="UI.insert_focused('ilaplace(')"
          title="ilaplace: transform&eacute;e de Laplace inverse">i
  </button>
  <button class="bouton" onclick="UI.insert_focused('laplace(')"
          title="Transform&eacute;e de Laplace">laplace
  </button>
  <button class="bouton" onclick="UI.insert_focused('odesolve(')"
          title="odesolve: r&eacute;solution approch&eacute;e d'&eacute;quation diff&eacute;rentielles">o
  </button>
  <button class="bouton" onclick="UI.insert_focused('desolve(')"
          title="R&eacute;solution exacte d'&eacute;quation diff&eacute;rentielle">desolve
  </button>
  <button class="bouton" onclick="UI.insert_focused('ifft(')"
          title="ifft: transform&eacute;e de Fourier rapide inverse">i
  </button>
  <button class="bouton" onclick="UI.insert_focused('fft(')"
          title="Transform&eacute;e de Fourier rapide">fft
  </button>
  <button class="bouton" onclick="UI.insert_focused('invztrans(')"
          title="invztrans: transform&eacute;e en z inverse d'une fraction rationnelle">inv
  </button>
  <button class="bouton" onclick="UI.insert_focused('ztrans(')"
          title="Transform&eacute;e en z d'une suite">ztrans
  </button>
  <button class="bouton" onclick="UI.insert_focused('grad(')"
          title="Gradient">grad
  </button>
  <button class="bouton" onclick="UI.insert_focused('hessian(')"
          title="Hessien">hess
  </button>
  <button class="bouton" onclick="UI.insert_focused('curl(')"
          title="Rotationnel">rot
  </button>
  <button class="bouton" onclick="UI.insert_focused('divergence(')"
          title="Divergence">div
  </button>
  <button class="bouton" onclick="UI.insert_focused('vpotential(')"
          title="vpotential: potentiel vecteur">v
  </button>
  <button class="bouton" onclick="UI.insert_focused('potential(')"
          title="Potentiel">poten.
  </button>
  <button class="bouton"
          onclick="$id('assistant_calculus').style.display='none'">Annul.
  </button>
  <div id="assistant_desolve" style="display:none">
    &Eacute;quation diff&eacute;rentielle
    <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
              id="desolveeq" title="Par exemple y'+t*y=t^2" rows=1
              cols=40></textarea>
    <br>
    Variable
    <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
              id="desolvevar" title="Par exemple t" rows=1 cols=3>t</textarea>,
    inconnue
    <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
              id="desolvey" title="Par exemple y" rows=1 cols=3>y</textarea>
    <br>
    Conditions initiales optionnelles
    <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
              id="desolveinit" title="Par exemple y(0)=1,y'(0)=0" rows=1
              cols=20></textarea>
    <br>
    <button class="bouton" onmousedown="event.preventDefault()"
            onclick="UI.set_focus('desolveeq');UI.insert_focused('t')">t
    </button>
    <button class="bouton" onmousedown="event.preventDefault()"
            onclick="UI.set_focus('desolveeq') ;UI.insert_focused('y\'\'')">y&quote;&quote;
    </button>
    <button class="bouton" onmousedown="event.preventDefault()"
            onclick="UI.insert_focused('y\'')">y&quote;
    </button>
    <button class="bouton" onmousedown="event.preventDefault()"
            onclick="UI.insert_focused('y')">y
    </button>
    <br>
    <button class="bouton"
            onclick="UI.assistant_desolve_ok();">Ok
    </button>
    <button class="bouton" onclick="UI.focused=UI.savefocused;$id('assistant_desolve').style.display='none'">Annul.</button>
    <button class="bouton" onclick="$id('desolveeq').value='';$id('desolvevar').value='';$id('desolvey').value='';$id('desolveinit').value='';">Effacer</button>
    <button class="bouton" onclick="$id('desolveeq').value='y\'+t*y=t';$id('desolvevar').value='t';$id('desolvey').value='y';$id('desolveinit').value='y(0)=2';">Ordre 1</button>
    <button class="bouton" onclick="$id('desolveeq').value='y\'\'+y=t^2';$id('desolvevar').value='t';$id('desolvey').value='y';$id('desolveinit').value='y(0)=1,y\'(0)=0';">Ordre 2</button>
    <button class="bouton" onclick="$id('desolveeq').value='y\'=[[1,2],[2,1]]*y+[t,t+1]';$id('desolvevar').value='t';$id('desolvey').value='y';$id('desolveinit').value='y(0)=[1,2]'">Syst&egrave;me</button>
  </div>
  <div id="assistant_series" style="display:none">
    D&eacute;veloppement limit&eacute; <br>
    expression <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                         id="seriesexpr" title="Expression, par exemple sin(x)" rows=1></textarea><br>
    variable <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                       id="seriesvarname" title="Nom de variable, par exemple x" rows=1>x</textarea><br>
    en <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                 id="seriesvarlim" title="Point limite" rows=1></textarea><br>
    ordre <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                    id="seriesvarorder" title="Ordre" rows=1></textarea><br>
    Polynome <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                       id="seriesvarstep" title="L'option polynom supprime le terme de reste du d&eacute;veloppement" rows=1>polynom</textarea>
    <br>
    <button class="bouton" onclick="UI.assistant_series_ok();">Ok</button>
    <button class="bouton" onclick="UI.focused=UI.savefocused;$id('assistant_series').style.display='none'">Annul.</button>
    <button class="bouton"
            onclick="$id('seriesexpr').value='';$id('seriesvarname').value='';$id('seriesvarlim').value='';$id('seriesvarorder').value='';">Effacer
    </button>
    <button class="bouton" onclick="$id('seriesexpr').value='sin(x)/x';$id('seriesvarname').value='x';$id('seriesvarlim').value='0';$id('seriesvarorder').value='5';$id('seriesvarstep').value='polynom';">Exemple</button>
  </div>
  <div id="assistant_limit" style="display:none">
    Limite de :<br>
    expression <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                         id="limitexpr" title="Expression, par exemple sin(x)/x" rows=1></textarea><br>
    variable <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                       id="limitvarname" title="Nom de variable, par exemple x" rows=1>x</textarea><br>
    en <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                 id="limitvarlim" title="Valeur limite" rows=1></textarea><br>
    Direction optionnelle <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                                    id="limitvardir" title="-1: limite &agrave; gauche, 1: &agrave; droite" rows=1></textarea>
    <br>
    <button class="bouton" onclick="UI.assistant_limit_ok();">Ok</button>
    <button class="bouton" onclick="UI.focused=UI.savefocused;$id('assistant_limit').style.display='none'">Annul.</button>
    <button class="bouton"
            onclick="$id('limitexpr').value='';$id('limitvarname').value='';$id('limitvarlim').value='';$id('limitvardir').value='';">Effacer
    </button>
    <button class="bouton" onclick="$id('limitexpr').value='sin(x)/x';$id('limitvarname').value='x';$id('limitvarlim').value='0';$id('limitvardir').value='1';">Exemple</button>
  </div>
  <div id="assistant_int" style="display:none">
    Int&eacute;grale de <br>
    expression <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                         id="intexpr" title="Expression, par exemple x^2" rows=1></textarea><br>
    variable <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                       id="intvarname" title="Nom de variable, par exemple x" rows=1>x</textarea><br>
    de (optionnel) <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                             id="intvarmin" title="Borne inf&eacute;rieure" rows=1></textarea><br>
    &agrave; (optionnel) <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                                   id="intvarmax" title="Borne sup&eacute;rieure" rows=1></textarea>
    <br>
    <button class="bouton" onclick="UI.assistant_int_ok();">Ok</button>
    <button class="bouton" onclick="UI.focused=UI.savefocused;$id('assistant_int').style.display='none'">Annul.</button>
    <button class="bouton"
            onclick="$id('intexpr').value='';$id('intvarname').value='';$id('intvarmin').value='';$id('intvarmax').value='';">Effacer
    </button>
    <button class="bouton" onclick="$id('intexpr').value='1/(1+x^2)^2';$id('intvarname').value='x';$id('intvarmin').value='';$id('intvarmax').value='';">Exemple 1</button>
    <button class="bouton" onclick="$id('intexpr').value='1/(1+x^2)^2';$id('intvarname').value='x';$id('intvarmin').value='0';$id('intvarmax').value='1';">Exemple 2</button>
  </div>
  <div id="assistant_sum" style="display:none">
    Somme de <br>
    expression <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                         id="sumexpr" title="Expression, par exemple j^2" rows=1></textarea><br>
    variable <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                       id="sumvarname" title="Nom de variable, par exemple j" rows=1>j</textarea><br>
    de (optionnel) <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                             id="sumvarmin" title="Borne inf&eacute;rieure" rows=1></textarea><br>
    &agrave; (optionnel) <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                                   id="sumvarmax" title="Borne sup&eacute;rieure" rows=1></textarea>
    <br>
    <button class="bouton" onclick="UI.assistant_sum_ok();">Ok</button>
    <button class="bouton" onclick="UI.focused=UI.savefocused;$id('assistant_sum').style.display='none'">Annul.</button>
    <button class="bouton" onclick="$id('sumexpr').value='j^2';$id('sumvarname').value='j';$id('sumvarmin').value='0';$id('sumvarmax').value='n';">Exemple</button>
    <button class="bouton"
            onclick="$id('sumexpr').value='';$id('sumvarname').value='';$id('sumvarmin').value='';$id('sumvarmax').value='';">Effacer
    </button>
  </div>
  <div id="assistant_diff" style="display:none">
    D&eacute;riv&eacute;e de <br>
    expression <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                         id="diffexpr" title="Expression, par exemple sin(x)^2" rows=1></textarea><br>
    variable <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                       id="diffvarname" title="Nom de variable, par exemple x" rows=1>x</textarea><br>
    Nombre de d&eacute;riv&eacute;es <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                                               id="diffnumber" title="Valeur par d&eacute;faut 1" rows=1>1</textarea><br>
    <br>
    <button class="bouton" onclick="UI.assistant_diff_ok();">Ok</button>
    <button class="bouton" onclick="UI.focused=UI.savefocused;$id('assistant_diff').style.display='none'">Annul.</button>
    <button class="bouton" onclick="$id('diffexpr').value='sin(x)^2';$id('diffvarname').value='x';$id('diffnumber').value='';">Exemple 1</button>
    <button class="bouton" onclick="$id('diffexpr').value='sin(x^2)';$id('diffvarname').value='x';$id('diffnumber').value='5';">Exemple 2</button>
    <button class="bouton"
            onclick="$id('diffexpr').value='';$id('diffvarname').value='';$id('diffnumber').value='';">Effacer
    </button>
  </div>
</div>
<div id="assistant_geo" style="display:none">
  <button class="bouton" onclick="UI.insert_focused('point(')"
          title="Point donn&eacute; par ses coordonn&eacute;es ou son affixe">point
  </button>
  <button class="bouton" onclick="UI.insert_focused('segment(')"
          title="Segment reliant 2 points ou 2 affixes">segment
  </button>
  <button class="bouton" onclick="UI.insert_focused('droite(')"
          title="Droite passant par 2 points">droite
  </button>
  <button class="bouton" onclick="UI.insert_focused('vecteur(')"
          title="Vecteur">vecteur
  </button>
  <button class="bouton" onclick="UI.insert_focused('equation(')"
          title="&Eacute;quation">equation
  </button>
  <button class="bouton" onclick="UI.insert_focused('parameq(')"
          title="&Eacute;quation param&eacute;trique">param
  </button>
  <button class="bouton" onclick="UI.insert_focused('milieu(')"
          title="Milieu de 2 points">milieu
  </button>
  <button class="bouton" onclick="UI.insert_focused('cercle(')"
          title="Cercle par centre, rayon ou diam&eacute;tre">&#x25ef;
  </button>
  <button class="bouton" onclick="UI.insert_focused('centre(')"
          title="Centre d'un cercle">centre
  </button>
  <button class="bouton" onclick="UI.insert_focused('isobarycentre(')"
          title="Centre de gravit&eacute;">gravit&eacute;
  </button>
  <button class="bouton" onclick="UI.insert_focused('inter(')"
          title="Liste des intersections, utiliser inter_unique pour un point">inter
  </button>
  <button class="bouton" onclick="UI.insert_focused('inter_unique(')"
          title="Premier ou unique point d'intersection">unique
  </button>
  <button class="bouton" onclick="var tmp=$id('assitant_geo_plus'); if(tmp.style.display=='none') tmp.style.display='block'; else tmp.style.display='none';">+</button>
  <div id="assitant_geo_plus" style="display:none">
    <button class="bouton" onclick="UI.insert_focused('triangle(')"
            title="Triangle">&#x25b3;
    </button>
    <button class="bouton" onclick="UI.insert_focused('A:=point(0);\nB:=point(1);\nassume(a=[0.3,-2,2,0.1]);\nassume(b=[0.6,-2,2,0.1]);\nC:=point(a,b);\ntriangle(A,B,C);\n')"
            title="Triangle symbolique">&#x25b3;ABC
    </button>
    <button class="bouton" onclick="UI.insert_focused('pointc(x):=(1+i*x)/(1-i*x);\nassume(a=[0.3,0,2,0.1]);\nassume(b=[0.6,0,2,0.1]);\nP1:=point(-1,display=hidden_name);\nP2:=point(pointc(a),display=hidden_name);\nP3:=point(pointc(-b),display=hidden_name);\nL1:=perpendicular(P1,line(0,P1)):;\nL2:=perpendicular(P2,line(0,P2)):;\nL3:=perpendicular(P3,line(0,P3)):;\nA:=single_inter(L1,L2);\nB:=single_inter(L2,L3);\nC:=single_inter(L3,L1);\ntriangle(A,B,C);circle(0,1);\n')"
            title="Triangle symbolique + cercle inscrit">&#x25ef;in&#x25b3;
    </button>
    <button class="bouton" onclick="UI.insert_focused('pointc(x):=(1+i*x)/(1-i*x);\nassume(b=[0.3,0,2,0.1]);\nassume(c=[0.6,0,2,0.1]);\nA:=point(-1);\nB:=point(pointc(b));\nC:=point(pointc(-c));\ncircle(0,1);triangle(A,B,C);\n')"
            title="Triangle symbolique + cercle circonscrit">&#x25b3;in&#x25ef;
    </button>
    <button class="bouton" onclick="UI.insert_focused('rectangle(')"
            title="Rectangle">&#x25ad;
    </button>
    <button class="bouton" onclick="UI.insert_focused('parallelogramme(')"
            title="Parallelogramme">&#x25b1;
    </button>
    <button class="bouton" onclick="UI.insert_focused('carre(')"
            title="Carre">&#x25a2;
    </button>
    <button class="bouton" onclick="UI.insert_focused('polygone(')"
            title="Polygone">polygone
    </button>
    <button class="bouton" onclick="UI.insert_focused('isopolygone(')"
            title="Polygone r&eacute;gulier">r&eacute;gulier
    </button>
    <button class="bouton" onclick="UI.insert_focused('parallele(')"
            title="Parall&egrave;le">//
    </button>
    <button class="bouton" onclick="UI.insert_focused('perpendiculaire(')"
            title="Perpendiculaire">&perp;
    </button>
    <button class="bouton" onclick="UI.insert_focused('mediatrice(')"
            title="Mediatrice">mediatrice
    </button>
    <button class="bouton" onclick="UI.insert_focused('bissectrice(')"
            title="Bissectrice">biss
    </button>
    <button class="bouton" onclick="UI.insert_focused('hauteur(')"
            title="Hauteur">hauteur
    </button>
    <button class="bouton" onclick="UI.insert_focused('tangent(')"
            title="Tangente &agrave; un graphe">tangent
    </button>
    <button class="bouton" onclick="UI.insert_focused('distance(')"
            title="Distance">dist.
    </button>
    <button class="bouton"
            onclick="$id('assistant_geo').style.display='none'">Annul.
    </button>
  </div>
</div>
<div id="assistant_arit" style="display:none">
  <button class="bouton" onclick="UI.insert_focused('gcd(')"
          title="PGCD d'entiers ou de polynomes">gcd
  </button>
  <button class="bouton" onclick="UI.insert_focused('iquo(')"
          title="iquo: quotient de la division euclidienne d'entiers">&nbsp;&nbsp;i
  </button>
  <button class="bouton" onclick="UI.insert_focused('quo(')"
          title="Quotient euclidien de 2 polynomes">quo
  </button>
  <button class="bouton" onclick="UI.insert_focused('irem(')"
          title="irem: reste de la division euclidienne d'entiers">&nbsp;&nbsp;i
  </button>
  <button class="bouton" onclick="UI.insert_focused('rem(')"
          title="Reste euclidien de 2 polynomes">rem
  </button>
  <button class="bouton" onclick="UI.insert_focused('iabcuv(')"
          title="iabcuv: r&eacute;soudre a*u+b*v=c pour a,b,c donn&eacute;s">&nbsp;&nbsp;i
  </button>
  <button class="bouton" onclick="UI.insert_focused('abcuv(')"
          title="Solution polynomiale de A*U+B*V=C">abcuv
  </button>
  <button class="bouton" onclick="UI.insert_focused('ifactor(')"
          title="ifactor: factorisation d'un entier">&nbsp;&nbsp;i
  </button>
  <button class="bouton" onclick="UI.insert_focused('factor(')"
          title="Factorisation d'un polynome">factor
  </button>
  <br>
  <button class="bouton" onclick="UI.insert_focused('lcm(')"
          title="PPCM d'entiers ou de polynomes">lcm
  </button>
  <button class="bouton" onclick="UI.insert_focused('ichinrem(')"
          title="Restes chinois entiers">ichrem
  </button>
  <button class="bouton" onclick="UI.insert_focused('isprime(')"
          title="Test de pseudo-primalit&eacute;">isprime
  </button>
  <button class="bouton" onclick="UI.insert_focused('nextprime(')"
          title="Prochain entier pseudo-premier">next
  </button>
  <button class="bouton" onclick="UI.insert_focused('powmod(')"
          title="powmod: puissance modulaire rapide">pow
  </button>
  <button class="bouton" onclick="UI.insert_focused('mod(')"
          title="Cr&eacute;ation d'un &eacute;l&eacute;ment de
                Z/nZ">mod
  </button>
  <button class="bouton" onclick="UI.insert_focused('GF(')"
          title="Cr&eacute;ation d'un corps fini non premier">GF
  </button>
  <br>
  <button class="bouton" onclick="UI.insert_focused('lcoeff(')"
          title="lcoeff: coefficient dominant">&nbsp;l
  </button>
  <button class="bouton" onclick="UI.insert_focused('coeff(')" title="Coefficient">coeff</button>
  <button class="bouton" onclick="UI.insert_focused('degree(')" title="Degr&eacute;">degree</button>
  <button class="bouton" onclick="UI.insert_focused('horner(')"
          title="&Eacute;valuation">horner
  </button>
  <button class="bouton" onclick="UI.insert_focused('ptayl(')"
          title="D&eacute;veloppement de Taylor">ptayl
  </button>
  <button class="bouton" onclick="UI.insert_focused('proot(')"
          title="Racines complexes approch&eacute;es d'un polyn&circ;ome">proot
  </button>
  <button class="bouton"
          onclick="$id('assistant_arit').style.display='none'">Annul.
  </button>
</div>
<div id="assistant_linalg" style="display:none">
  <button class="bouton" onclick="UI.insert_focused('dot(')"
          title="Produit scalaire de deux vecteurs">dot
  </button>
  <button class="bouton" onclick="UI.insert_focused('cross(')"
          title="Produit vectoriel de 2 vecteurs de R^2 ou R^3">cross
  </button>
  <button class="bouton" onclick="UI.insert_focused('tran(')"
          title="Transpos&eacute;e d'une matrice, utiliser trn(M) ou M^* pour la transconjugu&eacute;e de M">tran
  </button>
  <button class="bouton" onclick="UI.insert_focused('idn(')"
          title="Matrice identit&eacute; de taille n">idn
  </button>
  <button class="bouton" onclick="UI.insert_focused('matrix(')"
          title="Cr&eacute;e une matrice">matr
  </button>
  <button class="bouton" onclick="UI.insert_focused('hilbert(')"
          title="Matrice de Hilbert de taille n">hilb
  </button>
  <button class="bouton" onclick="UI.insert_focused('vandermonde(')"
          title="Matrice de Vandermonde de taille n">vand
  </button>
  <button class="bouton" onclick="UI.insert_focused('laplace(')"
          title="Matrice du laplacien discret 1-d de taille n">lapl.
  </button>
  <br>
  <button class="bouton" onclick="UI.insert_focused('rref(')"
          title="R&eacute;duction sous forme &eacute;chelonn&eacute;e">rref
  </button>
  <button class="bouton" onclick="UI.insert_focused('ker(')"
          title="ker(M) renvoie une base du noyau d'une application lin&eacute;aire de matrice M">ker
  </button>
  <button class="bouton" onclick="UI.insert_focused('det(')"
          title="D&eacute;terminant d'une matrice carr&eacute;e">det
  </button>
  <button class="bouton" onclick="UI.insert_focused('linsolve(')"
          title="R&eacute;solution d'un syst&egrave;me lin&eacute;aire">linsolve
  </button>
  <button class="bouton" onclick="UI.insert_focused('lu(')"
          title="Factorisation P*A=L*U d'une matrice A">lu
  </button>
  <button class="bouton" onclick="UI.insert_focused('qr(')"
          title="Factorisation A=Q*R d'une matrice A">qr
  </button>
  <button class="bouton" onclick="UI.insert_focused('cholesky(')"
          title="Factorisation de Cholesky A=L*L^* d'une matrice sym&eacute;trique d&eacute;finie positive">chol.
  </button>
  <button class="bouton" onclick="UI.insert_focused('cond(')"
          title="Nombre de condition d'une matrice relativement &agrave; la norme 1, 2 ou inf">cond
  </button>
  <br>
  <button class="bouton" onclick="UI.insert_focused('egv(')"
          title="Vecteurs propres d'une matrice">egv
  </button>
  <button class="bouton" onclick="UI.insert_focused('egvl(')"
          title="Valeurs propres d'une matrice">egvl
  </button>
  <button class="bouton" onclick="UI.insert_focused('jordan(')"
          title="R&eacute;duction de Jordan d'une matrice A*P=P*J">jordan
  </button>
  <button class="bouton" onclick="UI.insert_focused('pcar(')"
          title="Polynome caract&eacute;ristique">pcar
  </button>
  <button class="bouton" onclick="UI.insert_focused('pmin(')"
          title="Polynome minimal">pmin
  </button>
  <button class="bouton" onclick="UI.insert_focused('matrix_norm(')"
          title="Norme matricielle (1, 2 ou inf) ">norm
  </button>
  <button class="bouton"
          onclick="$id('assistant_linalg').style.display='none'">Annul.
  </button>
</div>
<div id="chooselawdiv" style="display:none">
  <form id="chooselawform">
    Loi actuelle <input class="bouton" type="text" id="rand_law" name="rand_law"
                        title="Loi" value='normald'>, param&egrave;tres optionnels
    <input class="bouton" type="number" name="rand_law1" id="rand_law1"
           title="1er param&egrave;tre" value=0 step=0.01>
    <input class="bouton" type="number" name="rand_law2" id="rand_law2"
           title="2&egrave;me param&egrave;tre" value=1 step=0.01>
    <input class="bouton" type="text" name="law_arg" id="law_arg"
           title="argument de la loi, par exemple 1 ou 2 ou 1.3 ou x" value=1>
    <br>
    Choisir une autre loi
    <input type="button" onclick="$id('rand_law').value='uniformd';$id('rand_law1').value=0;$id('rand_law1').step=0.01;$id('rand_law2').value=1;$id('rand_law1').style.display='inline';$id('rand_law2').style.display='inline';" value="uniformd">
    <input type="button" onclick="$id('rand_law').value='normald';$id('rand_law1').value=0;$id('rand_law1').step=0.01;$id('rand_law2').value=1;$id('rand_law1').style.display='inline';$id('rand_law2').style.display='inline';" value="normald">
    <input type="button" onclick="$id('rand_law').value='exponentiald';$id('rand_law1').value=0.5;$id('rand_law1').step=0.01;$id('rand_law1').style.display='inline';$id('rand_law2').style.display='none';" value="exponentiald">
    <input type="button" onclick="$id('rand_law').value='binomial';$id('rand_law1').value=10;$id('rand_law1').step=1;$id('rand_law2').value=0.5;$id('rand_law1').style.display='inline';$id('rand_law2').style.display='inline';" value="binomial">
    <input type="button" onclick="$id('rand_law').value='negbinomial';$id('rand_law1').value=10;$id('rand_law1').step=1;$id('rand_law2').value=0.5;$id('rand_law1').style.display='inline';$id('rand_law2').style.display='inline';" value="negbinomial">
    <input type="button" onclick="$id('rand_law').value='geometric';$id('rand_law1').value=0.5;$id('rand_law1').step=0.01;$id('rand_law1').style.display='inline';$id('rand_law2').style.display='none';" value="geometric">
    <input type="button" onclick="$id('rand_law').value='poisson';$id('rand_law1').value=0.5;$id('rand_law1').step=0.01;$id('rand_law1').style.display='inline';$id('rand_law2').style.display='none';" value="poisson">
  </form>
</div>
<form id="assistant_matr" style="display:none" onsubmit="setTimeout(UI.assistant_matr_ok()); return false">
  <div id="matr_type_chooser">
    <input class="bouton" type="checkbox" name="matr_formule"
           onclick="$id('assistant_matr').matr_formuleshadow.checked=!checked;UI.assistant_matr_setdisplay();"
           title="Cocher pour d&eacute;finir la matrice par une formule">
    <input class="bouton" type="button" value="formule" onclick="$id('assistant_matr').matr_formule.checked=true;$id('assistant_matr').matr_formuleshadow.checked=false;UI.assistant_matr_setdisplay();"> ou
    <input class="bouton" type="checkbox" name="matr_formuleshadow"
           onclick="$id('assistant_matr').matr_formule.checked=!checked;UI.assistant_matr_setdisplay();"
           title="Cocher pour d&eacute;finir la matrice &eacute;l&eacute;ment par &eacute;l&eacute;ment" checked>
    <input class="bouton" type="button" value="case" onclick="$id('assistant_matr').matr_formule.checked=false;$id('assistant_matr').matr_formuleshadow.checked=true;UI.assistant_matr_setdisplay();">
  </div>
  <div id="matr_stats" style="display:none">
    <input class="bouton" type="button"
           onclick="$id('chooselawdiv').style.display='block';$id('law_arg').style.display='inline';$id('matr_stat12').style.display='none';$id('matr_testhyp').style.display='none';$id('risque_alpha').style.display='none';$id('matr').style.display='none';$id('matr_matr').style.display='none';" value="lois usuelles">
    ou <input class="bouton" type="button"
              onclick="$id('chooselawdiv').style.display='block';$id('law_arg').style.display='none';$id('matr_stat12').style.display='none';$id('matr_testhyp').style.display='none';$id('risque_alpha').style.display='block';$id('matr').style.display='none';$id('matr_matr').style.display='none';" value="intervalle de fluctuation">
    ou <input class="bouton" type="button" onclick="$id('matr_stat12').style.display='block';$id('matr').style.display='block'; if(UI.is_sheet){ UI.spreadsheet2matrix(false);UI.matrix2spreadsheet();} UI.assistant_matr_setdisplay();$id('matr_testhyp').style.display='none';$id('risque_alpha').style.display='none';$id('chooselawdiv').style.display='none'; $id('matr_matr').style.display='block';$id('matr_submat').style.display='block';" value="statistiques descriptives">
    ou <input class="bouton" type="button" onclick="$id('matr_stat12').style.display='none';$id('matr').style.display='block'; $id('matr_testhyp').style.display='block';$id('risque_alpha').style.display='block';$id('chooselawdiv').style.display='none'; $id('matr_matr').style.display='block';$id('matr_submat').style.display='block';UI.adequation($id('assistant_matr'))" value="statistiques inf&eacute;rentielles">
    <div id="matr_stat12" style="display:none">
      <input class="bouton" type="checkbox" name="stat_mean">Moyenne,
      <input class="bouton" type="checkbox" name="stat_stddev">Ecart-type,
      <input class="bouton" type="checkbox" name="stat_quartiles">Quartiles,
      <input class="bouton" type="checkbox" name="stat_histo" onclick="form.stat_cmax.value=form.stat_cmin.value;">Histogramme,
      <input class="bouton" type="checkbox" name="stat_moustache">Boite a moustache,
      <br>
      <input class="bouton" type="checkbox" name="stat_scatter" onclick="form.stat_cmax.value=form.stat_cmin.value+1;">Nuage de points
      <input class="bouton" type="checkbox" name="stat_polygonscatter" onclick="form.stat_cmax.value=form.stat_cmin.value+1;">reli&eacute;s,
      <input class="bouton" type="checkbox" name="stat_linreg" onclick="form.stat_cmax.value=form.stat_cmin.value+1;">R&eacute;gression lin&eacute;aire
    </div>
    <div id="risque_alpha" style="display:none">
      Risque &alpha;= <input class="bouton" type="text"
                             id="adequation_alpha" name="adequation_alpha" value=0.05 size=4>
    </div>
    <div id="matr_testhyp" style="display:none">
      <ul>
        <li>
          Intervalle de confiance :
          <input type="button" class="bouton" onclick="form.adequation[0].checked=true;UI.adequation(form)" value="proportion"><input type="radio" name="adequation"
                                                                                                                                      onclick="UI.adequation(form)" title="Intervalle de confiance calcul&eacute; par la loi normale en supposant n*p et n*(1-p)>=5" checked>
          (n=<input name="confiance_n" class="bouton" type="number" value=30
                    min=30 step=1 title="Taille de la population. Pour n&gt;100, utilise sqrt(n/(n-1)*p*(1-p)) comme estimateur de l'ecart-type, sinon on majore par 0.5">&geq;30,
          p=<input name="confiance_p" class="bouton" type="number"
                   title="Proportion dans l'&eacute;chantillon"
                   value=0.5 min=0 max=1 step=0.001>),
          <input type="button" class="bouton" onclick="form.adequation[1].checked=true;UI.adequation(form)" value="Student &mu;&sigma;"><input type="radio"
                                                                                                                                               onclick="UI.adequation(form)" name="adequation" title="Intervalle calcul&eacute par la loi de Student">
          (&mu;=<input name="confiance_mu" class="bouton" type="number"
                       title="Moyenne de l'&eacute;chantillon" value=0
                       step=0.001>, &sigma;=<input name="confiance_sigma" class="bouton" type="number"
                                                   step=0.001 min=0 value=1 title="Ecart-type de la population">
          n=<input name="confiance_n_" class="bouton" type="number" value=30
                   min=30 step=1>)
          <br>
          <input type="button" class="bouton" onclick="form.adequation[2].checked=true;UI.adequation(form)" value="donn&eacute;es"><input type="radio" onclick="UI.adequation(form)" name="adequation"
                                                                                                                                          title="Intervalle calcul&eacute; par la loi de Student sur les donn&eacute;es des lignes et colonnes de la matrice m">,
        </li>
        <li> Ad&eacute;quation data/data :
          <input type="button" class="bouton" onclick="form.adequation[3].checked=true;UI.adequation(form)" value="Chi2"> <input type="radio" onclick="UI.adequation(form)"
                                                                                                                                 name="adequation" value="radio">,
          <input type="button" class="bouton" onclick="form.adequation[4].checked=true;UI.adequation(form)" value="Kolmogorov"> <input onclick="UI.adequation(form)"
                                                                                                                                       type="radio" name="adequation" value="radio" title="test de Kolmogorov-Smirnov d'ad&eacute;quation &agrave; une loi commune continue inconnue">,
          ou
          <input type="button" class="bouton" onclick="form.adequation[5].checked=true;UI.adequation(form)" value="Wilcoxon"> <input onclick="UI.adequation(form)"
                                                                                                                                     type="radio" name="adequation" value="radio" title="test de Wilcoxon-Mann-Whitney">
        </li>
        <li>
          Ad&eacute;quation data/loi : <input type="button" class="bouton" onclick="form.adequation[6].checked=true;UI.adequation(form)" value="normal"> <input type="radio"
                                                                                                                                                                name="adequation" value="radio" onclick="UI.adequation(form)">
          ou
          <input type="button" class="bouton" onclick="form.adequation[7].checked=true;UI.adequation(form)" value="Student"> <input type="radio" onclick="UI.adequation(form)"
                                                                                                                                    name="adequation" value="radio"> :
          &mu;=<input class="bouton" type="text" name="adequation_mu" size=4
                      value=0>
          (&sigma;=<input class="bouton" type="text"
                          name="adequation_sigma" size=4> optionnel),
          <br>
          <span title="Hypoth&egrave;se alternative a H0">Alternative H1 &lt;<input type="radio" name="adequation_alt">,
                            &ne;<input type="radio" name="adequation_alt">,
                            &gt;<input type="radio" name="adequation_alt"></span>
        </li>
      </ul>
    </div>
  </div>
  <div id="matr_matr">
    <input id="matr_name" name="matr_name" class="bouton" type="text"
           value="m" title="Nom de la matrice" size=3>:
    <input class="bouton" type="button" onclick="UI.sheet_rowadd(-1);" value="-">
    <input class="bouton" type="number" id="matr_nrows" name="matr_nrows" onkeypress="if (event.keyCode!=13) return true; UI.assistant_matr_setdisplay(); return false;"
           title="Nombre de lignes de la matrice" value=3 min=1 max=40>
    <input class="bouton" type="button" onclick="UI.sheet_rowadd(1)" value="+">
    par
    <input class="bouton" type="button" onclick="UI.sheet_coladd(-1)" value="-">
    <input class="bouton" type="number" id="matr_ncols" name="matr_ncols" onkeypress="if (event.keyCode!=13) return true; UI.assistant_matr_setdisplay(); return false;"
           title="Nombre de colonnes de la matrice" value=3 min=1 max=6>
    <input class="bouton" type="button" onclick="UI.sheet_coladd(1)" value="+">
  </div>
  <div id="matr_formulediv">
    (j,k)-&gt;<textarea rows="1" cols="20" style="font-size:18px"
                        onclick="UI.focused=this;" id="matr_expr" name="matr_expr" title="Expression de m[j,k] en fonction de j et k"></textarea>
    <input class="bouton" type="checkbox" name="matr_start0"
           title="Cochez pour utiliser les indices commencant a 0" checked>
    (indices de 0 &agrave; taille-1)
    <br>
    <input class="bouton" type="button" title="Matrice identit&eacute;" value="Identit&eacute;" onclick="form.matr_expr.value='si j==k alors 1; sinon 0; fsi';">
    <input class="bouton" type="button" title="Matrice de Hilbert" value="Hilbert" onclick="form.matr_expr.value='1/(j+k+1)';">
    <input class="bouton" type="button" title="Effacer" value="Effacer" onclick="if (form.matr_formule.checked) form.matr_expr.value='';">
  </div>
  <input class="bouton" type="submit" title="ok" value="Ok">
  <input class="bouton" type="button" title="Annuler" value="Annul." onclick="$id('chooselawdiv').style.display='none';form.style.display='none'; UI.focused=UI.savefocused; UI.focused.focus();"> &nbsp;
  <div id="matr" style="display:none">
    <div id="matr_submat" style="display:none">
      Lignes <input id="stat_lmin" name="stat_lmin" class="bouton" type="number" min=0 value=0>
      -
      <input id="stat_lmax" name="stat_lmax" class="bouton" type="number" min=0 value=2>,
      colonnes <input id="stat_cmin" name="stat_cmin" class="bouton" type="number" min=0 value=0>
      -
      <input id="stat_cmax" name="stat_cmax" class="bouton" type="number" min=0 value=1>
    </div>
    <input id="matr_or_sheet" name="matr_or_sheet" class="bouton"
           type="checkbox" title="Cocher pour passer en mode tableur"
           onchange="UI.is_sheet=checked; if (checked) UI.matrix2spreadsheet(); else UI.spreadsheet2matrix(false);" checked>
    <input type="button" onclick="form.matr_or_sheet.checked=!form.matr_or_sheet.checked;if (form.matr_or_sheet.checked) UI.matrix2spreadsheet(); else UI.spreadsheet2matrix(false);" value="Tableur">
    <input class="bouton" type="button"
           onclick="UI.sheet_edit_cmd(0)" onmousedown="event.preventDefault()"
           title="Copier vers le bas" value="cp↓">
    <input class="bouton" type="button"
           onclick="UI.sheet_edit_cmd(1)" onmousedown="event.preventDefault()"
           title="Copier vers la droite" value=" →">
    <input class="bouton" type="button"
           onclick="UI.sheet_edit_cmd(2)" onmousedown="event.preventDefault()"
           title="Ajouter une ligne" value="l+">
    <input class="bouton" type="button"
           onclick="UI.sheet_edit_cmd(3)" onmousedown="event.preventDefault()"
           title="Enlever une ligne" value="l-">
    <input class="bouton" type="button"
           onclick="UI.sheet_edit_cmd(4)" onmousedown="event.preventDefault()"
           title="Ajouter une colonne" value="c+">
    <input class="bouton" type="button"
           onclick="UI.sheet_edit_cmd(5)" onmousedown="event.preventDefault()"
           title="Enlever une colonne" value="c-">
    <input class="bouton" type="button"
           onclick="UI.insert_focused('=')" onmousedown="event.preventDefault()"
           title="Pr&eacute;fixe de formule tableur" value="=">
    <input class="bouton" type="button"
           onclick="UI.insert_focused('$')" onmousedown="event.preventDefault()"
           title="Pr&eacute;fixe de positionnement absolu" value="$">
    <div id="matr_casediv">
    </div>
  </div>
</form>
<form id="assistant_rand" style="display:none">
  G&eacute;n&eacute;rer
  <input class="bouton" type="button" onclick="form.rand_nrows.value--; if(form.rand_nrows.value<0) form.rand_nrows.value=0" value="-">
  <input class="bouton" type="number" id="rand_nrows" name="rand_nrows"
         title="Nombre de lignes de la matrice (0 pour un vecteur)" value=1 min=0>
  <input class="bouton" type="button" onclick="$id('rand_nrows').value++;" value="+">
  par
  <input class="bouton" type="button" onclick="form.rand_ncols.value--; if(form.rand_ncols.value<0) form.rand_ncols.value=0" value="-">
  <input class="bouton" type="number" id="rand_ncols" name="rand_ncols"
         title="Nombre de colonnes de la matrice (0 pour un seul nombre)"
         value=1 min=0>
  <input class="bouton" type="button" onclick="$id('rand_ncols').value++;" value="+">
  nombres
  <input class="bouton" type="checkbox" name="rand_int"
         onclick="$id('assistant_rand').rand_intshadow.checked=!checked;UI.assistant_rand_setdisplay();"
         title="Cocher pour entiers" checked>
  <input class="bouton" type="button" value="entiers"
         onclick="var checked=form.rand_int.checked;form.rand_int.checked=!checked;form.rand_intshadow.checked=checked;UI.assistant_rand_setdisplay();">
  ou selon une
  <input class="bouton" type="checkbox" name="rand_intshadow" value="loi"
         onclick="$id('assistant_rand').rand_int.checked=!checked;UI.assistant_rand_setdisplay();"
         title="Cocher pour choisir une loi">
  <input class="bouton" type="button" value="loi"
         onclick="var checked=form.rand_intshadow.checked;form.rand_intshadow.checked=!checked;form.rand_int.checked=checked;UI.assistant_rand_setdisplay();">
  <div id="rand_intdiv">
    Entiers entre 0 et n ou n et -n avec n=
    <input class="bouton" type="number" id="rand_maxint"
           title="Entier k tel que 0&lt;=k&lt;n ou n&lt;k&lt;-n si n est n&eacute;gatif" value=100>
  </div>
  <br><input class="bouton" type="button" title="ok" value="Ok"
             onclick="UI.assistant_rand_ok()">
  <input class="bouton" type="button" title="r&eacute;el al&eacute;atoire entre 0 et 1"
         value="rand" onclick="UI.insert_focused('rand()');"><input class="bouton" type="button" title="randint(a,b): entier al&eacute;atoire entre a et b inclus"
                                                                       value="int" onclick="UI.insert_focused('randint(');"><input class="bouton" type="button" title="r&eacute;el al&eacute;atoire selon la loi normale (centr&eacute;e r&eacute;duite par d&eacute;faut)"
                                                                                                                                      value="norm" onclick="UI.insert_focused('randNorm(');"><input class="bouton" type="button" title="r&eacute;el al&eacute;atoire selon la loi exponentielle de param&egrave;tre a"
                                                                                                                                                                                                       value="exp" onclick="UI.insert_focused('randexp(');">
  <input class="bouton" type="button" title="Permutation al&eacute;atoire d'une liste ou de n"
         value="perm" onclick="UI.insert_focused('randperm(');">
  <input class="bouton" type="button" title="sample(L,n) tirage de n parmi la liste L sans remise"
         value="sample" onclick="UI.insert_focused('sample(');">
  <input class="bouton" type="button" title="Annuler" value="Annul." onclick="$id('chooselawdiv').style.display='none';form.style.display='none'; UI.focused=UI.savefocused; UI.focused.focus();">
</form>
<div id="assistant_boucle" style="display:none">
  Choisir <strong>type de boucle</strong>
  <button class="bouton" onmousedown="event.preventDefault()" onclick="$id('assistant_pour').style.display='block';UI.set_focus('pourvarname'); $id('assistant_tantque').style.display='none';">pour</button>
  ou
  <button class="bouton" onmousedown="event.preventDefault()" onclick="$id('assistant_pour').style.display='none';$id('assistant_tantque').style.display='block';UI.set_focus('tantquecond'); $id('tantquecond').focus();">tantque</button>
  <div id="assistant_pour" style="display:none">
    pour <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                   id="pourvarname" title="Nom de variable, par exemple j" rows=1></textarea><br>
    de <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                 id="pourvarmin" title="Valeur de d&eacute;part" rows=1></textarea><br>
    jusque <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                     id="pourvarmax" title="Valeur de fin (non comprise en syntaxe Python, comprise en syntaxe Xcas)" rows=1></textarea><br>
    pas optionnel <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                            id="pourvarstep" title="on ajoute le pas &agrave; chaque it&eacute;ration, valeur par d&eacute;faut 1" rows=1></textarea>
    <br>
    <button class="bouton" onclick="UI.assistant_pour_ok();">Ok</button>
    <button class="bouton" onclick="UI.focused=UI.savefocused;$id('assistant_boucle').style.display='none';$id('assistant_pour').style.display='none'">Annul.</button>
    <button class="bouton"
            onclick="$id('pourvarname').value='';$id('pourvarmin').value='';$id('pourvarmax').value='';">Effacer
    </button>
    <button class="bouton" onclick="$id('pourvarname').value='j';$id('pourvarmin').value='1';$id('pourvarmax').value='10';">Exemple</button>
  </div>
  <div id="assistant_tantque" style="display:none">
    Tests :
    <button class="bouton" onmousedown="event.preventDefault()"
            onclick="UI.insert_focused('==')">==
    </button>
    <button class="bouton" onmousedown="event.preventDefault()"
            onclick="UI.insert_focused('!=')">!=
    </button>
    <button class="bouton" onmousedown="event.preventDefault()"
            onclick="UI.insert_focused('<=')">&lt;=
    </button>
    <button class="bouton" onmousedown="event.preventDefault()"
            onclick="UI.insert_focused('>=')">&gt;=
    </button>
    <button class="bouton" onmousedown="event.preventDefault()"
            onclick="UI.insert_focused('<')">&lt
    </button>
    <button class="bouton" onmousedown="event.preventDefault()"
            onclick="UI.insert_focused('>')">&gt
    </button>
    <button class="bouton" onmousedown="event.preventDefault()"
            onclick="UI.insert_focused(' et ')">et
    </button>
    <button class="bouton" onmousedown="event.preventDefault()"
            onclick="UI.insert_focused(' ou ')">ou
    </button>
    <button class="bouton" onmousedown="event.preventDefault()"
            onclick="UI.insert_focused('!')">!
    </button>
    <br>
    tantque <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                      id="tantquecond" title="Test de continuation de la boucle"
                      rows=1></textarea>
    <br>
    <button class="bouton" onclick="UI.assistant_tantque_ok();">Ok</button>
    <button class="bouton" onclick="UI.focused=UI.savefocused;$id('assistant_boucle').style.display='none';$id('assistant_pour').style.display='none'">Annul.</button>
  </div>
</div>
<div id="assistant_solve" style="display:none">
  R&eacute;soudre
  <button class="bouton" id="solvex" title="Cliquez ici pour une r&eacute;solution approch&eacute;e"
          onclick="style.display='none';$id('solvenum').style.display='inline'">exactement
  </button>
  <button class="bouton" style="display:none" id="solvenum" title="Cliquez ici pour une r&eacute;solution exacte"
          onclick="style.display='none';$id('solvex').style.display='inline'">de mani&egrave;re approch&eacute;ee
  </button>
  <button class="bouton" id="solveR" title="Cliquez ici pour une r&eacute;solution sur C"
          onclick="style.display='none';$id('solveC').style.display='inline'">sur R
  </button>
  <button class="bouton" style="display:none" id="solveC" title="Cliquez ici pour une r&eacute;solution sur R"
          onclick="style.display='none';$id('solveR').style.display='inline'">sur C
  </button>
  <br>
  l'&eacute;quation ou le syst&egrave;me
  <br>
  <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
            id="solveeq" title="Par exemple x^2-3x+1=0" rows=1
            cols=30></textarea>
  <br>
  d'inconnue(s)
  <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
            id="solvevar" title="Par exemple x" rows=1 cols=10></textarea>
  <br>
  <button class="bouton" onclick="UI.assistant_solve_ok();">Ok</button>
  <button class="bouton" onclick="UI.focused=UI.savefocused;$id('assistant_solve').style.display='none'">Annul.</button>
  <button class="bouton" onclick="$id('solveeq').value='';$id('solvevar').value='';">Effacer</button>
  <button class="bouton" onclick="$id('solveeq').value='x^2-3x+1';$id('solvevar').value='x';">Exemple</button>
  <button class="bouton" onclick="$id('solveeq').value='[2x^2-y^2=1,x+y=3]';$id('solvevar').value='[x,y]';">Syst&egrave;me</button>
</div>
<div id="assistant_suites" style="display:none">
  Choisir entre
  <button class="bouton"
          onclick="$id('assistant_rsolve').style.display='none';$id('assistant_fixe').style.display='block';UI.set_focus('rsolveexpr') ">&eacute;tude approch&eacute;e de u_(n+1)=f(u_n)
  </button>
  ou
  <button class="bouton"
          onclick="$id('assistant_rsolve').style.display='block';$id('assistant_fixe').style.display='none';UI.set_focus('rsolveeq');">
    trouver u_n en fonction de n
  </button>
  <button class="bouton"
          onclick="UI.focused=UI.savefocused;$id('assistant_suites').style.display='none'">Annul.
  </button>
  <br>
  <div id="assistant_rsolve" style="display:none">
    Relation(s) de r&eacute;currence
    <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
              id="rsolveeq" title="Par exemple u(n+1)===2*u(n)+3" rows=1
              cols=40></textarea>
    <br>
    Suite(s) inconnue(s)
    <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
              id="rsolvevar" title="Par exemple u(n)" rows=1 cols=20>u(n)</textarea>
    <br>
    Conditions initiales
    <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
              id="rsolveinit" title="Par exemple u(0)===1" rows=1
              cols=20>u(0)===1</textarea>
    <br>
    <button class="bouton" onmousedown="event.preventDefault()"
            onclick="UI.set_focus('rsolveeq') ;UI.insert_focused('u(n+2)')">u(n+2)
    </button>
    <button class="bouton" onmousedown="event.preventDefault()"
            onclick="UI.set_focus('rsolveeq') ;UI.insert_focused('u(n+1)')">u(n+1)
    </button>
    <button class="bouton" onmousedown="event.preventDefault()"
            onclick="UI.insert_focused('u(n)')">u(n)
    </button>
    <button class="bouton" onmousedown="event.preventDefault()"
            onclick="UI.set_focus('rsolveeq') ;UI.insert_focused('u(n-1)')">u(n-1)
    </button>
    <button class="bouton" onmousedown="event.preventDefault()"
            onclick="UI.set_focus('rsolveinit') ;UI.insert_focused('u(0)===')">u(0)=
    </button>
    <button class="bouton" onmousedown="event.preventDefault()"
            onclick="UI.set_focus('rsolveinit');UI.insert_focused('u(1)===')">u(1)=
    </button>
    <br>
    <button class="bouton"
            onclick="UI.assistant_rsolve_ok();">Ok
    </button>
    <button class="bouton" onclick="UI.focused=UI.savefocused;$id('assistant_suites').style.display='none'">Annul.</button>
    <button class="bouton" onclick="$id('rsolveeq').value='';$id('rsolvevar').value='';$id('rsolveinit').value='';">Effacer</button>
    <button class="bouton" onclick="$id('rsolveeq').value='u(n+1)===2*u(n)+3';$id('rsolvevar').value='u(n)';$id('rsolveinit').value='u(0)===1';">Arit-geo</button>
    <button class="bouton" onclick="$id('rsolveeq').value='u(n+1)===(u(n)+2)/(u(n)+1)';$id('rsolvevar').value='u(n)';$id('rsolveinit').value='u(0)===1';">Fixe</button>
    <button class="bouton" onclick="$id('rsolveeq').value='u(n+2)===u(n+1)+u(n)';$id('rsolvevar').value='u(n)';$id('rsolveinit').value='u(0)===1,u(1)===1';">Fibonacci</button>
    <button class="bouton" onclick="$id('rsolveeq').value='[u(n+1)===3*v(n)+u(n),v(n+1)===v(n)+u(n)]';$id('rsolvevar').value='[u(n),v(n)]';$id('rsolveinit').value='u(0)===1,v(0)===2'">Syst&egrave;me</button>
  </div>
  <div id="assistant_fixe" style="display:none">
    u_(n+1)=<textarea onkeyup="$id('rsolvefshadow').innerHTML=value;" onclick="UI.focused=this;" style="height:25px;font-size:large"
                      id="rsolvef" title="Nom de la fonction" rows=1
                      cols=2>f</textarea>(u_n) avec
    <span id="rsolvefshadow">f</span>(<textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                                                id="rsolvevarf" title="" rows=1 cols=2>x</textarea>):=
    <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
              id="rsolveexpr" title="Par exemple (x+2)/(x+1)" rows=1 cols=20></textarea>
    et u(0)=
    <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
              id="rsolveu0" title="Par exemple 1" rows=1
              cols=10></textarea>
    <br>
    Nombre de termes n=
    <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
              id="rsolven" title="Par exemple 10" rows=1
              cols=3>10</textarea>
    <br>
    Repr&eacute;sentation graphique entre
    <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
              id="rsolvemin" title="Par exemple 0" rows=1
              cols=3>0</textarea> et
    <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
              id="rsolvemax" title="Par exemple 2" rows=1
              cols=3>2</textarea>
    <br>
    <button class="bouton"
            onclick="UI.assistant_fixe_ok();">Ok
    </button>
    <button class="bouton" onclick="UI.focused=UI.savefocused;$id('assistant_suites').style.display='none'">Annul.</button>
    <button class="bouton" onclick="$id('rsolvef').value='';$id('rsolvevarf').value='';$id('rsolveexpr').value='';$id('rsolveu0').value='';$id('rsolven').value='';$id('rsolvemin').value='';$id('rsolvemax').value='';">Effacer</button>
    <button class="bouton" onclick="$id('rsolvef').value='f';$id('rsolvevarf').value='x';$id('rsolveexpr').value='(x+2)/(x+1)';$id('rsolveu0').value='1';$id('rsolven').value='10';$id('rsolvemin').value='1';$id('rsolvemax').value='2';">Exemple</button>
  </div>
</div>
<div id="assistant_test" style="display:none">
  Tests :
  <button class="bouton" onmousedown="event.preventDefault()"
          onclick="UI.insert_focused('==')">==
  </button>
  <button class="bouton" onmousedown="event.preventDefault()"
          onclick="UI.insert_focused('!=')">!=
  </button>
  <button class="bouton" onmousedown="event.preventDefault()"
          onclick="UI.insert_focused('<=')">&lt;=
  </button>
  <button class="bouton" onmousedown="event.preventDefault()"
          onclick="UI.insert_focused('>=')">&gt;=
  </button>
  <button class="bouton" onmousedown="event.preventDefault()"
          onclick="UI.insert_focused('<')">&lt
  </button>
  <button class="bouton" onmousedown="event.preventDefault()"
          onclick="UI.insert_focused('>')">&gt
  </button>
  <button class="bouton" onmousedown="event.preventDefault()"
          onclick="UI.insert_focused(' et ')">et
  </button>
  <button class="bouton" onmousedown="event.preventDefault()"
          onclick="UI.insert_focused(' ou ')">ou
  </button>
  <button class="bouton" onmousedown="event.preventDefault()"
          onclick="UI.insert_focused('!')">!
  </button>
  <br>
  si <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
               id="sicond" title="Test, par exemple j!=0"
               rows=1></textarea>
  <br>
  alors <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                  id="sialors" title="Clause vraie, par exemple j:=-j;"
                  rows=1></textarea>
  <br>
  sinon (optionnel) <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                              id="sisinon" title="Clause fausse"
                              rows=1></textarea>
  <br>
  <button class="bouton" onclick="UI.assistant_test_ok();">Ok</button>
  <button class="bouton"
          onclick="UI.focused=UI.savefocused;$id('assistant_test').style.display='none'">Annul.
  </button>
  <button class="bouton"
          onclick="$id('sicond').value='';$id('sialors').value='';">Effacer
  </button>
  <button class="bouton"
          onclick="$id('sicond').value='j<0';$id('sialors').value=UI.python_mode?'j=-j':'j:=-j;';">Exemple 1
  </button>
  <button class="bouton"
          onclick="$id('sicond').value='j<0';$id('sialors').value=UI.python_mode?'absj=-j':'absj:=-j;';$id('sisinon').value=UI.python_mode?'absj=j':'absj:=j;';">Exemple 2
  </button>
</div>
<div id="assistant_prog" style="display:none">
  <strong>Nouvelle fonction</strong><br>
  nom de la fonction <textarea onclick="UI.focused=this;" style="height:25px;font-size:large" id="funcname" title="Nom de la fonction, par exemple f" rows=1>f</textarea><br>
  liste des arguments <textarea onclick="UI.focused=this;" style="height:25px;font-size:large" id="argsname" title="Arguments de la fonction s&eacute;par&eacute;s par des virgules" rows=1>x</textarea><br>
  <span id="localvarspan">variables locales <textarea onclick="UI.focused=this;" style="height:25px;font-size:large" id="localvars" title="Variables locales, s&eacute;par&eacute;es par des virgule. Laisser vide pour une fonction d&eacute;finie par une expression. Pour utiliser des variables locales formelles, purgez-les apr&egrave;s les avoir d&eacute;clar&eacute;." rows=1></textarea><br></span>
  valeur renvoy&eacute;e <textarea onclick="UI.focused=this;" style="height:25px;font-size:large" id="returnedvar" title="Valeur de retour" rows=1></textarea><br>
  <button class="bouton" onclick="UI.assistant_prog_ok();">Ok</button>
  <button class="bouton" onclick="UI.focused=UI.savefocused;$id('assistant_prog').style.display='none'">Annul.</button>
  <button class="bouton"
          onclick="$id('funcname').value='';$id('argsname').value='';$id('localvars').value='';$id('returnedvar').value='';">Effacer
  </button>
  <button class="bouton" onclick="$id('funcname').value='f';$id('argsname').value='x,y';$id('localvars').value='';$id('returnedvar').value='x*y';">Exemple 1</button>
  <button class="bouton" onclick="$id('funcname').value='f';$id('argsname').value='x,y';$id('localvars').value='z';$id('returnedvar').value='x*z';">Exemple 2</button>
</div>
<div id="assistant_seq" style="display:none">
  Cr&eacute;ation d'une s&eacute;quence ou tableau de valeurs, <br>
  expression <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                       id="seqexpr" title="Expression, par exemple j^2" rows=1></textarea><br>
  variable <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                     id="seqvarname" title="Nom de variable, par exemple j" rows=1></textarea><br>
  de <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
               id="seqvarmin" title="Valeur de d&eacute;part" rows=1></textarea><br>
  jusque <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                   id="seqvarmax" title="Valeur de fin" rows=1></textarea><br>
  Pas optionnel <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                          id="seqvarstep" title="on ajoute le pas &agrave; chaque it&eacute;ration, valeur par d&eacute;faut 1" rows=1></textarea>
  <br>
  <button class="bouton" onclick="UI.assistant_seq_ok();">Ok</button>
  <button class="bouton" onclick="UI.focused=UI.savefocused;$id('assistant_seq').style.display='none'">Annul.</button>
  <button class="bouton" onclick="$id('seqexpr').value='j^2';$id('seqvarname').value='j';$id('seqvarmin').value='1';$id('seqvarmax').value='10';$id('seqvarstep').value=''">Exemple 1</button>
  <button class="bouton" onclick="$id('seqexpr').value='[j,j^2]';$id('seqvarname').value='j';$id('seqvarmin').value='-2';$id('seqvarmax').value='2';$id('seqvarstep').value='0.25'">Exemple 2</button>
  <button class="bouton"
          onclick="$id('seqexpr').value='';$id('seqvarname').value='';$id('seqvarmin').value='';$id('seqvarmax').value='';$id('seqvarstep').value=''">Effacer
  </button>
</div>
<div id="assistant_tabvar" style="display:none">
  Choisir entre &eacute;tude de
  <button class="bouton" onclick="$id('assistant_tabvarfunc').style.display='block';UI.xtn='x';$id('assistant_tabvarparam').style.display='none';UI.set_focus('tabvarfuncexpr')">fonction</button>
  ou de
  <button class="bouton"
          onclick="$id('assistant_tabvarfunc').style.display='none';$id('assistant_tabvarparam').style.display='block';UI.xtn='t';UI.set_focus('tabvarparamexprx');">courbe
    param&eacute;tr&eacute;e
  </button>
  <button class="bouton"
          onclick="UI.focused=UI.savefocused;$id('assistant_tabvar').style.display='none'">Annul.
  </button>
  <br>
  <div id="assistant_tabvarfunc" style="display:none">
    &Eacute;tude de fonction (dans la console) et trac&eacute; de <br>
    <textarea rows=1 cols=3 onclick="UI.focused=this;" style="height:25px;font-size:large"
              id="tabvarfuncname" title="Nom de fonction">f</textarea>(
    <textarea rows=1 cols=2 onclick="UI.focused=this;" style="height:25px;font-size:large"
              id="tabvarfuncvarname" title="Nom de variable, par exemple x">x</textarea>)
    :=<textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                id="tabvarfuncexpr" title="Expression, par exemple x^2" rows=1></textarea><br>
    xmin <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                   id="tabvarfuncvarmin" title="Minimum" rows=1>-4</textarea><br>
    xmax <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                   id="tabvarfuncvarmax" title="Maximum" rows=1>4</textarea><br>
    xstep <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                    id="tabvarfuncvarstep" title="Pas entre 2 &eacute;valuations successives de l'expression" rows=1>0.0625</textarea>
    <br>
    Option : <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                       id="tabvarfuncopt" title="diff: pas de convexit&eacute;, plot: renvoie le graphe, tabvar: renvoie le tableau de variations, equation ou coordonnees: des points particuliers," rows=1>diff</textarea>
    <br>
    <button class="bouton" onclick="UI.assistant_tabvarfunc_ok();">Ok</button>
    <button class="bouton"
            onclick="UI.focused=UI.savefocused;$id('assistant_tabvar').style.display='none'">Annul.
    </button>
    <button class="bouton"
            onclick="$id('tabvarfuncname').value='';$id('tabvarfuncexpr').value='';$id('tabvarfuncvarname').value='';$id('tabvarfuncvarmin').value='';$id('tabvarfuncvarmax').value='';$id('tabvarfuncvarstep').value='';">Effacer
    </button>
    <button class="bouton" onclick="$id('tabvarfuncname').value='f';$id('tabvarfuncexpr').value='x/(x^2-1)';$id('tabvarfuncvarname').value='x';$id('tabvarfuncvarmin').value='-inf';$id('tabvarfuncvarmax').value='inf';">Exemple</button>
    <button class="bouton"
            onclick="$id('assistant_tabvar').style.display='none';$id('assistant_seq').style.display='block';$id('seqexpr').value= '['+$id('tabvarfuncvarname').value+','+$id('tabvarfuncexpr').value+']';$id('seqvarname').value=$id('tabvarfuncvarname').value;var tmp=$id('tabvarfuncvarmin').value; if(tmp=='-inf') tmp=-5;$id('seqvarmin').value=tmp;tmp=$id('tabvarfuncvarmax').value; if(tmp=='inf') tmp=5;$id('seqvarmax').value=tmp;$id('seqvarstep').value=$id('tabvarfuncxstep').value;">Tableau valeurs
    </button>
    .
  </div>
  <div id="assistant_tabvarparam" style="display:none">
                <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                          id="tabvarparamnamex" title="Nom de la fonction en abscisse"
                          rows=1 cols=3>x1</textarea>
    (<textarea onkeyup="$id('tabvarparamvarnameshadow').innerHTML=value;" onclick="UI.focused=this;" style="height:25px;font-size:large"
               id="tabvarparamvarname" title="Nom de variable, par exemple t"
               rows=1 cols=2>t</textarea>):= <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                                                       id="tabvarparamexprx" title="Expression de x(t), par exemple 2*cos(t)" rows=1></textarea><br>
    <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
              id="tabvarparamnamey" title="Nom de la fonction en ordonn&eacute;e"
              rows=1 cols=3>y1</textarea>(<span id="tabvarparamvarnameshadow">t</span>):= <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                                                                                                    id="tabvarparamexpry" title="Expression de y(t), par exemple 3*sin(t)" rows=1></textarea><br>
    tmin <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                   id="tabvarparamvarmin" title="Valeur de d&eacute;part" rows=1>-4</textarea><br>
    tmax <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                   id="tabvarparamvarmax" title="Valeur de fin" rows=1>4</textarea><br>
    tstep <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                    id="tabvarparamvarstep" title="Pas entre 2 &eacute;valuations successives" rows=1>0.0625</textarea>
    <br>
    <button class="bouton" onclick="UI.assistant_tabvarparam_ok();">Ok</button>
    <button class="bouton"
            onclick="UI.focused=UI.savefocused;$id('assistant_tabvar').style.display='none'">Annul.
    </button>
    <button class="bouton"
            onclick="$id('tabvarparamnamex').value='';$id('tabvarparamnamey').value='';$id('tabvarparamexprx').value='';$id('tabvarparamexpry').value='';$id('tabvarparamvarname').value='';$id('tabvarparamvarnameshadow').innerHTML='';$id('tabvarparamvarmin').value='';$id('tabvarparamvarmax').value='';$id('tabvarparamvarstep').value='';">Effacer
    </button>
    <button class="bouton" onclick="$id('tabvarparamnamex').value='x1';$id('tabvarparamnamey').value='y1';$id('tabvarparamexprx').value='cos(2t)';$id('tabvarparamexprx').value='cos(2t)';$id('tabvarparamexpry').value='sin(3t)';$id('tabvarparamvarname').value='t';$id('tabvarparamvarnameshadow').innerHTML='t';$id('tabvarparamvarmin').value='-pi';$id('tabvarparamvarmax').value='pi';">Exemple</button>
  </div>
</div>
<table border="0" align="center" summary="" id="alpha_keyboard"
       style="display:none" onmousedown="event.preventDefault()">
  <tr>
    <td>
      <input type="button" id="add_alpha_a" value="a"
             onmousedown="event.preventDefault()" onClick="UI.insert_focused(value)">
      <input type="button" id="add_alpha_z" value="z"
             onmousedown="event.preventDefault()" onClick="UI.insert_focused(value)">
      <input type="button" id="add_alpha_e" value="e"
             onmousedown="event.preventDefault()" onClick="UI.insert_focused(value)">
      <input type="button" id="add_alpha_r" value="r"
             onmousedown="event.preventDefault()" onClick="UI.insert_focused(value)">
      <input type="button" id="add_alpha_t" value="t"
             onmousedown="event.preventDefault()" onClick="UI.insert_focused(value)">
      <input type="button" id="add_alpha_y" value="y"
             onmousedown="event.preventDefault()" onClick="UI.insert_focused(value)">
      <input type="button" id="add_alpha_u" value="u"
             onmousedown="event.preventDefault()" onClick="UI.insert_focused(value)">
      <input type="button" id="add_alpha_i" value="i"
             onmousedown="event.preventDefault()" onClick="UI.insert_focused(value)">
      <input type="button" id="add_alpha_o" value="o"
             onmousedown="event.preventDefault()" onClick="UI.insert_focused(value)">
      <input type="button" id="add_alpha_p" value="p"
             onmousedown="event.preventDefault()" onClick="UI.insert_focused(value)">
    </td>
  </tr>
  <tr>
    <td>
      <input type="button" id="add_alpha_q" value="q"
             onmousedown="event.preventDefault()" onClick="UI.insert_focused(value)">
      <input type="button" id="add_alpha_s" value="s"
             onmousedown="event.preventDefault()" onClick="UI.insert_focused(value)">
      <input type="button" id="add_alpha_d" value="d"
             onmousedown="event.preventDefault()" onClick="UI.insert_focused(value)">
      <input type="button" id="add_alpha_f" value="f"
             onmousedown="event.preventDefault()" onClick="UI.insert_focused(value)">
      <input type="button" id="add_alpha_g" value="g"
             onmousedown="event.preventDefault()" onClick="UI.insert_focused(value)">
      <input type="button" id="add_alpha_h" value="h"
             onmousedown="event.preventDefault()" onClick="UI.insert_focused(value)">
      <input type="button" id="add_alpha_j" value="j"
             onmousedown="event.preventDefault()" onClick="UI.insert_focused(value)">
      <input type="button" id="add_alpha_k" value="k"
             onmousedown="event.preventDefault()" onClick="UI.insert_focused(value)">
      <input type="button" id="add_alpha_l" value="l"
             onmousedown="event.preventDefault()" onClick="UI.insert_focused(value)">
      <input type="button" id="add_alpha_m" value="m"
             onmousedown="event.preventDefault()" onClick="UI.insert_focused(value)">
    </td>
  </tr>
  <tr>
    <td>
      <input type="button"
             onmousedown="event.preventDefault()"
             onClick='var kbd_a=["a","b","c","d","e",
                        "f","j","n","r","u","x",
                        "g","k","o","s","v","y",
                        "h","l","p","t","w","z",
                        "i","m","q"];
                        for (var i=0;i<kbd_a.length;i++){
                        var tmp=$id("add_alpha_"+kbd_a[i]);
                        if (tmp.value<="Z") tmp.value=String.fromCharCode(tmp.value.charCodeAt(0)+32); else tmp.value=String.fromCharCode(tmp.value.charCodeAt(0)-32);
                        }' id="add_alpha_" value="maj">
      <input type="button" id="add_alpha_w" value="w"
             onmousedown="event.preventDefault()" onClick="UI.insert_focused(value)">
      <input type="button" id="add_alpha_x" value="x"
             onmousedown="event.preventDefault()" onClick="UI.insert_focused(value)">
      <input type="button" id="add_alpha_c" value="c"
             onmousedown="event.preventDefault()" onClick="UI.insert_focused(value)">
      <input type="button" id="add_alpha_v" value="v"
             onmousedown="event.preventDefault()" onClick="UI.insert_focused(value)">
      <input type="button" id="add_alpha_b" value="b"
             onmousedown="event.preventDefault()" onClick="UI.insert_focused(value)">
      <input type="button" id="add_alpha_n" value="n"
             onmousedown="event.preventDefault()" onClick="UI.insert_focused(value)">
      <input type="button" id="add_alpha_{" value="{"
             onmousedown="event.preventDefault()" onClick="UI.insert_focused(value)">
      <input type="button" id="add_alpha_}" value="}"
             onmousedown="event.preventDefault()" onClick="UI.insert_focused(value)">
      <input type="button" id="add_alpha_space" value=" "
             onmousedown="event.preventDefault()" onClick="UI.insert_focused(' ')">
    </td>
  </tr>
</table>
<hr>
<div id="divoutput" style="max-height: 400px; overflow:auto">
  <table id="mathoutput" contextmenu="cmdmenu" title="Historique"
         style="max-width:1000px "></table>
</div>
<div id="history4" style="display:none">
  <button class="bouton" onclick="var tmp=$id('variables'); if(tmp.style.display=='inline') tmp.style.display='none'; else {tmp.style.display='inline';UI.listvars(3);}"><strong>Vars</strong></button>
  <span id="variables" style="display:none">
            <button class="bouton" onclick="UI.insert_focused('python(')"
                    title="python(f) affiche la conversion en syntaxe Python d'une fonction stock&eacute; dans la variable f ">→python</button>
            <button class="bouton" onclick="UI.insert_focused('xcas(')"
                    title="xcas(f) affiche la conversion en syntaxe Xcas d'une fonction stock&eacute; dans la variable f ">→xcas</button>
            <button class="bouton" name="add_purge"
                    onmousedown="event.preventDefault()"
                    onClick="UI.insert_focused('purge(')" title="Efface le contenu d'une ou plusieurs variables, par exemple purge(a) ou purge(a,b,c)">efface</button>
            <button class="bouton" onclick="UI.addhelp(' ','rm_all_vars(1)')"
                    title="Effacer le contenu de toutes les variables">tout</button>
            <span id="listvars"> </span>
            <br>
            </span>
  <span id="historique">
            <button class="bouton" onclick="UI.exec($id('mathoutput'),0)"
                    title="Executer toutes les commandes de l'historique">Exec</button>
            <button class="bouton" id="button_show_answers" onclick="UI.show_answers(true)" title="Montrer les r&eacute;ponses">+</button>
            <button class="bouton" id="button_hide_answers" onclick="UI.show_answers(false)" title="Cacher les r&eacute;ponses">-</button>
            <button class="bouton" onclick="UI.erase_all($id('mathoutput'))"
                    title="Placer tout les niveaux de l'historique dans la
                corbeille">→Corbeille</button>
            <button class="bouton" onclick="UI.restoretrash()" title="Restaurer les niveaux plac&eacute;s dans la corbeille">Restaure</button>
            <button class="bouton" onclick="UI.emptytrash()"
                    title="Vider la corbeille">Vide</button>
            </span>
</div>
<div contextmenu="cmdmenu" title="F1: aide sur le mot-clef avant le curseur.">
            <textarea name="entree" id="entree" title="Taper une commande ici puis Entree pour valider" style="font-size:18px;width:98%"
                      rows=1 onclick="UI.focused=this;" onkeypress="UI.focused=this; if (event.keyCode==13 && event.shiftKey){UI.insert(this,'\n'); UI.indentline(this); return false;} if (event.keyCode!=13 || event.shiftKey) return true;UI.eval_cmdline1(value,true); return false;"></textarea>
  <span>
            <button class="bouton" style="color:green" id="button_ok" onclick="if (UI.assistant_ok()) return; if (UI.focused==cmentree || UI.focused==entree) UI.eval_cmdline(); else {UI.reeval(UI.focused,'',false);}" title="Evaluer la ligne de commande">
  <strong>&nbsp;&nbsp;Ok&nbsp;&nbsp;</strong></button>
  <button class="bouton xcas" title="Xcas evaluation" onclick="UI.micropy=0; UI.python_mode=0;$id('button_ok').click();">x</button><button class="bouton cas" title="Xcas Python mode evaluation" onclick="UI.micropy=0; UI.python_mode=1;$id('button_ok').click();">Cas</button><button class="bouton micropy" title="MicroPython evaluation" onclick="UI.micropy=1; UI.python_mode=4;$id('button_ok').click();">Py</button><button class="bouton js" id="bouton_js" title="Javascript evaluation" onclick="UI.micropy=-1; UI.python_mode=0;$id('button_ok').click();">JS</button>
            <button class="bouton" onmousedown="event.preventDefault()" onClick="UI.completion(cmentree)" title="Donne une aide courte et quelques exemples d'utilisation d'une commande.">&nbsp;?&nbsp;</button>
            <button class="bouton" onmousedown="event.preventDefault()" onClick="UI.move_caret_or_focus(UI.focused,-1)" title="Deplace vers la gauche le curseur">&nbsp;&nbsp;←&nbsp;&nbsp;</button><button class="bouton" id="button_droit" onmousedown="event.preventDefault()" onClick="UI.move_caret_or_focus(UI.focused,1)" title="Deplace vers la droite le curseur"> &nbsp;&nbsp;→&nbsp;&nbsp;</button><button class="bouton" onmousedown="event.preventDefault()" onClick="UI.moveCaretUpDown(UI.focused,-1)" title="Deplace vers le haut le curseur">&nbsp;↑&nbsp;&nbsp;</button><button class="bouton" onmousedown="event.preventDefault()" onClick="UI.moveCaretUpDown(UI.focused,1)" title="Deplace vers le bas le curseur">&nbsp;&nbsp;↓&nbsp;</button><button class="bouton" onmousedown="event.preventDefault()"
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            onClick="UI.indentline(UI.focused)"
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            title="Indente">→|</button>
            <button class="bouton" onmousedown="event.preventDefault()" onClick="UI.backspace(UI.focused)" title="Efface">&nbsp;&#x232b;&nbsp;</button>
            <button class="bouton" onmousedown="event.preventDefault()" onClick="UI.insert_focused('\n')" title="Saut de ligne">\n</button>
            <button class="bouton" onmousedown="event.preventDefault()" onclick="UI.search(this,6)" title="Annuler"><img width="16" height="16" src="undo.png" alt="Annuler" align="center"></button><button class="bouton" onmousedown="event.preventDefault()" onclick="UI.search(this,7)" title="Refaire"><img width="16" height="16" src="redo.png" alt="Refaire" align="center"></button><button class="bouton" onmousedown="event.preventDefault()" onclick="UI.search(this,0)" title="Rechercher">find</button><button class="bouton" onmousedown="event.preventDefault()" onclick="UI.search(this,1)" title="Rechercher suivant">&#x21D2;</button><button class="bouton" onmousedown="event.preventDefault()" onclick="UI.search(this,2)" title="Rechercher pr&eacute;c&eacute;dent">&#x21D0;</button><button
      class="bouton"
      onmousedown="event.preventDefault()"
      onclick="UI.search(this,3)"
      title="Remplacer">rep</button><button
      class="bouton" onmousedown="event.preventDefault()" onclick="UI.search(this,5)" title="Aller ligne">go</button>
            <button class="bouton" name="select_button"
                    id="select_button" onmousedown="event.preventDefault()"
                    onClick="UI.selectionne()" title="Selectionne la ligne de commande">&nbsp;sel&nbsp;</button>  <button id="stop_button" class="bouton" style="display:none"
                                                                                                                          onclick="if (UI.webworker && confirm('Voulez-vous vraiment terminer la session ?')){
                UI.webworker.terminate(); UI.busy=0;UI.webworker=0; alert('Session redemarree. Toutes les variables ont ete effacees.');}" title="Termine la session en cours">STOP</button>
            </span>
</div>
<div id="restoresession" style="display:none">
  <h1> Restauration de la session en cours</h1>
</div>
<div id="consolediv" style="display:none">
  <hr>
  <h3>Console</h3>
  <button class="bouton" title="Effacer la console (Ctrl-N)" onclick="var field=$id('output');field.innerHTML='';$id('consolediv').style.display='none';UI.set_config_width();">Efface</button>
  <button class="bouton" title="Augmenter le nombre de lignes" onclick="var field=$id('output');var s=field.style.maxHeight; s=s.substr(0,s.length-2);s=eval(s)+20 ;s=s+'px';field.style.maxHeight =s ;">+</button>
  <button class="bouton" title="Diminuer le nombre de lignes" onclick="var field=$id('output');var s=field.style.maxHeight; s=s.substr(0,s.length-2);s=Math.max(eval(s)-20,40) ;s=s+'px';field.style.maxHeight =s ;">-</button>
</div>
<div id="output" style="max-height: 200px; overflow:auto"></div>
<div id="table_3d" style="display:none">
  <hr>
  <table border="0" align="left" summary="">
    <tr>
      <td>
        <button id="boutons_3d0" class="bouton" onclick="
                            if($id('table_3d').style.display=='none'){
                            $id('table_3d').style.display='inherit';
                            }
                            else {
                            $id('table_3d').style.display='none';
                            }"
                title="Montre ou cache le graphe 3d">Graphe 3d
        </button>
        <span id="boutons_3d">
                        <button class="bouton" onclick="UI.giac_renderer('-')">out</button>
                        <button class="bouton" onclick="UI.giac_renderer('+')">in</button>
                        <button class="bouton" onclick="UI.giac_renderer('l')"> ← </button>
                        <button class="bouton" onclick="UI.giac_renderer('r')"> → </button>
                        <button class="bouton" onclick="UI.giac_renderer('u')"> ↑ </button>
                        <button class="bouton" onclick="UI.giac_renderer('d')"> ↓ </button>
                        </span>
      </td>
    </tr>
    <tr>
      <td>
        <canvas id='canvas' width=0 height=0
                onmousedown="UI.canvas_pushed=true;UI.canvas_lastx=event.clientX; UI.canvas_lasty=event.clientY;"
                onmouseup="UI.canvas_pushed=false;">
        </canvas>
      </td>
    </tr>
  </table>
</div>
<div class="emscripten" id="status">Downloading...</div>
<div class="emscripten">
  <progress value="0" max="100" id="progress" hidden=1></progress>
</div>
<script src="w3data.js"></script>
<div w3-include-html="menufr.js"></div>
<script src="FileSaver.js"></script>
<script src="codemirror.js"></script>
<link rel="stylesheet" href="codemirror.css">
<link rel="stylesheet" href="show-hint.css">
<script src="search.js"></script>
<script src="searchcursor.js"></script>
<script src="jump-to-line.js"></script>
<script src="dialog.js"></script>
<link rel="stylesheet" href="dialog.css">
<script src="xcasmode.js"></script>
<script src="python.js"></script>
<script src="micropy.js"></script>
<script src="matchbrackets.js"></script>
<script src="show-hint.js"></script>
<style type="text/css">
  .CodeMirror {
    border: 1px solid black;
    height: auto;
  }

  dt {
    font-family: monospace;
    color: #666;
  }
</style>
<script src="xcas.js"></script>
<script src="numworks.js"></script>
<script src="nws_sig.js"></script>
<script type='text/javascript'>
    // remove existing codemirror field
    prog = $id('prog');
    if (prog && prog.nextSibling) {
        prog.parentNode.removeChild(prog.nextSibling);
    }
    if (entree && entree.nextSibling) {
        entree.parentNode.removeChild(entree.nextSibling);
    }
    $id('canvas').onmousemove = function (event) {
        UI.canvas_mousemove(event, '');
    };
    $id('output').style.display = 'none';
    $id("config").reset();
    // connect to canvas
    var Module = {
        // TOTAL_MEMORY:134217728,
        worker: false,
        htmlcheck: true,
        htmlbuffer: '',
        preRun: [],
        postRun: [],
        lastrefresh:0,
        print: (function () {
            var element = $id('output');
            element.innerHTML = '';// element.value = ''; // clear browser cache
            return function (text) {
                //console.log(text.charCodeAt(0));
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                    element.innerHTML = '';
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                }
                if (text.length >= 1 && text.charCodeAt(0) == 2) {
                    console.log('STX');
                    Module.htmlcheck = false;
                    htmlbuffer = '';
                    return;
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                if (text.length >= 1 && text.charCodeAt(0) == 3) {
                    console.log('ETX');
                    Module.htmlcheck = true;
                    element.style.display = 'inherit';
                    element.innerHTML += htmlbuffer;
                    htmlbuffer = '';
                    element.scrollTop = 99999;
                    return;
                }
                if (Module.htmlcheck) {
                    // These replacements are necessary if you render to raw HTML
                    text = '' + text;
                    console.log(text);
                    text = text.replace(/&/g, "&amp;");
                    text = text.replace(/</g, "&lt;");
                    text = text.replace(/>/g, "&gt;");
                    text = text.replace(/\n/g, '<br>');
                    text += '<br>';
                    var tmp = $id('consolediv');
                    if (tmp.style.display != 'block') {
                        tmp.style.display = 'block';
                        UI.set_config_width();
                    }
                    element.style.display = 'inherit';
                    element.innerHTML += text; // element.value += text + "\n";
                    element.scrollTop = 99999; // focus on bottom
                } else htmlbuffer += text;
                element.scrollIntoView();
           };
        })(),
        printErr: function (text) {
            if (0) { // XXX disabled for safety typeof dump == 'function') {
                dump(text + '\n'); // fast, straight to the real console
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                console.log(text);
            }
        },
        canvas: $id('canvas'),
        setStatus: function (text) {
            if (Module.setStatus.interval) clearInterval(Module.setStatus.interval);
            var m = text.match(/([^(]+)\((\d+(\.\d+)?)\/(\d+)\)/);
            var statusElement = $id('status');
            var progressElement = $id('progress');
            if (m) {
                text = m[1];
                progressElement.value = parseInt(m[2]) * 100;
                progressElement.max = parseInt(m[4]) * 100;
                progressElement.hidden = false;
            } else {
                progressElement.value = null;
                progressElement.max = null;
                progressElement.hidden = true;
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            statusElement.innerHTML = text;
        },
        totalDependencies: 0,
        monitorRunDependencies: function (left) {
            this.totalDependencies = Math.max(this.totalDependencies, left);
            Module.setStatus(left ? 'Preparation... (' + (this.totalDependencies - left) + '/' + this.totalDependencies + ')' : 'Telechargements termines.');
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    };
    Module.setStatus('T&eacute;l&eacute;chargement et pr&eacute;paration (peut prendre 1 ou 2 minutes la premi&egrave;re fois)');
    Module['onRuntimeInitialized'] = function () {
        console.log('UI is ready');
        UI.ready = true;
    }
</script>
<script type='text/javascript'></script>
<script async>
    var script = document.createElement("script");
    script.type = "text/javascript";
    var supported = (function () {
        try {
            if (typeof WebAssembly === "object" && typeof WebAssembly.instantiate === "function") {
                var module = new WebAssembly.Module(Uint8Array.of(0x0, 0x61, 0x73, 0x6d, 0x01, 0x00, 0x00, 0x00));
                if (module instanceof WebAssembly.Module)
                    return new WebAssembly.Instance(module) instanceof WebAssembly.Instance;
            }
        } catch (e) {}
        return false;
    })();
    if (Boolean(window.chrome))
      if (UI.detectmob() || window.location.href.substr(0,4)=='file') supported=false;
    else  
      if (UI.detectmob() && window.location.href.substr(0,4)=='file') supported=false;
    var webAssemblyAvailable = supported;
    /*
    if (Boolean(window.chrome)){
    if (!UI.detectmob()) webAssemblyAvailable = !!window.WebAssembly && window.location.href.substr(0,4)!='file';
    }
    else {
    var ua = window.navigator.userAgent;
    var old_ie = ua.indexOf('MSIE ');
    var new_ie = ua.indexOf('Trident/');
    if (!UI.detectmob() && old_ie<=-1 && new_ie<=-1)
      webAssemblyAvailable =!!window.WebAssembly;
    } */
    if (webAssemblyAvailable) {
        var ck = UI.readCookie('xcas_wasm');
        if (ck) {
            var form = $id('config');
            form.wasm_mode.checked = (ck == '1');
            webAssemblyAvailable = form.wasm_mode.checked;
        }
     }
    //alert(webAssemblyAvailable?'true':'false');
    console.log('wasm ', supported, webAssemblyAvailable);
    if (webAssemblyAvailable) // fixme: enable
        script.src = "giacwasm.js";
    else
        script.src = "giac.js";
    document.getElementsByTagName("head")[0].appendChild(script);
</script>
<script src="longhelp.js"></script>
<script language="javascript">
    $id('thelink').innerHTML='<a href="'+UI.forum_url+'" target=_blank>Forum</a>';
    CodeMirror.registerHelper("hintWords", "simplemode", UI.xcascmd);
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    var old_ie = ua.indexOf('MSIE ');
    var new_ie = ua.indexOf('Trident/');
    var isSafari = /^((?!chrome|android).)*safari/i.test(ua);
    if ((old_ie > -1) || (new_ie > -1) 
        || Boolean(window.chrome) || isSafari
        ) {
        (function () {
            var script = document.createElement("script");
            script.type = "text/javascript";
            if (0) {script.src = "load-mathjax.js"; UI.mathjax_version=3; } else
            { script.src = "file:///usr/share/javascript/mathjax/MathJax.js?config=TeX-AMS_CHTML"; UI.mathjax_version=2; }
            document.getElementsByTagName("head")[0].appendChild(script);
        })();
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</script>
<script language="javascript">
    window.onbeforeunload = function (e) {
        var dialogText = "Etes-vous sur?";
        return dialogText;
    };
    $id('shift_key').style.backgroundColor = "cyan";
    cmentree = entree;
    window.onresize = UI.set_config_width;
    // En ajoutant async a la fin de script src=giac.js on accelere les chargements
    // de la page nue (cache), mais pas si il y a un lien
    window.onload = function (e) {
        console.log('init');
        var mth = $id('bouton_math');
        //mth.style.backgroundImage = "url('logo.png')";
        //mth.style.backgroundSize = '100%';
        //UI.caseval('abc(x=0); [x, y]; z+1;');
        var form = $id('config');
        var hw = window.innerWidth - 50;
        var access = true;
        if (hw >= 900) {
            UI.qa = true;
            UI.usecm = true;
            form.qa.checked = true;
            form.usecm.checked = true;
        } else {
            UI.qa = false;
            UI.usecm = true;
            form.qa.checked = false;
            form.usecm.checked = true;
            access = false;
            $id('button_show_answers').style.display = 'none';
            $id('button_hide_answers').style.display = 'none';
        }
        var ua = window.navigator.userAgent;
        var old_ie = ua.indexOf('MSIE ');
        var new_ie = ua.indexOf('Trident/');
        var isSafari = /^((?!chrome|android).)*safari/i.test(ua);
        if ( (isSafari || Boolean(window.chrome)) && window.location.href.substr(0, 4) != 'file') UI.prettyprint = false;
        if ((old_ie > -1) || (new_ie > -1)) UI.isie = true;
        var bt = UI.browser_type();
        if (UI.isie || (bt!=1 && bt!=2 )) {
            UI.usemathjax = true;
            var alertmsg = "Les calculs seraient plus rapides avec Firefox.";
            if (0 && Boolean(window.chrome)) {
                if (window.location.href.substr(0, 4) == 'file')
                    alertmsg = "Les cookies ne fonctionnent pas en local avec Chrome, la sauvegarde/restauration de sessions est impossible. " + alertmsg;
                else
                    alertmgs = "L'affichage 2d ne fonctionne pas en distant avec Chrome. " + alertmsg;
            }
            //alert(alertmsg);
        }
        //console.log(window.location.href);
        var mobile = UI.detectmob();
        if (mobile) {
            $id('historyload').style.display = 'none';
            $id('loadbutton_cookie').style.display = 'inline';
            $id('loadbutton_file').style.display = 'none';
            $id('bouton_js').style.display = 'none';
        }
        else {
            $id('historyload').style.display = 'inline';
            $id('loadbutton_cookie').style.display = 'none';
            $id('loadbutton_file').style.display = 'inline';
        }
        if (!UI.is_touch_device() && !UI.isie) w3IncludeHTML(); // contextmenu
        //if (bt==1 && hw>=1000 && window.location.href.substr(0,4)=="http") w3IncludeHTML();
        $id('apropos').style.display = 'none';
        $id('help').style.display = 'none';
        console.log("window.onload");
        // config in cookies
        var ck;
        ck = UI.readCookie('xcas_lang');
        if (ck) {
            var test = eval(ck) - 1; //console.log(test);
            if (test >= 0 && test < 5) {
                form.lang[1].checked = false;
                form.lang[test].checked = true;
            }
            if (test >= -1) UI.langue = -test - 1;
        }
        ck = UI.readCookie('xcas_calc');
        if (ck) {
            var test = eval(ck) - 1; //console.log(test);
            if (test >= 0 && test < 3) {
                form.calc[0].checked = false;
                form.calc[test].checked = true;
                UI.set_calc_type(test+1);
            }
        }
        ck = UI.readCookie('xcas_from');
        if (ck) {
            form.from.value = ck;
            UI.from = ck;
        }
        ck = UI.readCookie('xcas_to');
        if (ck) {
            form.to.value = ck;
            UI.mailto = ck;
        }
        ck = UI.readCookie('xcas_digits');
        if (ck) form.digits_mode.value = eval(ck);
        ck = UI.readCookie('xcas_angle_radian');
        if (ck) form.angle_mode.checked = (ck == '1');
        ck = UI.readCookie('xcas_warnpy');
        if (ck) UI.warnpy = form.warnpy_mode.checked = (ck == '1');
        ck = UI.readCookie('xcas_python_mode');
        var hashParams = window.location.hash.substr(1);
        var forcepy=hashParams.substr(0,6)=='python';
        if (forcepy) ck='1';
        if (!ck) {
           var tmp=prompt("Choisir l'interpreteur. 1: Xcas compatible Python (defaut), 0: Xcas en francais, 4: MicroPython");
           if (tmp=='0' || tmp=='4') ck=tmp; else ck='1'; 
           if (tmp=='xcas' || tmp=='Xcas') ck='0';
           if (tmp=='python' || tmp=='Python') ck='4';
           //if (confirm('Voulez-vous activer la compatibilite de syntaxe Python ?')) ck = 1; else ck = 0;
        }
        form.python_mode.checked = (ck == '1' || ck=='4');
        form.python_xor.checked = (ck=='4');
        UI.python_mode = eval(ck);
        if (UI.python_mode==4) UI.micropy=1;
        $id('add_//').value = UI.python_mode ? '#' : '//';
        if (!UI.kbdshift) $id('add_:').value = UI.python_mode ? ':' : ':=';
        UI.createCookie('xcas_python_mode', UI.python_mode, 10000);
        ck = UI.readCookie('xcas_complex_mode');
        if (ck) form.complex_mode.checked = (ck == '1');
        ck = UI.readCookie('xcas_with_sqrt');
        if (ck) form.sqrt_mode.checked = (ck == '1');
        ck = UI.readCookie('xcas_step_infolevel');
        if (ck) form.step_mode.checked = (ck == '1');
        ck = UI.readCookie('xcas_autosimplify');
        if (ck) form.autosimp_level.value = eval(ck);
        ck = UI.readCookie('xcas_docprefix');
        if (ck) UI.docprefix = ck;
        ck = UI.readCookie('xcas_withworker');
        if (ck) form.worker_mode.checked = (ck == '1');
        UI.withworker = form.worker_mode.checked;
        ck = UI.readCookie('xcas_prettyprint');
        if (ck) form.prettyprint.checked = (ck == '1');
        UI.prettyprint = form.prettyprint.checked;
        ck = UI.readCookie('xcas_qa');
        if (ck) form.qa.checked = UI.qa = (ck == '1');
        ck = UI.readCookie('xcas_usecm');
        if (ck) form.usecm.checked = UI.usecm = (ck == '1');
        ck = UI.readCookie('xcas_fixeddel');
        if (ck) form.fixeddel.checked = UI.fixeddel = (ck == '1');
        ck = UI.config_string();
        console.log(ck);
        //UI.sleep(200);
        if (0) UI.caseval(ck); else UI.initconfigstring = ck; //UI.set_config_width();
        ck = UI.readCookie('xcas_canvas_w');
        ck = eval(ck);
        if (ck > 0 && ck <= 1000)
            ;
        else {
            console.log('qa', UI.qa);
            ck = (UI.qa ? Math.floor(window.innerWidth / 2.5) : window.innerWidth - 110);
        }
        console.log('canvas_w', ck);
        UI.canvas_w = ck;
        $id('config').canvas_w.value = ck;
        ck = UI.readCookie('xcas_canvas_h');
        ck = eval(ck);
        if (ck > 0 && ck <= 1000) ; else ck = Math.floor(window.innerHeight / 2);
        if (ck > 200 && mobile) ck = 200;
        console.log('canvas_h', ck);
        UI.canvas_h = ck;
        $id('config').canvas_h.value = ck;
        ck = UI.readCookie('xcas_matrix_maxrows');
        ck = eval(ck);
        if (ck > 0 && ck <= 1000) {
            UI.assistant_matr_maxrows = ck;
            $id('matr_cfg_rows').value = ck;
        }
        ck = UI.readCookie('xcas_matrix_maxcols');
        ck = eval(ck);
        if (ck > 0 && ck <= 100) {
            UI.assistant_matr_maxcols = ck;
            $id('matr_cfg_cols').value = ck;
        }
        ck = UI.readCookie('xcas_matrix_textarea');
        ck = eval(ck);
        if (ck > 0 && ck <= 100) {
            UI.assistant_matr_textarea = ck;
            $id('matr_textarea').checked = ck;
        }
        UI.assistant_matr_setmatrix(UI.assistant_matr_maxrows, UI.assistant_matr_maxcols);
        $id('assistant_matr').adequation[0].checked = true;
        var hist = $id('mathoutput');
        var doexec = false;
        var asked = false;
        if (hist.firstChild) {
            asked = true;
            if (!UI.withworker && confirm('Voulez-vous executer les commandes de l\'historique?')) {
                doexec = true;
            }
            // else {alert('Historique non execute');}
        }
        // substr(1) to remove the `#`
        if (UI.readCookie('xcas_session') != null) {
            $id('startup_restore').style.display = 'inline';
            $id('startup1').style.display = 'none';
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        else { if (!forcepy) $id('help').style.display = 'block'; }
        //UI.restoresession(hashParams,hist,asked,doexec);
        //console.log(UI.wasm_mode);
        var cons = $id('restoresession');
        cons.style.display = 'inherit';
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            window.setTimeout(UI.restoresession, 0, hashParams, hist, asked, doexec);
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            window.setTimeout(UI.restoresession, (UI.wasm_mode ? 10 : 400), hashParams, hist, asked, doexec);
        if (access)
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</script>
</body>
</html>