File: xcasen.html

package info (click to toggle)
giac 1.6.0.41%2Bdfsg1-1
links: PTS, VCS
area: main
in suites: bullseye
size: 64,540 kB
sloc: cpp: 351,842; ansic: 105,138; python: 30,545; javascript: 8,675; yacc: 2,690; lex: 2,449; makefile: 1,243; sh: 579; perl: 314; lisp: 216; asm: 62; java: 41; sed: 16; csh: 7; pascal: 6
file content (3893 lines) | stat: -rw-r--r-- 287,260 bytes
<!DOCTYPE HTML>
<html id="fulldocument" lang="en">
<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, browser, computer algebra system, online, offline">
  <title>
    xcas or python
  </title>
  <style>
    html {
      background-color: #FFFFFF;
    }

    body {
      color: black;
      text-align: justify;
      background-color: #FFFFFF;
    }

    .curseur {
      min-width: 25px;
      height: 35px
    }

    .emscripten {
      padding-right: 0;
      margin-left: auto;
      margin-right: auto;
      display: block;
    }

    canvas.emscripten {
      border: 1px solid black;
    }

    textarea.emscripten {
      font-family: monospace;
      width: 100%;
    }

    div.emscripten {
      text-align: center;
    }
  </style>
  <style id="document_style" type="text/css">
    h3 {
      display: inline;
      font-size: 1em;
    }

    input[type="number"] {
      width: 40px;
      font-size: 24px;
    }

    input[type="text"] {
      width: 40px;
      font-size: 24px;
    }

    input[type="button"] {
      width: 40px;
      font-size: 24px;
    }

    .outdiv {
      width: 410px;
      max-height: 200px;
      overflow: auto;
    }

    .filenamecss {
      width: 80px;
      height: 20px
    }

    .historyinput {
      width: 400px;
    }
  </style>
  <style type="text/css">
    .matrixcell {
      font-size: 18px;
      width: 80px;
    }

    td.matrixcell {
      border: 1px solid;
    }

    input.matrixcell {
      width: 80px;
    }

    input.matrixcell:hover {
      background-color: #eee;
    }

    input.matrixcell:focus {
      background-color: #ccf;
    }

    input.matrixcell:not(:focus) {
      text-align: right;
    }

    textarea.matrixcell {
      width: 80px;
      height: 22px;
    }

    textarea.matrixcell:hover {
      background-color: #eee;
    }

    textarea.matrixcell:focus {
      background-color: #ccf;
    }

    textarea.matrixcell:not(:focus) {
      text-align: right;
    }

    div.matrixcell:hover {
      background-color: #eee;
    }

    div.matrixcell:focus {
      background-color: #ccf;
    }

    div.matrixcell:not(:focus) {
      text-align: right;
    }
  </style>
  <script>
      // Redirect to HTTPS page if not testing locally
      if (location.protocol === 'http:' && location.hostname !== 'localhost' && location.hostname !== '127.0.0.1') {
          location.href = 'https:' + window.location.href.substring(window.location.protocol.length);
      }
  </script>
  <script>
    function $id(id) { return document.getElementById(id); }
  </script>
</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...
    -->
<script language="javascript">
    if (window.location.href.substr(0, 4) == "http") {
        if ('serviceWorker' in navigator) {
            navigator.serviceWorker.register('service-worker.js');
        }
    }
    KEY_DOWN = 40;
    KEY_UP = 38;
    KEY_LEFT = 37;
    KEY_RIGHT = 39;

    KEY_END = 35;
    KEY_BEGIN = 36;


    KEY_BACK_TAB = 8;
    KEY_TAB = 9;
    KEY_SH_TAB = 16;
    KEY_ENTER = 13;
    KEY_ESC = 27;
    KEY_SPACE = 32;
    KEY_DEL = 46;

    KEY_A = 65;
    KEY_B = 66;
    KEY_C = 67;
    KEY_D = 68;
    KEY_E = 69;
    KEY_F = 70;
    KEY_G = 71;
    KEY_H = 72;
    KEY_I = 73;
    KEY_J = 74;
    KEY_K = 75;
    KEY_L = 76;
    KEY_M = 77;
    KEY_N = 78;
    KEY_O = 79;
    KEY_P = 80;
    KEY_Q = 81;
    KEY_R = 82;
    KEY_S = 83;
    KEY_T = 84;
    KEY_U = 85;
    KEY_V = 86;
    KEY_W = 87;
    KEY_X = 88;
    KEY_Y = 89;
    KEY_Z = 90;

    KEY_PF1 = 112;
    KEY_PF2 = 113;
    KEY_PF3 = 114;
    KEY_PF4 = 115;
    KEY_PF5 = 116;
    KEY_PF6 = 117;
    KEY_PF7 = 118;
    KEY_PF8 = 119;

    REMAP_KEY_T = 5019;

    function checkEventObj(_event_) {
        // --- IE explorer
        if (window.event)
            return window.event;
        // --- Netscape and other explorers
        else
            return _event_;
    }

    function applyKey(_event_) {
        // --- Retrieve event object from current web explorer
        var winObj = checkEventObj(_event_);
        var intKeyCode = winObj.keyCode;
        var intShiftKey = winObj.shiftKey;
        var intAltKey = winObj.altKey;
        var intCtrlKey = winObj.ctrlKey;
        var done = false;
        if (intShiftKey && intKeyCode == KEY_ENTER) {
            UI.insert(UI.focused, '\n');
            done = true;
        }
        // raccourcis avec Alt
        // F1 aide, c cmdline, m menu,
        if (!done && (intAltKey || intCtrlKey)) {
            if (intKeyCode == KEY_D || intKeyCode == KEY_RIGHT) {
                UI.move_focus(UI.focused, 1);
                done = true;
            }
            if (intKeyCode == KEY_G || intKeyCode == KEY_LEFT) {
                UI.move_focus(UI.focused, -1);
                done = true;
            }
            if (intKeyCode == KEY_DOWN) {
                UI.move_focus(UI.focused, 1);
                UI.move_focus(UI.focused, 1);
                done = true;
            }
            if (intKeyCode == KEY_UP) {
                UI.move_focus(UI.focused, -1);
                UI.move_focus(UI.focused, -1);
                done = true;
            }
            if (intKeyCode == KEY_A) {
                var tmp = $id('helptxt');
                tmp.focus();
                tmp.scrollIntoView(false);
                done = true;
            }
            if (intKeyCode == KEY_C && intAltKey) {
                if (UI.focused != cmentree) {
                    if (UI.focused.type == 'textarea') UI.insert(cmentree, UI.focused.value);
                    if (UI.focused.getValue) UI.insert(cmentree, UI.focused.getValue());
                    cmentree.focus();
                }
                done = true;
            }
            if (intKeyCode == KEY_B) {
                cmentree.focus();
                done = true;
            }
            if (intKeyCode == KEY_M) {
                UI.show_menu();
                done = true;
            }
            if (intKeyCode == KEY_T) {
                $id('progbuttons').style.display = 'block';
                $id('boutons_tortue').style.display = 'block';
                UI.hide_show_xcas('boutons_tortue_xcas');
                done = true;
            }
            if (intKeyCode == KEY_P) {
                $id('prog_key').click();
                done = true;
            }
            if (intKeyCode == KEY_TAB || intKeyCode == KEY_PF1) {
                UI.completion(cmentree);
                done = true;
            }
            if (intKeyCode == KEY_E || intKeyCode == KEY_F) {
                UI.exec($id('mathoutput'), 0);
                done = true;
            }
            if (intKeyCode == KEY_N) {
                var field = $id('output');
                field.innerHTML = '';
                $id('consolediv').style.display = 'none';
                $id('settings').scrollIntoView();
                UI.set_config_width();
            }
        }
        if (done) {
            // --- Map the keyCode in another keyCode not used
            winObj.keyCode = REMAP_KEY_T;
            winObj.returnValue = false;
            return false;
        }
        return true;
    }

    document.onkeydown = applyKey;

</script>
<div id="startup2" style="display:none">
  <button onclick="if (UI.usecm){ $id('config').usecm.checked=false;  UI.set_config(false);} cmentree.focus();">Version
  </button>
  for visually impaired,
  <a href="xcasfr.html#lang=fr" target="_blank">version francaise</a>.
</div>
<div id="startup1">
  Welcome to Xcas for Firefox or compatible browser
  (c) 2020, B. Parisse and R. De Graeve, Institut Fourier,
  Universit&eacute; de Grenoble.
</div>
<div id="startup">
  If Xcas doesn't work
  <a
      href="https://en.wikipedia.org/wiki/Wikipedia:Bypass_your_cache"
      target="_blank">clear your browser cache</a> and reload
  <span id="startup_restore" style="display:none">
            <br>
            Restore last session
            <button title="Load last session and execute it automatically"
                    onclick="var s=UI.readCookie('xcas_session');UI.restoresession(s,$id('mathoutput'),false,true);">evaled</button> or
            <button title="Load last session, you must execute it manually"
                    onclick="var s=UI.readCookie('xcas_session');UI.restoresession(s,$id('mathoutput'),false,false);">not</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>
        personal e-mail <input class="bouton" type="text" name="from"
                               title="Fill with your personal email address"
                               value="">
        default to <input class="bouton" type="text" name="to"
                          title="Fill with the email address of the person who you are sending frequently sessions, for example the teacher email for a student"
                          value="">,
        help language
        <input type="radio" name="lang" value="radio" title="French">fr
        <input type="radio" name="lang" value="radio" title="English" checked>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 to
        <input type="radio" name="calc" value="radio" title="Casio" checked>Casio Prizm or Fx-9750GIII
        <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>
        Digits:<input class="bouton" type="number" name="digits_mode"
                      title="Number of digits. If &gt; 14, computations are more accurate but slower"
                      value=12>
        Autosimplification: <input class="bouton"
                                   type="number" name="autosimp_level"
                                   title="0: none, 1: minimum, 2: maximum" value=1
                                   max=2 min=0>
        Syntax <input class="bouton" type="button" value="Python"
	onclick="python_mode.checked=!python_mode.checked;">
	<input
          class="bouton" type="checkbox" name="python_mode" title="Check to enable Python syntax compatibility">,
	MicroPython <input class="bouton" type="checkbox" name="python_xor"
	title="If checked, interpreter is MicroPython, otherwise Xcas">,
        <input class="bouton" type="button" title="Display Python alerts" value="warnings" onclick="warnpy_mode.checked=!warnpy_mode.checked">
        <input class="bouton" type="checkbox" name="warnpy_mode"
               title="Check to display Python alerts" checked>
      </td>
    </tr>
    <tr>
      <td>
        <input class="bouton" type="button"
               title="Choose angle unit: degrees or radians"
               value="Radians" onclick="angle_mode.checked=!angle_mode.checked;">
        <input class="bouton" type="checkbox" name="angle_mode"
               title="Check for radians, uncheck for degrees" checked>,
        <input class="bouton" type="button" title="Complex or real mode"
               value="Complex"
               onclick="complex_mode.checked=!complex_mode.checked"> <input
          class="bouton" type="checkbox" name="complex_mode" title="If checked, some commands like factor will work on C by default">,
        <input class="bouton" type="button" title="Factor degree 2 polynomials even if they are irreducible over Q" value=" √ " onclick="sqrt_mode.checked=!sqrt_mode.checked"> <input class="bouton" type="checkbox" name="sqrt_mode" title="Check if you want to factor degree 2 polynomials even if they are irreducible over Q">,
        <input class="bouton" type="button" title="Show intermediate steps" value="step" onclick="step_mode.checked=!step_mode.checked">
        <input class="bouton" type="checkbox" name="step_mode" title="Check if you want to display intermediate steps">,
        <input class="bouton" type="button" title="Run computations with a webworker" value="worker"
               onclick="worker_mode.checked=!worker_mode.checked"> <input
          class="bouton" type="checkbox" name="worker_mode" title="Check to run computations with a webworker">
        <input class="bouton" type="button" title="Use web-assembly if possible" value="wasm" onclick="wasm_mode.checked=!wasm_mode.checked"> <input class="bouton" type="checkbox" name="wasm_mode" title="Check to run computations with web-assembly">
      </td>
    </tr>
    <tr>
      <td>
        <input class="bouton" type="button" title="2d display switch" value="2d" onclick="prettyprint.checked=!prettyprint.checked"> <input class="bouton" type="checkbox" name="prettyprint"
                                                                                                                                            title="Check for 2d display" checked>,
        <input class="bouton" type="button"
               title="Questions and answers on the same line"
               value="Q/A on 1 line"
               onclick="qa.checked=!qa.checked"> <input class="bouton" type="checkbox" name="qa"
                                                        title="Check to have questions and answers on the same line"
      >,
        <input class="bouton" type="button"
               title="Syntax highlighting"
               value="Syntax highlighting"
               onclick="usecm.checked=!usecm.checked"> <input class="bouton" type="checkbox" name="usecm"
                                                              title="Check to have syntax highlighting"
      >
        <input class="bouton" type="button"
               title="Move and del buttons always visible"
               value="Del visible" onclick="fixeddel.checked=!fixeddel.checked"> <input class="bouton" type="checkbox" name="fixeddel"
                                                                                        title="Move and del buttons always visible"
                                                                                        checked>
      </td>
    </tr>
    <tr>
      <td>
        Turtle <input class="bouton" type="number" name="canvas_w" value=400
                      title="Turtle graph width">
        by <input class="bouton" type="number" name="canvas_h" value=300
                  title="Turtle graph height">
        Out <input class="bouton" type="number" name="outdiv_width" value=410
                   title="Max width for answer fields"
      >
        by <input class="bouton" type="number" name="outdiv_height" value=190
                  title="Max height for answer fields"
      >
      </td>
    </tr>
    <tr>
      <td>
        Maximal size for matrix assistant
        <input class="bouton" type="number" name="matr_cfg_rows" id="matr_cfg_rows"
               title="Lines number" value=40 min=1 max=1000>,
        <input class="bouton" type="number" name="matr_cfg_cols" id="matr_cfg_cols"
               title="Columns number" 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="Check for resizable cells"
        >
        resizable
      </td>
    </tr>
    <tr>
      <td>
        Documentation <input class="bouton" type="checkbox" name="online_doc"
                             title="Check if Xcas is not installed, documentation will be retrieved from Internet"
                             checked>online
        <input class="bouton" type="text" name="doc_path" size="60"
               value="/usr/share/giac/doc/en/cascmd_en/"
               title="Offline documentation path on linux, for Mac add /Applications prefix"
        >
      </td>
    </tr>
  </table>
  <input class="bouton" type="submit" title="ok" value="&#x2705;">
  <input class="bouton" type="button"
         title="Cancel configuration changes"
         value="&#x274C;" onclick="form.style.display='none';  UI.focused.focus();">
  <hr>
</form>
<button id="settings" class="bouton" onclick="UI.show_config()"
        title="Modify settings"
>
  <img WIDTH="28" HEIGHT="28" SRC="config.png" alt="Configuration" align="center">
  <span id='curcfg'></span>
</button>
<span id='themailto'></span>
<span id='thelink'></span>
<textarea id='theforumlink' style="display:none"></textarea>
<span id="history1" style="display:none">
        <button class="bouton"
                title="Click here to save history (filename in the next textfield)"
                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="Saving session filename.">session</textarea>
        <button id="exportbutton" class="bouton"
                title="Export session to KhiCas (Casio Prizm or Fx-9750GIII, Numworks, TI Nspire CX, to be configured in the Settings)"
                onclick='UI.savesession(1);'>Export</button>
        </span>
<button id="loadbutton_cookie" class="bouton"
        title="Load session"
        onclick="$id('loadfile_cookie').innerHTML=UI.listCookies();">Load
</button>
<span id="loadfile_cookie"></span>
<form id="loadbutton_file" style="display:none">
  <label for="loadfileinput">Load</label>
  <input id="loadfileinput" accept=".xw" type="file" title="Insert a session" onchange="UI.loadfile(this.files);this.value=''">
</form>
<span id="help" style="display:none">
        <ul>
            <li style="display:inline">
                <button class="bouton"
                        onclick="$id('help').style.display='none';">
                <em>Hide documentation</em></button>
            </li>
            <li style="display:inline">
                <button class="bouton"
                        onclick="var tmp=$id('tutointro'); if (tmp.style.display=='none') tmp.style.display='block'; else tmp.style.display='none';">
                <strong>Introduction</strong></button>
                <div id="tutointro" style="display:none">
                    Type a computation or program in the commandline, for
                    example <tt>1/3+1/6</tt>.
                    Helpers are available by pressing <tt>Math</tt>
                    or <tt>Prog</tt> or <tt>123</tt> (scientific keyboard).
                    Press enter or hit &#x2705; to run the computation.
                    <br>
                    Find commandnames with the helpers or by reading the sections
                    below or in the
                    <a
                        href="http://www-fourier.univ-grenoble-alpes.fr/~parisse/giac/doc/en/cascmd_en"
                        target="_blank">Xcas manual</a>.
                    To get online help on a command, enter the commandname and press
                    the <tt>?</tt> button or F1 key.
                </div>
            <li style="display:inline">
                <button class="bouton"
                        onclick="var tmp=$id('tutonet'); if (tmp.style.display=='none') tmp.style.display='block'; else tmp.style.display='none';">
                <strong>Share</strong></button>
                <div id="tutonet" style="display:none">
                    You can share a session by clicking on the &#x282A; button.
                    You can exchange Xcas sessions by email. Fill in once the email
                    fields in the Settings (topleft button).
                    You can send a session by clicking on the &#x2709; link, modify the To
                    field if necessary (if you are using a webmail that is not gmail, copy
                    the x2 link content inside a mail or configure your browser settings for
                    this webmail).
                    When you receive an Xcas session by email, click on the link, this
                    should open the session in your browser. You can modify the
                    session and send it back with the &#x2709; link.
                    <br>
                    When you send a session by email, the filename of the session
                    will be modified by prefixing the sender email, except if the
                    sessionname contains @ (it remains unchanged, except if the filename begins
                    with @, then the leading @ is removed).
                    <br>
                    Example: a teacher sends to his students a session named
                    <tt>@exercise</tt> with a mail alias or by sharing on the forum (&#x282A;),
                    the students filename session will be <tt>exercise</tt>,
                    they do the work and send it back to the teacher (&#x2709; link),
                    the session received by the teacher is named with the email
                    address of the student prefixed, it's easy for him to know
                    who he is correcting. The teacher can send the session back,
                    the session name remains unchanged.
                </div>
            </li>
          </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>Install</strong></button>
                <div id="tutoinst" style="display:none">
                    You can optionally install Xcas on your device, in order to run it
                    in airplane mode (without Internet connection).
                    <br>
                    To install Xcas for Firefox on a mobile device, download
                    <a
                        href="http://www-fourier.univ-grenoble-alpes.fr/~parisse/giac/xcashtml.zip"
                        target="_blank">
                    xcashtml.zip</a>,
                    unzip it (for example with Androzip on Android),
                    search the <tt>xcasen.html</tt> file and open it with your
                    browser (Firefox recommended). You can create a shortcut
                    on your welcome screen for easy access.
                    <br>
                    On PC/Mac: if you have Xcas native &gt;1.4.9-57 already installed, Xcas for
                    Firefox is already installed, otherwise do like on mobile.
                    <ul>
                        <li> Windows: locate the file <tt>xcasen.html</tt>
                            in the <tt>doc</tt> subdirectory inside the install directory
                            of Xcas, by default <tt>c:\xcas</tt>.
                        <li> Mac:<a href="file:///Applications/usr/share/giac/doc/xcasen.html"
                                    target="_blank"><tt>/Applications/usr/share/giac/doc/xcasen.html</tt></a>,
                        <li> Linux: <a href="file:///usr/share/giac/doc/xcasen.html"
                                       target="_blank"><tt>/usr/share/giac/doc/xcasen.html</tt></a>,
                    </ul>
		    If Xcas for Firefox does not work locally with
		    Firefox, disable
		    <tt>security.fileuri.strict_origin_policy</tt>
		    in <tt>about:config</tt>.
                </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>Examples (highschool)</strong></button>
                <div id="tutoex" style="display:none">
                    Sessions examples
                    <ul>
                        <li>Variables,
                            types, affectation, tests, loop, function, syntax
                            <a
                                href="#exec&python=0&+///Enter%20commandlines%20in%20algebraic%20syntax,%20take%20care%20of%20parenthesis.%20Implicit%20multiplication%20is%20not%20supported%20except%20for%20number*symbol.&+1.2%3B%202*3%2B4%3B%202*(3%2B4)&+expand((x%2B1)%5E2)%3B%0Afactor(x%5E2%2B4x%2B4)%3B%0Asin(pi%2F3)&+///Variables,%20infix%20:=%20stores%20a%20value%20in%20a%20variable.&+a%3A%3D2&+2*a%2B5&+a%3A%3D2%3B%20type(a)&+a%3A%3D2.3%3B%20type(a)&+a%3A%3D%22hello%22%3B%20type(a)&+///A%20test&+a%3A%3D1%3B%20%0Aif%20a%3E0%20then%20%22positive%22%3B%20%0Aelse%20%22negative%22%3B%20fi%3B&+///A%20loop%20with%20known%20number%20of%20iterations.%20The%20output%20of%20print%20is%20visible%20in%20the%20console%20at%20the%20bottom.%0a&+for%20j%20from%201%20to%2010%20do%0A%20%20print(j%2B%22%20squared%20is%20%22%2Bj%5E2)%3B%20%0Aod%3B&+///A%20while%20loop,%20number%20of%20iterations%20is%20not%20known%20at%20the%20beginning.%20Illustrates%20the%20test%20precision%20with%20approx%20numbers.&+j%3A%3D1.0%3B%20%0Awhile%20j-1!%3Dj%20do%20%0A%20%20j%3D2*j%3B%20%0Aod%3B&+///Creation%20of%20a%20simple%20function,%20for%20example%20the%20midpoint%20of%20$A$%20and%20$B$.%20We%20first%20construct%20the%20midpoint%20interactively.&+A%3A%3Dpoint(1%2C2)%3B%20B%3A%3Dpoint(-2%2C-2)&+Ax%3A%3Dabscissa(A)%3B%20%0AAy%3A%3Dordinate(A)%3B%0ABx%3A%3Dabscissa(B)%3B%20%0ABy%3A%3Dordinate(B)&+///Now%20we%20compute%20the%20coordinates%20of%20$M$%20and%20we%20display%20the%203%20points.&+M%3A%3Dpoint((Ax%2BBx)%2F2%2C(Ay%2BBy)%2F2)%3B%0AA%3B%0AB%3B&+///Then%20we%20regroup%20these%20instructions%20in%20a%20function%20and%20we%20test%20it.&+function%20Midpoint(A%2CB)%0A%20%20var%20Ax%2CAy%2CBx%2CBy%3B%0A%20%20Ax%3A%3Dabscissa(A)%3B%20%0A%20%20Ay%3A%3Dordinate(A)%3B%0A%20%20Bx%3A%3Dabscissa(B)%3B%20%0A%20%20By%3A%3Dordinate(B)%3B%20%0A%20%20return%20point((Ax%2BBx)%2F2%2C(Ay%2BBy)%2F2)%3B%0Affunction%3A%3B&+A%3BB%3BM%3A%3DMidpoint(A%2CB)&+///%3Ch1%3eExercice%3C/h1%3e%20%0aWrite%20a%20%3Ctt%3eCircle(A,B,C)%3C/tt%3e%20function%20that%20compute%20the%20circumcircle%20of%20a%20triangle%20$ABC$%20using%20the%20commands%20%3Ctt%3eperpen_bissector,%20single_inter,%20distance,%20circle(center,%20radius)%3C/tt%3e&"
                                target="_blank">
                            Xcas</a> or
                            <a
                                href="#exec&python=1&+///Enter%20commandlines%20in%20algebraic%20syntax,%20take%20care%20of%20parenthesis.%20Implicit%20multiplication%20is%20not%20supported%20except%20for%20number*symbol.&+%23%20%0A1.2%0A2*3%2B4%0A2*(3%2B4)&+%23%20symbolics%0Anormal((x%2B1)%5E2)%0Afactor(x%5E2%2B4x%2B4)%0Asin(pi%2F3)&+///Variables,%20infix%20:=%20stores%20a%20value%20in%20a%20variable.&+a%3D2&+2*a%2B5&+type(a)&+a%3D2.3&+type(a)&+%23%0Aa%3D%22%22%0Atype(a)&+///A%20test&+%23%0Aa%3D1%0Aif%20a%3E0%3A%20%0A%20%20%20%20%22positive%22%0Aelse%3A%0A%20%20%20%20%22negati%22&+///A%20loop%20with%20known%20number%20of%20iterations.%20The%20output%20of%20print%20is%20visible%20in%20the%20console%20at%20the%20bottom.%0a&+for%20j%20in%20range(10)%3A%0A%20%20%20%20print(j%2B%22%20square%20is%20%22%2Bj%5E2)&+///A%20while%20loop,%20number%20of%20iterations%20is%20not%20known%20at%20the%20beginning.%20Illustrates%20the%20test%20precision%20with%20approx%20numbers.&+%23%0Aj%3D1.0%0Awhile%20j-1!%3Dj%3A%0A%20%20%20%20j%3D2*j&+///Creation%20of%20a%20simple%20function,%20for%20example%20the%20midpoint%20of%20$A$%20and%20$B$.%20We%20first%20construct%20the%20midpoint%20interactively.&+%23%20create%202%20points%0AA%3Dpoint(1%2C2)%20%0AB%3Dpoint(-2%2C-2)&+%23%20compute%20coordinates%0AAx%3Dabscissa(A)%20%0AAy%3Dordinate(A)%0ABx%3Dabscissa(B)%0ABy%3Dordinate(B)&+%23%20compute%20M%20and%20display%20it%0AM%3Dpoint((Ax%2BBx)%2F2%2C(Ay%2BBy)%2F2)%0AA%0AB&+///Now%20we%20compute%20the%20coordinates%20of%20$M$%20and%20we%20display%20the%203%20points.&+def%20Midpoint(A%2CB)%3A%0A%20%20%20%20%23%20local%20Ax%2CAy%2CBx%2CBy%3B%0A%20%20%20%20Ax%3Dabscissa(A)%0A%20%20%20%20Ay%3Dordinate(A)%0A%20%20%20%20Bx%3Dabscissa(B)%0A%20%20%20%20By%3Dordinate(B)%0A%20%20%20%20return%20point((Ax%2BBx)%2F2%2C(Ay%2BBy)%2F2)&+%23%0AA%0AB%0AM%3DMidpoint(A%2CB)&+///%3Ch1%3eExercice%3C/h1%3e%20%0aWrite%20a%20%3Ctt%3eCircle(A,B,C)%3C/tt%3e%20function%20that%20compute%20the%20circumcircle%20of%20a%20triangle%20$ABC$%20using%20the%20commands%20%3Ctt%3eperpen_bissector,%20single_inter,%20distance,%20circle(center,%20radius)%3C/tt%3e&"
                                target="_blank">Python</a>
                        </li>
                        <li> Turtle
                            Click on      <button onclick="$id('tutotortue').style.display='block';$id('tutoprog').style.display='none' ">
                            <strong>Turtle</strong>
                            </button> for examples (not translated).
                        </li>
                        <li> Step by step curve, syntax
                            <a
                                href="#exec&python=0&+///Define%20$f$%20by%20$f(x)=-x^2-3$%20if%20$x%3C0$%20and%20$f(x)=x^2+1$%20otehrwise.&+f(x)%3A%3Dif%20x%3C0%20then%20-x%5E2-3%20%0A%20%20else%20x%5E2%2B1%20fi%3B&+///First%20do%20a%20table%20of%20values.&+L%3A%3D%5B%5D%3B%20%0Afor%20x%20from%20-3%20to%203%20step%200.5%20do%0A%20%20L.append(%5Bx%2Cf(x)%5D)%3B%0Aod%3B&+open_polygon(L)&+///There%20is%20a%20step%20in%20the%20representation,%20we%20should%20make%202%20polygonal%20lines,%20it's%20a%20good%20idea%20to%20make%20a%20function%20and%20call%20it%20twice.&+function%20tabval(f%2Cxmin%2Cxmax%2Cdx)%0A%20%20var%20x%2CL%3B%0A%20%20L%3A%3D%5B%5D%3B%0A%20%20for%20x%20from%20xmin%20to%20xmax%20step%20dx%20do%0A%20%20%20%20L.append(%5Bx%2Cf(x)%5D)%3B%0A%20%20od%3B%0A%20%20return%20L%3B%0Affunction%3A%3B&+open_polygon(tabval(f%2C-3%2C-0.1%2C0.1))%3B%0Aopen_polygon(tabval(f%2C0.1%2C3%2C0.1))%3B&"
                                target="_blank">
                            Xcas</a> or
                            <a
                                href="#exec&python=1&+///Define%20$f$%20by%20$f(x)=-x^2-3$%20if%20$x%3C0$%20and%20$f(x)=x^2+1$%20otehrwise.&+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&+///First%20do%20a%20table%20of%20values.&+%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)&+open_polygon(L)&+///There%20is%20an%20ugly%20%20step%20in%20the%20representation,%20we%20should%20make%202%20polygonal%20lines,%20it's%20a%20good%20idea%20to%20make%20a%20function%20and%20call%20it%20twice.&+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&+open_polygon(tabval(f%2C-3%2C-0.1%2C0.1))%3B%0Aopen_polygon(tabval(f%2C0.1%2C3%2C0.1))%3B&"
                                target="_blank">Python</a>
                        </li>
                        <li> approximate curve arc length
                            <a href="#exec&python=1&+///Approx%20curve%20arc%20length%20with%20a%20polygonal%20line.%0a$1/x$%20may%20be%20replaced%20by%20another%20expression%20$f(x)$.&+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)%5E2%2B(yb-ya)%5E2)&+Distance(1%2C2)%2BDistance(2%2C3)%2BDistance(3%2C4)&+def%20Length(xa%2Cxb%2CN)%3A%0A%20%20%20%20%23%20local%20h%2Cd%2Ck%0A%20%20%20%20h%3D(xb-xa)%2FN%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%3DLength(1%2C4%2C10)&+arclen(1%2Fx%2C1.0%2C4)%3B%20evalf(l)&"
                               target="_blank">Python</a>
                        </li>
                        <li> Line equation
                            <a
                                href="#exec&python=0&+A%3A%3Dpoint(-2%2C3)%3B%20%0AB%3A%3Dpoint(1%2C-1)%3B%20%0AD%3A%3Dline(A%2CB)&+function%20eqline(A%2CB)%0A%20%20var%20Ax%2CAy%2CBx%2CBy%2Cm%3B%0A%20%20Ax%2CAy%3A%3Dcoordinates(A)%3B%0A%20%20Bx%2CBy%3A%3Dcoordinates(B)%3B%0A%20%20if%20Ax%3DBx%20then%20return%20%22x%3D%22%2BAx%3B%20fi%3B%0A%20%20m%3A%3D(By-Ay)%2F(Bx-Ax)%3B%0A%20%20%2F%2F%20m*Ax%2Bp%3DAy%0A%20%20return%20%22y%3D%22%2Bm%2B%22*x%2B%22%2B(Ay-m*Ax)%3B%0Affunction%3A%3B&+eqline(A%2CB)%3B%20equation(D)&"
                                target="_blank">Xcas</a>
                            or
                            <a
                                href="#exec&python=1&+%23%20%0AA%3Dpoint(-2%2C3)%0AB%3A%3Dpoint(1%2C-1)%3B%20%0AD%3A%3Dline(A%2CB)&+def%20eqline(A%2CB)%3A%0A%20%20%20%20%23%20local%20Ax%2CAy%2CBx%2CBy%2Cm%3B%0A%20%20%20%20Ax%2CAy%3Dcoordinates(A)%0A%20%20%20%20Bx%2CBy%3Dcoordinates(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)&+eqline(A%2CB)%3B%20equation(D)&"
                                target="_blank">
                            Python</a>
                        </li>
                        <li> Minimum by mean of a table of value
                            <a
                                href="#exec&python=0&+///Find%20a%20local%20minimum%20of%20a%20function%20$f$%20in%20$[a,b]$.%20Cut%20the%20interval%20in%2010,%20find%20the%20minimum.%20Do%20that%20again%20with%20the%20interval%20containing%20the%20minimum,%20until%20required%20precision%20is%20reached.&+function%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%20for%20j%20from%201%20to%2010%20do%0A%20%20%20%20xcur%3A%3Da%2Bj*h%3B%0A%20%20%20%20fxcur%3A%3Df(xcur)%3B%0A%20%20%20%20if%20fxcur%3Cfxmin%20then%0A%20%20%20%20%20%20xmin%3A%3Dxcur%3B%0A%20%20%20%20%20%20fxmin%3A%3Dfxcur%3B%0A%20%20%20%20fi%3B%0A%20%20od%3B%0A%20%20return%20xmin%3B%0Affunction%3A%3B&+posmin10(cos%2C0%2C6)%0A&+function%20posmin(f%2Ca%2Cb%2Ceps)%0A%20%20local%20x%2Ch%3B%0A%20%20x%3A%3Da%3B%0A%20%20while%20b-a%3Eeps%20do%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%20if%20x!%3Da%20then%20a%3A%3Dx-h%3B%20fi%3B%0A%20%20%20%20if%20x!%3Db%20then%20b%3A%3Dx%2Bh%3B%20fi%3B%0A%20%20od%3B%0A%20%20return%20x%3B%0Affunction%3A%3B&+posmin(cos%2C0%2C6%2C1e-2)&"
                                target="_blank">Xcas</a>,
                            <a href="#exec&python=1&+///Find%20a%20local%20minimum%20of%20a%20function%20$f$%20in%20$[a,b]$.%20Cut%20the%20interval%20in%2010,%20find%20the%20minimum.%20Do%20that%20again%20with%20the%20interval%20containing%20the%20minimum,%20until%20required%20precision%20is%20reached.&+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(cos%2C0%2C6)&+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(cos%2C0%2C6%2C1e-2)&"
                               target="_blank">Python</a>
                        </li>
                        <li> Frequency in a sample
                            <a
                                href="#exec&python=0&+///Algorithm%20computing%20frequency%20of%20%3Ctt%3eval%3C/tt%3e%20in%20a%20sample.&+function%20freq(sampl%2Cval)%0A%20%20var%20j%2Ctotal%3B%0A%20%20total%3A%3D0%3B%0A%20%20for%20j%20from%201%20to%20dim(sampl)%20do%0A%20%20%20%20if%20sampl(j)%3Dval%20then%20%0A%20%20%20%20%20%20total%3A%3Dtotal%2B1%3B%20%0A%20%20%20%20fi%3B%0A%20%20od%3B%0A%20%20return%20total%2Fdim(sampl)%3B%0Affunction%3A%3B&+sampl%3A%3Dranv(100%2C2)&+freq(sampl%2C1)%3B%20%0Afreq(sampl%2C0)&+///Fluctuation%20of%20a%20frequency,%20here%200.4.%20We%20draw%20100%20samples%20of%20$N=200$%20values%20according%20to%20the%20binomial%20law%20and%20we%20return%20the%20frequency%20of%201.&+f%3A%3D0.4%3B%20N%3A%3D200%0A&+sampl%3A%3D%0Aranv(100%2Cbinomial%2CN%2Cf)%2FN&+count(x-%3E%0A%20%20abs(x-f)%3C1%2Fsqrt(N)%2Csampl)&+///If%20we%20do%20not%20want%20to%20call%20%3Ctt%3eranv%3C/tt%3e,%20we%20can%20simulate%20a%20frequency%20$f$%20with%20%3Ctt%3erand()%3C/tt%3e%20and%20compare%20with%20$f$&+rand()&+dr(f)%3A%3Drand()%3Cf&+seq(dr(f)%2C10)&+function%20simu(N%2Cf)%0A%20%20var%20j%2Cres%3B%0A%20%20res%3A%3D0%3B%0A%20%20for%20j%20from%201%20to%20N%20do%0A%20%20%20%20if%20dr(f)%20then%20res%3A%3Dres%2B1%3B%20fi%3B%0A%20%20od%3B%0A%20%20return%20res%2FN%3B%0Affunction%3A%3B&+simu(200%2C.4)&+l%3A%3Dseq(simu(200%2C.4)%2C100)%0A&+count(x-%3Eabs(x-f)%3C1%2Fsqrt(N)%2Cl)&+///Click%20on%20Exec%20to%20run%20again%20with%20different%20random%20input.&"
                                target="_blank">
                            Xcas</a> or
                            <a href="#exec&python=0&+///Algorithm%20computing%20frequency%20of%20%3Ctt%3eval%3C/tt%3e%20in%20a%20sample.&+def%20Freq(sampl%2Cval)%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%20sampl%3A%0A%20%20%20%20%20%20%20%20if%20j%3D%3Dval%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20total%3Dtotal%2B1%0A%20%20%20%20return%20total%2Fdim(sampl)&+sampl%3Dranv(100%2C2)&+%23%0AFreq(sampl%2C1)%0AFreq(sampl%2C0)&+///Fluctuation%20of%20a%20frequency,%20here%200.4.%20We%20draw%20100%20samples%20of%20$N=200$%20values%20according%20to%20the%20binomial%20law%20and%20we%20return%20the%20frequency%20of%201.&+%23%0Af%3D0.4%0AN%3D200%0A&+sampl%3D%0Aranv(100%2Cbinomial%2CN%2Cf)%2FN&+def%20Ok(sampl%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%20sampl%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(sampl%2Cf%2CN)&+///If%20we%20do%20not%20want%20to%20call%20%3Ctt%3eranv%3C/tt%3e,%20we%20can%20simulate%20a%20frequency%20$f$%20with%20%3Ctt%3erand()%3C/tt%3e%20and%20compare%20with%20$f$&+random()&+def%20dr(f)%3A%0A%20%20%20%20return%20random()%3Cf&+seq(dr(f)%2C10)&+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%20dr(f)%3A%20%0A%20%20%20%20%20%20%20%20%20%20%20%20res%3Dres%2B1%0A%20%20%20%20return%20res%2FN&+Simu(200%2C.4)&+l%3Dseq(Simu(200%2C.4)%2C100)&+Ok(l%2Cf%2CN)&+///Click%20on%20Exec%20to%20run%20again%20with%20different%20random%20input.&"
                               target="_blank">Python</a>
                        </li>
                        <li>
                            Trial division for prime factorization
                            <a href="#exec&python=0&+function%20tdiv(n)%0A%20%20local%20r%2Cj%3B%0A%20%20r%3A%3Dmakelist(0)%3B%0A%20%20for%20j%20from%202%20to%2010000%20do%0A%20%20%20%20if%20j*j%3En%20then%0A%20%20%20%20%20%20if%20n!%3D1%20then%20r.append(n)%3B%20fi%3B%0A%20%20%20%20%20%20return%20r%3B%20%0A%20%20%20%20fi%3B%0A%20%20%20%20while%20irem(n%2Cj)%3D0%20do%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%20od%3B%0A%20%20%20%20if%20j%3E2%20then%20j%2B%2B%3B%20fi%3B%20%2F%2F%20step%202%0A%20%20fpour%3B%0A%20%20return%20%22Too%20large%22%3B%0Affunction%3A%3B&+tdiv(1007)&"
                               target="_blank">Xcas</a>,
                            <a
                                href="#exec&python=1&+def%20tdiv(n)%3A%0A%20%20%20%20%23%20local%20r%2Cj%0A%20%20%20%20r%3Dmakelist(0)%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%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%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%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%0A%20%20%20%20%20%20%20%20%20%20%20%20j%2B%2B%0A%20%20%20%20return(%22Too%20large%22)%0A&+tdiv(1007)&"
                                target="_blank">Python</a>
                        </li>
                        <li> Second order equation
                            <a
                                href="#exec&python=0&+function%20resolution2(a%2Cb%2Cc)%0A%20%20var%20delta%3B%0A%20%20delta%3A%3Db%5E2-4*a*c%3B%0A%20%20if%20delta%3C0%20then%20return%20%22no%20roots%22%3B%20fi%3B%0A%20%20if%20delta%3D0%20then%20return%20-b%2F(2*a)%3B%20fi%3B%0A%20%20delta%3A%3Dsqrt(delta)%3B%0A%20%20return%20(-b-delta)%2F(2*a)%2C(-b%2Bdelta)%2F(2*a)%3B%0Affunction%3A%3B&+resolution2(1%2C2%2C3)&+resolution2(1%2C2%2C1)&+resolution2(1%2C1%2C-1)&"
                                target="_blank">
                            Xcas</a>,
                            <a
                                href="#exec&python=1&+def%20resolution2(a%2Cb%2Cc)%3A%0A%20%20%20%20%23%20local%20delta%2Cs%0A%20%20%20%20delta%3Db%5E2-4*a*c%0A%20%20%20%20if%20delta%3C0%3A%0A%20%20%20%20%20%20%20%20return%20%22no%20roots%22%0A%20%20%20%20if%20delta%3D%3D0%3A%0A%20%20%20%20%20%20%20%20return%20-b%2F(2*a)%0A%20%20%20%20s%3Dsqrt(delta)%0A%20%20%20%20return%20%5B(-b-s)%2F(2*a)%2C(-b%2Bs)%2F(2*a)%5D&+resolution2(1%2C2%2C3)&+resolution2(1%2C2%2C1)&+resolution2(1%2C1%2C-1)&"
                                target="_blank">Python</a>
                        </li>
                        <li> Sequences
                            <a
                                href="#exec&python=0&+///First%20terms%20of%20an%20explicit%20sequence%20(given%20by%20an%20expression)&+u(n)%3A%3D1%2Fn&+s%3A%3Dseq(u(n)%2Cn%2C1%2C10)&+seq(point(n%2Cu(n))%2Cn%2C1%2C10)&+///Computation%20of%20the%20first%20terms%20of%20a%20recurrent%20sequence%20$u[n+1]=f(u[n])$&+function%20nterms(f%2Cu0%2CN)%20%0A%20%20var%20n%2Cu%3B%0A%20%20u%3A%3D%5Bu0%5D%3B%0A%20%20for%20n%20from%201%20to%20N%20do%0A%20%20%20%20u%5Bn%5D%3A%3Df(u%5Bn-1%5D)%3B%0A%20%20od%3B%0A%20%20return%20u%3B%20%0A%20%20%2F%2F%20ou%20retourne%20u%5BN%5D%20pour%20le%20dernier%20terme%0Affunction%3A%3B&+f(x)%3A%3D1%2F2*(x%2B2%2Fx)&+nterms(f%2C1.0%2C1)&+U%3A%3Dnterms(f%2C1.0%2C5)&+nterms(f%2C1%2C5)&+seq(point(n%2CU%5Bn%5D)%2Cn%2C0%2Csize(U)-1)&"
                                target="_blank">Xcas
                            </a>,
                            <a
                                href="#exec&python=1&+///First%20terms%20of%20an%20explicit%20sequence%20(given%20by%20an%20expression)&+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&+///Computation%20of%20the%20first%20terms%20of%20a%20recurrent%20sequence%20$u[n+1]=f(u[n])$&+def%20nterms(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%201%2F2*(x%2B2%2Fx)&+nterms(f%2C1.0%2C1)&+U%3Dnterms(f%2C1.0%2C5)&+nterms(f%2C1%2C5)&+%5Bpoint(n%2CU%5Bn%5D)%20for%20n%20in%20range(size(U))%5D%0A&"
                                target="_blank">Python</a>
                        </li>
                        <li> Binomial and truncated geometric law
                            <a
                                href="#exec&python=0&+python_compat(0)&+///$n$%20samples%20with%20success%20probability%20$p$&+function%20f(n%2Cp)%0A%20%20var%20total%2Cj%2Ch%3B%0A%20%20total%3A%3D0%3B%0A%20%20for%20j%20from%201%20to%20n%20do%0A%20%20%20%20h%3A%3Drand(0%2C1)%3B%0A%20%20%20%20if%20h%3C%3Dp%20then%20total%3A%3Dtotal%2B1%3B%20fi%3B%0A%20%20%20od%3B%0A%20%20return%20total%3B%0Affunction%3A%3B&+f(10%2C0.4)%0A&+///Histogram%20of%201000%20samples%20and%20comparison%20with%20the%20histogram%20of%20the%20binomial%20law.&+s%3A%3Dseq(f(10%2C0.4)%2C1000)&+histogram(s%2C-0.5%2C1%2Ccolor%3Dred)%3B%20%0Ahistogram(binomial%2C10%2C0.4)&+///Symmetric%20confidence%20interval%20for%20the%20binomial%20law.&+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%0Aline(x%3Dxmin%2Ccolor%3Dred)%3B%0Aline(x%3Dxmax%2Ccolor%3Dred)%3B&+///Algorithm%20to%20compute%20the%20confidence%20interval%20for%20the%20binomial%20law.&+function%20confidence(n%2Cp%2Cseuil)%0A%20%20var%20k%2Ctotal%3B%0A%20%20total%3A%3D0%3B%0A%20%20for%20k%20from%200%20to%20n%20do%0A%20%20%20%20total%3A%3Dtotal%2Bbinomial(n%2Cp%2Ck)%3B%0A%20%20%20%20if%20total%3E%3Dseuil%20then%20retourne%20k%3B%20fi%3B%0A%20%20od%3B%0Affunction%3A%3B&+confidence(100%2C.16%2C0.025)&+confidence(100%2C.16%2C0.975)&+///Comparison%20with%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&+///Truncated%20geometric%20law%20(returns%20the%20first%20success%20or%200)&+function%20geo(n%2Cp)%0A%20%20var%20k%2Ct%3B%0A%20%20for%20k%20from%201%20to%20n%20do%0A%20%20%20%20t%3A%3Drand(0%2C1)%3B%0A%20%20%20%20if%20t%3C%3Dp%20then%20return%20k%3B%20fi%3B%0A%20%20od%3B%0A%20%20return%200%3B%0Affunction%3A%3B&+geo(10%2C.4)%0A&+s%3A%3Dseq(geo(10%2C.4)%2C1000)&+histogram(s%2C-0.5%2C1%2Ccolor%3Dred)%3B%20%0Ahistogram(geometric%2C0.4)&"
                                target="_blank">Xcas</a>,
                            <a
                                href="#exec&python=1&+///$n$%20samples%20with%20success%20probability%20$p$&+def%20f(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&+f(10%2C0.4)&+///Histogram%20of%201000%20samples%20and%20comparison%20with%20the%20histogram%20of%20the%20binomial%20law.&+s%3Dseq(f(10%2C0.4)%2C1000)&+histogram(s%2C-0.5%2C1%2Ccolor%3Dred)%3B%0Ahistogram(binomial%2C10%2C0.4)&+///Symmetric%20confidence%20interval%20for%20the%20binomial%20law.&+%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(line(equal(x%2Cxmin))%2Cred)%0Acolor(line(equal(x%2Cxmax))%2Cred)&+///Algorithm%20to%20compute%20the%20confidence%20interval%20for%20the%20binomial%20law.&+def%20confidence(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&+confidence(100%2C.16%2C0.025)&+confidence(100%2C.16%2C0.975)&+///comparison%20with%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)&+///Truncated%20geometric%20law%20(returns%20the%20first%20success%20or%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%3Dseq(geo(10%2C.4)%2C1000)&+%23%0Acolor(histogram(s%2C-0.5%2C1)%2Cred)%20%0Ahistogram(geometric%2C0.4)&"
                                target="_blank">Python</a>
                        </li>
                        <li> Pascal triangle
                            <a
                                href="#exec&python=0&+///Pascal%20triangle%20to%20compute%20binomial%20coefficients.&+function%20Pascal(n)%0A%20%20var%20tab%2Cj%2Ck%3B%0A%20%20tab%3A%3Dmatrix(n%2Cn)%3B%0A%20%20for%20j%20from%200%20to%20n-1%20do%0A%20%20%20%20tab%5Bj%2C0%5D%3A%3D1%3B%0A%20%20%20%20for%20k%20from%201%20to%20j%20do%0A%20%20%20%20%20%20tab%5Bj%2Ck%5D%3A%3Dtab%5Bj-1%2Ck-1%5D%2Btab%5Bj-1%2Ck%5D%3B%0A%20%20%20%20od%3B%0A%20%20od%3B%0A%20%20return%20tab%3B%0Affunction%3A%3B&+Pascal(6)&"
                                target="_blank">
                            Xcas</a>
                            <a
                                href="#exec&python=1&+///Pascal%20triangle%20to%20compute%20binomial%20coefficients.&+def%20Pascal(n)%3A%0A%20%20%20%20%23%20local%20tab%2Cj%2Ck%3B%0A%20%20%20%20tab%3Dmatrix(n%2Cn)%0A%20%20%20%20for%20j%20in%20range(n)%3A%0A%20%20%20%20%20%20%20%20tab%5Bj%2C0%5D%3D1%0A%20%20%20%20%20%20%20%20for%20k%20in%20range(1%2Cj%2B1)%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20tab%5Bj%2Ck%5D%3Dtab%5Bj-1%2Ck-1%5D%2Btab%5Bj-1%2Ck%5D%0A%20%20%20%20return%20tab%0A&+Pascal(6)&"
                                target="_blank">Python</a>
                        </li>
                        <li>
                            Dichotomy
                            <a
                                href="#exec&python=0&+///Find%20a%20root%20of%20$f$%20between%20$a$%20and%20$b$%20with%20precision%20%3Ctt%3eeps%3C/tt%3e.%0aThe%20%3Ctt%3edicho%3C/tt%3e%20function%20begins%20with%20a%20test%20that%20the%20sign%20differ%20at%20$a$%20and%20$b$.&+function%20dicho(f%2Ca%2Cb%2Ceps)%0A%20%20var%20c%2Cniter%3B%0A%20%20if%20f(a)*f(b)%3E%3D0%20then%20retorn%20%22error%3A%20no%20sign%20change%22%3B%20fi%3B%0A%20%20while%20abs(b-a)%3Eeps%20do%0A%20%20%20%20c%3D(a%2Bb)%2F2%3B%0A%20%20%20%20if%20f(a)*f(c)%3E0%20then%20a%3Dc%3B%20else%20b%3Dc%3B%20fi%3B%0A%20%20od%3B%0A%20%20return%20c%3B%0Affunction%3A%3B&+f(x)%3A%3Dcos(x)-x%3B&+plot(f(x)%2Cx%2C0%2C2)%0A&+dicho(f%2C0.0%2C1.0%2C1e-8)&"
                                target="_blank">
                            Xcas
                            </a>,
                            <a
                                href="#exec&python=1&+///Find%20a%20root%20of%20$f$%20between%20$a$%20and%20$b$%20with%20precision%20%3Ctt%3eeps%3C/tt%3e.%0aThe%20%3Ctt%3edicho%3C/tt%3e%20function%20begins%20with%20a%20test%20that%20the%20sign%20differ%20at%20$a$%20and%20$b$.&+def%20dicho(f%2Ca%2Cb%2Ceps)%3A%0A%20%20%20%20%23%20local%20var%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%22error%3A%20f(a)*f(b)%3E%3D0%22%0A%20%20%20%20while%20abs(b-a)%3Eeps%3A%0A%20%20%20%20%20%20%20%20c%3D(a%2Bb)%2F2%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">Python</a>
                        </li>
                        <li>
                            Approximate area under curve
                            <a
                                href="#exec&python=0&+///Numeric%20integration&+f(x)%3A%3Dsin(x)%0A&+plot(f(x)%2Cx%2C0%2C1)%3B%20line(y%3D0)%3B&+function%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%20for%20j%20from%201%20to%20N%20do%0A%20%20%20%20S%3A%3DS%2Bf(a%2Bj*h)%3B%0A%20%20od%3B%0A%20%20return%20S*h%3B%0Affunction%3A%3B&+rect(f%2C0%2C1%2C100)%0A&+integrate(f(x)%2Cx%2C0%2C1.0)%0A&+///For%20the%20midpoint%20method,%20replace%20f(a+j*h)%20by%20f(a-h/2+j*h)&+fonction%20Midpoint(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%20for%20j%20from%201%20to%20N%20do%0A%20%20%20%20S%3A%3DS%2Bf(a-h%2F2%2Bj*h)%3B%0A%20%20od%3B%0A%20%20return%20S*h%3B%0Affunction%3A%3B&+Midpoint(f%2C0%2C1%2C100)&+///It%20is%20more%20accurate%20for%20(almost)%20the%20same%20computational%20cost,%20as%20graphically%20illustrated%20below.&+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%20by%20Monte-Carlo%20method&+function%20Montecarlo(f%2Ca%2Cb%2Cn)%0A%20%20local%20k%2Cr%3B%0A%20%20r%3A%3D0%3B%0A%20%20for%20k%20from%201%20to%20n%20do%0A%20%20%20%20r%3A%3Dr%2Bf(rand(uniformd%2Ca%2Cb))%3B%0A%20%20od%3B%0A%20%20return%20r*(b-a)%2Fn%3B%0Affunction%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%0Aline(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&+///Numeric%20integration&+f(x)%3A%3Dsin(x)&+plot(f(x)%2Cx%2C0%2C1)%3B%20line(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)%2FN%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)&+///For%20the%20midpoint%20method,%20replace%20f(a+j*h)%20by%20f(a-h/2+j*h)&+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)%2FN%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)&+///It%20is%20more%20accurate%20for%20(almost)%20the%20same%20computational%20cost,%20as%20graphically%20illustrated%20below.&+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%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)&+%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%2C0.005)%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">Python</a>
                        </li>
                        <li>
                            Cumulated frequency
                            <a href="#exec&python=0&+///Cumulated%20distribution%20between%202%20values%20$a$%20and%20$b$.%0aFor%20another%20law,%20e.g.%20exponentiald(1),%20take%20care%20of%20the%20values%20of%20$a$%20and%20$b$%20and%20modify%20%3Ctt%3ex=-5..5%3C/tt%3e%20for%20example%20to%20%3Ctt%3ex=0..6%3C/tt%3e.&+law%3A%3Dnormald(0%2C1)&*a,-2,-5,5,0.125&*b,0,-5,5,0.125&+plotarea(law(x)%2Cx%3Dmin(a%2Cb)..max(a%2Cb))%3B%0Aplotfunc(law(x)%2Cx%3D-5..5)%3B%0A&+///Symmetric%20confidence%20interval%20for%20the%20law%20with%20$alpha$%20risk.&+alpha%3A%3D0.05%3A%3B%0Aicdf(law%2Calpha%2F2)%2Cicdf(law%2C1-alpha%2F2)&"
                               target="_blank">normal law</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">
                            Central-limit theorem illustration
                            </a>
                        </li>
                    </ul>
                </div>
            </li>
            <li style="display:inline">
                <button class="bouton"
                        onclick="var tmp=$id('tutoex2'); if (tmp.style.display=='none') tmp.style.display='block'; else tmp.style.display='none';">
                <strong>Examples</strong></button>
                <div id="tutoex2" style="display:none">
                    Sessions examples
                    <ul>
                        <li>
                            <a
                                href="#exec&python=0&+///%3Ch1%3eFloats%3C/h1%3e&+1.0-0.9-0.1&+///As%20illustrated%20above,%20Xcas%20does%20not%20compute%20in%20basis%2010.%0aThe%20program%20below%20will%20find%20the%20basis%20used%20for%20computation.&+function%20Base()%0A%20%20local%20A%2CB%3B%0A%20%20A%3A%3D1.0%3B%20B%3A%3D1.0%3B%0A%20%20while%20evalf(evalf(A%2B1.0)-A)-1.0%3D0.0%20do%20%20A%3A%3D2*A%3B%20od%3B%0A%20%20while%20evalf(evalf(A%2BB)-A)-B!%3D0%20do%20B%3A%3DB%2B1%3B%20od%3B%0A%20%20return%20B%3B%0Affunction%3A%3B%20Base()&+///Smallest%20and%20largest%20representable%20strictly%20positive%20reals%20(normal%20precision).&+MINREAL%3BMAXREAL&+///Xcas%20precision%20for%20floats%20in%20bits.%20If%20%3Ctt%3eDigits%3C/tt%3e%20is%20larger%20than%2014,%20computations%20are%20slower%20but%20more%20accurate.&+epsilon%3A%3D0%3A%3B%20Digits%3A%3D14%3B%0Apour%20j%20de%201%20jusque%201000%20faire%20%0A%20%20si%20evalf(1)%2B2%5E(-j)%3D%3Devalf(1)%20alors%20break%3B%20fsi%3B%20%0Afpour%3A%3B%0Aj&+///Relative%20error,%20example%20with%20the%20computation%20of%20a%20derivative.%20The%20optimal%20value%20of%20$h$%20depends%20on%20the%20precision%20(%3Ctt%3eDigits%3C/tt%3e).&+der(f%2Cx%2Ch)%3A%3D(f(x%2Bh)-f(x))%2Fh&+Digits%3A%3D14&+seq(der(exp%2C0.0%2C10%5E(-j))-1%0A%20%20%2Cj%2C1%2C15))&+der2(f%2Cx%2Ch)%3A%3D(f(x%2Bh)-f(x-h))%2F2%2Fh&+seq(der2(exp%2C0.0%2C10%5E(-j))-1%0A%20%20%2Cj%2C1%2C15))&+///Relative%20error%20on%20$f(x)$%20is%20equivalent%20to%20$abs(x*f'(x)/f(x))$.%20Illustration%20with%20interval%20arithmetic.&+x%3A%3Dconvert(pi%2Cinterval)&+err%3A%3D(right(x)-left(x))%2Fpi&+f(x)%3A%3Dexp(x)%3A%3By%3A%3Df(x)&+(right(y)-left(y))%2Fexp(pi)%3B%20%0Aerr*pi*f'(pi)%2Ff(pi)&+///Sum%20of%20$n$%20independant%20absolute%20errors.%0aThe%20majoration%20of%20the%20absolute%20error%20of%20the%20sum%20is%20multiplied%20by%20$n$%20but%20this%20is%20too%20pessimistic,%20most%20of%20the%20time%20error%20is%20multiplied%20by%20a%20factor%20$sqrt(n)$.%0aExample%20of%20simulation%20:%20sum%20of%20$n=400$%20numbers%20on%20(-1,1),%20uniform%20law,%20divide%20by%20$sqrt(n)=20$,%20make%20this%201000%20times,%20draw%20the%20histogram%20and%20compare%20with%20the%20normal%20law%20(mean=0,%20stddev=stddev%20of%20the%20uniform%20law%20on%20(-1,1)).&+n%3A%3D400%3B%0Am%3A%3Dranm(n%2C1000%2C-1..1)%3A%3B%0Agl_x%3D-2..2%3B%0Ahistogram(sum(m)%2Fsqrt(n)%2C-1%2C0.1)%3B%20%0Aplot(normald(0%2Cstddev(uniform%2C-1%2C1))%2C-2..2)&+///Correction%20of%20rounding%20errors%20in%20the%20sum%20of%20the%20components%20of%20a%20list.%20We%20accumulate%20in%20$c$%20almost%20the%20opposite%20of%20the%20roundings%20errors%20from%20%3Ctt%3es+=x%3C/tt%3e&+function%20Somme(l)%0A%20%20local%20x%2Cs%2Cc%3B%0A%20%20s%3A%3D0.0%3B%0A%20%20c%3A%3D0.0%3B%0A%20%20pour%20x%20in%20l%20faire%0A%20%20%20%20c%20%2B%3D%20(x-((s%2Bx)-s))%3B%0A%20%20%20%20s%20%2B%3D%20x%3B%0A%20%20fpour%3B%0A%20%20print(c)%3B%0A%20%20return%20s%2Bc%3B%0Affunction%3A%3B&+n%3A%3D6000%3B%0Al%3A%3Dseq(1%2Fj%2Cj%2C1%2Cn)%3A%3B%0ASomme(l)%3B&+///Comparison%20with%20the%20approx%20value%20of%20the%20exact%20value%20of%20$S$%20and%20of%20the%20approx%20computation%20without%20correction.&+S%3A%3Dsum(1%2Fj%2Cj%2C1%2Cn)%3A%3B%20evalf(S)%3B%0Asum(1.%20%2Fj%2Cj%2C1%2Cn)%3B&"
                                target="_blank">Floating point numbers</a>
                        </li>
                        <li>
                            <a
                                href="#exec&python=0&+///Computation%20time%20and%20accuracy%20of%20a%20LU%20factorization%20as%20the%20size%20$n$%20of%20the%20matrix%20increases.&+t%3A%3D%5B%5D%3A%3B%20err%3A%3D%5B%5D%3A%3B%0Afor%20n%20from%201%20to%208%20do%0A%20%20m%3A%3Dranm(n*50%2Cn*50%2Cuniformd%2C-1%2C1)%3B%20%0A%20%20t.append(time(p%2Cl%2Cu%3A%3Dlu(m)))%3B%20%0A%20%20err.append(maxnorm(permu2mat(p)*m-l*u))%3B%0Aod%3A%3B%0At%3Berr%3B&+N%3A%3Dseq(ln(n)%2Cn%2C2%2C8)%3B%0AT%3A%3Dln(t)%5B1..11%5D%3B%0Apolygonscatterplot(N%2CT)%3B%0Alinear_regression_plot(N%2CT%2Ccolor%3Dred)&+linear_regression(N%2CT)&+///It's%20better%20than%20the%20expected%20$O(n^3)$,%20there%20are%20some%20optimizations%20as%20the%20matrix%20size%20increases%20and%20Xcas%20is%20using%20more%20efficient%20bloc%20algorithms.%0aFor%20specific%20matrices,%20like%20sparse%20matrices%20(e.g.%20discrete%20laplacian)%20or%20symmetric%20defined,%20some%20algorithms%20will%20give%20better%20timings%20(like%20Cholesky%20factorization%20for%20symmetric%20defined%20matrices).&+n%3A%3D7%3B%20a%3A%3Dlaplacian(n)%3B&+///Comparison%20:%20linear%20solving%20assuming%20LU%20is%20known%20in%20$O(n^2)$%20vs%20direct%20solving.&+function%20f(n)%0A%20%20local%20t1%2Ct2%2Cp%2Cl%2Cu%2Ca%2Cb%2Cv%2Cw%3B%0A%20%20p%2Cl%2Cu%3A%3Dlu(a%3A%3Dranm(n%2Cn%2Cuniformd%2C-1%2C1))%3A%3B%20%0A%20%20b%3A%3Dranv(n%2Cuniformd%2C-1%2C1)%3A%3B%20%0A%20%20t1%3A%3Dtime(v%3A%3Dlinsolve(p%2Cl%2Cu%2Cb))%3B%0A%20%20t2%3A%3Dtime(w%3A%3Dlinsolve(a%2Cb))%3B%0A%20%20return%20t1%2Ct2%2Cmaxnorm(v-w)%3B%0Affunction%3A%3B&+f(600)&+///Condition%20number%20of%20a%20matrix,%20example%20of%20resolution%20of%20a%20system%20with%202%20second%20members%20that%20are%20close%20together,%20the%20relative%20error%20of%20the%20corresponding%20solutions%20is%20almost%20increased%20by%20the%20condition%20number.&+a%3A%3D%5B%5B10%2C7%2C8%2C7%5D%2C%0A%20%20%5B7%2C5%2C6%2C5%5D%2C%0A%20%20%5B8%2C6%2C10%2C9%5D%2C%0A%20%20%5B7%2C5%2C9%2C10%5D%5D&+b%3A%3D%5B32%2C23%2C33%2C31%5D&+v%3A%3Dlinsolve(a%2Cb)&+delta_b%3A%3D%5B1%2C-1%2C1%2C-1%5D%2F100&+w%3A%3Dlinsolve(a%2Cb%2Bdelta_b)&+err1%3A%3Dl2norm(evalf(delta_b))%2Fl2norm(b)%3B%0Aerr2%3A%3Dl2norm(evalf(w-v))%2Fl2norm(v)%3B&+cond(a%2C2)%3B%20err2%2Ferr1&"
                                target="_blank">Linear systems, LU, condition number</a>
                        </li>
                        <li>
                            <a
                                href="#exec&python=0&+///$Q*R$%20decomposition%20and%20least%20squares.%0aExample:%20linear%20regression.&+///Given%20a%20sequence%20of%20values%20that%20are%20on%20a%20line%20modulo%20a%20small%20random%20error,%20we%20are%20searching%20the%20best%20line%20$y=a*x+b$%20near%20these%20points%20minimizing%20the%20square%20vertical%20distance.&+n%3A%3D30%3B%20b%3A%3Dseq(2*j%2B5*rand()%2Cj%2C1%2Cn)&+x%3A%3Dseq(j%2Cj%2C1%2Cn)%3B%20scatterplot(x%2Cb)%3B%0Alinear_regression_plot(x%2Cb)&+///Matrix%20translation%20of%20the%20problem%20$A*x=b$%20with%20$x=[m,p]$&+A%3A%3Dtrn(%5Bx%2Cseq(1%2Cn)%5D)&+A*%5Bm%2Cp%5D%3Db&+///The%20system%20is%20overdetermined.%20It%20can%20only%20be%20solve%20as%20a%20least%20square%20problem,%20find%20$x$%20such%20that%20$abs(A*x-b)$%20is%20minimal,%20i.e.%20$A^t*A*x=A^t*b$&+///Let%20$A=Q_1*R_1$%20with%20$R_1$%20upper%20triangular%20invertible%20be%20the%20thin%20$QR$%20factorization%20of%20$A$.%20We%20have%20$R_1*x=Q_1^t*b$&+q%2Cr%3A%3Dqr(evalf(A))&+q1%3A%3Dq%5B%3A%2C0..1%5D&+r1%3A%3Dr%5B0..1%2C0..1%5D&+linsolve(r1%2Ctran(q1)*b)&+///Comparison%20with%20the%20builtin%20linear%20regression%20command%20of%20Xcas.&+linear_regression(x%2Cb)&+///Solving%20like%20above%20is%20more%20accurate%20than%20solving%20$A^t*A*x=A^t*b$%20because%20the%20condition%20number%20is%20smaller.&+cond(A%2C2)&+///We%20might%20loose%20at%20most%201.5%20digits%20instead%20of%203.&"
                                target="_blank">QR decomposition, least squares, example linear regression</a>
                        </li>
                        <li> Univariate polynomials
                            <a href="#exec&python=0&+///Horner%20method%20to%20evaluate%20a%20polynomial%20at%20a%20point,%20comparison%20with%20the%20builtin%20horner%20command.&+function%20Horner(p%2Ca)%0A%20%20%2F%2F%20p%20list%20of%20coefficients%20by%20decreasing%20order%0A%20%20%2F%2F%20returns%20p%20evaled%20at%20a%0A%20%20local%20c%2Cr%3B%0A%20%20r%3A%3D0%3B%0A%20%20for%20c%20in%20p%20do%0A%20%20%20%20r%3A%3Dr*a%2Bc%3B%0A%20%20od%3B%0A%20%20return%20r%3B%0Affunction%3A%3B&+Horner(%5B1%2C2%2C3%5D%2C4)%3B%20%0Ahorner(%5B1%2C2%2C3%5D%2C4)&+///We%20modify%20the%20previous%20program%20to%20also%20return%20the%20euclidean%20quotient%20of%20$p$%20by%20$x-a$.%0a&+function%20Horner2(p%2Ca)%0A%20%20local%20c%2Cr%2Cq%3B%0A%20%20r%3A%3D0%3B%20q%3A%3D%5B%5D%3B%0A%20%20for%20c%20in%20p%20do%0A%20%20%20%20r%3A%3Dr*a%2Bc%3B%0A%20%20%20%20q.append(r)%3B%0A%20%20od%3B%0A%20%20q%3A%3Dq%5B0..-2%5D%3B%0A%20%20return%20q%2Cr%3B%0Affunction%3A%3B&+Horner2(%5B1%2C2%2C3%5D%2C4)&+///Calling%20Horner2,%20we%20make%20a%20change%20of%20origin,%20i.e.%20express%20$P(X)$%20in%20terms%20of%20the%20$(X-a)^k$,%20and%20compare%20with%20the%20builtin%20ptayl%20command.&+function%20Taylor(p%2Ca)%0A%20%20local%20q%2Cj%2Cn%3B%0A%20%20q%3A%3Dp%3B%0A%20%20n%3A%3Ddegree(p)%3B%0A%20%20for%20j%20from%200%20to%20n%20do%0A%20%20%20%20p%2Cq%5Bj%5D%3A%3DHorner2(p%2Ca)%3B%0A%20%20od%3B%0A%20%20return%20reverse(q)%3B%0Affunction%3A%3B&+Taylor(%5B1%2C2%2C3%5D%2C4)%3B%0Aptayl(%5B1%2C2%2C3%5D%2C4)&"
                               target="_blank">Horner and Taylor</a>
                        </li>
                        <li> Polynomial interpolation
                            <a href="#exec&python=0&+///Interpolation%20of%20$ln(x^2+1)$%20at%2011%20equispaced%20points%20on%20$[0,1]$.&+f(x)%3A%3Dln(x%5E2%2B1)%3B%20n%3A%3D10%3B%20%0AX%3A%3Devalf(seq(j%2Fn%2Cj%2C0%2Cn))%3B%20%0AY%3A%3Dmap(X%2Cf)%3B&+P%3A%3Dinterp(X%2CY)%3B%0A&+plot(%5Bf(x)%2CP%5D%2Cx%3D-1..2%2Ccolor%3D%5Bred%2Cblue%5D)&+plot(1e7*abs(f(x)-P)%2Cx%3D0..1)&+///Runge's%20phenomenon:%20adding%20more%20equispaced%20points%20does%20not%20help.%20Here%20we%20take%20$n+1$%20points%20on%20[-1,1]%20with%20$n=20$.&+f(x)%3A%3D1%2F(1%2B25x%5E2)%3B%20n%3A%3D20%3B%20%0AX%3A%3Dseq(2*j%2Fn-1.0%2Cj%2C0%2Cn)%3A%3B&+gl_y%3D-2..2%3B%0Al%3A%3Dlagrange(X%2Cmap(X%2Cf))%3A%3B%20%0Aplot(%5Bl%2Cf(x)%5D%2Cx%3D-1..1)&+plot(l-f(x)%2Cx%3D-1..1)%0A&+///This%20does%20not%20happen%20with%20Tchebyshev%20points.&+T%3A%3Dseq(cos((j%2B0.5)*pi%2F(n%2B1))%2C%0A%20%20j%2C0%2Cn)%3B&+apply(point%2CT)&+l%3A%3Dlagrange(T%2Cmap(T%2Cf))%3A%3B%20%0Aplot(%5Bl%2Cf(x)%5D%2Cx%3D-1..1)&+plot((l-f(x))%2Cx%3D-1..1)&"
                               target="_blank"> Runge's phenomenom, Tchebyshev points</a>
                        </li>
                        <li> Polynomial GCD
                            <a href="#exec&python=0&+///GCD%20of%20univariate%20polynomials%20with%20integer%20coefficients.&+a%3A%3D(x-1)%5E8*(x%5E2%2B2)%3B%0Ab%3A%3D(x-1)*(x%5E2%2B2)%5E4&+function%20Euclide(a%2Cb)%0A%20%20while%20b!%3D0%20do%0A%20%20%20%20print(b)%3B%0A%20%20%20%20a%2Cb%3A%3Db%2Crem(a%2Cb)%3B%0A%20%20od%3B%0A%20%20return%20a%3B%0Affunction%3A%3B&+Euclide(a%2Cb)&+///Coefficients%20are%20rationals,%20hence%20computations%20are%20more%20expensive%20(numerator%20and%20denominator%20size%20grows%20in%20the%20Euclide%20algorithm).%20To%20avoid%20rationals,%20we%20replace%20division%20by%20pseudo-division%20(this%20does%20not%20change%20the%20gcd).&+function%20Euclide1(a%2Cb)%0A%20%20if%20degree(a)%3Cdegree(b)%20then%20return%20Euclide1(b%2Ca)%3B%20fi%3B%0A%20%20while%20b!%3D0%20do%0A%20%20%20%20print(b)%3B%0A%20%20%20%20a%2Cb%3A%3Db%2Crem(lcoeff(b)%5E(degree(a)-degree(b)%2B1)*a%2Cb)%3B%0A%20%20od%3B%0A%20%20return%20a%3B%0Affunction%3A%3B&+Euclide1(a%2Cb)&+///We%20observe%20that%20the%20coefficient%20sizes%20grows%20rapidly.%20To%20avoid%20that%20we%20can%20replace%20$b$%20by%20it's%20primitive%20part%20(divide%20by%20the%20gcd%20of%20the%20coefficients).&+function%20Euclide2(a%2Cb)%0A%20%20if%20degree(a)%3Cdegree(b)%20then%20return%20Euclide2(b%2Ca)%3B%20fi%3B%0A%20%20while%20b!%3D0%20do%0A%20%20%20%20b%3A%3Dprimpart(b)%3B%0A%20%20%20%20print(b)%3B%0A%20%20%20%20a%2Cb%3A%3Db%2Crem(lcoeff(b)%5E(degree(a)-degree(b)%2B1)*a%2Cb)%3B%0A%20%20od%3B%0A%20%20return%20a%3B%0Affunction%3A%3B&+Euclide2(a%2Cb)&+///It's%20better,%20but%20computing%20the%20content%20(gcd%20of%20coefficients)%20of%20$b$%20at%20each%20step%20is%20still%20expensive.%0aThe%20subresultant%20algorithm%20computes%20a%20divisor%20of%20the%20content.%20This%20coefficient%20is%20not%20optimal,%20but%20almost%20and%20it%20is%20easy%20to%20%0acompute.&+function%20Euclide3(a%2Cb)%0A%20%20local%20g%2Ch%2Cq%3B%0A%20%20if%20degree(a)%3Cdegree(b)%20then%20return%20Euclide3(b%2Ca)%3B%20fi%3B%0A%20%20g%3A%3D1%3B%20h%3A%3D1%3B%20%0A%20%20while%20b!%3D0%20do%0A%20%20%20%20d%3A%3Ddegree(a)-degree(b)%3B%0A%20%20%20%20q%3A%3Dlcoeff(b)%3B%0A%20%20%20%20a%2Cb%3A%3Db%2Crem(q%5E(d%2B1)*a%2Cb)%3B%0A%20%20%20%20b%3A%3Dratnormal(b%2F(g*h%5Ed))%3B%0A%20%20%20%20g%3A%3Dq%3B%20h%3A%3Dq%5Ed%2Fh%5E(d-1)%3B%0A%20%20od%3B%0A%20%20return%20a%3B%0Affunction%3A%3B&+Euclide3(a%2Cb)&+///Modular%20methods%20are%20more%20efficient.%20If%20the%20polynomials%20are%20prime%20together,%20they%20will%20be%20modulo%20any%20prime%20not%20dividing%20the%20resultant%20of%20the%20polynomials,%20it%20will%20easily%20be%20detected.%0aOtherwise,%20we%20rebuild%20the%20GCD%20modulo%20one%20or%20more%20prime%20numbers%20(by%20Chinese%20remaidering)%20that%20return%20the%20minimal%20degree%20and%20we%20test%20divisibility%20of%20$a$%20and%20$b$.%20%0a&+Euclide(a%20mod%2011%2Cb%2B1%20mod%2011)&+g%3A%3DEuclide(a%20mod%2011%2Cb%20mod%2011)&+normal(g%2Flcoeff(g))%20mod%200&"
                               target="_blank">from Euclide to sub-resultant</a>
                        </li>
                        <li>
                            <a
                                href="#exec&python=0&+///%3Ch1%3eLinear%20algebra%20on%20a%20finite%20field.%3C/h1%3e%0aLU%20decomposition%20and%20application%20to%20linear%20system%20solving.&+n%3A%3D5%3B%20p%3A%3D17%3B%20a%3A%3Drandmatrix(n%2Cn%2C1%20mod%20p)&+p%2Cl%2Cu%3A%3Dlu(a)&+function%20myinv(a)%0A%20%20local%20b%2Cc%2Cj%2Cp%2Cl%2Cu%3B%0A%20%20n%3A%3Dsize(a)%3B%0A%20%20b%3A%3Da%3B%20%0A%20%20c%3A%3Didentity(n)%3B%0A%20%20p%2Cl%2Cu%3A%3Dlu(a)%3B%0A%20%20for%20j%20from%200%20to%20n-1%20do%20%0A%20%20%20%20b%5Bj%5D%3A%3Dlinsolve(p%2Cl%2Cu%2Cc%5Bj%5D)%3B%0A%20%20od%3B%0A%20%20return%20b%3B%0Affunction%3A%3B&+myinv(a)%3B%20inv(a)&+///Algorithm%20to%20compute%20the%20characteristic%20polynomial%20by%20interpolation%20in%20$O(n^4)$%20operations.&+function%20polchar(a)%0A%20%20local%20j%2Cp%2Cn%2CI%2CN%2Cg%2Cgj%2CX%2CY%3B%0A%20%20if%20type(a%5B0%2C0%5D)!%3D15%20then%20%0A%20%20%20%20return%20%22expecting%20matrix%20with%20coefficients%20in%20Z%2FpZ%22%3B%20%0A%20%20fi%3B%0A%20%20p%3A%3Da%5B0%2C0%2C2%5D%3B%20%2F%2F%20field%20char.%0A%20%20if%20!isprime(p)%20then%20%0A%20%20%20%20return%20p%2B%22%20is%20not%20prime%22%3B%20%0A%20%20fi%3B%0A%20%20n%3A%3Dsize(a)%3B%0A%20%20I%3A%3Didentity(n)%3B%0A%20%20X%3A%3D%5B%5D%3B%20Y%3A%3D%5B%5D%3B%0A%20%20if%20n%3Cp%20then%0A%20%20%20%20for%20j%20from%200%20to%20n%20do%0A%20%20%20%20%20%20X%5Bj%5D%3A%3Dj%3B%0A%20%20%20%20%20%20Y%5Bj%5D%3A%3Ddet(j*I-a)%3B%0A%20%20%20%20od%3B%0A%20%20%20%20return%20normal(interp(X%2CY))%3B%0A%20%20fi%3B%0A%20%20%2F%2F%20construct%20an%20extension%20of%20Z%2FpZ%0A%20%20N%3A%3Dceil(log(n%2B1)%2Flog(p))%3B%0A%20%20purge(g)%3B%0A%20%20GF(p%2CN%2Cg)%3B%0A%20%20%2F%2F%20interpolation%20at%20g%5Ej%0A%20%20gj%3A%3D1%3B%0A%20%20for%20j%20from%200%20to%20n%20do%0A%20%20%20%20X%5Bj%5D%3A%3Dgj%3B%0A%20%20%20%20Y%5Bj%5D%3A%3Ddet(gj*I-a)%3B%0A%20%20%20%20gj%3A%3Dg*gj%3B%0A%20%20od%3B%0A%20%20return%20normal(interp(X%2CY))%3B%0Affunction%3A%3B&+polchar(a)%3B%20charpoly(a%2Cx)&+a%3A%3Drandmatrix(8%2C8%2C1%20mod%205)&+polchar(a)%3B%20charpoly(a%2Cx)&"
                                target="_blank">
                            Linear algebra over a finite field
                            </a>
                        </li>
                        <li> Groebner  basis
                            <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>.
                            For more intensive computations, activate
			wasm in the settings and open
                            <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 (modular)</a>.
If you want to see informations while a computation is running, run first
<tt>debug_infolevel:=1</tt> (or more), then open the browser console.
                            For really large computations, use native Xcas versions.
                        </li>
                        <li> Arithmetic on multivariate polynomials (requires a browser
                            compatible with Web-Assembly, like 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">Fateman benchmark for 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>
                      <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>
                        <li>
                            Fractals:
                            <ul>
                                <li>
                                    Mandelbrot
                                    <a
                                        href="#exec&python=0&+///Mandelbrot%20fractal,%20not%20using%20symmetry.&+function%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%20for%20y%20from%200%20to%20Y%20do%0A%20%20%20%20c%3A%3D-2.1%2Bi*(h*y%2B0.935)%3B%0A%20%20%20%20for%20x%20from%200%20to%20X-1%20do%0A%20%20%20%20%20%20z%3A%3D0%3B%0A%20%20%20%20%20%20for%20j%20from%200%20to%20Nmax-1%20do%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%20od%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%20od%3B%0A%20%20od%3B%0A%20%20return%20res1%3B%0Affunction%3A%3B&+///Faster%20program%20using%20symmetry.&+function%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%20for%20y%20from%200%20to%20Y%2F2%20do%0A%20%20%20%20c%3A%3D-2.1%2Bi*(h*y%2B0.935)%3B%0A%20%20%20%20for%20x%20from%200%20to%20X-1%20do%0A%20%20%20%20%20%20z%3A%3D0%3B%0A%20%20%20%20%20%20for%20j%20from%200%20to%20Nmax-1%20do%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%20od%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%20od%3B%0A%20%20od%3B%0A%20%20return%20res1%2Cres2%3B%0Affunction%3A%3B&+pixon(1)&+fra1(260%2C222%2C10)&"
                                        target="_blank">Xcas</a>,
                                    <a href="#exec&python=1&+///Mandelbrot%20fractal,%20Python%20compatible%20syntax,%20without%20symmetry%20trick.&+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&+///Mandelbrot%20fractal%20with%20symmetry.&+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>
                                    Newton fractals
                                    <a href="#exec&python=0&+///We%20iterate%20Newton%20method%20to%20find%20the%20roots%20of%20a%20polynomial%20$P$,%20$z[n+1]=z[n]-P(z[n])/P'(z[n])$,%20if%20there%20is%20numeric%20convergence%20we%20color%20the%20initial%20point%20$z[0]$%20of%20the%20sequence%20with%20a%20color%20depending%20on%20the%20root%20number.%0aTwo%20versions%20are%20proposed,%20fsym%20is%20using%20complex%20conjugation%20symmetry%20to%20speedup%20computations%20by%20a%20factor%20about%202.&+function%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%20if%20distance((z%3A%3Dhorner(P%2C(zp%3A%3Dhorner(P%2Cz%2Cnewton))%2Cnewton))%2Czp)%3C1e-4%20or%20abs(z)%3E1e20%20then%20%0A%20%20%20%20%20%20%20%20%20%20break%3B%20%0A%20%20%20%20%20%20%20%20fi%3B%0A%20%20%20%20%20%20od%3B%0A%20%20%20%20%20%20if%20z%3D%3Dundef%20then%20continue%3B%20fi%3B%0A%20%20%20%20%20%20for%20n%20from%200%20to%20rs%20do%0A%20%20%20%20%20%20%20%20if%20distance(z%2Cr%5Bn%5D)%3C1e-4%20then%20break%3B%20fi%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%0Affunction%3A%3B&+function%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%20if%20size(im(P))!%3D0%20then%20return%20%22Polynomial%20must%20have%20real%20coefficients%22%3B%20fi%3B%0A%20%20r%3A%3Dproot(P)%3B%0A%20%20%2F%2F%20extract%20roots%20with%20imaginary%20part%20%3E%3D0%2C%20put%20reals%20at%20the%20end%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%20if%20distance((z%3A%3Dhorner(P%2C(zp%3A%3Dhorner(P%2Cz%2Cnewton))%2Cnewton))%2Czp)%3C1e-4%20or%20abs(z)%3E1e20%20then%20%0A%20%20%20%20%20%20%20%20%20%20break%3B%20%0A%20%20%20%20%20%20%20%20fi%3B%0A%20%20%20%20%20%20od%3B%0A%20%20%20%20%20%20if%20z%3D%3Dundef%20then%20continue%3B%20fi%3B%0A%20%20%20%20%20%20for%20n%20from%200%20to%20rs%20do%0A%20%20%20%20%20%20%20%20if%20distance(z%2Cr%5Bn%5D)%3C1e-4%20then%20break%3B%20fi%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*when(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%0Affunction%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="#exec&python=1&+///We%20iterate%20Newton%20method%20to%20find%20the%20roots%20of%20a%20polynomial%20$P$,%20$z[n+1]=z[n]-P(z[n])/P'(z[n])$,%20if%20there%20is%20numeric%20convergence%20we%20color%20the%20initial%20point%20$z[0]$%20of%20the%20sequence%20with%20a%20color%20depending%20on%20the%20root%20number.%0aTwo%20versions%20are%20proposed%20in%20Python-compatible%20syntax,%20fsym%20is%20using%20complex%20conjugation%20symmetry%20to%20speedup%20computations%20by%20a%20factor%20about%202.&+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(%22Polynomial%20must%20have%20real%20coefficients!%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>
                            </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">
                    From the top you will see:
                    <ul>
                        <li>
                            a panel of buttons: settings, save/restore session,
                            helpers (Xcas logo maths, programming, scientific keyboard, documentation).
                            Some buttons or links are not visible at startup like the x2 or
                            &#x2709; links:
                            <ul>
                                <li> the <strong>x2</strong> (resp. local) link may be used to replicate a
                                    session, right-click to copy/paste the link in Xcas native or
                                    on a static web
                                    page. It is also useful if you stop a computation that would
                                    take too long.
                                <li> the <strong>&#x2709;</strong> link lets you share your session by e-mail.
                                </li>
                            </ul>
                        </li>
                        <li> a <strong>help</strong> area, where you will see short descriptions of the
                            commands you asked the syntax. You can clear the help area with
                            the erase button at the right of the help search field.
                        </li>
                        <li> the <strong>history</strong> area contains levels (0 at the
                            beginning), a level is a pair commandline (written in
                            black)/answer (in blue).
                            You can move levels with the ↑ and ↓ buttons.
                            You can modify an existing commandline, update it with the
                            &#x2705; button or Enter key at the beginning of the field.
                            You can throw a level to the trash with the erase button at the
                            right of the level. You can restore levels from the trash with
                            the Restore button at the bottom of the history, or empty
                            the trash.
                            The link <tt>+</tt> right to the Empty button lets you open
                            a new empty session in a new tab.
                        </li>
                        <li>
                            a <strong>commandline</strong>,
                            type your command or program there,  then tap &#x2705;
                            or hit Enter (type Ctrl-Enter if your input has several lines, or
                            Enter on a blank line).
                            If you want to force a new line, hit Shift-Enter or tap the <tt>\n</tt> button.
                            <br>
                            For example, type <tt>1/2+1/3</tt>
                            or <tt>sin(pi/4)</tt> or <tt>sin(pi/4.0)</tt>.
                            <br>
                            The <tt>Math</tt>, <tt>prog</tt> and <tt>123</tt>
                            buttons may be used to help you fill the commandline.
                            <br>
                            If you know a commandname, type it (or its first letters),
                            for example <tt>factor</tt> then press
                            the <button>F1</button> key or the <button>?</button>
                            button. This will display a
                            <strong>short help</strong> on the command if it exists
                            or give some commandname hints if it does not or is incomplete.
                            <br>
                            For example, click on <tt>math</tt> then <tt>rewrite</tt> then
                            <tt>factor</tt> then <tt>?</tt>, look at the short help at the top,
                            click on one example or complete with x^4-1 then type Enter.
                            <br>
                            You can
                            <strong>select</strong> text  with the <tt>beg</tt>
                            and <tt>end</tt> buttons, remove selection
                            with <tt>del</tt> and paste selection with <tt>cp</tt>.
                            <br>
                            If you evaluate a blank commandline, this will add a
                            <strong>comment</strong> field. You can convert
                            a commandline into a comment (or a comment into a commandline):
                            type /// at the beginning then Enter.
                            You can comment an exisiting level by pressing
                            the &#x270e; key. You can write boldface, italic, etc. in a comment
                            using the buttons below the comment or typing HTML code.
                            If you want to render maths, you have two methods
                            <ul>
                                <li>enter a valid Xcas input between two dollars
                                    (<tt>$...$</tt>), the input will be parsed unevaled and converted to MathML for 2d
                                    display. For example <tt>$x[n+1]^2$</tt> will display x with
                                    exponent n+1, <tt>$A=[[1,2],[3,4]]$</tt> will display a matrix
                                    (it will not modify A), <tt>$integrate(sin(x),x,0,pi)$</tt>
                                    will display the integral of sin(x) between 0 and pi (the integral will not be
                                    computed), <tt>vector(u), vector(A,B)</tt> will display an arrow
                                    over u or AB.
                                    Symbols of sets like ℤ,ℕ may be obtained by entering
                                    <tt>$ZZ$, $NN$</tt>, for example type <tt>$x in QQ$</tt> to get x∈ℚ. HTML code may
                                    also help like <tt>&amp;forall;</tt> for &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.
                                    or copy/paste a symbol from
                                    <a href="https://www.w3schools.com/charsets/ref_utf_math.asp">here</a>.
                                <li> or enter a comment containing at least one pair of
                                    double dollars (<tt>$$...$$</tt>), the whole comment will be
                                    rendered as a LaTeX formatted comment by loading MathJax
                                    (beware that this will not work offline).
                            </ul>
                        </li>
                        <li>
                            a <strong>console</strong> that will display CAS messages,
                            syntax errors or step by step computation for commands that
                            support step by step (like derivative).
                            The console is not displayed if it is empty. You can clear
                            the console or adjust it's height.
                        </li>
                        <li>
                            a <strong>graph 3d</strong> area for 3d commands. This area
                            is not displayed if it is empty.
                        </li>
                    </ul>
                    You can <strong>save</strong> the history by hitting the <tt>&#x1f4be;</tt>
                    button. The filename of the session is displayed in a modifiable text
                    field at the right of the <tt>&#x1f4be;</tt> button, it is <tt>session</tt>
                    by default. You can open a saved session by hitting the <tt>Load</tt>
                    button.
                    You can <strong>export</strong> your worksheet on desktops, this
                    will save the whole HTML code (instead of the commandlines for a
                    session).
                    2d graphs can be saved as SVG 1.2 files (save button at the right of
                    the level).
                    <br>
                    If you have a native Xcas session, you can open it in Xcas for Firefox
                    (native Xcas menu menu File, Clone or from commandline
                    <tt>xcas --online nom_fichier.xws</tt>).
                    <br>
                    Note that Chrome (or the builtin browser of your device) is
                    much slower than Firefox (about 5 times). Moreover Chrome
                    does not have builtin support to display 2d maths with
                    MathML, an additional javascript library (Mathjax) must
                    be retrieved from Internet which is slower and does not
                    work in airplane mode.
                    <br>
                    <strong>It is therefore recommended to run Xcas for Firefox from Firefox</strong>
                    <br>
                    <button class="bouton"
                            onclick="$id('tutointerface').style.display='none';">Hide
                    interface help</button>
                </div>
            </li>
            <li style="display:inline">
                <button class="bouton"
                        onclick="var tmp=$id('tutokbd'); if (tmp.style.display=='none') tmp.style.display='block'; else tmp.style.display='none';">
                <strong>Keyboard</strong></button>
                <div id="tutokbd" style="display:none">
                    Keyboard shortcuts with Alt (or Ctrl if Alt-key is already
                    interpreted by the browser or the OS)
                    <ul>
                        <li> D, cursor right: move focus to the right (or down)
                        <li> G, cursor left: move focus to the left (or up)
                        <li> cursor down: move focus to the right/down twice
                        <li> curseur up: move focus to the left/up twice
                        <li> B: move focus to commandline
                        <li> C: copy current field to command line and move focus to commandline
                        <li> A: move focus to help field
                        <li> TAB: display help on the command at the left of the cursor
                            in the commandline.
                        <li> M: display or hide Math menu
                        <li> P: display or hide Program menu
                        <li> T: show turtle menu
                        <li> E or F: exec history
                        <li> N: clears console
                    </ul>
                </div>
            </li>
            <li style="display:inline">
                <button class="bouton"
                        onclick="var tmp=$id('tutocfg'); if (tmp.style.display=='none') tmp.style.display='block'; else tmp.style.display='none';">
                <strong>Configuration</strong></button>
                <div id="tutocfg" style="display:none">
                    Click on the button at the topleft to modify settings. You can
                    change
                    the default digits number, the angle unit, the step by step mode,
                    etc.
                    If you have a compatible browser, like Firefox&geq;58, you can
                    enable the <tt>wasm</tt> option (Web-Assembly), this makes most
                    computations faster and give access to PARI-GP commands after
                    running <tt>pari()</tt>.
                </div>
            </li>
            <li style="display:inline">
                <button class="bouton" onclick="var tmp=$id('manuels'); if (tmp.style.display=='none') tmp.style.display='block'; else tmp.style.display='none';">
                <strong>Manuals</strong>
                </button>
                <span id="manuels" style="display:none">
                    <strong>Xcas manals</strong> <button class="bouton"
                                                         onclick="$id('manuels').style.display='none';">Hide</button>
                    <br>
                    Most of the documentation is in French, not yet translated.
                    The "hard disk" version of the documentation is available on
                    Linux if you have <tt>giac</tt> installed.
                    Otherwise, please select the Internet version.
                    <ul>
                        <li> Xcas reference guide
                            <a href="file:///usr/share/giac/doc/en/cascmd_en.html"
                               target="_blank">hard disk</a>,
                            <a href="http://www-fourier.univ-grenoble-alpes.fr/~parisse/giac/doc/en/cascmd_en.html"
                               target="_blank">Internet</a>,
                        </li>
                        <li> Symbolic and numeric algorithms (FR):
                            PDF <a href="file:///usr/share/giac/doc/fr/algo.pdf"
                                   target="_blank">hard disk</a>,
                            <a href="http://www-fourier.univ-grenoble-alpes.fr/~parisse/giac/doc/fr/algo.pdf"
                               target="_blank">Internet</a>,
                            HTML <a href="file:///usr/share/giac/doc/fr/algo.html"
                                    target="_blank">hard disk</a>,
                            <a href="http://www-fourier.univ-grenoble-alpes.fr/~parisse/giac/doc/fr/algo.html"
                               target="_blank">Internet</a>,
                        </li>
                        <li> Programmation (FR):
                            <a href="irem/algolycee.html" target="_blank">algorithmique lyc&eacute;e</a>,
                            <a href="file:///usr/share/giac/doc/fr/casrouge/index.html"
                               target="_blank">hard disk</a>,
                            <a href="http://www-fourier.univ-grenoble-alpes.fr/~parisse/giac/doc/fr/casrouge/index.html"
                               target="_blank">Internet</a>,
                        </li>
                        <li> Geometry (FR):
                            <a href="file:///usr/share/giac/doc/fr/casgeo/index.html"
                               target="_blank">hard disk</a>,
                            <a href="http://www-fourier.univ-grenoble-alpes.fr/~parisse/giac/doc/fr/casgeo/index.html"
                               target="_blank">Internet</a>,
                        </li>
                        <li> Simulation (FR):
                            <a href="file:///usr/share/giac/doc/fr/cassim/index.html"
                               target="_blank">hard disk</a>,
                            <a href="http://www-fourier.univ-grenoble-alpes.fr/~parisse/giac/doc/fr/cassim/index.html"
                               target="_blank">Internet</a>,
                        </li>
                        <li> Logo turtle (FR):
                            <a href="file:///usr/share/giac/doc/fr/castor/index.html"
                               target="_blank">hard disk</a>,
                            <a href="http://www-fourier.univ-grenoble-alpes.fr/~parisse/giac/doc/fr/castor/index.html"
                               target="_blank">Internet</a>,
                        </li>
                        <li> Exercises (FR):
                            <a href="file:///usr/share/giac/doc/fr/casexo/index.html"
                               target="_blank">hard disk</a>,
                            <a href="http://www-fourier.univ-grenoble-alpes.fr/~parisse/giac/doc/fr/casexo/index.html"
                               target="_blank">Internet</a>,
                        </li>
                        <li> Amusement (FR):
                            <a href="file:///usr/share/giac/doc/fr/cascas/index.html"
                               target="_blank">hard disk</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>About</strong>
                </button>
                <span id="apropos" style="display:none">
                xcasen.html is a javascript interface, optimized for Firefox, of the
                <a
                    href="http://www-fourier.univ-grenoble-alpes.fr/~parisse/giac/emgiac.tgz">Giac</a>
                computer algebra system compiled with emscripten. The text editors
                are using the <a href="http://codemirror.net">CodeMirror</a>
                javascript library.
                Unlike many CAS web-interfaces, once the page is loaded,
                it does not require a server,
                it runs entirely locally with the javascript engine of your browser.
                It is slower than native code, about 2 times slower for numeric code,
                up to 8 times slower for symbolic code.
                If you run large computations, consider installing
                <a href="http://www-fourier.univ-grenoble-alpes.fr/~parisse/install_en.html">Xcas native</a>!
                <br>
                Giac/Xcas (c) 2018 B. Parisse, R. De Graeve, Institut Fourier, Université
                de Grenoble, GPL3 license. For commercial license,
	    contact us.
	    <br>
	        Optimization, signalprocessing, graph theory code: Luka Marohnić.
	    <br>
                Mathml and SVG code initially written by J.P. Branchard.
                </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>Simplify</strong></button>
                <span id="tutosimplifier" style="display:none">
                    There is no universal method to simplify an expression,
                    sometimes it's better to expand, sometimes to factor, sometimes
                    linearize, etc.. It is therefore important to know
                    some <strong>rewriting</strong>
                    commands, the most important are available by hitting Math then rewrite.
                    <ul>
                        <li>
                            For example, hit <tt>math</tt>, <tt>rewrite</tt>, <tt>simpl</tt>
                            this will insert the command
                            <button onclick="UI.insert(UI.focused,'simplify(')">simplify(</button>,
                            type the expression you want to expand and simplify, then Enter.<br>
                            <button onclick="UI.insert(UI.focused,'normal(')">normal</button>,
                            <button onclick="UI.insert(UI.focused,'reorder(')">reorder</button>,
                            <button onclick="UI.insert(UI.focused,'ratnormal(')">ratnormal</button>
                            are somewhat similar, less powerfull and faster: normal
                            does not search relations between trigonometric functions,
                            ratnormal does only rational simplifications.
                            <tt>reorder</tt> reorders a polynomial according to a list of variables.
                        </li>
                        <li>
                            <button onclick="UI.insert(UI.focused,'factor(')">factor</button>
                            factorizes over R
                            <button onclick="UI.insert(UI.focused,'cfactor(')">cfactor</button>
                            over C
                        </li>
                        <li>
                            <button onclick="UI.insert(UI.focused,'partfrac(')">partfrac</button>
                            partial fraction decomposition over R,
                            <button onclick="UI.insert(UI.focused,'cpartfrac(')">cpartfrac</button>
                            over C.
                        </li>
                        <li>
                            <button onclick="UI.insert(UI.focused,'texpand(')">texpand</button>
                            expand trigonometrics, exponentials and logarithms,
                            <button onclick="UI.insert(UI.focused,'lin(')">lin</button>
                            linearizes exponentials,
                            <button onclick="UI.insert(UI.focused,'tlin(')">tlin</button>
                            linearizes trigonometrics,
                        </li>
                        <li> <button onclick="UI.insert(UI.focused,'subst(')">subst</button>
                            substitution of one or more variables by one or more values
                        </li>
                        <li> Trigonometric conversions <button onclick="UI.insert(UI.focused,'trigcos(')">trigcos</button>,
                            <button onclick="UI.insert(UI.focused,'trigsin(')">trigsin</button>,
                            <button onclick="UI.insert(UI.focused,'trigtan(')">trigtan</button>,
                            <button onclick="UI.insert(UI.focused,'halftan(')">halftan</button>,
                            <button onclick="UI.insert(UI.focused,'tan2sincos(')">tan2sincos</button>
                        </li>
                        <li> Others: <button onclick="UI.insert(UI.focused,'trig2exp(')">trig2exp</button>,
                            <button onclick="UI.insert(UI.focused,'exp2trig(')">exp2trig</button>
                            <button onclick="UI.insert(UI.focused,'pow2exp(')">pow2exp</button>,
                            <button onclick="UI.insert(UI.focused,'exp2pow(')">exp2pow</button>
                            <button onclick="UI.insert(UI.focused,'lncollect(')">lncollect</button>
                            <button onclick="UI.insert(UI.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>Linear algebra </strong>
                </button>
                <span id="tutolinalg" style="display:none">
                    <ul>
                        <li>
                            To create a vector, type the coordinates with comma as separator and
                            [] as delimiters.
                            <button onclick="UI.insert(UI.focused,'dot(')">dot</button>
                            scalar product,
                            <button onclick="UI.insert(UI.focused,'cross(')">cross</button>
                            cross product in dimension 2 or 3
                        </li>
                        <li>
                            Matrices are vectors of vectors of the same size and can be typed in
                            the commandline like <tt>A:=[[1,2],[3,4]]</tt>. Alternatively, you can
                            hit <tt>Math</tt> then <tt>matrix</tt> to open the matrix assistant
                            or <tt>rand</tt> for a matrix with random coefficients.
                        </li>
                        <li>
                            Line and column indices begin at 0 when indexed by <tt>[]</tt> and 1 when
                            indexed by <tt>[[]]</tt>, for
                            example
                            <button onclick="UI.insert(UI.focused,'A[0,1]')">A[0,1]</button>
                            or <button onclick="UI.insert(UI.focused,'A[[1,2]]')">A[[1,2]]</button>.
                        <li>
                            You can use <tt>+,-,*</tt> and <button onclick="UI.insert(UI.focused,'matpow(')">matpow</button>
                            for usual arithmetic operations on matrices.
                        </li>
                        <li>
                            <button onclick="UI.insert(UI.focused,'tran(')">tran</button>
                            transposed, <button onclick="UI.insert(UI.focused,'tran(')">trn</button>: transconjugate,
                            <button onclick="UI.insert(UI.focused,'idn(')">idn</button> identity;
                        </li>
                        <li>
                            <button onclick="UI.insert(UI.focused,'linsolve(')">linsolve</button>
                            linear system,
                            <button onclick="UI.insert(UI.focused,'rref(')">rref</button> :
                            row reduction to echelon form,
                            <button onclick="UI.insert(UI.focused,'p,l,u:=lu(')">det</button>
                            : determinant,
                            <button onclick="UI.insert(UI.focused,'inv(')">inv</button>
                            : inverse,
                            <button onclick="UI.insert(UI.focused,'p,l,u:=lu(')">lu</button>
                            : LU decomposition, can be used in
                            <button onclick="UI.insert(UI.focused,'linsolve(p,l,u,')">linsolve</button>,
                        </li>
                        <li>
                            <button onclick="UI.insert(UI.focused,'charpoly(')">charpoly(</button>
                            characteristic polynomial
                            <button onclick="UI.insert(UI.focused,'pmin(')">pmin(</button>
                            minimal polynomial,
                            <button onclick="UI.insert(UI.focused,'p,d:=jordan(')">p,d:=jordan(</button>
                            eigenvectors and eigenvalues,
                        </li>
                        <li>
                            Matrix factorizations
                            <button onclick="UI.insert(UI.focused,'lu(')">lu</button>,
                            <button onclick="UI.insert(UI.focused,'cholesky(')">cholesky</button>,
                            <button onclick="UI.insert(UI.focused,'qr(')">qr</button>,
                            <button onclick="UI.insert(UI.focused,'svd(')">svd</button>
                        </li>
                        <li> Norms
                            <button onclick="UI.insert(UI.focused,'l1norm(')">l1norm</button>,
                            <button onclick="UI.insert(UI.focused,'l2norm(')">l2norm</button>,
                            <button onclick="UI.insert(UI.focused,'maxnorm(')">maxnorm</button> :
                            <button onclick="UI.insert(UI.focused,'matrix_norm(')">matrix_norm</button>
                            (w.r.t L1, L2 or Linf vector space norm)
                        </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>Arithmetic</strong>
            </button>
            <span id="tutoarit" style="display:none">
            Hit <tt>math</tt> then <tt>arit</tt>.
            Some commands work on integers and polynomials, for example
            <tt>gcd</tt> or <tt>lcm</tt>.
            Otherwise, there are two versions,
            the one working on integers begins with
            <tt>i</tt>, like <tt>irem</tt> (euclidean
            remainder for integers) vs <tt>rem</tt> (euclidean remainder for polynomials).
            <ul>
            <li>
            <button onclick="UI.insert(UI.focused,'gcd(')">gcd</button>,
            <button onclick="UI.insert(UI.focused,'lcm(')">lcm</button> GCD and LCM
            </li>
            <li>
            <button onclick="UI.insert(UI.focused,'irem(')">irem</button>,
            <button onclick="UI.insert(UI.focused,'iquo(')">iquo</button>,
            <button onclick="UI.insert(UI.focused,'iquorem(')">iquorem</button>:
            remainder and quotient (euclidean integer division)
            </li>
            <li>
            <button onclick="UI.insert(UI.focused,'iegcd(')">iegcd</button>
            extended GCD for integers
            <button onclick="UI.insert(UI.focused,'iabcuv(')">iabcuv</button>
            integer solutions of au+bv=c,
            <button onclick="UI.insert(UI.focused,'isprime(')">isprime</button>
            pseudo-primality test,
            <button onclick="UI.insert(UI.focused,'nextprime(')">nextprime</button>,
            <button onclick="UI.insert(UI.focused,'ifactor(')">ifactor</button>
            integer factorization,
            <button onclick="UI.insert(UI.focused,'euler(')">Euler</button> indicatrix,
            <button onclick="UI.insert(UI.focused,'powmod(')">powmod</button>
            fast modular powering.
            </li>
            <li>
            <button onclick="UI.insert(UI.focused,'rem(')">rem</button>,
            <button onclick="UI.insert(UI.focused,'quo(')">quo</button>,
            <button onclick="UI.insert(UI.focused,'quorem(')">quorem</button>:
            remainder and quotient for polynomial euclidean division.
            The default variable is <tt>x</tt>, it can be specified as 3rd argument.
            <li>
            <button onclick="UI.insert(UI.focused,'egcd(')">egcd</button>
            extended gcd for polynomials
            <button onclick="UI.insert(UI.focused,'abcuv(')">abcuv</button>
            polynomial solutions for au+bv=c
            <button onclick="UI.insert(UI.focused,'horner(')">horner</button>
            Horner evaluation,
            <button onclick="UI.insert(UI.focused,'interp(')">interp</button>
            polynomial interpolation
            </li>
            <li>
            Use infix <tt>mod</tt> to work in ℤ/nℤ, for
            example <tt>x^3+5x-11 mod 17</tt>
            is a polynomial with coefficients in ℤ/17ℤ.
            If you must work in a non prime finite field, run
            <button onclick="UI.insert(UI.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>Solve</strong>
            </button>
            <span id="tutosolve" style="display:none">
            <ul>
            <li> Equation and system solving:
            Hit <tt>math</tt>
            then <tt>solve</tt>, select exact or approx. and real or
            complex,
            or enter the commands
            <button onclick="UI.insert(UI.focused,'solve(')">solve</button>
            <button onclick="UI.insert(UI.focused,'csolve(')">csolve</button>
            <button onclick="UI.insert(UI.focused,'fsolve(')">fsolve</button>
            <button onclick="UI.insert(UI.focused,'cfsolve(')">cfsolve</button>)
            </li>
            <li> Differential equation/system solving:
            Hit <tt>math</tt>
            then <tt>calc</tt>
            <button onclick="UI.insert(UI.focused,'desolve(')">desolve</button>
            exact solver,
            <button onclick="UI.insert(UI.focused,'odesolve(')">odesolve</button>
            approx. solver, or <tt>math</tt>, <tt>graph</tt>
            <button onclick="UI.insert(UI.focused,'odeplot(')">ode</button>
            approx. graph.
            </li>
            <li>
            Recurrent sequences:
            hit <tt>math</tt> then <tt>u_n</tt>.
            The
            <button onclick="UI.insert(UI.focused,'rsolve(')">rsolve</button>
            command tries to find an explicit expression for a recurrent sequence.
            </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>Calculus</strong>
            </button>
            <span id="tutoanalyse" style="display:none">
            Hit <tt>math</tt> then <tt>f(x)</tt>
            to study a function, or <tt>u_n</tt> for a sequence,
            or <tt>calc</tt> for calculus commands and assistants for
            discrete sums (<tt>∑</tt>), limits (<tt>limit</tt>),
            derivatives (<tt>∂</tt>),
            antiderivatives and definite integrals (<tt>∫</tt>),
            series expansions
            (<tt>series</tt>).
            <br>
            For example, let's define an univariate function
            <tt>f</tt>, hit <tt>prog</tt> then
            <tt>func</tt>, set
            <tt>f</tt> as function
            <tt>x</tt> as list of arguments and <tt>sin(x^2)</tt> as
            returned value. Or type in the commandline
            <button onclick="UI.insert(UI.focused,'f(x):=sin(x^2):;')"><tt>f(x):=sin(x^2)</tt></button>
            Once <tt>f</tt> is defined, we can compute the value of the function
            and derivative like this:
            <button onclick="UI.insert(UI.focused,'f(sqrt(pi)); f\'(2);f\'(y);')">
            <tt>f(sqrt(pi)); f'(2); f'(y) </tt></button>.
            <br>
            <tt>'</tt> denotes the derivative with respect to <tt>x</tt>,
            for other variables, use
            <button onclick="UI.insert(UI.focused,'diff(')">diff</button>.
            The antiderivative command is
            <button onclick="UI.insert(UI.focused,'integrate(')">integrate</button>, for
            example <button onclick="UI.insert(UI.focused,'integrate(1/(x^4-1))')">integrate(1/(x^4-1));</button>,
            or for a definite integral
            <button onclick="UI.insert(UI.focused,'integrate(1/(x^4+1),x,0,+infinity)')">
            integrate(1/(x^4+1)^4,x,0,+infinity);</button>.
            <br>
            The <button onclick="UI.insert(UI.focused,'limit(')">limit</button> et
            <button onclick="UI.insert(UI.focused,'series(')">series</button>
            commands compute a limit or Taylor series (or asymptotic series expansion)
            for example
            <button onclick="UI.insert(UI.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>Probability </strong></button>
            <span id="tutoproba" style="display:none">
            Hit <tt>math</tt> <tt>rand</tt> opens an assistant that build
            random numbers.
            <br>
            Continuous distributions commands
            <button onclick="UI.insert(UI.focused,'uniformd(')">uniformd</button>,
            <button onclick="UI.insert(UI.focused,'normald(')">normald</button>,
            <button onclick="UI.insert(UI.focused,'studentd(')">studentd</button>,
            <button onclick="UI.insert(UI.focused,'chisquared(')">chisquared</button>,
            <button onclick="UI.insert(UI.focused,'gammad(')">gammad</button>,
            <button onclick="UI.insert(UI.focused,'exponentiald(')">exponentiald</button>,
            <button onclick="UI.insert(UI.focused,'cauchyd(')">cauchyd</button>,
            <button onclick="UI.insert(UI.focused,'fisherd(')">fisherd</button>,
            <button onclick="UI.insert(UI.focused,'betad(')">betad</button>.
            <br>
            Discrete distributions commands
            <button onclick="UI.insert(UI.focused,'binomial(')">binomial</button>,
            <button onclick="UI.insert(UI.focused,'negbinomial(')">negbinomial</button>,
            <button onclick="UI.insert(UI.focused,'geometric(')">geometric</button>,
            <button onclick="UI.insert(UI.focused,'poisson(')">poisson</button>.
            <br>
            Cumulated distributions commands have a
            <tt>_cdf</tt> suffix, one can also get them by passing the
            distribution law and arguments to the <button onclick="UI.insert(UI.focused,'cdf(')">cdf</button> command.
            Inverse cumulated distributions have an
            <tt>_icdf</tt> suffix, there is also an  <button onclick="UI.insert(UI.focused,'icdf(')">icdf</button> command.
            <br>
            The   <button onclick="UI.insert(UI.focused,'histogram(')">histogram</button>
            will display an histogram of a list of value
            (default class minimum 0, default class
            size 1, otherwise pass them as arguments).
            <br>
            The   <button onclick="UI.insert(UI.focused,'markov(')">markov</button>
            command splits a Markov chain transition matrix.
            </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>Graphs </strong>
            </button>
            <span id="tutograph" style="display:none">
            Hit <tt>math</tt>  then <tt>graph</tt>
            (see also <tt>f(x)</tt> for function variations).,
            <br>
            Examples of commands
            <button onclick="UI.insert(UI.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>
            displays the 2d graph of two expressions simultaneously
            (sin(x) and x-x^3/6),
            <button onclick="UI.insert(UI.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>
            displays the 3d graph of x^2-y^2 together with a plane.
            You can move the viewpoint with the mouse.
            <br>
            Some geometry commands:
            <button onclick="UI.insert(UI.focused,'point(')">point</button>,
            <button onclick="UI.insert(UI.focused,'midpoint(')">milieu</button>,
            <button onclick="UI.insert(UI.focused,'line(')">line</button>,
            <button onclick="UI.insert(UI.focused,'bisector(')">bisector</button>,
            <button onclick="UI.insert(UI.focused,'perpen_bisector(')">perpen_bisector</button>,
            <button onclick="UI.insert(UI.focused,'segment(')">segment</button>,
            <button onclick="UI.insert(UI.focused,'triangle(')">triangle</button>,
            <button onclick="UI.insert(UI.focused,'circle(')">circle</button>,
            <button onclick="UI.insert(UI.focused,'ellipse(')">ellipse</button>,
            <button onclick="UI.insert(UI.focused,'hyperbola(')">hyperbola</button>,
            <button onclick="UI.insert(UI.focused,'parabola(')">parabola</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">
            The <tt>Prog</tt> displays assistants
            that will help you enter programmation structures
            (test, loop, function). You can add newlines with the <tt>\n</tt>
            button, or with Shift-Enter (or Enter alone if you modify an
            existing level). <tt>→|</tt> indents the current line.
            Hit <tt>debug</tt> to run a function in step by step mode,
            this will display local variables, it's very useful to debug
            a function.
            <br>
            You can choose syntax compatibility with C/javascript or Python.
            <button onclick="var tmp=$id('progex'); if (tmp.style.display=='none') tmp.style.display='block'; else tmp.style.display='none';">
            <strong>example of program</strong>
            </button>
            <div id="progex" style="display:none">
            Example of program: sum of squares in Xcas syntax
            <br>
            <tt>function f(x)
            <br>
            &nbsp;&nbsp;local y,s;
            <br>
            &nbsp;&nbsp;if x &gt; 100000 then return "Number too large"; fi;
            <br>
            &nbsp;&nbsp;s:=0;
            <br>
            &nbsp;&nbsp;for y from 1 to x do
            <br>
            &nbsp;&nbsp;&nbsp;&nbsp;s:=s+y^2;
            <br>
            &nbsp;&nbsp;od
            <br>
            &nbsp;&nbsp;return s;
            <br>
            end:;
            </tt><br>
            Python compatible syntax<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 "Number too large"<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(UI.focused,'function f(x)\n  local y,s;\n  if x &gt; 100 then return &quot;Number too large&quot; fi;\n  s:=0;\n  for y from 1 to x do\n    s:=s+y^2;\n  od\n  return s;\nend:; ')">Test (Xcas)</button>
            <button onclick="UI.insert(UI.focused,'def f(x):\n    # local y,s\n    if x > 100000:\n        return &quot;Number too large&quot;\n    s=0\n    for y in range(x+1):\n        s=s+y**2\n    return s\n')">Test (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>Turtle</strong>
            </button>
            <span id="tutotortue" style="display:none">
            The turtle is a small robot that moves following the user commands,
            it will trace the moves with a pen with a selectable color. It may
            be used to learn programming.
            <br>
            Click on <tt>Prog</tt> then <tt>Turtle</tt> then <tt>new</tt>
            <br>
            Two levels are created, the first one is for programs/functions that
            will be used to make a figure, the second field begins with the
            command <tt>clearscreen</tt>, it will contain the move commands, including
            calls to functions defined in the first level.
            At the right of the <tt>new</tt> button, you can select move commands,
            <tt>forward</tt>
            (turtle moves forward n steps, default n=10),
            <tt>backward</tt>, <tt>tright</tt>
            (<tt>right</tt> n degrees, default n=90), etc.
            <br>
            For example, click on the line after <tt>clearscreen</tt>,
            then <tt>forward</tt> then <tt>tleft</tt>, press Enter, the turtle
            moves 10 pixels left and will turn left, heading to the top.
            <br>
            The first field is a normal level where you can write utilities
            functions,
            with the help of the prog assistants (test, loop, func).
            <br>
            Example: square, regular polygons
            <a
                href="#exec&python=0&+function%20Square(l)%0A%20%20local%20k%3B%0A%20%20for%20k%20from%201%20to%204%20do%0A%20%20%20%20forward(l)%3B%0A%20%20%20%20left()%3B%0A%20%20od%3B%0Affunction%3A%3B&+%23%0Aclearscreen%0ASquare(40)%0Ajump%2080%0ASquare(40)&+function%20Polygon(l%2Cn)%0A%20%20local%20k%2Ct%3B%0A%20%20t%3A%3D360%2Fn%3B%0A%20%20for%20k%20from%201%20to%20n%20do%0A%20%20%20%20forward(l)%3B%0A%20%20%20%20left(t)%3B%0A%20%20od%3B%0Affunction%3A%3B&+%23%0Aclearscreen%0APolygon(50%2C5)&"
                target="_blank">
            Xcas</a> or
            <a
                href="#exec&python=1&+def%20Square(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%20forward(l)%0A%20%20%20%20%20%20%20%20left()&+%23%0Aclearscreen%0ASquare(40)%0Ajump%2080%0ASquare(40)&+def%20Polygon(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%20forward(l)%0A%20%20%20%20%20%20%20%20left(t)&+%23%0Aclearscreen%0APolygon(50%2C5)&"
                target="_blank">Python</a>,
            <a
                href="#exec&python=0&+sap(n)%3A%3D%7B%0A%20%20triangle_plein(5*n%2C5*n)%3B%0A%20%20left()%20%3B%0A%20%20triangle_plein(5*n%2C5*n)%3B%0A%20%20jump%204*n%3B%0A%20%20triangle_plein(4*n%2C4*n)%3B%0A%20%20right()%20%3B%0A%20%20triangle_plein(4*n%2C4*n)%3B%0A%20%20skip%20-4*n%3B%0A%7D%3A%3B&+sapins2(n)%3A%3D%7B%0A%20%20if%20n%3C%3D1%20then%20%0A%20%20%20%20pencolor%20yellow%3B%20disque%2010%3B%20pencolor%20green%3B%20return%3B%20%0A%20%20fi%3B%0A%20%20pencolor%20green%3B%0A%20%20sap(n)%3B%0A%20%20left(30)%3B%0A%20%20jump%2010*n%3B%0A%20%20right(30)%3B%0A%20%20sapins2(n-2)%3B%0A%20%20right(30)%3B%0A%20%20jump%2010*n%3B%0A%20%20left(30)%3B%0A%20%20sap(n)%3B%0A%7D%3A%3B&+clearscreen%3B%0Askip%2050%3B%0Ajump%20-75%3B%0Asapins2(8)%3B%0Apencolor%20blue%3B%0Asigne%20%22Merry%20Xcas%22&"
                target="_blank">
            Merry Xcas</a>,
            <a
                href="#exec&python=1&+def%20sap(n)%3A%0A%20%20%20%20triangle_plein(5*n%2C5*n)%0A%20%20%20%20left()%0A%20%20%20%20triangle_plein(5*n%2C5*n)%0A%20%20%20%20jump%204*n%0A%20%20%20%20triangle_plein(4*n%2C4*n)%0A%20%20%20%20right()%0A%20%20%20%20triangle_plein(4*n%2C4*n)%0A%20%20%20%20skip%20-4*n&+def%20sapins2(n)%3A%0A%20%20%20%20if%20n%3C%3D1%3A%0A%20%20%20%20%20%20%20%20pencolor%20yellow%0A%20%20%20%20%20%20%20%20disque%2010%20%0A%20%20%20%20%20%20%20%20pencolor%20green%20%0A%20%20%20%20%20%20%20%20return%0A%20%20%20%20pencolor%20green%0A%20%20%20%20sap(n)%0A%20%20%20%20left(30)%0A%20%20%20%20jump%2010*n%0A%20%20%20%20right(30)%0A%20%20%20%20sapins2(n-2)%0A%20%20%20%20right(30)%0A%20%20%20%20jump%2010*n%0A%20%20%20%20left(30)%0A%20%20%20%20sap(n)&+%23%0Aclearscreen%0Askip%2050%0Ajump%20-75%0Asapins2(8)%0Apencolor%20blue%0Asigne%20%22Merry%20Xcas%22&"
                target="_blank">Merry Xcas (Python version)</a>
            <br>
            The French <a
                href="https://www-fourier.univ-grenoble-alpes.fr/~parisse/giac/doc/fr/castor/index.html"
                target="_blank">turtle
            manual</a> explain all these commands and contains many examples
            of scenarios to teach programming to young childrens.
            </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) $id(l[i]).style.display='none';">
            <em>Fold all</em>
            </button>
        </ul>
        </span>
<div id="divhelpoutput" style="max-height: 200px; overflow:auto">
  <table id="helpoutput" title="Aide"
         style="max-width:1000px "></table>
</div>
<div>
  <button id="bouton_math" class="bouton" onclick="UI.show_menu();"
          title="Show or hide math assistants"
  >
    <img WIDTH="28" HEIGHT="28" SRC="logo.png" alt="Maths" align="center">
    Math
  </button>
  <button id="prog_key" class="bouton" title="Programmation" onclick="var tmp=$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'; $id('alpha_keyboard').style.display='none';} else UI.kbdonfuncoff(); if (UI.focusaftereval){ UI.focused.focus(); }"
          title="Show or hide scientific keyboard"
  >123
  </button>
  <button class="bouton" style="vertical-align:bottom"
          onclick="if($id('help').style.display=='none')
                $id('help').style.display='block';
                else $id('help').style.display='none';"
          title="Show or hide documentation"
  >
    <strong>Doc</strong>
  </button>
  <textarea cols="9" class="bouton" style="font-size:large;vertical-align:bottom" id="helptxt"
            title="Short help on a commandname"
            rows=1 onclick="UI.focused=this;" onkeypress="if (event.keyCode!=13) return true;UI.addhelp('?',value); return false;"></textarea>
  <button class="bouton" style="vertical-align:bottom" onmousedown="event.preventDefault()"
          title="Clear help"
          onclick="var helptxt=$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(UI.focused,' \n') ; else UI.insert(UI.focused,' ');">
      <input type="button" style="width:29px;height:35px;"
             name="add_sin" id="add_sin" value="sin"
             onmousedown="event.preventDefault()"
             onClick="UI.insert(UI.focused,value+'(')"
      >
      <input type="button" style="width:29px;height:35px;" name="add_cos"
             id="add_cos"
             value="cos" onmousedown="event.preventDefault()"
             onClick="UI.insert(UI.focused,value+'(')"
      >
      <input type="button" style="width:29px;height:35px;" name="add_tan"
             id="add_tan"
             value="tan" onmousedown="event.preventDefault()" onClick="UI.insert(UI.focused,value+'(')">
      <input type="button" style="width:29px;height:35px;" name="add_ln"
             id="add_ln"
             value="exp" onmousedown="event.preventDefault()" onClick="UI.insert(UI.focused,value+'(')">
      <input type="button" style="width:29px;height:35px;" name="add_^" id="add_^" value="^" onmousedown="event.preventDefault()" onClick="UI.insert(UI.focused,'^')">
      <input type="button" style="width:29px;height:35px;" name="add_7" id="add_7" value="7" onmousedown="event.preventDefault()" onClick="UI.insert(UI.focused,'7')">
      <input type="button" style="width:29px;height:35px;" name="add_8" id="add_8" value="8" onmousedown="event.preventDefault()" onClick="UI.insert(UI.focused,'8')">
      <input type="button" style="width:29px;height:35px;" name="add_9" id="add_9" value="9" onmousedown="event.preventDefault()" onClick="UI.insert(UI.focused,'9')">
      <input type="button" style="width:29px;height:35px;" name="add_/"
             id="add_/"
             value="/" onmousedown="event.preventDefault()"
             onClick="UI.insert(UI.focused,value)"
             title="Division. // is a comment, type mod to work in 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(UI.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(UI.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(UI.focused,UI.xtn)" title="Insert x or t or 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(UI.focused,'∞'); else UI.insert(UI.focused,'pi')">
      <input type="button" style="width:29px;height:35px;" name="add_i"
             id="add_i"
             value="i" onmousedown="event.preventDefault()"
             onClick="UI.insert(UI.focused,'i')" title="Complex square root of -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(UI.focused,'^2'); else  UI.insert(UI.focused,'sqrt(');" title="square root">
      <input type="button" style="width:29px;height:35px;" name="add_4" id="add_4" value="4" onmousedown="event.preventDefault()" onClick="UI.insert(UI.focused,'4')">
      <input type="button" style="width:29px;height:35px;" name="add_5" id="add_5" value="5" onmousedown="event.preventDefault()" onClick="UI.insert(UI.focused,'5')">
      <input type="button" style="width:29px;height:35px;" name="add_6" id="add_6" value="6" onmousedown="event.preventDefault()" onClick="UI.insert(UI.focused,'6')">
      <input type="button" style="width:29px;height:35px;" name="add_*" id="add_*" value="*" onmousedown="event.preventDefault()" onClick="UI.insert(UI.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="alpha keyboard">
      <input type="button" style="width:29px;height:35px;" name="add-=" id="add-=" value="=" onmousedown="event.preventDefault()" onClick="UI.insert(UI.focused,value)">
      <input type="button" style="width:29px;height:35px;" name="add_,"
             id="add_,"
             value="," onmousedown="event.preventDefault()"
             onClick="UI.insert(UI.focused,value)"
             title=", is a field separator for a vector/list component. ' suspends evaluation"
      >
      <input type="button" id="add_infer" value="&lt;"
             onmousedown="event.preventDefault()" onClick="UI.insert(UI.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="move cursor up">
      <input type="button" style="width:29px;height:35px;" name="copy_button" id="copy_button" value="cp"
             onmousedown="event.preventDefault()"
             onClick="UI.insert(UI.focused,UI.selection)"
             title="Copy last commandline to focus"
      >
      <input type="button" style="width:29px;height:35px;" name="add_dosel"
             id="add_dosel"
             value="sel" onmousedown="event.preventDefault()" onClick="UI.selectionne()" title="Select">
      <input type="button" style="width:29px;height:35px;" name="add_1" id="add_1" value="1" onmousedown="event.preventDefault()" onClick="UI.insert(UI.focused,'1')">
      <input type="button" style="width:29px;height:35px;" name="add_2" id="add_2" value="2" onmousedown="event.preventDefault()" onClick="UI.insert(UI.focused,'2')">
      <input type="button" style="width:29px;height:35px;" name="add_3" id="add_3" value="3" onmousedown="event.preventDefault()" onClick="UI.insert(UI.focused,'3')">
      <input type="button" style="width:29px;height:35px;" name="add_-" id="add_-" value="-" onmousedown="event.preventDefault()" onClick="UI.insert(UI.focused,'-')">
    </td>
  </tr>
  <tr>
    <td>
      <input type="button" style="width:29px;height:35px"
             id="shift_key" value="alt" title="Alternatives keys"
             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(UI.focused,value)"
             title=":= stores a value to a variable, for example a:=pi/2; sin(a). ! computes a factorial"
      >
      <input type="button" style="width:29px;height:35px;"
             name="add_semi" id="add_semi" value=";" onmousedown="event.preventDefault()" onClick="UI.insert(UI.focused,value)"
             title="; ends a commands, for example inside a program"
      >
      <input type="button" id="add_super" value="&gt;"
             title=""
             onmousedown="event.preventDefault()" onClick="UI.insert(UI.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="move cursor down"
      >
      <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="End selection">
      <input type="button" style="width:29px;height:35px;" name="add_e"
             id="add_e"
             value="e" onmousedown="event.preventDefault()"
             onClick="UI.insert(UI.focused,'e')"
             title="e is either the basis of exponential or separator between mantissa and exponent of a floating point number"
      >
      <input type="button" style="width:29px;height:35px;" name="add_0" id="add_0" value="0" onmousedown="event.preventDefault()" onClick="UI.insert(UI.focused,'0')">
      <input type="button" style="width:29px;height:35px;" name="add_." id="add_." value="." onmousedown="event.preventDefault()" onClick="UI.insert(UI.focused,'.')">
      <input type="button" style="width:29px;height:35px;" name="add_+" id="add_+" value="+" onmousedown="event.preventDefault()" onClick="UI.insert(UI.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="rewrite"
             onmousedown="event.preventDefault()"
             onClick="$id('assistant_rewrite').style.display='block';UI.funcoff();"
             title="Commands to rewrite expressions"
      >
      <input type="button" style="width:29px;height:35px" name="add_calculus"
             id="add_calculus"
             value="calc" onClick="$id('assistant_calculus').style.display='block';UI.funcoff();"
             title="Calculus commands (diff, integrate, ...)"
      >
      <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; $id('assistant_solve').style.display='block';UI.set_focus('solveeq') ;"
             title="Solve assistant"
      >
      <input type="button" style="width:60px;height:35px"
             name="add_graph" id="add_graph" value="graph"
             onmousedown="event.preventDefault()"
             onClick="$id('assistant_graph').style.display='block';UI.funcoff();"
             title="Graph commands (function, parametric, etc.)"
      >
      <input type="button" style="width:29px;height:35px" name="add_geo"
             id="add_geo"
             value="geometry" onClick="$id('assistant_geo').style.display='block';UI.funcoff();"
             title="Geometry commands">
      <input type="button" style="width:60px;height:35px"
             name="add_arit" id="add_arit" value="arit"
             onmousedown="event.preventDefault()"
             onClick="$id('assistant_arit').style.display='block';UI.funcoff();"
             title="Arithmetic commands">
      <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="Linear algebra commands">
      <input type="button" style="width:29px;height:35px" name="add_mathcomment"
             id="add_mathcomment"
             value="text" onmousedown="event.preventDefault()"
             onClick="UI.eval_cmdline1('///Type a comment, use $...$ (math button) to render math formula (in Xcas syntax)',true)" title="Create a new comment entry.">
    </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;$id('assistant_tabvar').style.display='block';"
             title="Function study assistant"
      >
      <input type="button" style="width:60px;height:35px"
             name="add_rsolve" id="add_rsolve" value="u_n"
             onmousedown="event.preventDefault()"
             onClick="UI.funcoff();UI.savefocused=UI.focused;$id('assistant_suites').style.display='block';UI.xtn='n';"
             title="Recurrent sequence assistant"
      >
      <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;$id('assistant_seq').style.display='block';UI.set_focus('seqexpr')"
             title="Create a sequence of values from an explicit expression"
      >
      <input type="button" style="width:60px;height:35px"
             name="add_tableur" id="add_tableur" value="tabl."
             onmousedown="event.preventDefault()"
             onClick="UI.open_sheet(true);"
             title="Spreadsheet">
      <input type="button" style="width:60px;height:35px"
             name="add_matr" id="add_matr" value="matrx"
             onmousedown="event.preventDefault()"
             onClick="UI.open_sheet(false);"
             title="Matrix assistant">
      <input type="button" style="width:60px;height:35px"
             name="add_stats" id="add_stats" value="stats"
             title="Probability and statistics"
             onmousedown="event.preventDefault()"
             onClick="UI.funcoff();UI.savefocused=UI.focused;var mat=$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';$id('risque_alpha').style.display='none';"
      >
      <input type="button" style="width:60px;height:35px"
             name="add_rand" id="add_rand" value="rand"
             onmousedown="event.preventDefault()"
             onClick="UI.savefocused=UI.focused;$id('assistant_rand').style.display='block';UI.assistant_rand_setdisplay();UI.funcoff();"
             title="assistant to create a random number, list or matrix"
      >
      <input type="button" value="slider" id="add_curseur"
             style="height:35px"
             onclick="UI.addcurseur(String.fromCharCode(UI.paramname),0,-5,5,0.125); UI.paramname++;"
             title="Create a slider"
      >
    </td>
  </tr>
</table>
<div id="progbuttons" style="display:none">
  <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(UI.focused,'\nsi  alors  sinon  fsi; ');UI.moveCaret(UI.focused,-20);UI.funcoff();"
         title="if/then/else test assistant"
  >
  <input type="button" style="width:40px;height:35px"
         id="add_boucle" value="loop" onclick="UI.savefocused=UI.focused; $id('assistant_boucle').style.display='block';$id('assistant_test').style.display='none';$id('assistant_prog').style.display='none'"
         title="for/while loop assistant"
  >
  <input type="button" value="func" title="Function creation assistant" style="width:55px;height:35px" id="add_function" onclick="UI.savefocused=UI.focused;  $id('assistant_boucle').style.display='none';  $id('assistant_test').style.display='none'; $id('assistant_prog').style.display='block';UI.set_focus('funcname');$id('localvarspan').style.display=UI.python_mode?'none':'inline';">
  <input type="button" style="width:46px;height:35px" name="add_debug"
         id="add_debug"
         value="debug" onmousedown="event.preventDefault()"
         onClick="UI.insert(UI.focused,'debug(')"
         title="Debugger, for example debug(f(2,3)) will execute step by step the f function with arguments 2 and 3"
  >
  <input type="button" style="width:29px;height:35px" name="add_//"
         id="add_//"
         value="//" onmousedown="event.preventDefault()" onClick="UI.insert(UI.focused,UI.python_mode?'#':'//');UI.funcoff();" title="comment">
  <input type="button" style="width:29px;height:35px" name="add_nlprog"
         id="add_nlprog"
         value="cmds" onmousedown="event.preventDefault()"
         onClick="UI.hide_show($id('list_cmds')); UI.hide_show_xcas('list_cmds_xcas'); UI.hide_show_python('python_mods');"
         title="List commands">
  <input type="button" style="width:29px;height:35px" name="add_listechaine"
         id="add_listechaine"
         value='graph' onmousedown="event.preventDefault()"
         onClick="UI.hide_show($id('prog_graph_cmds'));"
         title="Strings and sets commands">
  <input type="button" style="width:29px;height:35px"
         id="add_tortue"
         value="Turtle" 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="turtle commands">
  <div id="list_cmds" style="display:none">
    <button class="bouton" onclick="UI.insert(UI.focused,'range(');">range</button>
    <button class="bouton" onclick="UI.insert(UI.focused,'len(');">len</button>
    <button class="bouton" onclick="UI.insert(UI.focused,'append(');">append</button>
    <button class="bouton" onclick="UI.insert(UI.focused,'sorted(');">sort</button>
    <div id="list_cmds_xcas">
    <button class="bouton" onclick="UI.insert(UI.focused,'seq(');">seq</button>
    <button class="bouton" onclick="UI.insert(UI.focused,'concat(');">concat</button>
    <button class="bouton" onclick="UI.insert(UI.focused,'head(');">head</button>
    <button class="bouton" onclick="UI.insert(UI.focused,'tail(');">tail</button>
    <button class="bouton" onclick="UI.insert(UI.focused,'makelist(');">makelist</button>
    <button class="bouton" onclick="UI.insert(UI.focused,'member(');">member</button>
    <button class="bouton" onclick="UI.insert(UI.focused,'revlist(');">revlist</button>
    <button class="bouton" onclick="UI.insert(UI.focused,'mid(');">mid</button>
    <button class="bouton" onclick="UI.insert(UI.focused,'suppress(');">suppress</button>
    <button class="bouton" onclick="UI.insert(UI.focused,'select(');">select</button>
    <button class="bouton" onclick="UI.insert(UI.focused,'count(');">count</button>
    <strong>set[]</strong>
    <button class="bouton" onclick="UI.insert(UI.focused,'intersect(');">intersect</button>
    <button class="bouton" onclick="UI.insert(UI.focused,'minus(');">minus</button>
    <button class="bouton" onclick="UI.insert(UI.focused,'union(');">union</button>
    <button class="bouton" onclick="UI.insert(UI.focused,'est_element(');">est_element</button>
    <button class="bouton" onclick="UI.insert(UI.focused,'est_inclus(');">est_inclus</button>
    <br>
    <strong> ""</strong>
    <button class="bouton" onclick="UI.insert(UI.focused,'asc(');">asc</button>
    <button class="bouton" onclick="UI.insert(UI.focused,'char(');">char</button>
    <button class="bouton" onclick="UI.insert(UI.focused,'inString(');">inString</button>
    <button class="bouton" onclick="UI.insert(UI.focused,'gauche(');">gauche</button>
    <button class="bouton" onclick="UI.insert(UI.focused,'ord(');">ord</button>
    <button class="bouton" onclick="UI.insert(UI.focused,'droit(');">droit</button>
    <button class="bouton" onclick="UI.insert(UI.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="Type ; on an empty commandline to display graph." 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(');">circle</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');">red</button><button class="bouton" onclick="UI.insert_focused('green');">green</button><button class="bouton" onclick="UI.insert_focused('blue');">blue</button><button class="bouton" onclick="UI.insert_focused('yellow');">yellow</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="Inside MicroPython, type , on an empty commandline to display graph." 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="clear" onmousedown="event.preventDefault()"
           onClick="if (UI.python_mode){ UI.eval_cmdline1('# script functions\nfrom turtle import *\nreset()\n',true);UI.eval_cmdline1(UI.micropy?'.':'clearscreen # Move script\n',true);} else {UI.eval_cmdline1('/* utility functions for the script */\n',true); UI.eval_cmdline1('/* Move script*/\nclearscreen;\n',true);}" title="Create a turtle picture. Type . in an empty commandline to display turtle.">
    <input type="button" style="width:46px;height:35px" name="add_avance"
           id="add_avance"
           value="forward" onmousedown="event.preventDefault()"
           onClick="UI.insertsemi(UI.focused,'forward(');" title="n steps forward (defaut 10)">
    <input type="button" style="width:46px;height:35px" name="add_recule"
           id="add_recule"
           value="backward" onmousedown="event.preventDefault()"
           onClick="UI.insertsemi(UI.focused,'backward(');" title="n steps backward (defaut 10)">
    <input type="button" style="width:46px;height:35px" name="add_tourne_droite"
           id="add_tourne_droite"
           value="tright" onmousedown="event.preventDefault()"
           onClick="UI.insertsemi(UI.focused,'right(');" title="turn right n degrees (default 90)">
    <input type="button" style="width:46px;height:35px" name="add_tourne_gauche"
           id="add_tourne_gauche"
           value="tleft" onmousedown="event.preventDefault()"
           onClick="UI.insertsemi(UI.focused,'left(');" title="turn left n degrees (default 90)">
    <input type="button" style="width:46px;height:35px" name="add_crayon"
           id="add_crayon"
           value="pen" onmousedown="event.preventDefault()"
           onClick="UI.insertsemi(UI.focused,'pencolor(');" title="change color for the turtle pen">
    <input type="button" style="width:46px;height:35px" name="add_rond"
           id="add_rond"
           value="arc" onmousedown="event.preventDefault()"
           onClick="UI.insertsemi(UI.focused,UI.micropy?'circle(':'rond ');" title="Arc of circle">
    <input type="button" style="width:46px;height:35px" name="add_ecris"
           id="add_ecris"
           value="write" onmousedown="event.preventDefault()"
           onClick="UI.insertsemi(UI.focused,UI.micropy?'write(':'ecris ');" title="Write a string">
    <span id="boutons_tortue_xcas">
    <input type="button" style="width:46px;height:35px" name="add_pas_de_cote"
           id="add_pas_de_cote"
           value="skip" onmousedown="event.preventDefault()"
           onClick="UI.insertsemi(UI.focused,'skip ');" title="turtle jumps n step to the right (default 10)">
    <input type="button" style="width:46px;height:35px" name="add_saute"
           id="add_saute"
           value="jump" onmousedown="event.preventDefault()"
           onClick="UI.insertsemi(UI.focused,'jump ');" title="turtle jumps n steps (default 10)">
    <br>
    <input type="button" style="width:46px;height:35px" name="add_disque"
           id="add_disque"
           value="farc" onmousedown="event.preventDefault()"
           onClick="UI.insertsemi(UI.focused,'disque ');" title="Filled arc of circle">
    <input type="button" style="width:46px;height:35px" name="add_rectangle_plein"
           id="add_rectangle_plein"
           value="rectangle" onmousedown="event.preventDefault()"
           onClick="UI.insertsemi(UI.focused,'rectangle_plein ');" title="Filled rectangle">
    <input type="button" style="width:46px;height:35px" name="add_triangle_plein"
           id="add_triangle_plein"
           value="triangle" onmousedown="event.preventDefault()"
           onClick="UI.insertsemi(UI.focused,'triangle_plein ');" title="Filled triangle">
    <input type="button" style="width:46px;height:35px" name="add_repete"
           id="add_repete"
           value="repeat" onmousedown="event.preventDefault()"
           onClick="UI.insertsemi(UI.focused,'repete ');"
           title="Repeat one or more instructions">
    <input type="button" style="width:46px;height:35px" name="tortue_maillage"
           id="tortue_maillage"
           value="mesh" onmousedown="event.preventDefault()"
           onClick="UI.turtle_maillage=(UI.turtle_maillage+1)%3" title="Change mesh type (quad, triang, none)">
</span>
    <input type="button" style="width:46px;height:35px" name="tortue_clear"
           id="tortue_clear"
           value="&#x274C;" onmousedown="event.preventDefault()"
           onClick="$id('boutons_tortue').style.display='none'" title="Remove turtle buttons">
  </div>
</div>
<div id="assistant_rewrite" style="display:none">
  <button class="bouton" onclick="UI.insert(UI.focused,'simplify(')"
          title="Tries to simplify an expression.">simpl.
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'normal(')"
          title="Expands, reduce to an irreducible fraction">normal
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'c')" title="Prefix for factorization over C">c</button>
  <button class="bouton" onclick="UI.insert(UI.focused,'factor(')" title="Factorization, for example factor(x^4-1). Use cfactor to factor over C">factor</button>
  <button class="bouton" onclick="UI.insert(UI.focused,'partfrac(')" title="Partial fraction decomposition. Use cpartfrac over C">partf</button>
  <button class="bouton" onclick="UI.insert(UI.focused,'subst(')" title="Substitution">subst</button>
  <button class="bouton" onclick="UI.insert(UI.focused,'reorder(')" title="Change variable order in a polynomial">reord</button>
  <br>
  <button class="bouton" onclick="UI.insert(UI.focused,'texpand(')"
          title="Expand sin/cos/tan/exp/ln">texpand
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'tlin(')"
          title="Linearize trigonometric expressions">tlin
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'tcollect(')"
          title="Collect trigonometric expressions">tcoll.
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'trigsin(')"
          title="Rewrite with sin">trigsin
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'trigcos(')"
          title="Rewrite with cos">cos
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'trigtan(')"
          title="Rewrite with tan">tan
  </button>
  <button class="bouton"
          onclick="UI.insert(UI.focused,'halftan(')"
          title="Rewrite in terms of tan of the half angle">halftan
  </button>
  <br>
  <button class="bouton" onclick="UI.insert(UI.focused,'trig2exp(')"
          title="sin/cos/tan in terms of exp(i*.)">trig2exp
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'exp2trig(')" title="exp(i*.)->cos(.)+i*sin(.)">exp2trig</button>
  <button class="bouton" onclick="UI.insert(UI.focused,'lin(')" title="Linearize exponentials">lin</button>
  <button class="bouton" onclick="UI.insert(UI.focused,'lncollect(')"
          title="Collect logarithms">lncoll.
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'exp2pow(')" title="e^(a*ln(b))->b^a">exp2^</button>
  <button class="bouton" onclick="UI.insert(UI.focused,'pow2exp(')" title="b^a->e^(a*ln(b))">^2exp</button>
  <button class="bouton"
          onclick="$id('assistant_rewrite').style.display='none'">&#x274C;
  </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="Graph an expression, for example plotfunc(sin(x),x===-5..5,xstep===0.1)">plot
  </button>
  <button class="bouton" onmousedown="event.preventDefault()"
          onClick="UI.funcoff();UI.savefocused=UI.focused;
                $id('assistant_plotimplicit').style.display='block';UI.set_focus('plotimplicitexprf');"
          title="Graphe an implicit curve, for example plotimplicit(x^2+x*y+y^2===3)">implicit
  </button>
  <button class="bouton" onmousedown="event.preventDefault()"
          onClick="UI.funcoff();UI.savefocused=UI.focused;$id('assistant_plotparam').style.display='block';UI.xtn='t';"
          title="Graph a parametric curve, for example 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; $id('assistant_plotpolar').style.display='block';UI.xtn='t'; UI.set_focus('plotpolarexpr');"
          title="Graph a polar curve, for example plotpolar(sin(3*t),t)">polar
  </button>
  <button class="bouton" onmousedown="event.preventDefault()" onClick="UI.funcoff();UI.savefocused=UI.focused;$id('assistant_plotfield').style.display='block';UI.set_focus('plotfieldexprf');"
          title="Slopefield of a differential equation, for example plotfield(sin(t*y),[t===-5..5,y===-3..3],xstep===0.5,ystep===0.5))">field
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'plotode(')"
          title="Graph of a solution of a differential equation">ode
  </button>
  <br>
  <button class="bouton" onclick="UI.insert(UI.focused,'plotseq(')"
          title="Web graph of a recurrent sequence"
  >suite
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'plotlist(')"
          title="Draw points (i,y_i) for a list [y_i]"
  >liste
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'moustache(')"
          title="Boxwhiskers">whisker
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'histogram(')"
          title="Histogram">histo.
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'scatterplot(')"
          title="Scatterplot">scatter
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'polygonplot(')"
          title="Polygonal line from a list of points"
  >polyg.
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'linear_regression_plot(')"
          title="Linear regression plot"
  >regr.
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'bar_plot(')"
          title="Barplot">bar
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'plotcdf(')"
          title="Cumulated frequency graph for a probability distribution"
  >cdf
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'plotcontour(')"
          title="Level curves for a 2-var function"
  >level
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'plotarea(')"
          title="Area under the curve"
  >area
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'bezier(')"
          title="Bezier curve">bezier
  </button>
  <button class="bouton"
          onclick="$id('assistant_graph').style.display='none'">&#x274C;
  </button>
  <div id="assistant_plotfunc" style="display:none">
    Choose
    <button class="bouton" onclick="$id('assistant_plotfunc1var').style.display='block';$id('assistant_plotfunc2var').style.display='none';UI.set_focus('plotfuncexpr');">curve</button>
    or
    <button class="bouton" onclick="$id('assistant_plotfunc1var').style.display='none';$id('assistant_plotfunc2var').style.display='block';UI.set_focus('plotfunc2expr');">surface</button>
    <div id="assistant_plotfunc1var" style="display:none">
      Expression <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                           id="plotfuncexpr" title="Expression, for example x^2" rows=1></textarea><br>
      variable <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                         id="plotfuncvarname" title="Variable name, for example x" rows=1>x</textarea><br>
      xmin <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                     id="plotfuncvarmin" title="Start value" rows=1>-4</textarea><br>
      xmax <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                     id="plotfuncvarmax" title="End value" rows=1>4</textarea><br>
      xstep <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                      id="plotfuncvarstep" title="Step (between two successive evaluations of the expression)" rows=1>0.0625</textarea>
      <br>
      <button class="bouton" onclick="UI.assistant_plotfunc1var_ok();">&#x2705;</button>
      <button class="bouton"
              onclick="UI.focused=UI.savefocused;$id('assistant_plotfunc').style.display='none'">&#x274C;
      </button>
      <button class="bouton"
              onclick="$id('plotfuncexpr').value='';$id('plotfuncvarname').value='';$id('plotfuncvarmin').value='';$id('plotfuncvarmax').value='';$id('plotfuncvarstep').value='';">Clear
      </button>
      <button class="bouton" onclick="$id('plotfuncexpr').value='x^2';$id('plotfuncvarname').value='x';$id('plotfuncvarmin').value='-4';$id('plotfuncvarmax').value='4';">Example</button>
    </div>
    <div id="assistant_plotfunc2var" style="display:none">
      Expression <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                           id="plotfunc2expr" title="Expression, for example x^2-y^2" rows=1></textarea><br>
      1&egrave;re variable <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                                     id="plotfunc2varx" title="First variable, for example x===-3..3" rows=1>x===-3..3</textarea><br>
      2&egrave;me variable <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                                     id="plotfunc2vary" title="second variable, for example y===-3..3" rows=1>y===-3..3</textarea><br>
      xstep <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                      id="plotfunc2varxstep" title="Pas entre 2 &eacute;valuations successives de l'expression" rows=1>0.25</textarea><br>
      ystep <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                      id="plotfunc2varystep" title="Step (between two successive evaluations of the expression)" rows=1>0.25</textarea>
      <br>
      <button class="bouton" onclick="UI.assistant_plotfunc2var_ok();">&#x2705;</button>
      <button class="bouton"
              onclick="UI.focused=UI.savefocused;$id('assistant_plotfunc').style.display='none'">&#x274C;
      </button>
      <button onclick="$id('plotfunc2expr').value='';$id('plotfunc2varx').value='x';$id('plotfunc2vary').value='y';$id('plotfunc2varxstep').value='';$id('plotfunc2varystep').value='';">Clear
      </button>
      <button onclick="$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';">Example</button>
    </div>
  </div>
  <div id="assistant_plotparam" style="display:none">
    Choose parametric
    <button class="bouton"
            onclick="$id('assistant_plotparam1var').style.display='block';$id('assistant_plotparam2var').style.display='none';UI.set_focus('plotparamexprx');">curve
    </button>
    or parametric
    <button class="bouton"
            onclick="$id('assistant_plotparam1var').style.display='none';$id('assistant_plotparam2var').style.display='block';UI.set_focus('plotparam2exprx');">surface
    </button>
    <button class="bouton"
            onclick="UI.focused=UI.savefocused;$id('assistant_plotparam').style.display='none'">&#x274C;
    </button>
    <br>
    <div id="assistant_plotparam1var" style="display:none">
      x(t)= <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                      id="plotparamexprx" title="Expression of x(t), for example 2*cos(t)" rows=1></textarea><br>
      y(t)= <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                      id="plotparamexpry" title="Expression of y(t), for example 3*sin(t)" rows=1></textarea><br>
      variable<textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                        id="plotparamvarname" title="variable name, for example t" rows=1>t</textarea><br>
      tmin <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                     id="plotparamvarmin" title="start value" rows=1>-4</textarea><br>
      tmax <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                     id="plotparamvarmax" title="end value" rows=1>4</textarea><br>
      tstep <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                      id="plotparamvarstep" title="Step (between two successive evaluations of the expression)" rows=1>0.0625</textarea>
      <br>
      <button class="bouton" onclick="UI.assistant_plotparam_ok();;">&#x2705;</button>
      <button class="bouton"
              onclick="UI.focused=UI.savefocused;$id('assistant_plotparam').style.display='none'">&#x274C;
      </button>
      <button class="bouton"
              onclick="$id('plotparamexprx').value='';$id('plotparamexpry').value='';$id('plotparamvarname').value='';$id('plotparamvarmin').value='';$id('plotparamvarmax').value='';$id('plotparamvarstep').value='';">Clear
      </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';">Example</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, for example 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, for example 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, for example v" rows=1></textarea><br>
      1&egrave;re variable <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                                     id="plotparam2varx" title="First variable, for example 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="second variable, for example 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="Step (between two successive evaluations of the expression)" rows=1>0.25</textarea><br>
      vstep <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                      id="plotparam2varystep" title="Step (between two successive evaluations of the expression)" rows=1>0.25</textarea>
      <br>
      <button class="bouton" onclick="UI.assistant_plotparam2var_ok();">&#x2705;</button>
      <button class="bouton"
              onclick="UI.focused=UI.savefocused;$id('assistant_plotparam').style.display='none'">&#x274C;
      </button>
      <button class="bouton"
              onclick="$id('plotparam2exprx').value='';$id('plotparam2expry').value='';$id('plotparam2exprz').value='';$id('plotparam2varx').value='u';$id('plotparam2vary').value='v';$id('plotparam2varxstep').value='';$id('plotparam2varystep').value='';">Clear
      </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';$id('plotparam2varystep').value='0.25';">Example</button>
    </div>
  </div>
  <div id="assistant_plotimplicit" style="display:none">
    f(x,y)= <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                      id="plotimplicitexprf" title="Expression, for example x^3+x-y^2-1" rows=1></textarea><br>
    Variable x<textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                        id="plotimplicitvarx" title="First variable, for example x===-3..3" rows=1>x===-3..3</textarea><br>
    Variable y<textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                        id="plotimplicitvary" title="Second variable, for example y===-3..3" rows=1>y===-3..3</textarea><br>
    xstep <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                    id="plotimplicitvarxstep" title="Step (between two successive evaluations of the expression)" rows=1>0.25</textarea><br>
    ystep <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                    id="plotimplicitvarystep" title="Step (between two successive evaluations of the expression)" rows=1>0.25</textarea><br>
    niveaux=<textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                      id="plotimplicitlevel" title="Levels to be plotted, keep empty for none, or input a list"
                      rows=1></textarea>
    <br>
    <button class="bouton" onclick="UI.assistant_plotimplicit_ok();">&#x2705;</button>
    <button class="bouton"
            onclick="UI.focused=UI.savefocused;$id('assistant_plotimplicit').style.display='none'">&#x274C;
    </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=''">Clear
    </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=''">Example 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]'">Example 2</button>
  </div>
  <div id="assistant_plotfield" style="display:none">
    Slopefield for a differential equation dx/dt=f(x,t) or autonomous 2-d system d[x,y]/dt=f(x,y)<br>
    f=<textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                id="plotfieldexprf" title="Expression, for example x^3+x-y^2-1" rows=1></textarea><br>
    Variable t (or x)<textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                               id="plotfieldvarx" title="First variable, for example 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="second variable, for example 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="Step (between two successive evaluations of the expression)" rows=1>0.25</textarea><br>
    ystep <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                    id="plotfieldvarystep" title="Step (between two successive evaluations of the expression)" rows=1>0.25</textarea><br>
    init=<textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                   id="plotfieldinit" title="Optionnal list of initial conditions" rows=1></textarea>
    <br>
    <button class="bouton" onclick="UI.assistant_plotfield_ok();">&#x2705;</button>
    <button class="bouton"
            onclick="UI.focused=UI.savefocused;$id('assistant_plotfield').style.display='none'">&#x274C;
    </button>
    <button class="bouton"
            onclick="$id('plotfieldexprf').value='';$id('plotfieldvarx').value='x';$id('plotfieldvary').value='y';$id('plotfieldvarxstep').value='';$id('plotfieldvarystep').value='';$id('plotfieldinit').value=''">Clear
    </button>
    <button class="bouton" onclick="$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';$id('plotfieldinit').value='[[0,1],[0,2]]'">Example 1d</button>
    <button class="bouton" onclick="$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';$id('plotfieldinit').value='seq([0,j],j,-3,3)'">Example a 2d</button>
    <button class="bouton" onclick="$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';$id('plotfieldinit').value='seq([0,j],j,-3,3)'">Example b 2d</button>
  </div>
  <div id="assistant_plotpolar" style="display:none">
    Polar curve <br>
    expression <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                         id="plotpolarexpr" title="Expression, for example sin(3*t)" rows=1></textarea><br>
    variable θ <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                         id="plotpolarvarname" title="variable name, for example t" rows=1>t</textarea><br>
    θmin <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                   id="plotpolarvarmin" title="start value" rows=1></textarea><br>
    θmax <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                   id="plotpolarvarmax" title="end value" rows=1></textarea><br>
    θstep <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                    id="plotpolarvarstep" title="Step (between two successive evaluations of the expression)" rows=1></textarea>
    <br>
    <button class="bouton" onclick="UI.assistant_plotpolar_ok();">&#x2705;</button>
    <button class="bouton" onclick="UI.focused=UI.savefocused;$id('assistant_plotpolar').style.display='none'">&#x274C;</button>
    <button class="bouton"
            onclick="$id('plotpolarexpr').value='';$id('plotpolarvarname').value='';$id('plotpolarvarmin').value='';$id('plotpolarvarmax').value='';$id('plotpolarvarstep').value='';">Clear
    </button>
    <button class="bouton" onclick="$id('plotpolarexpr').value='sin(3*t)';$id('plotpolarvarname').value='t';$id('plotpolarvarmin').value='0';$id('plotpolarvarmax').value='pi';$id('plotpolarvarstep').value='';">Example</button>
  </div>
</div>
<div id="assistant_calculus" style="display:none">
  <button class="bouton" onmousedown="event.preventDefault()" onClick="UI.funcoff();UI.savefocused=UI.focused; $id('assistant_limit').style.display='block';UI.set_focus('limitexpr') ;" title="limit of an expression as a variable tends to a limite, for example limit(sin(x)/x,x,0). For unidirectional limit add 1 or -1 as last argument">limit</button>
  <button class="bouton" onmousedown="event.preventDefault()"
          onClick="UI.funcoff();UI.savefocused=UI.focused;$id('assistant_diff').style.display='block';UI.set_focus('diffexpr')
                ;" title="Derivative of an expression. For a function f, for example f(x):=sin(x^2), the derivative of f is f', for example g:=f' or f'(2)">∂
  </button>
  <button class="bouton" onmousedown="event.preventDefault()"
          onClick="UI.funcoff();UI.savefocused=UI.focused;
                $id('assistant_series').style.display='block';UI.set_focus('seriesexpr')
                ;" title="Taylor/series expansion, for example series(sin(x),x=0,5,polynom). Without the polynom option, no remainder term is returned. For unidirectional series expansion, add optional parameter 1 or -1 before polynom"> series
  </button>
  <button class="bouton" onmousedown="event.preventDefault()"
          onClick="UI.funcoff();UI.savefocused=UI.focused;$id('assistant_sum').style.display='block';UI.set_focus('sumexpr'); " title="Discrete sum, for example ∑(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; $id('assistant_int').style.display='block';UI.set_focus('intexpr');"
          title="Integrals computation, for example ∫(x^2*sin(x)*exp(x),x) or ∫(1/(x^4+1),x,0,inf)">∫
  </button>
  <button class="bouton"
          onmousedown="event.preventDefault()"
          onClick="UI.funcoff();UI.savefocused=UI.focused;$id('assistant_desolve').style.display='block';UI.set_focus('desolveeq');"
          title="Differential equation solver, for example desolve(y''+y=0), desolve(y'+y=0,y(0)=1)">desolve
  </button>
  <br>
  <button class="bouton" onclick="UI.insert(UI.focused,'ilaplace(')"
          title="ilaplace: inverse Laplace transform">i
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'laplace(')"
          title="Laplace transform">laplace
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'odesolve(')"
          title="odesolve: approx differential equation solver">o
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'desolve(')"
          title="Differential equation solver">desolve
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'ifft(')"
          title="ifft: inverse Fast Fourier transform">i
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'fft(')"
          title="Fast Fourier transform">fft
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'invztrans(')"
          title="invztrans: inverse z-transform of a rational fraction">inv
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'ztrans(')"
          title="z-transform">ztrans
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'grad(')"
          title="Gradient">grad
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'hessian(')"
          title="Hessian">hess
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'curl(')"
          title="Rotationnal">curl
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'divergence(')"
          title="Divergence">div
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'vpotential(')"
          title="vpotential: vector potential">v
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'potential(')"
          title="Potentiel">poten.
  </button>
  <button class="bouton"
          onclick="$id('assistant_calculus').style.display='none'">&#x274C;
  </button>
  <div id="assistant_desolve" style="display:none">
    Differential equation
    <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
              id="desolveeq" title="for example y'+t*y=t^2" rows=1
              cols=40></textarea>
    <br>
    time-variable
    <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
              id="desolvevar" title="for example t" rows=1 cols=3>t</textarea>,
    unknown
    <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
              id="desolvey" title="for example y" rows=1 cols=3>y</textarea>
    <br>
    Initial conditions (optional)
    <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
              id="desolveinit" title="for example y(0)=1,y'(0)=0" rows=1
              cols=20></textarea>
    <br>
    <button class="bouton" onmousedown="event.preventDefault()"
            onclick="UI.set_focus('desolveeq');UI.insert(UI.focused,'t')">t
    </button>
    <button class="bouton" onmousedown="event.preventDefault()"
            onclick="UI.set_focus('desolveeq') ;UI.insert(UI.focused,'y\'\'')">y''
    </button>
    <button class="bouton" onmousedown="event.preventDefault()"
            onclick="UI.insert(UI.focused,'y\'')">y'
    </button>
    <button class="bouton" onmousedown="event.preventDefault()"
            onclick="UI.insert(UI.focused,'y')">y
    </button>
    <br>
    <button class="bouton"
            onclick="UI.assistant_desolve_ok();">&#x2705;
    </button>
    <button class="bouton" onclick="UI.focused=UI.savefocused;$id('assistant_desolve').style.display='none'">&#x274C;</button>
    <button class="bouton" onclick="$id('desolveeq').value='';$id('desolvevar').value='';$id('desolvey').value='';$id('desolveinit').value='';">Clear</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';">Order 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';">Order 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]'">System</button>
  </div>
  <div id="assistant_series" style="display:none">
    Series expansion <br>
    expression <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                         id="seriesexpr" title="Expression, for example sin(x)" rows=1></textarea><br>
    variable <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                       id="seriesvarname" title="variable name, for example x" rows=1>x</textarea><br>
    at <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                 id="seriesvarlim" title="Limit point" rows=1></textarea><br>
    order <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                    id="seriesvarorder" title="Order" rows=1></textarea><br>
    Polynom <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                      id="seriesvarstep" title="The 'polynom' option suppress the remainder term in the Taylor expansion" rows=1>polynom</textarea>
    <br>
    <button class="bouton" onclick="UI.assistant_series_ok();">&#x2705;</button>
    <button class="bouton" onclick="UI.focused=UI.savefocused;$id('assistant_series').style.display='none'">&#x274C;</button>
    <button class="bouton"
            onclick="$id('seriesexpr').value='';$id('seriesvarname').value='';$id('seriesvarlim').value='';$id('seriesvarorder').value='';">Clear
    </button>
    <button class="bouton" onclick="$id('seriesexpr').value='sin(x)/x';$id('seriesvarname').value='x';$id('seriesvarlim').value='0';$id('seriesvarorder').value='5';$id('seriesvarstep').value='polynom';">Example</button>
  </div>
  <div id="assistant_limit" style="display:none">
    Limit :<br>
    expression <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                         id="limitexpr" title="Expression, for example sin(x)/x" rows=1></textarea><br>
    variable <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                       id="limitvarname" title="variable name, for example x" rows=1>x</textarea><br>
    at <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                 id="limitvarlim" title="Limit at value" rows=1></textarea><br>
    Direction (optional) <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                                   id="limitvardir" title="-1: limite from left, 1: from right" rows=1></textarea>
    <br>
    <button class="bouton" onclick="UI.assistant_limit_ok();">&#x2705;</button>
    <button class="bouton" onclick="UI.focused=UI.savefocused;$id('assistant_limit').style.display='none'">&#x274C;</button>
    <button class="bouton"
            onclick="$id('limitexpr').value='';$id('limitvarname').value='';$id('limitvarlim').value='';$id('limitvardir').value='';">Clear
    </button>
    <button class="bouton" onclick="$id('limitexpr').value='sin(x)/x';$id('limitvarname').value='x';$id('limitvarlim').value='0';$id('limitvardir').value='1';">Example</button>
  </div>
  <div id="assistant_int" style="display:none">
    Integration <br>
    expression <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                         id="intexpr" title="Expression, for example x^2" rows=1></textarea><br>
    variable <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                       id="intvarname" title="variable name, for example x" rows=1>x</textarea><br>
    from (optional) <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                              id="intvarmin" rows=1></textarea><br>
    to (optional) <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                            id="intvarmax" rows=1></textarea>
    <br>
    <button class="bouton" onclick="UI.assistant_int_ok();">&#x2705;</button>
    <button class="bouton" onclick="UI.focused=UI.savefocused;$id('assistant_int').style.display='none'">&#x274C;</button>
    <button class="bouton"
            onclick="$id('intexpr').value='';$id('intvarname').value='';$id('intvarmin').value='';$id('intvarmax').value='';">Clear
    </button>
    <button class="bouton" onclick="$id('intexpr').value='1/(1+x^2)^2';$id('intvarname').value='x';$id('intvarmin').value='';$id('intvarmax').value='';">Example 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';">Example 2</button>
  </div>
  <div id="assistant_sum" style="display:none">
    Discrete sum <br>
    expression <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                         id="sumexpr" title="Expression, for example j^2" rows=1></textarea><br>
    variable <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                       id="sumvarname" title="variable name, for example j" rows=1>j</textarea><br>
    from (optional) <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                              id="sumvarmin" rows=1></textarea><br>
    to (optional) <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                            id="sumvarmax" rows=1></textarea>
    <br>
    <button class="bouton" onclick="UI.assistant_sum_ok();">&#x2705;</button>
    <button class="bouton" onclick="UI.focused=UI.savefocused;$id('assistant_sum').style.display='none'">&#x274C;</button>
    <button class="bouton" onclick="$id('sumexpr').value='j^2';$id('sumvarname').value='j';$id('sumvarmin').value='0';$id('sumvarmax').value='n';">Example</button>
    <button class="bouton"
            onclick="$id('sumexpr').value='';$id('sumvarname').value='';$id('sumvarmin').value='';$id('sumvarmax').value='';">Clear
    </button>
  </div>
  <div id="assistant_diff" style="display:none">
    Derivative <br>
    expression <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                         id="diffexpr" title="Expression, for example sin(x)^2" rows=1></textarea><br>
    variable <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                       id="diffvarname" title="variable name, for example x" rows=1>x</textarea><br>
    Number of derivatives <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                                    id="diffnumber" title="Default value 1" rows=1>1</textarea><br>
    <br>
    <button class="bouton" onclick="UI.assistant_diff_ok();">&#x2705;</button>
    <button class="bouton" onclick="UI.focused=UI.savefocused;$id('assistant_diff').style.display='none'">&#x274C;</button>
    <button class="bouton" onclick="$id('diffexpr').value='sin(x)^2';$id('diffvarname').value='x';$id('diffnumber').value='';">Example 1</button>
    <button class="bouton" onclick="$id('diffexpr').value='sin(x^2)';$id('diffvarname').value='x';$id('diffnumber').value='5';">Example 2</button>
    <button class="bouton"
            onclick="$id('diffexpr').value='';$id('diffvarname').value='';$id('diffnumber').value='';">Clear
    </button>
  </div>
</div>
<div id="assistant_geo" style="display:none">
  <button class="bouton" onclick="UI.insert(UI.focused,'point(')"
          title="Point by coordinates or affix">point
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'segment(')"
          title="Segment by 2 points or 2 affixes">segment
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'line(')"
          title="Line by 2 points or equation">line
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'vector(')"
          title="Vector">vector
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'equation(')"
          title="Equation">equation
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'parameq(')"
          title="Parametric equation">param
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'midpoint(')"
          title="Midpoint">milieu
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'circle(')"
          title="Circle by center and radius or diameter">&#x25ef;
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'isobarycenter(')"
          title="Isobarycenter">Isobary.
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'center(')"
          title="Circle center">center
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'inter(')"
          title="List of intersections, run inter_unique for one point">inter
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'inter_unique(')"
          title="First or unique intersection point">unique
  </button>
  <button class="bouton" onclick="var tmp=$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(UI.focused,'triangle(')"
            title="Triangle">&#x25b3;
    </button>
    <button class="bouton" onclick="UI.insert(UI.focused,'rectangle(')"
            title="Rectangle">&#x25ad;
    </button>
    <button class="bouton" onclick="UI.insert(UI.focused,'parallelogram(')"
            title="Parallelogram">&#x25b1;
    </button>
    <button class="bouton" onclick="UI.insert(UI.focused,'square(')"
            title="Square">&#x25a2;
    </button>
    <button class="bouton" onclick="UI.insert(UI.focused,'isopolygon(')"
            title="Isopolygon">iso
    </button>
    <button class="bouton" onclick="UI.insert(UI.focused,'polygon(')"
            title="Polygon">polygon
    </button>
    <button class="bouton" onclick="UI.insert(UI.focused,'parallel(')"
            title="Parallel">//
    </button>
    <button class="bouton" onclick="UI.insert(UI.focused,'perpendicular(')"
            title="Perpendicular">&perp;
    </button>
    <button class="bouton" onclick="UI.insert(UI.focused,'perpen_bisector(')"
            title="Perpendicular bisector">perpen_
    </button>
    <button class="bouton" onclick="UI.insert(UI.focused,'bisector(')"
            title="Bisector">bisector
    </button>
    <button class="bouton" onclick="UI.insert(UI.focused,'altitude(')"
            title="Altitude">hauteur
    </button>
    <button class="bouton" onclick="UI.insert(UI.focused,'tangent(')"
            title="Tangent to a graphe">tangent
    </button>
    <button class="bouton" onclick="UI.insert(UI.focused,'distance(')"
            title="Distance">dist.
    </button>
    <button class="bouton"
            onclick="$id('assistant_geo').style.display='none'">&#x274C;
    </button>
  </div>
</div>
<div id="assistant_arit" style="display:none">
  <button class="bouton" onclick="UI.insert(UI.focused,'gcd(')"
          title="GCD of integers or polynomials">gcd
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'iquo(')"
          title="iquo: quotient de la division euclidienne d'entiers">&nbsp;&nbsp;i
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'quo(')"
          title="Polynomial euclidean quotient">quo
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'irem(')"
          title="irem: integer euclidean remainder">&nbsp;&nbsp;i
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'rem(')"
          title="Polynomial euclidean remainder">rem
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'iabcuv(')"
          title="iabcuv: solve a*u+b*v=c where a,b,c are integers">&nbsp;&nbsp;i
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'abcuv(')"
          title="Polynomial solution of A*U+B*V=C">abcuv
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'ifactor(')"
          title="ifactor: integer factorization">&nbsp;&nbsp;i
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'factor(')"
          title="Polynomial factorization">factor
  </button>
  <br>
  <button class="bouton" onclick="UI.insert(UI.focused,'lcm(')"
          title="Least common multiple (integer or polynomials)">lcm
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'ichinrem(')"
          title="Integer chinese remainder">ichrem
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'isprime(')"
          title="Pseudo-primality test">isprime
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'nextprime(')"
          title="Next pseudo-prime integer">next
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'powmod(')"
          title="powmod: fast modular powering">pow
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'mod(')"
          title="Create an element of Z/nZ">mod
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'GF(')"
          title="Create a finite field (of cardinal p^n with n>1)">GF
  </button>
  <br>
  <button class="bouton" onclick="UI.insert(UI.focused,'lcoeff(')"
          title="lcoeff: leading coefficient">&nbsp;l
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'coeff(')" title="Coefficient">coeff</button>
  <button class="bouton" onclick="UI.insert(UI.focused,'degree(')"
          title="Degree">degree
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'horner(')"
          title="Evaluation">horner
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'ptayl(')"
          title="Polynomial Taylor expansion (aka shift)">ptayl
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'proot(')"
          title="Approx. complex roots for a polynomial">proot
  </button>
  <button class="bouton"
          onclick="$id('assistant_arit').style.display='none'">&#x274C;
  </button>
</div>
<div id="assistant_linalg" style="display:none">
  <button class="bouton" onclick="UI.insert(UI.focused,'dot(')"
          title="Scalar product">dot
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'cross(')"
          title="Vector product in R^2 or R^3">cross
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'tran(')"
          title="Matrix transpose, for the transconjugate use trn(M) or M^*">tran
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'idn(')"
          title="Identity matrix of size n">idn
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'matrix(')"
          title="Create a matrix">matr
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'hilbert(')"
          title="Hilbert matrix of size n">hilb
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'vandermonde(')"
          title="Vandermonde matrix">vand
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'laplace(')"
          title="1-d discrete Laplacian matrix of size n">lapl.
  </button>
  <br>
  <button class="bouton" onclick="UI.insert(UI.focused,'rref(')"
          title="Row reduction to echelon form">rref
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'ker(')"
          title="ker(M) basis of the nullspace of a linear application of matrix M">ker
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'det(')"
          title="Determinant">det
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'linsolve(')"
          title="Linear system solver">linsolve
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'lu(')"
          title="Factorization P*A=L*U">lu
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'qr(')"
          title="Factorization A=Q*R">qr
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'cholesky(')"
          title="Cholesky factorization A=L*L^* for A definite positive">chol.
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'cond(')"
          title="Condition number with respect to 1, 2 or inf norm">cond
  </button>
  <br>
  <button class="bouton" onclick="UI.insert(UI.focused,'egv(')"
          title="Eigenvectors">egv
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'egvl(')"
          title="Eigenvalues">egvl
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'jordan(')"
          title="Jordan matrix reduction A*P=P*J">jordan
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'pcar(')"
          title="Characteristic polynomial">pcar
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'pmin(')"
          title="Minimal polynomial">pmin
  </button>
  <button class="bouton" onclick="UI.insert(UI.focused,'matrix_norm(')"
          title="Matrix norm (1, 2 or inf) ">norm
  </button>
  <button class="bouton"
          onclick="$id('assistant_linalg').style.display='none'">&#x274C;
  </button>
</div>
<div id="chooselawdiv" style="display:none">
  <form id="chooselawform">
    Selected law <input class="bouton" type="text" id="rand_law" name="rand_law"
                        title="Loi" value='normald'>, optional parameters
    <input class="bouton" type="number" name="rand_law1" id="rand_law1"
           title="1er param&egrave;tre" value=0 step=0.01>
    <input class="bouton" type="number" name="rand_law2" id="rand_law2"
           title="2&egrave;me param&egrave;tre" value=1 step=0.01>
    <input class="bouton" type="text" name="law_arg" id="law_arg"
           title="argument de la loi, for example 1 ou 2 ou 1.3 ou x" value=1>
    <br>
    Choose a law
    <input type="button" onclick="$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="$id('assistant_matr').matr_formuleshadow.checked=!checked;UI.assistant_matr_setdisplay();"
           title="Check to define the matrix using an expression">
    <input class="bouton" type="button" value="expression" onclick="$id('assistant_matr').matr_formule.checked=true;$id('assistant_matr').matr_formuleshadow.checked=false;UI.assistant_matr_setdisplay();"> or
    <input class="bouton" type="checkbox" name="matr_formuleshadow"
           onclick="$id('assistant_matr').matr_formule.checked=!checked;UI.assistant_matr_setdisplay();"
           title="Check to define each element of the matrix"
           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';$id('matr_matr').style.display='none';" value="usual laws">
    or <input class="bouton" type="button"
              onclick="$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="fluctuation interval">
    or <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="descriptive statistics">
    or <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="inferential statistics">
    <div id="matr_stat12" style="display:none">
      <input class="bouton" type="checkbox" name="stat_mean">Mean,
      <input class="bouton" type="checkbox" name="stat_stddev">Standard deviation,
      <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;">Histogram,
      <input class="bouton" type="checkbox" name="stat_moustache">Boxwhisker,
      <br>
      <input class="bouton" type="checkbox" name="stat_scatter" onclick="form.stat_cmax.value=form.stat_cmin.value+1;">Scatterplot
      <input class="bouton" type="checkbox" name="stat_polygonscatter" onclick="form.stat_cmax.value=form.stat_cmin.value+1;">Polygonplot,
      <input class="bouton" type="checkbox" name="stat_linreg"
             onclick="form.stat_cmax.value=form.stat_cmin.value+1;">Linear regression
    </div>
    <div id="risque_alpha" style="display:none">
      Risk &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>
          Confidence interval:
          <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="Confidence interval according to normal law assuming n*p and n*(1-p)>=5" checked>
          (n=<input name="confiance_n" class="bouton" type="number" value=30
                    min=30 step=1 title="Population size. For n&gt;100, standard deviation is estimated by sqrt(n/(n-1)*p*(1-p)), otherwise 0.5">&geq;30,
          p=<input name="confiance_p" class="bouton" type="number"
                   title="Proportion in sample"
                   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="Confidence interval according to Student law">
          (&mu;=<input name="confiance_mu" class="bouton" type="number"
                       title="Sample mean" value=0
                       step=0.001>, &sigma;=<input name="confiance_sigma" class="bouton" type="number"
                                                   step=0.001 min=0 value=1 title="Sample stddev">
          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="data"><input type="radio" onclick="UI.adequation(form)" name="adequation"
                                                                                                                                title="Confidence interval according to Student on data from matrix">,
        </li>
        <li> Adequation 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="Kolmogorov-Smirnov adequation test (assumes common continuous unknown law)">,
          or
          <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="Wilcoxon-Mann-Whitney test">
        </li>
        <li>
          Adequation data/law : <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)">
          or
          <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> optional),
          <br>
          <span title="Alternative to 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="Matrix name" 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="Number of rows" value=3 min=1 max=40>
    <input class="bouton" type="button" onclick="UI.sheet_rowadd(1)" value="+">
    by
    <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="Number of columns" 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 of m[j,k] in terms of j and k"></textarea>
    <input class="bouton" type="checkbox" name="matr_start0"
           title="Check for indices starting at 0" checked>
    (indices from 0 to size-1)
    <br>
    <input class="bouton" type="button" title="Identity matrix" value="Identity" onclick="form.matr_expr.value='si j==k alors 1; sinon 0; fsi';">
    <input class="bouton" type="button" title="Hilbert matrix" value="Hilbert" onclick="form.matr_expr.value='1/(j+k+1)';">
    <input class="bouton" type="button" title="Clear" value="Clear" onclick="if (form.matr_formule.checked) form.matr_expr.value='';">
  </div>
  <input class="bouton" type="submit" title="ok" value="&#x2705;">
  <input class="bouton" type="button" title="Cancel" value="&#x274C;" 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">
      Lines <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>,
      columns <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="Switch spreadsheet/matrix mode"
           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="Spreadsheet">
    <input class="bouton" type="button"
           onclick="UI.sheet_edit_cmd(0)" onmousedown="event.preventDefault()"
           title="Copy down" value="cp↓">
    <input class="bouton" type="button"
           onclick="UI.sheet_edit_cmd(1)" onmousedown="event.preventDefault()"
           title="Copy right" value=" →">
    <input class="bouton" type="button"
           onclick="UI.sheet_edit_cmd(2)" onmousedown="event.preventDefault()"
           title="Add line" value="l+">
    <input class="bouton" type="button"
           onclick="UI.sheet_edit_cmd(3)" onmousedown="event.preventDefault()"
           title="Remove line" value="l-">
    <input class="bouton" type="button"
           onclick="UI.sheet_edit_cmd(4)" onmousedown="event.preventDefault()"
           title="Add column" value="c+">
    <input class="bouton" type="button"
           onclick="UI.sheet_edit_cmd(5)" onmousedown="event.preventDefault()"
           title="Remove column" value="c-">
    <input class="bouton" type="button"
           onclick="UI.insert(UI.focused,'=')" onmousedown="event.preventDefault()"
           title="Spreadsheet formula prefix" value="=">
    <input class="bouton" type="button"
           onclick="UI.insert(UI.focused,'$')" onmousedown="event.preventDefault()"
           title="Absolute position prefix" value="$">
    <div id="matr_casediv">
    </div>
  </div>
</form>
<form id="assistant_rand" style="display:none">
  Generation of
  <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="Number of rows of the matrix (0 for a vector)" value=1 min=0>
  <input class="bouton" type="button" onclick="$id('rand_nrows').value++;" value="+">
  by
  <input class="bouton" type="button" onclick="form.rand_ncols.value--; if(form.rand_ncols.value<0) form.rand_ncols.value=0" value="-">
  <input class="bouton" type="number" id="rand_ncols" name="rand_ncols"
         title="Number of columns of the matrix (0 for a single number)"
         value=1 min=0>
  <input class="bouton" type="button" onclick="$id('rand_ncols').value++;" value="+">
  <input class="bouton" type="checkbox" name="rand_int"
         onclick="$id('assistant_rand').rand_intshadow.checked=!checked;UI.assistant_rand_setdisplay();"
         title="Check for integers" checked>
  <input class="bouton" type="button" value="integers"
         onclick="var checked=form.rand_int.checked;form.rand_int.checked=!checked;form.rand_intshadow.checked=checked;UI.assistant_rand_setdisplay();">
  or according to a
  <input class="bouton" type="checkbox" name="rand_intshadow" value="law"
         onclick="$id('assistant_rand').rand_int.checked=!checked;UI.assistant_rand_setdisplay();"
         title="Check to choose a law">
  <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">
    Integers between 0 and n or n and -n with n=
    <input class="bouton" type="number" id="rand_maxint"
           title="Integer k such that 0&lt;=k&lt;n or n&lt;k&lt;-n if n<0" value=100>
  </div>
  <br><input class="bouton" type="button" title="ok" value="&#x2705;"
             onclick="UI.assistant_rand_ok()">
  <input class="bouton" type="button" title="random real in 0..1"
         value="rand" onclick="UI.insert(UI.focused,'rand()');"><input class="bouton" type="button" title="randint(a,b): random integer between a and b included"
                                                                       value="int" onclick="UI.insert(UI.focused,'randint(');"><input class="bouton" type="button" title="random real, normal law (default mean=0 and stddev=1)"
                                                                                                                                      value="norm" onclick="UI.insert(UI.focused,'randNorm(');"><input class="bouton" type="button" title="random real, exponential law parameter a"
                                                                                                                                                                                                       value="exp" onclick="UI.insert(UI.focused,'randexp(');">
  <input class="bouton" type="button" title="Random permutation of a list or of n integers"
         value="perm" onclick="UI.insert(UI.focused,'randperm(');">
  <input class="bouton" type="button" title="sample(L,n) sample of n in list L without replacement"
         value="sample" onclick="UI.insert(UI.focused,'sample(');">
  <input class="bouton" type="button" title="Cancel" value="&#x274C;" onclick="$id('chooselawdiv').style.display='none';form.style.display='none'; UI.focused=UI.savefocused; UI.focused.focus();">
</form>
<div id="assistant_boucle" style="display:none">
  Choose <strong>loop</strong>
  <button class="bouton" onmousedown="event.preventDefault()" onclick="$id('assistant_pour').style.display='block';UI.set_focus('pourvarname'); $id('assistant_tantque').style.display='none';">for</button>
  or
  <button class="bouton" onmousedown="event.preventDefault()" onclick="$id('assistant_pour').style.display='none';$id('assistant_tantque').style.display='block';UI.set_focus('tantquecond'); $id('tantquecond').focus();">while</button>
  <div id="assistant_pour" style="display:none">
    for <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                  id="pourvarname" title="variable name, for example j" rows=1></textarea><br>
    from <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                   id="pourvarmin" title="start value" rows=1></textarea><br>
    to <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                 id="pourvarmax" title="end value (not included in Python syntax, included in Xcas syntax)" rows=1></textarea><br>
    step (optional) <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                              id="pourvarstep" title="step, default to 1" rows=1></textarea>
    <br>
    <button class="bouton" onclick="UI.assistant_pour_ok();">&#x2705;</button>
    <button class="bouton" onclick="UI.focused=UI.savefocused;$id('assistant_boucle').style.display='none';$id('assistant_pour').style.display='none'">&#x274C;</button>
    <button class="bouton"
            onclick="$id('pourvarname').value='';$id('pourvarmin').value='';$id('pourvarmax').value='';">Clear
    </button>
    <button class="bouton" onclick="$id('pourvarname').value='j';$id('pourvarmin').value='1';$id('pourvarmax').value='10';">Example</button>
  </div>
  <div id="assistant_tantque" style="display:none">
    Tests :
    <button class="bouton" onmousedown="event.preventDefault()"
            onclick="UI.insert(UI.focused,'==')">==
    </button>
    <button class="bouton" onmousedown="event.preventDefault()"
            onclick="UI.insert(UI.focused,'!=')">!=
    </button>
    <button class="bouton" onmousedown="event.preventDefault()"
            onclick="UI.insert(UI.focused,'<=')">&lt;=
    </button>
    <button class="bouton" onmousedown="event.preventDefault()"
            onclick="UI.insert(UI.focused,'>=')">&gt;=
    </button>
    <button class="bouton" onmousedown="event.preventDefault()"
            onclick="UI.insert(UI.focused,'<')">&lt
    </button>
    <button class="bouton" onmousedown="event.preventDefault()"
            onclick="UI.insert(UI.focused,'>')">&gt
    </button>
    <button class="bouton" onmousedown="event.preventDefault()"
            onclick="UI.insert(UI.focused,' and ')">and
    </button>
    <button class="bouton" onmousedown="event.preventDefault()"
            onclick="UI.insert(UI.focused,' or ')">or
    </button>
    <button class="bouton" onmousedown="event.preventDefault()"
            onclick="UI.insert(UI.focused,'!')">!
    </button>
    <br>
    while <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                    id="tantquecond" title="Loops while this condition is true"
                    rows=1></textarea>
    <br>
    <button class="bouton" onclick="UI.assistant_tantque_ok();">&#x2705;</button>
    <button class="bouton" onclick="UI.focused=UI.savefocused;$id('assistant_boucle').style.display='none';$id('assistant_pour').style.display='none'">&#x274C;</button>
  </div>
</div>
<div id="assistant_solve" style="display:none">
  Solve
  <button class="bouton" id="solvex" title="Click here for approx"
          onclick="style.display='none';$id('solvenum').style.display='inline'">exact
  </button>
  <button class="bouton" style="display:none" id="solvenum"
          title="Click here for exact"
          onclick="style.display='none';$id('solvex').style.display='inline'">approx
  </button>
  <button class="bouton" id="solveR" title="Click to solve in C"
          onclick="style.display='none';$id('solveC').style.display='inline'">in R
  </button>
  <button class="bouton" style="display:none" id="solveC"
          title="Click to solve in R"
          onclick="style.display='none';$id('solveR').style.display='inline'">in C
  </button>
  <br>
  equation or system
  <br>
  <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
            id="solveeq" title="for example x^2-3x+1=0" rows=1
            cols=30></textarea>
  <br>
  unknown(s)
  <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
            id="solvevar" title="for example x" rows=1 cols=10></textarea>
  <br>
  <button class="bouton" onclick="UI.assistant_solve_ok();">&#x2705;</button>
  <button class="bouton" onclick="UI.focused=UI.savefocused;$id('assistant_solve').style.display='none'">&#x274C;</button>
  <button class="bouton" onclick="$id('solveeq').value='';$id('solvevar').value='';">Clear</button>
  <button class="bouton" onclick="$id('solveeq').value='x^2-3x+1';$id('solvevar').value='x';">Example</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">
  Choose
  <button class="bouton"
          onclick="$id('assistant_rsolve').style.display='none';$id('assistant_fixe').style.display='block';UI.set_focus('rsolveexpr')
                ">numerical study of u_(n+1)=f(u_n)
  </button>
  or
  <button class="bouton"
          onclick="$id('assistant_rsolve').style.display='block';$id('assistant_fixe').style.display='none';UI.set_focus('rsolveeq');">
    find expression of u_n
  </button>
  <button class="bouton"
          onclick="UI.focused=UI.savefocused;$id('assistant_suites').style.display='none'">&#x274C;
  </button>
  <br>
  <div id="assistant_rsolve" style="display:none">
    Recurrence
    <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
              id="rsolveeq" title="for example u(n+1)=2*u(n)+3" rows=1
              cols=40></textarea>
    <br>
    Unknown(s)
    <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
              id="rsolvevar" title="for example u(n)" rows=1 cols=20>u(n)</textarea>
    <br>
    Initial conditions
    <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
              id="rsolveinit" title="for example u(0)===1" rows=1
              cols=20>u(0)===1</textarea>
    <br>
    <button class="bouton" onmousedown="event.preventDefault()"
            onclick="UI.set_focus('rsolveeq') ;UI.insert(UI.focused,'u(n+2)')">u(n+2)
    </button>
    <button class="bouton" onmousedown="event.preventDefault()"
            onclick="UI.set_focus('rsolveeq') ;UI.insert(UI.focused,'u(n+1)')">u(n+1)
    </button>
    <button class="bouton" onmousedown="event.preventDefault()"
            onclick="UI.insert(UI.focused,'u(n)')">u(n)
    </button>
    <button class="bouton" onmousedown="event.preventDefault()"
            onclick="UI.set_focus('rsolveeq') ;UI.insert(UI.focused,'u(n-1)')">u(n-1)
    </button>
    <button class="bouton" onmousedown="event.preventDefault()"
            onclick="UI.set_focus('rsolveinit') ;UI.insert(UI.focused,'u(0)===')">u(0)=
    </button>
    <button class="bouton" onmousedown="event.preventDefault()"
            onclick="UI.set_focus('rsolveinit');UI.insert(UI.focused,'u(1)===')">u(1)=
    </button>
    <br>
    <button class="bouton"
            onclick="UI.assistant_rsolve_ok();">&#x2705;
    </button>
    <button class="bouton" onclick="UI.focused=UI.savefocused;$id('assistant_suites').style.display='none'">&#x274C;</button>
    <button class="bouton" onclick="$id('rsolveeq').value='';$id('rsolvevar').value='';$id('rsolveinit').value='';">Clear</button>
    <button class="bouton" onclick="$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)';$id('rsolveinit').value='u(0)===1';">Fixed
    </button>
    <button class="bouton" onclick="$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)]';$id('rsolveinit').value='u(0)===1,v(0)===2'">System</button>
  </div>
  <div id="assistant_fixe" style="display:none">
    u_(n+1)=<textarea onkeyup="$id('rsolvefshadow').innerHTML=value;" onclick="UI.focused=this;" style="height:25px;font-size:large"
                      id="rsolvef" title="Function name" rows=1
                      cols=2>f</textarea>(u_n) with
    <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="for example (x+2)/(x+1)" rows=1 cols=20></textarea>
    and u(0)=
    <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
              id="rsolveu0" title="for example 1" rows=1
              cols=10></textarea>
    <br>
    Number of terms n=
    <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
              id="rsolven" title="for example 10" rows=1
              cols=3>10</textarea>
    <br>
    Function graph between
    <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
              id="rsolvemin" title="for example 0" rows=1
              cols=3>0</textarea> and
    <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
              id="rsolvemax" title="for example 2" rows=1
              cols=3>2</textarea>
    <br>
    <button class="bouton"
            onclick="UI.assistant_fixe_ok();">&#x2705;
    </button>
    <button class="bouton" onclick="UI.focused=UI.savefocused;$id('assistant_suites').style.display='none'">&#x274C;</button>
    <button class="bouton" onclick="$id('rsolvef').value='';$id('rsolvevarf').value='';$id('rsolveexpr').value='';$id('rsolveu0').value='';$id('rsolven').value='';$id('rsolvemin').value='';$id('rsolvemax').value='';">Clear</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';$id('rsolvemax').value='2';">Example</button>
  </div>
</div>
<div id="assistant_test" style="display:none">
  Tests :
  <button class="bouton" onmousedown="event.preventDefault()"
          onclick="UI.insert(UI.focused,'==')">==
  </button>
  <button class="bouton" onmousedown="event.preventDefault()"
          onclick="UI.insert(UI.focused,'!=')">!=
  </button>
  <button class="bouton" onmousedown="event.preventDefault()"
          onclick="UI.insert(UI.focused,'<=')">&lt;=
  </button>
  <button class="bouton" onmousedown="event.preventDefault()"
          onclick="UI.insert(UI.focused,'>=')">&gt;=
  </button>
  <button class="bouton" onmousedown="event.preventDefault()"
          onclick="UI.insert(UI.focused,'<')">&lt
  </button>
  <button class="bouton" onmousedown="event.preventDefault()"
          onclick="UI.insert(UI.focused,'>')">&gt
  </button>
  <button class="bouton" onmousedown="event.preventDefault()"
          onclick="UI.insert(UI.focused,' et ')">et
  </button>
  <button class="bouton" onmousedown="event.preventDefault()"
          onclick="UI.insert(UI.focused,' ou ')">ou
  </button>
  <button class="bouton" onmousedown="event.preventDefault()"
          onclick="UI.insert(UI.focused,'!')">!
  </button>
  <br>
  if <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
               id="sicond" title="Test, for example j!=0"
               rows=1></textarea>
  <br>
  then <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                 id="sialors" title="True clause, for example j:=-j;"
                 rows=1></textarea>
  <br>
  else (optional) <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                            id="sisinon" title="False clause"
                            rows=1></textarea>
  <br>
  <button class="bouton" onclick="UI.assistant_test_ok();">&#x2705;</button>
  <button class="bouton"
          onclick="UI.focused=UI.savefocused;$id('assistant_test').style.display='none'">&#x274C;
  </button>
  <button class="bouton"
          onclick="$id('sicond').value='';$id('sialors').value='';">Clear
  </button>
  <button class="bouton"
          onclick="$id('sicond').value='j<0';$id('sialors').value=UI.python_mode?'j=-j':'j:=-j;';">Example
  </button>
</div>
<div id="assistant_prog" style="display:none">
  <strong>New function</strong><br>
  function name<textarea onclick="UI.focused=this;"
                         style="height:25px;font-size:large" id="funcname" title="Function name, for example f" rows=1>f</textarea><br>
  arguments <textarea onclick="UI.focused=this;"
                      style="height:25px;font-size:large" id="argsname" title="Function arguments, use comma as separator" rows=1>x</textarea><br>
  <span id="localvarspan">local variables <textarea onclick="UI.focused=this;"
                            style="height:25px;font-size:large" id="localvars"
                            title="Local variables, use comma as separator. Leave empty if you do not need local variables. Symbolic variables should be declared as local and purged after."
                            rows=1></textarea><br></span>
  returned value <textarea onclick="UI.focused=this;"
                           style="height:25px;font-size:large" id="returnedvar" title="Returned value" rows=1></textarea><br>
  <button class="bouton" onclick="UI.assistant_prog_ok();">&#x2705;</button>
  <button class="bouton" onclick="UI.focused=UI.savefocused;$id('assistant_prog').style.display='none'">&#x274C;</button>
  <button class="bouton"
          onclick="$id('funcname').value='';$id('argsname').value='';$id('localvars').value='';$id('returnedvar').value='';">Clear
  </button>
  <button class="bouton" onclick="$id('funcname').value='f';$id('argsname').value='x,y';$id('localvars').value='';$id('returnedvar').value='x*y';">Example 1</button>
  <button class="bouton" onclick="$id('funcname').value='f';$id('argsname').value='x,y';$id('localvars').value='z';$id('returnedvar').value='x*z';">Example 2</button>
</div>
<div id="assistant_seq" style="display:none">
  Create a sequence or a table of values, <br>
  expression <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                       id="seqexpr" title="Expression, for example j^2" rows=1></textarea><br>
  variable <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                     id="seqvarname" title="variable name, for example j" rows=1></textarea><br>
  from <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                 id="seqvarmin" title="start value" rows=1></textarea><br>
  to <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
               id="seqvarmax" title="end value" rows=1></textarea><br>
  Step (optional) <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                            id="seqvarstep" title="step value, default 1" rows=1></textarea>
  <br>
  <button class="bouton" onclick="UI.assistant_seq_ok();">&#x2705;</button>
  <button class="bouton" onclick="UI.focused=UI.savefocused;$id('assistant_seq').style.display='none'">&#x274C;</button>
  <button class="bouton" onclick="$id('seqexpr').value='j^2';$id('seqvarname').value='j';$id('seqvarmin').value='1';$id('seqvarmax').value='10';$id('seqvarstep').value=''">Example 1</button>
  <button class="bouton" onclick="$id('seqexpr').value='[j,j^2]';$id('seqvarname').value='j';$id('seqvarmin').value='-2';$id('seqvarmax').value='2';$id('seqvarstep').value='0.25'">Example 2</button>
  <button class="bouton"
          onclick="$id('seqexpr').value='';$id('seqvarname').value='';$id('seqvarmin').value='';$id('seqvarmax').value='';$id('seqvarstep').value=''">Clear
  </button>
</div>
<div id="assistant_tabvar" style="display:none">
  Choose
  <button class="bouton" onclick="$id('assistant_tabvarfunc').style.display='block';UI.xtn='x';$id('assistant_tabvarparam').style.display='none';UI.set_focus('tabvarfuncexpr')">function</button>
  or
  <button class="bouton"
          onclick="$id('assistant_tabvarfunc').style.display='none';$id('assistant_tabvarparam').style.display='block';UI.xtn='t';UI.set_focus('tabvarparamexprx');">parametric curve
  </button>
  <button class="bouton"
          onclick="UI.focused=UI.savefocused;$id('assistant_tabvar').style.display='none'">&#x274C;
  </button>
  <br>
  <div id="assistant_tabvarfunc" style="display:none">
    Function study (console) and graph of <br>
    <textarea rows=1 cols=3 onclick="UI.focused=this;" style="height:25px;font-size:large"
              id="tabvarfuncname" title="Function name">f</textarea>(
    <textarea rows=1 cols=2 onclick="UI.focused=this;" style="height:25px;font-size:large"
              id="tabvarfuncvarname" title="variable name, for example x">x</textarea>)
    :=<textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                id="tabvarfuncexpr" title="Expression, for example 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="Step (between two successive evaluations of the expression)" rows=1>0.0625</textarea>
    <br>
    Option : <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                       id="tabvarfuncopt" title="diff: no convexity, plot: returns the graph, tabvar: returns the variations table" rows=1>diff</textarea>
    <br>
    <button class="bouton" onclick="UI.assistant_tabvarfunc_ok();">&#x2705;</button>
    <button class="bouton"
            onclick="UI.focused=UI.savefocused;$id('assistant_tabvar').style.display='none'">&#x274C;
    </button>
    <button class="bouton"
            onclick="$id('tabvarfuncname').value='';$id('tabvarfuncexpr').value='';$id('tabvarfuncvarname').value='';$id('tabvarfuncvarmin').value='';$id('tabvarfuncvarmax').value='';$id('tabvarfuncvarstep').value='';">Clear
    </button>
    <button class="bouton" onclick="$id('tabvarfuncname').value='f';$id('tabvarfuncexpr').value='x/(x^2-1)';$id('tabvarfuncvarname').value='x';$id('tabvarfuncvarmin').value='-inf';$id('tabvarfuncvarmax').value='inf';">Example</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=$id('tabvarfuncxstep').value;">Table
    </button>
    .
  </div>
  <div id="assistant_tabvarparam" style="display:none">
                <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                          id="tabvarparamnamex" title="x-function name"
                          rows=1 cols=3>x1</textarea>
    (<textarea onkeyup="$id('tabvarparamvarnameshadow').innerHTML=value;" onclick="UI.focused=this;" style="height:25px;font-size:large"
               id="tabvarparamvarname" title="variable name, for example t"
               rows=1 cols=2>t</textarea>):= <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                                                       id="tabvarparamexprx" title="Expression of x(t), for example 2*cos(t)" rows=1></textarea><br>
    <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
              id="tabvarparamnamey" title="y-function name"
              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 of y(t), for example 3*sin(t)" rows=1></textarea><br>
    tmin <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                   id="tabvarparamvarmin" title="start value" rows=1>-4</textarea><br>
    tmax <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                   id="tabvarparamvarmax" title="end value" rows=1>4</textarea><br>
    tstep <textarea onclick="UI.focused=this;" style="height:25px;font-size:large"
                    id="tabvarparamvarstep" title="Step (between two successive evaluations of the expression)" rows=1>0.0625</textarea>
    <br>
    <button class="bouton" onclick="UI.assistant_tabvarparam_ok();">&#x2705;</button>
    <button class="bouton"
            onclick="UI.focused=UI.savefocused;$id('assistant_tabvar').style.display='none'">&#x274C;
    </button>
    <button class="bouton"
            onclick="$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='';">Clear
    </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';">Example</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(UI.focused,value)">
      <input type="button" id="add_alpha_z" value="z"
             onmousedown="event.preventDefault()" onClick="UI.insert(UI.focused,value)">
      <input type="button" id="add_alpha_e" value="e"
             onmousedown="event.preventDefault()" onClick="UI.insert(UI.focused,value)">
      <input type="button" id="add_alpha_r" value="r"
             onmousedown="event.preventDefault()" onClick="UI.insert(UI.focused,value)">
      <input type="button" id="add_alpha_t" value="t"
             onmousedown="event.preventDefault()" onClick="UI.insert(UI.focused,value)">
      <input type="button" id="add_alpha_y" value="y"
             onmousedown="event.preventDefault()" onClick="UI.insert(UI.focused,value)">
      <input type="button" id="add_alpha_u" value="u"
             onmousedown="event.preventDefault()" onClick="UI.insert(UI.focused,value)">
      <input type="button" id="add_alpha_i" value="i"
             onmousedown="event.preventDefault()" onClick="UI.insert(UI.focused,value)">
      <input type="button" id="add_alpha_o" value="o"
             onmousedown="event.preventDefault()" onClick="UI.insert(UI.focused,value)">
      <input type="button" id="add_alpha_p" value="p"
             onmousedown="event.preventDefault()" onClick="UI.insert(UI.focused,value)">
    </td>
  </tr>
  <tr>
    <td>
      <input type="button" id="add_alpha_q" value="q"
             onmousedown="event.preventDefault()" onClick="UI.insert(UI.focused,value)">
      <input type="button" id="add_alpha_s" value="s"
             onmousedown="event.preventDefault()" onClick="UI.insert(UI.focused,value)">
      <input type="button" id="add_alpha_d" value="d"
             onmousedown="event.preventDefault()" onClick="UI.insert(UI.focused,value)">
      <input type="button" id="add_alpha_f" value="f"
             onmousedown="event.preventDefault()" onClick="UI.insert(UI.focused,value)">
      <input type="button" id="add_alpha_g" value="g"
             onmousedown="event.preventDefault()" onClick="UI.insert(UI.focused,value)">
      <input type="button" id="add_alpha_h" value="h"
             onmousedown="event.preventDefault()" onClick="UI.insert(UI.focused,value)">
      <input type="button" id="add_alpha_j" value="j"
             onmousedown="event.preventDefault()" onClick="UI.insert(UI.focused,value)">
      <input type="button" id="add_alpha_k" value="k"
             onmousedown="event.preventDefault()" onClick="UI.insert(UI.focused,value)">
      <input type="button" id="add_alpha_l" value="l"
             onmousedown="event.preventDefault()" onClick="UI.insert(UI.focused,value)">
      <input type="button" id="add_alpha_m" value="m"
             onmousedown="event.preventDefault()" onClick="UI.insert(UI.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(UI.focused,value)">
      <input type="button" id="add_alpha_x" value="x"
             onmousedown="event.preventDefault()" onClick="UI.insert(UI.focused,value)">
      <input type="button" id="add_alpha_c" value="c"
             onmousedown="event.preventDefault()" onClick="UI.insert(UI.focused,value)">
      <input type="button" id="add_alpha_v" value="v"
             onmousedown="event.preventDefault()" onClick="UI.insert(UI.focused,value)">
      <input type="button" id="add_alpha_b" value="b"
             onmousedown="event.preventDefault()" onClick="UI.insert(UI.focused,value)">
      <input type="button" id="add_alpha_n" value="n"
             onmousedown="event.preventDefault()" onClick="UI.insert(UI.focused,value)">
      <input type="button" id="add_alpha_{" value="{"
             onmousedown="event.preventDefault()" onClick="UI.insert(UI.focused,value)">
      <input type="button" id="add_alpha_}" value="}"
             onmousedown="event.preventDefault()" onClick="UI.insert(UI.focused,value)">
      <input type="button" id="add_alpha_space" value=" "
             onmousedown="event.preventDefault()" onClick="UI.insert(UI.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=$id('variables'); if(tmp.style.display=='inline') tmp.style.display='none'; else {tmp.style.display='inline';UI.listvars(3);}"><strong>Vars</strong></button>
  <span id="variables" style="display:none">
            <button class="bouton" onclick="UI.insert(UI.focused,'python(')"
                    title="python(f) displays in Python syntax a function stored in a variable f">→python</button>
            <button class="bouton" onclick="UI.insert(UI.focused,'xcas(')"
                    title="xcas(f) displays in Xcas syntax a function stored in a variable f">→xcas</button>
            <button class="bouton" name="add_purge"
                    onmousedown="event.preventDefault()"
                    onClick="UI.insert(UI.focused,'purge(')" title="Clear one or more variables, for example purge(a) or purge(a,b,c)">clear</button>
            <button class="bouton" onclick="UI.addhelp(' ','rm_all_vars(1)')"
                    title="Clear all variables">tout</button>
            <span id="listvars"> </span>
            <br>
            </span>
  <span id="historique">
            <button class="bouton" onclick="UI.exec($id('mathoutput'),0)"
                    title="Execute all history commands">Exec</button>
            <button class="bouton" id="button_show_answers" onclick="UI.show_answers(true)" title="Show answers">+</button>
            <button class="bouton" id="button_hide_answers"
                    onclick="UI.show_answers(false)" title="Hide answers">-</button>
            <button class="bouton" onclick="UI.erase_all($id('mathoutput'))"
                    title="Move all levels to the trash">→Trash</button>
            <button class="bouton" onclick="UI.restoretrash()"
                    title="Restore levels from the trash">Restore</button>
            <button class="bouton" onclick="UI.emptytrash()"
                    title="Empty trash">Empty</button>
            </span>
</div>
<div contextmenu="cmdmenu" title="F1: help on commandname before cursor">
            <textarea name="entree" id="entree" title="Type a command, e.g. 2/3+1/6, then Enter" 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="Eval commandline">
            <strong>&nbsp;&nbsp;&#x2705;&nbsp;&nbsp;</strong></button>
            <button class="bouton" onmousedown="event.preventDefault()"
                    onClick="UI.completion(cmentree)" title="Short help on a command">&nbsp;?&nbsp;</button>
            <button class="bouton" onmousedown="event.preventDefault()" onClick="UI.move_caret_or_focus(UI.focused,-1)" title="Cursor left">&nbsp;&nbsp;←&nbsp;&nbsp;</button><button class="bouton" id="button_droit" onmousedown="event.preventDefault()" onClick="UI.move_caret_or_focus(UI.focused,1)" title="Cursor right"> &nbsp;&nbsp;→&nbsp;&nbsp;</button><button class="bouton" onmousedown="event.preventDefault()" onClick="UI.moveCaretUpDown(UI.focused,-1)" title="Cursor up">&nbsp;↑&nbsp;&nbsp;</button><button class="bouton" onmousedown="event.preventDefault()" onClick="UI.moveCaretUpDown(UI.focused,1)" title="Cursor down">&nbsp;&nbsp;↓&nbsp;</button><button class="bouton" onmousedown="event.preventDefault()" onClick="UI.indentline(UI.focused)" title="Indent">→|</button>
            <button class="bouton" onmousedown="event.preventDefault()" onClick="UI.backspace(UI.focused)" title="Erase">&nbsp;&#x232b;&nbsp;</button>
            <button class="bouton" onmousedown="event.preventDefault()" onClick="UI.insert(UI.focused,'\n')" title="Newline">\n</button>
            <button class="bouton" onmousedown="event.preventDefault()" onclick="UI.search(this,6)" title="Undo"><img width="16" height="16" src="undo.png" alt="Undo" align="center"></button><button class="bouton" onmousedown="event.preventDefault()" onclick="UI.search(this,7)" title="Redo"><img width="16" height="16" src="redo.png" alt="Redo" align="center"></button><button class="bouton" onmousedown="event.preventDefault()" onclick="UI.search(this,0)" title="Find">find</button><button class="bouton" onmousedown="event.preventDefault()" onclick="UI.search(this,1)" title="find next">&#x21D2;</button><button class="bouton" onmousedown="event.preventDefault()" onclick="UI.search(this,2)" title="Find previous">&#x21D0;</button><button class="bouton" onmousedown="event.preventDefault()"
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      onclick="UI.search(this,3)" title="Replace">rep</button><button
      class="bouton" onmousedown="event.preventDefault()" onclick="UI.search(this,5)" title="Go line">go</button>
            <button class="bouton" name="select_button"
                    id="select_button" onmousedown="event.preventDefault()"
                    onClick="UI.selectionne()" title="Select commandline">&nbsp;sel&nbsp;</button>  <button id="stop_button" class="bouton" style="display:none"
                                                                                                            onclick="if (UI.webworker && confirm('Really end session ?')){
                UI.webworker.terminate(); UI.busy=0;UI.webworker=0; alert('Session restarted. All variables have been cleared.');}" title="End current session">STOP</button>
            </span>
</div>
<div id="restoresession" style="display:none">
  <h1>Restoring session</h1>
</div>
<div id="consolediv" style="display:none">
  <hr>
  <h3>Console</h3>
  <button class="bouton" title="Clear console" onclick="var field=$id('output');field.innerHTML='';$id('consolediv').style.display='none';UI.set_config_width();">Clear</button>
  <button class="bouton" title="Increase line number" onclick="var field=$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="Decrease line number" 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">3d Graph
        </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="menuen.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 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: [],
        print: (function () {
            var element = $id('output');
            element.innerHTML = '';// element.value = ''; // clear browser cache
            return function (text) {
                //console.log(text.charCodeAt(0));
                if (text.length == 1 && text.charCodeAt(0) == 12) {
                    element.innerHTML = '';
                    return;
                }
                if (text.length >= 1 && text.charCodeAt(0) == 2) {
                    console.log('STX');
                    Module.htmlcheck = false;
                    htmlbuffer = '';
                    return;
                }
                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;
                    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
            } else {
                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;
            }
            statusElement.innerHTML = text;
        },
        totalDependencies: 0,
        monitorRunDependencies: function (left) {
            this.totalDependencies = Math.max(this.totalDependencies, left);
            Module.setStatus(left ? 'Preparing... (' + (this.totalDependencies - left) + '/' + this.totalDependencies + ')' : 'Download finished.');
        }
    };
    Module.setStatus('Downloading and preparing (may take 1 or 2 minutes the first time)');
    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;
    })();
    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;
        }
    }
    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_en.js"></script>
<script language="javascript">
    $id('thelink').innerHTML='<a href="'+UI.forum_url+'" target=_blank>Forum</a>';
    CodeMirror.registerHelper("hintWords", "simplemode", UI.xcascmd);
    var ua = window.navigator.userAgent;
    var old_ie = ua.indexOf('MSIE ');
    var new_ie = ua.indexOf('Trident/');
    if ((old_ie > -1) || (new_ie > -1) || Boolean(window.chrome)) {
        (function () {
            var script = document.createElement("script");
            script.type = "text/javascript";
            script.src = "file:///usr/share/javascript/mathjax/MathJax.js?config=TeX-AMS_CHTML";
            document.getElementsByTagName("head")[0].appendChild(script);
        })();
    }
</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/');
        if (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 = "Computations would be faster with 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('loadbutton_cookie').style.display = 'inline';
            $id('loadbutton_file').style.display = 'none';
        }
        else {
            $id('loadbutton_cookie').style.display = 'none';
            $id('loadbutton_file').style.display = 'inline';
        }
        if (!UI.is_touch_device()) 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");
        UI.langue = 0;
        // 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[2].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, 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 ck = (UI.qa ? Math.floor(window.innerWidth / 2) : 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('Execute history commands?')) {
                doexec = true;
            }
            // else {alert('History not executed');}
        }
        // substr(1) to remove the `#`
        if (UI.readCookie('xcas_session') != null) {
            $id('startup_restore').style.display = 'inline';
            $id('startup1').style.display = 'none';
        }
        else { if (!forcepy) $id('help').style.display = 'block'; }
        //UI.restoresession(hashParams,hist,asked,doexec);
        var cons = $id('restoresession');
        cons.style.display = 'inherit';
        if (1 || UI.ready)
            window.setTimeout(UI.restoresession, 0, hashParams, hist, asked, doexec);
        else
            window.setTimeout(UI.restoresession, 400, hashParams, hist, asked, doexec);
        if (access)
            $id('startup2').style.display = 'block';
    };
</script>
</body>
</html>