<!DOCTYPE html> <html xmlns="http://www.w3.org/1999/xhtml"><head> <!--[ GuppY v5.0.9 CeCILL Copyright (C) 2004-2014 by Laurent Duveau - http://www.freeguppy.org/ ]--> <meta http-equiv="content-type" content="text/html; charset=UTF-8"> <meta name="application-name" content="Casyopée - Manipulation d expressions"> <title>Casyopée - Manipulation d expressions</title> <meta name="description" content="Casyopée: a learning environment dedicated to functions"> <meta name="generator" content="GuppY CMS"> <meta name="author" content="lagrange"> <meta name="keywords" content="casyopée, functions, mathematics, geodynamic geometry, cas, symbolic computation,"> <meta name="viewport" content="width=device-width, initial-scale=1, maximum-scale=1"> <meta name="apple-mobile-web-app-capable" content="yes"> <meta name="apple-mobile-web-app-status-bar-style" content="black"> <link rel="shortcut icon" href="https://casyopee.math.univ-paris-diderot.fr/guppy.ico"> <link rel="alternate" type="application/rss+xml" title="Casyopée : Actualité" hreflang="fr" href="https://casyopee.math.univ-paris-diderot.fr/data/fr-news.xml"> <link type="text/css" rel="stylesheet" href="skins/casyop/style.css"> <link type="text/css" rel="stylesheet" href="skins/casyop/jqstyle.css"> <style type="text/css" media="screen"> @import url(inc/auto.css); </style> <style type="text/css" media="print"> @import url(inc/print.css); </style> <link type="text/css" rel="stylesheet" href="inc/csshead/fotorama.css"> <link type="text/css" rel="stylesheet" href="inc/csshead/menubox.css"> <link type="text/css" rel="stylesheet" href="inc/csshead/slidesjs.css"> <script type="text/javascript"> //<![CDATA[ <!-- var charset = "UTF-8"; var site0 = "Casyopée"; var site3 = "https://casyopee.math.univ-paris-diderot.fr/"; var sValue = screen.width + "||" + screen.height + "||" + screen.availWidth + "||" + screen.availHeight; var today = new Date(), expires = new Date(); expires.setTime(today.getTime() + (365*24*60*60*1000)); document.cookie = "GuppYScreen" + "=" + encodeURIComponent(sValue) + ";expires=" + expires.toGMTString(); //--> //]]> </script> <script type="text/javascript" src="inc/hpage.js"></script> <script type="text/javascript" src="inc/jquery-min.js"></script> <script type="text/javascript" src="inc/jquery-migrate-min.js"></script> <script type="text/javascript" src="inc/jqscript.js"></script> <script type="text/javascript" src="inc/jshead/boxmenu_toggle.js"></script> <script type="text/javascript" src="inc/jshead/fotorama.js"></script> <script type="text/javascript" src="inc/jshead/jquery.imagecube.min.js"></script> <script type="text/javascript" src="inc/jshead/sidephoto.js"></script> <script type="text/javascript" src="inc/jshead/slides.min.jquery.js"></script> <script type="text/javascript" src="inc/jshead/slidesjs.js"></script> </head><body> <table style="margin: auto auto auto 0px; width: 100%; text-align: left;"> <tbody> <tr> <td style="width: 100%; vertical-align: top;"> <br> <div id="AboveBoxes"> </div> <br> <br> <div class="tbl tblout" onmouseover="this.className = 'tbl tblover'" onmouseout="this.className = 'tbl tblout'"> <div style="padding: 6px;"> <h1 style="text-align: center;">Manipulation d expressions</h1> <p style="margin-left: 24pt;"><a href="pg88.htm#_Toc364184518"><em>Créer une expression.</em></a></p> <p style="margin-left: 24pt;"><a href="pg88.htm#_Toc364184520"><em>Evaluer une formule. </em></a></p> <p style="margin-left: 24pt;"><a href="pg88.htm#_Toc364184521"><em>Transformer&nbsp; une expression. </em></a></p> <p style="margin-left: 24pt;"><a href="pg88.htm#_Toc364184522"><em>Modifier une expression. </em></a></p> <h3><a name="_Toc364184518"><span style="font-family: &quot;Times New Roman&quot;;">Créer une expression</span></a><span><o:p></o:p></span></h3> <p class="MsoNormal">Dans le menu de la <i>liste des expressions</i>, cliquez sur <b style="">Créer Expression</b>. Une <i style="">boite</i> s'ouvre, entrez la formule <sub><span style=""><!--[if gte vml 1]><v:shape id="_x0000_i1038" type="#_x0000_t75" style='width:56.25pt;height:17.25pt'> <v:imagedata src="/help/imgFrHelp/image019.gif" o:title="" cropbottom="4821f" cropleft="18503f"/> </v:shape><![endif]--><!--[if !vml]--><img src="/help/imgFrHelp/image020.gif" v:shapes="_x0000_i1038" height="23" width="75"><!-- [endif]--></span></sub>. Notez la case à cocher <span style="background: silver none repeat scroll 0% 50%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;">Vérification Existence</span>. Si vous la cochez, Casyopée donnera un diagnostic sur les problèmes que peut poser la formule. Ici, il n y a pas de problème à prévoir.</p> <p class="MsoNormal" style="text-align: center;" align="center"><!--[if !vml]--><img src="/help/imgFrHelp/image022.jpg" v:shapes="_x0000_i1039" height="156" width="546"><!--[endif]--></p> <p class="MsoCaption" style="text-align: center;" align="center"><a name="_Toc364193768"></a><a name="_Ref364186056"><span style="">Figure </span></a><span style=""><span style="">: Boite de création des expressions</span></span></p> <p class="MsoNormal">Dans <span style="font-family: &quot;Andika Basic&quot;;">Casyopée</span>, tous les objets ont un nom, qui est composé d'un caractère alphabétique. Vous avez pu le choisir dans la liste à gauche du bouton <span style="background: silver none repeat scroll 0% 50%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;">Créer</span>.</p> <p class="MsoCaption" style="text-align: center;" align="center"><!--[if gte vml 1]><v:shape id="_x0000_i1040" type="#_x0000_t75" style='width:282pt;height:46.5pt'> <v:imagedata src="/help/imgFrHelp/image023.gif" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img src="/help/imgFrHelp/image023.gif" v:shapes="_x0000_i1040" height="62" width="376"><!--[endif]--></p> <p class="MsoCaption" style="text-align: center;" align="center"><a name="_Toc364193769">Figure </a><!--[if supportFields]><span style='mso- bookmark: _Toc364193769'></span><span style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc364193769'><span style='mso-spacerun:yes'> </span>SEQ Figure * ARABIC <span style='mso-element:field-separator'></span></span><! [endif]--><span style=""><span>4</span></span><!--[if supportFields]><span style='mso-bookmark:_Toc364193769'></span><span style='mso-element:field- end'></span><![endif]--><span style=""> : Affichage de l'expression dans la liste dédiée</span></p> <h3><a name="_Toc364184520"><span style="font-family: &quot;Times New Roman&quot;;">Evaluer une formule</span></a><span><o:p></o:p></span></h3> <p class="MsoNormal">On a souvent besoin d évaluer une formule, soit par calcul formel, soit par approximation numérique, sans conserver le résultat. Il y a une entrée dans la barre de menus de la liste des expressions pour cela. Divers transformations sont proposées. Le résultat est affiché dans le bloc note et peut être copié aux différents formats.</p> <p class="MsoNormal" style="text-align: center;" align="center"><!--[if gte vml 1]><v:shape id="_x0000_i1044" type="#_x0000_t75" style='width:409.5pt;height:191.25pt'> <v:imagedata src="/help/imgFrHelp/image030.png" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img src="/help/imgFrHelp/image031.jpg" v:shapes="_x0000_i1044" height="255" width="546"><!--[endif]--></p> <p class="MsoCaption" style="text-align: center;" align="center"><a name="_Toc364193772">Figure </a><!--[if supportFields]><span style='mso- bookmark: _Toc364193772'></span><span style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc364193772'><span style='mso-spacerun:yes'> </span>SEQ Figure * ARABIC <span style='mso-element:field-separator'></span></span><! [endif]--><span style=""><span>7</span></span><!--[if supportFields]><span style='mso-bookmark:_Toc364193772'></span><span style='mso-element:field- end'></span><![endif]--><span style=""> : Evaluer une formule</span></p> <p class="MsoNormal">Pour les experts, il est possible d entrer toute commande avec la syntaxe Maxima (bouton radio dans Syntaxe Entrée).</p> <h3><a name="_Toc364184521"><span>Transformer <span style="">&nbsp;</span>une expression</span></a><span style="font-family: &quot;Times New Roman&quot;;"><o:p></o:p></span></h3> <p class="MsoNormal">On peut appliquer différents calculs à une expression. Nous allons développer l'expression A.</p> <p class="MsoNormal">En cliquant sur l'expression, elle est mise en surbrillance, le menu <b style="">Calculer</b> apparaît aussi. Cliquez dessus et choisissez <b>développement</b>.</p> <p class="MsoNormal" style="text-align: center;" align="center"><!--[if gte vml 1]><v:shape id="_x0000_i1045" type="#_x0000_t75" style='width:372.75pt;height:121.5pt'> <v:imagedata src="/help/imgFrHelp/image032.gif" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img src="/help/imgFrHelp/image032.gif" v:shapes="_x0000_i1045" height="162" width="497"><!--[endif]--></p> <p class="MsoCaption" style="text-align: center;" align="center"><a name="_Toc364193773">Figure </a><!--[if supportFields]><span style='mso- bookmark: _Toc364193773'></span><span style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc364193773'><span style='mso-spacerun:yes'> </span>SEQ Figure * ARABIC <span style='mso-element:field-separator'></span></span><! [endif]--><span style=""><span>8</span></span><!--[if supportFields]><span style='mso-bookmark:_Toc364193773'></span><span style='mso-element:field- end'></span><![endif]--><span style=""> : Menu Calculer / développement</span></p> <p class="MsoNormal" style="text-align: center;" align="center">Une boîte de confirmation apparait.</p> <p class="MsoNormal" style="text-align: center;" align="center"><!--[if gte vml 1]><v:shape id="_x0000_i1046" type="#_x0000_t75" style='width:429pt;height:69pt'> <v:imagedata src="/help/imgFrHelp/image033.png" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img src="/help/imgFrHelp/image034.jpg" v:shapes="_x0000_i1046" height="92" width="572"><!--[endif]--></p> <p class="MsoCaption" style="text-align: center;" align="center"><a name="_Toc364193774"></a><a name="_Toc307472224"><span style="">Figure </span></a><!--[if supportFields]><span style='mso- bookmark: _Toc307472224'><span style='mso-bookmark:_Toc364193774'></span></span><span style='mso-element:field-begin'></span><span style='mso- bookmark:_Toc307472224'><span style='mso-bookmark:_Toc364193774'><span style='mso-spacerun:yes'> </span>SEQ Figure * ARABIC <span style='mso-element:field- separator'></span></span></span><![endif]--><span style=""><span><span style="">9</span></span></span><!--[if supportFields]><span style='mso-bookmark:_Toc307472224'><span style='mso- bookmark:_Toc364193774'></span></span><span style='mso-element:field-end'></span><![endif]--><span style=""><span style=""> - Confirmation pour nouvelle expression</span></span></p> <p class="MsoNormal">La nouvelle expression est placée dans la <i style="">liste des expressions</i>.</p> <p class="MsoNormal" style="text-align: center;" align="center"><!--[if gte vml 1]><v:shape id="_x0000_i1047" type="#_x0000_t75" style='width:178.5pt;height:70.5pt'> <v:imagedata src="/help/imgFrHelp/image035.gif" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img src="/help/imgFrHelp/image035.gif" v:shapes="_x0000_i1047" height="94" width="238"><!--[endif]--></p> <p class="MsoCaption" style="text-align: center;" align="center"><a name="_Toc364193775">Figure </a><!--[if supportFields]><span style='mso- bookmark: _Toc364193775'></span><span style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc364193775'><span style='mso-spacerun:yes'> </span>SEQ Figure * ARABIC <span style='mso-element:field-separator'></span></span><! [endif]--><span style=""><span>10</span></span><!--[if supportFields]><span style='mso-bookmark:_Toc364193775'></span><span style='mso-element:field- end'></span><![endif]--><span style=""> : Expression développée dans la liste des expressions</span></p> <h3><a name="_Toc364184522"><span>Modifier une expression</span></a><span><o:p></o:p></span></h3> <p class="MsoNormal">Les expressions sont définies dynamiquement c'est-à-dire qu'on peut les modifier grâce au double-clic.</p> <p class="MsoNormal">Double-cliquez sur l'expression A. Une <i>boite de dialogue</i> demande confirmation, cliquez sur <b style="">Oui</b>.</p> <p class="MsoNormal" style="text-align: center;" align="center"><!--[if gte vml 1]><v:shape id="_x0000_i1048" type="#_x0000_t75" style='width:172.5pt;height:82.5pt'> <v:imagedata src="/help/imgFrHelp/image036.png" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img src="/help/imgFrHelp/image037.jpg" v:shapes="_x0000_i1048" height="110" width="230"><!--[endif]--></p> <p class="MsoCaption" style="text-align: center;" align="center"><a name="_Toc364193776">Figure </a><!--[if supportFields]><span style='mso- bookmark: _Toc364193776'></span><span style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc364193776'><span style='mso-spacerun:yes'> </span>SEQ Figure * ARABIC <span style='mso-element:field-separator'></span></span><! [endif]--><span style=""><span>11</span></span><!--[if supportFields]><span style='mso-bookmark:_Toc364193776'></span><span style='mso-element:field- end'></span><![endif]--><span style=""> : Boite de confirmation de modification</span></p> <p class="MsoNormal">Modifiez l'expression pour obtenir<sub><span style="line-height: 115%;"><!--[if gte vml 1]><v:shape id="_x0000_i1049" type="#_x0000_t75" style='width:71.25pt;height:16.5pt'> <v:imagedata src="/help/imgFrHelp/image038.gif" o:title="" cropbottom="6786f" cropleft="13963f"/> </v:shape><![endif]--><!--[if !vml]--><img src="/help/imgFrHelp/image039.gif" v:shapes="_x0000_i1049" height="22" width="95"><!-- [endif]--></span></sub>.</p> <p class="MsoNormal" style="text-align: center;" align="center"><!--[if gte vml 1]><v:shape id="_x0000_i1050" type="#_x0000_t75" style='width:409.5pt;height:117pt'> <v:imagedata src="/help/imgFrHelp/image040.png" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img src="/help/imgFrHelp/image041.jpg" v:shapes="_x0000_i1050" height="156" width="546"><!--[endif]--></p> <p class="MsoCaption" style="text-align: center;" align="center"><a name="_Toc364193777">Figure </a><!--[if supportFields]><span style='mso- bookmark: _Toc364193777'></span><span style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc364193777'><span style='mso-spacerun:yes'> </span>SEQ Figure * ARABIC <span style='mso-element:field-separator'></span></span><! [endif]--><span style=""><span>12</span></span><!--[if supportFields]><span style='mso-bookmark:_Toc364193777'></span><span style='mso-element:field- end'></span><![endif]--><span style=""> : Boite de modification des expressions</span></p> <p class="MsoNormal">Une <i style="">boite</i> demande la confirmation de création d'un nouveau paramètre. Cliquez sur <b style=""><span style="background: silver none repeat scroll 0% 50%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;">Confirmer</span></b>.</p> <p class="MsoNormal" style="text-align: center;" align="center"><!--[if gte vml 1]><v:shape id="_x0000_i1051" type="#_x0000_t75" style='width:217.5pt;height:82.5pt'> <v:imagedata src="/help/imgFrHelp/image042.png" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img src="/help/imgFrHelp/image043.jpg" v:shapes="_x0000_i1051" height="110" width="290"><!--[endif]--></p> <p class="MsoCaption" style="text-align: center;" align="center"><a name="_Toc364193778">Figure </a><!--[if supportFields]><span style='mso- bookmark: _Toc364193778'></span><span style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc364193778'><span style='mso-spacerun:yes'> </span>SEQ Figure * ARABIC <span style='mso-element:field-separator'></span></span><! [endif]--><span style=""><span>13</span></span><!--[if supportFields]><span style='mso-bookmark:_Toc364193778'></span><span style='mso-element:field- end'></span><![endif]--><span style=""> : Boite demandant la création d'un paramètre</span></p> <p class="MsoNormal">L'expression A a été modifiée et la forme transformée (le développement) changée en conséquence.</p> <p class="MsoNormal" style="text-align: center;" align="center"><!--[if gte vml 1]><v:shape id="_x0000_i1052" type="#_x0000_t75" style='width:275.25pt;height:126.75pt'> <v:imagedata src="/help/imgFrHelp/image044.png" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img src="/help/imgFrHelp/image045.jpg" v:shapes="_x0000_i1052" height="169" width="367"><!--[endif]--></p> <p class="MsoCaption" style="text-align: center;" align="center"><a name="_Toc364193779">Figure </a><!--[if supportFields]><span style='mso- bookmark: _Toc364193779'></span><span style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc364193779'><span style='mso-spacerun:yes'> </span>SEQ Figure * ARABIC <span style='mso-element:field-separator'></span></span><! [endif]--><span style=""><span>14</span></span><!--[if supportFields]><span style='mso-bookmark:_Toc364193779'></span><span style='mso-element:field- end'></span><![endif]--><span style=""> : Expressions modifiées</span></p> <p class="MsoNormal">Notez figure 13 le bouton et la valeur donnée au paramètre <i style="">a</i>. Le paramètre est ici en mode formel. Sa valeur n est pas prise en compte dans le développement. En cliquant sur le bouton <span style="background: silver none repeat scroll 0% 50%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;">a=</span>, on passe en mode piloté. Un curseur permet d animer le paramètre et les valeurs sont prises en compte dans le développement.</p> <p class="MsoCaption" style="text-align: center;" align="center"><!--[if gte vml 1]><v:shape id="_x0000_i1053" type="#_x0000_t75" style='width:318pt;height:127.5pt'> <v:imagedata src="/help/imgFrHelp/image046.png" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img src="/help/imgFrHelp/image047.jpg" v:shapes="_x0000_i1053" height="170" width="424"><!--[endif]--><span style="">&nbsp;</span></p> <p class="MsoCaption" style="text-align: center;" align="center"><a name="_Toc364193780">Figure </a><!--[if supportFields]><span style='mso- bookmark: _Toc364193780'></span><span style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc364193780'><span style='mso-spacerun:yes'> </span>SEQ Figure * ARABIC <span style='mso-element:field-separator'></span></span><! [endif]--><span style=""><span>15</span></span><!--[if supportFields]><span style='mso-bookmark:_Toc364193780'></span><span style='mso-element:field- end'></span><![endif]--><span style=""> : paramètres, animation</span></p> <p class="MsoNormal" style="text-align: center;" align="center"><o:p>&nbsp;</o:p></p> <p class="MsoNormal">Notez aussi que <i style="">a</i> prend des valeurs entières de -9 à 11. En fait, <i style="">a</i> a été créé comme «&nbsp;réel&nbsp;» sans restriction de domaine. Pour changer cela ou créer un paramètre ayant d autres caractéristiques, il suffit d appeler la boîte de dialogue correspondante par le bouton <span style="background: silver none repeat scroll 0% 50%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;">Paramètres</span>.</p> <p class="MsoNormal" style="text-align: center;" align="center"><!--[if gte vml 1]><v:shape id="_x0000_i1054" type="#_x0000_t75" style='width:362.25pt;height:66.75pt'> <v:imagedata src="/help/imgFrHelp/image048.png" o:title=""/> </v:shape><![endif]--><!--[if !vml]--><img src="/help/imgFrHelp/image049.jpg" v:shapes="_x0000_i1054" height="89" width="483"><!--[endif]--></p> <p class="MsoCaption" style="text-align: center;" align="center"><a name="_Toc364193781">Figure </a><!--[if supportFields]><span style='mso- bookmark: _Toc364193781'></span><span style='mso-element:field-begin'></span><span style='mso-bookmark:_Toc364193781'><span style='mso-spacerun:yes'> </span>SEQ Figure * ARABIC <span style='mso-element:field-separator'></span></span><! [endif]--><span style=""><span>16</span></span><!--[if supportFields]><span style='mso-bookmark:_Toc364193781'></span><span style='mso-element:field- end'></span><![endif]--><span style=""> : paramètres, réglage du pas</span></p> </div> <hr> <div class="tbl tblout" onmouseover="this.className = 'tbl tblover'" onmouseout="this.className = 'tbl tblout'"> <form name="react" action="postguest.php?lng=fr&amp;typ=ra&amp;pg=88" method="post"></form> <table style="border: medium none ; margin: auto; text-align: center;"> <tbody> <tr> <td><br> </td> </tr> </tbody> </table> </div> </div> <div id="UnderBoxes"> </div> <br> </td> </tr> </tbody> </table> </body></html>