{"id":6085,"date":"2021-05-08T16:22:28","date_gmt":"2021-05-08T14:22:28","guid":{"rendered":"https:\/\/www.mathweb.fr\/euclide\/?p=6085"},"modified":"2021-05-08T16:39:39","modified_gmt":"2021-05-08T14:39:39","slug":"ensembles-et-python","status":"publish","type":"post","link":"https:\/\/www.mathweb.fr\/euclide\/2021\/05\/08\/ensembles-et-python\/","title":{"rendered":"Ensembles et Python"},"content":{"rendered":"\n<p>Dans les programmes scolaires fran\u00e7ais du lyc\u00e9e, il est question d&#8217;ensembles d\u00e8s la classe de Seconde, et il est question de Python. On a l&#8217;habitude de repr\u00e9senter les ensembles par des listes ou des dictionnaires, mais il existe un autre type pouvant \u00eatre utile : le type <em>set<\/em>.<\/p>\n\n\n\n<!--more-->\n\n\n\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_82_2 counter-hierarchy ez-toc-counter ez-toc-white ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Au menu sur cette page...<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 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ez-toc-heading-2\" href=\"https:\/\/www.mathweb.fr\/euclide\/2021\/05\/08\/ensembles-et-python\/#Les_methodes_importantes_associees_au_type_%E2%80%9Cset%E2%80%9D\" >Les m\u00e9thodes importantes associ\u00e9es au type &#8220;set&#8221;<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/www.mathweb.fr\/euclide\/2021\/05\/08\/ensembles-et-python\/#Ensembles_en_Python_ajouter_un_element_add\" >Ensembles en Python: ajouter un \u00e9l\u00e9ment: add()<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/www.mathweb.fr\/euclide\/2021\/05\/08\/ensembles-et-python\/#Vider_lensemble_clear\" >Vider l&#8217;ensemble: clear()<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/www.mathweb.fr\/euclide\/2021\/05\/08\/ensembles-et-python\/#Ensembles_en_Python_supprimer_le_premier_element_pop\" >Ensembles en Python: supprimer le premier \u00e9l\u00e9ment: pop()<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/www.mathweb.fr\/euclide\/2021\/05\/08\/ensembles-et-python\/#Reunion_de_deux_ensembles_union\" >R\u00e9union de deux ensembles: union()<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/www.mathweb.fr\/euclide\/2021\/05\/08\/ensembles-et-python\/#Intersection_de_deux_ensembles_intersection\" >Intersection de deux ensembles: intersection()<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/www.mathweb.fr\/euclide\/2021\/05\/08\/ensembles-et-python\/#Supprimer_un_element_discard\" >Supprimer un \u00e9l\u00e9ment: discard()<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/www.mathweb.fr\/euclide\/2021\/05\/08\/ensembles-et-python\/#Difference_de_deux_ensembles_difference\" >Diff\u00e9rence de deux ensembles: difference()<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/www.mathweb.fr\/euclide\/2021\/05\/08\/ensembles-et-python\/#La_difference_symetrique_jointure_dexclusion_symmetric_difference\" >La diff\u00e9rence sym\u00e9trique (jointure d&#8217;exclusion): symmetric_difference()<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/www.mathweb.fr\/euclide\/2021\/05\/08\/ensembles-et-python\/#Ensembles_en_Python_ajouter_plusieurs_elements_update\" >Ensembles en Python: ajouter plusieurs \u00e9l\u00e9ments: update()<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/www.mathweb.fr\/euclide\/2021\/05\/08\/ensembles-et-python\/#Les_tests\" >Les tests<\/a><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/www.mathweb.fr\/euclide\/2021\/05\/08\/ensembles-et-python\/#Est-ce_un_sous-ensemble_issubset\" >Est-ce un sous-ensemble ? issubset()<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/www.mathweb.fr\/euclide\/2021\/05\/08\/ensembles-et-python\/#Les_deux_ensembles_sont-ils_disjoints\" >Les deux ensembles sont-ils disjoints ?<\/a><\/li><\/ul><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ensembles_en_Python_type_%E2%80%9Cset%E2%80%9D\"><\/span>Ensembles en Python: type &#8220;set&#8221;<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>Ce type d&#8217;objet est un peu sp\u00e9cial par rapport aux listes et aux dictionnaires: c&#8217;est un m\u00e9lange des deux du point de vue syntaxique.<\/p>\n\n\n\n<p>On peut d\u00e9clarer un ensemble de la mani\u00e8re suivante:<\/p>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\" data-enlighter-theme=\"dracula\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"false\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">E = {'1','2','3'}<\/pre>\n\n\n\n<p>ou encore:<\/p>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\" data-enlighter-theme=\"dracula\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"false\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">E = set('123')<\/pre>\n\n\n\n<p>Ces deux fa\u00e7ons de d\u00e9clarer E donne le m\u00eame r\u00e9sultat :<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>&gt;&gt;&gt; E\n{'1','2','3'}<\/code><\/pre>\n\n\n\n<p>Remarquez alors que les \u00e9l\u00e9ments de l&#8217;ensemble sont de type <em>string<\/em>. Pour avoir un ensemble de nombres, il faudra utiliser la premi\u00e8re syntaxe:<\/p>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\" data-enlighter-theme=\"droide\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"false\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">E = {1,2,3}<\/pre>\n\n\n\n<pre class=\"wp-block-code\"><code>&gt;&gt;&gt; E\n{1, 2, 3}<\/code><\/pre>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Les_methodes_importantes_associees_au_type_%E2%80%9Cset%E2%80%9D\"><\/span>Les m\u00e9thodes importantes associ\u00e9es au type &#8220;set&#8221;<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>Nous allons partir d&#8217;un ensemble vide E :<\/p>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\" data-enlighter-theme=\"dracula\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"false\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">E = set()<\/pre>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ensembles_en_Python_ajouter_un_element_add\"><\/span>Ensembles en Python: ajouter un \u00e9l\u00e9ment: add()<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\" data-enlighter-theme=\"dracula\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"false\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">E.add(1)<\/pre>\n\n\n\n<p>Ici, on ajoute le nombre 1 \u00e0 l&#8217;ensemble. Donc on a maintenant :<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>&gt;&gt;&gt; E\n{1}<\/code><\/pre>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Vider_lensemble_clear\"><\/span>Vider l&#8217;ensemble: clear()<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\" data-enlighter-theme=\"dracula\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"false\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">E.clear()<\/pre>\n\n\n\n<p>\u00c0 ce stade, il n&#8217;y a plus rien dans E: on est revenu \u00e0 l&#8217;ensemble vide.<\/p>\n\n\n\n<p><em>Pour les besoins de la suite, nous allons construire l&#8217;ensemble des nombres pairs de 0 \u00e0 20:<\/em><\/p>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\" data-enlighter-theme=\"dracula\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"false\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">E = set( 2*k for k in range(11) )<\/pre>\n\n\n\n<pre class=\"wp-block-code\"><code>&gt;&gt;&gt; E\n{0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20}<\/code><\/pre>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ensembles_en_Python_supprimer_le_premier_element_pop\"><\/span>Ensembles en Python: supprimer le premier \u00e9l\u00e9ment: pop()<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\" data-enlighter-theme=\"dracula\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"false\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">E.pop()<\/pre>\n\n\n\n<pre class=\"wp-block-code\"><code>&gt;&gt;&gt; E\n{2, 4, 6, 8, 10, 12, 14, 16, 18, 20}<\/code><\/pre>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Reunion_de_deux_ensembles_union\"><\/span>R\u00e9union de deux ensembles: union()<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p><em>Pour les besoins de ce paragraphe, je vais d&#8217;abord construire l&#8217;ensemble des multiples de 3 de 0 \u00e0 20:<\/em><\/p>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\" data-enlighter-theme=\"dracula\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"false\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">F = set( 3*k for k in range(7) )<\/pre>\n\n\n\n<pre class=\"wp-block-code\"><code>&gt;&gt;&gt; F\n{0, 3, 6, 9, 12, 15, 18}<\/code><\/pre>\n\n\n\n<p>Pour obtenir la r\u00e9union des ensembles E et F, on \u00e9crit:<\/p>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\" data-enlighter-theme=\"dracula\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"false\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">U = E.union(F)<\/pre>\n\n\n\n<pre class=\"wp-block-code\"><code>&gt;&gt;&gt; U\n{2, 4, 6, 8, 10, 12, 14, 16, 18, 20}<\/code><\/pre>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Intersection_de_deux_ensembles_intersection\"><\/span>Intersection de deux ensembles: intersection()<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\" data-enlighter-theme=\"dracula\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"false\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">R = E.intersection(F)<\/pre>\n\n\n\n<pre class=\"wp-block-code\"><code>&gt;&gt;&gt; R\n{18, 12, 6}<\/code><\/pre>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Supprimer_un_element_discard\"><\/span>Supprimer un \u00e9l\u00e9ment: discard()<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\" data-enlighter-theme=\"dracula\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"false\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">E.discard(10)<\/pre>\n\n\n\n<pre class=\"wp-block-code\"><code>&gt;&gt;&gt; E\n{2, 4, 6, 8, 12, 14, 16, 18, 20}<\/code><\/pre>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Difference_de_deux_ensembles_difference\"><\/span>Diff\u00e9rence de deux ensembles: difference()<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\" data-enlighter-theme=\"dracula\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"false\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">D = E.difference(F)  # ensemble E auquel on a enlev\u00e9 tous les \u00e9l\u00e9ments de F\nDD = F.difference(E) # ensemble F auquel on a enlev\u00e9 tous les \u00e9l\u00e9ments de E<\/pre>\n\n\n\n<pre class=\"wp-block-code\"><code>&gt;&gt;&gt; D \n{2, 4, 8, 14, 16, 20}\n&gt;&gt;&gt; DD # ensemble F auquel on a enlev\u00e9 tous les \u00e9l\u00e9ments de E\n{0, 9, 3, 15}<\/code><\/pre>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"La_difference_symetrique_jointure_dexclusion_symmetric_difference\"><\/span>La diff\u00e9rence sym\u00e9trique (jointure d&#8217;exclusion): symmetric_difference()<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\" data-enlighter-theme=\"dracula\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"false\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">S = E.symmetric_difference(F)<\/pre>\n\n\n\n<pre class=\"wp-block-code\"><code>&gt;&gt;&gt; S\n{0, 2, 3, 4, 8, 9, 14, 15, 16, 20}<\/code><\/pre>\n\n\n\n<p>La jointure d&#8217;exclusion de E et F est l&#8217;ensemble des \u00e9l\u00e9ments qui sont dans E ou dans F, mais pas dans leur intersection.<\/p>\n\n\n\n<p>On peut aussi utiliser la syntaxe suivante:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>&gt;&gt;&gt; S = E ^ F<\/code><\/pre>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ensembles_en_Python_ajouter_plusieurs_elements_update\"><\/span>Ensembles en Python: ajouter plusieurs \u00e9l\u00e9ments: update()<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\" data-enlighter-theme=\"dracula\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"false\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">X = {1,2,3,4,5}\nY = {50,60,70,80}\nX.update(Y)<\/pre>\n\n\n\n<pre class=\"wp-block-code\"><code>&gt;&gt;&gt; X\n{1, 2, 3, 4, 5, 70, 80, 50, 60}<\/code><\/pre>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Les_tests\"><\/span>Les tests<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<h4 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Est-ce_un_sous-ensemble_issubset\"><\/span>Est-ce un sous-ensemble ? issubset()<span class=\"ez-toc-section-end\"><\/span><\/h4>\n\n\n\n<pre class=\"wp-block-code\"><code>&gt;&gt;&gt; F.issubset(E)\nFalse<\/code><\/pre>\n\n\n\n<p>En effet, F n&#8217;est pas un sous-ensemble de E.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Les_deux_ensembles_sont-ils_disjoints\"><\/span>Les deux ensembles sont-ils disjoints ?<span class=\"ez-toc-section-end\"><\/span><\/h4>\n\n\n\n<pre class=\"wp-block-code\"><code>&gt;&gt;&gt; E.isdisjoint(F)\nFalse<\/code><\/pre>\n\n\n\n<p>En effet, nos ensembles E et F ne sont pas ici disjoints car ils ont des \u00e9l\u00e9ments en commun.<\/p>\n\n\n\n<p>Ce type est en compl\u00e9ment de ce que l&#8217;on peut voir au lyc\u00e9e (voir <a href=\"https:\/\/www.mathweb.fr\/euclide\/ressources-python\/\">cette page<\/a> par exemple).<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Dans les programmes scolaires fran\u00e7ais du lyc\u00e9e, il est question d&#8217;ensembles d\u00e8s la classe de Seconde, et il est question de Python. On a l&#8217;habitude de repr\u00e9senter les ensembles par des listes ou des dictionnaires, mais il existe un autre type pouvant \u00eatre utile : le type set.<\/p>\n","protected":false},"author":1,"featured_media":6087,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5],"tags":[],"class_list":["post-6085","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-python"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.3 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Ensembles et Python, le type set apr\u00e8s le type list et dict - Mathweb.fr<\/title>\n<meta name=\"description\" content=\"On peut repr\u00e9senter les ensembles en Python par des listes ou des dictionnaires, mais il existe un type pouvant \u00eatre utile : le type set.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.mathweb.fr\/euclide\/2021\/05\/08\/ensembles-et-python\/\" \/>\n<meta property=\"og:locale\" content=\"fr_FR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Ensembles et Python, le type set apr\u00e8s le type list et dict - 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