{"id":5806,"date":"2021-02-16T17:33:43","date_gmt":"2021-02-16T16:33:43","guid":{"rendered":"https:\/\/www.mathweb.fr\/euclide\/?p=5806"},"modified":"2021-10-26T16:13:46","modified_gmt":"2021-10-26T14:13:46","slug":"calculer-la-frequence-des-lettres-dans-la-langue-francaise-avec-python","status":"publish","type":"post","link":"https:\/\/www.mathweb.fr\/euclide\/2021\/02\/16\/calculer-la-frequence-des-lettres-dans-la-langue-francaise-avec-python\/","title":{"rendered":"Calculer la fr\u00e9quence des lettres dans la langue fran\u00e7aise avec Python"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">Calculer la fr\u00e9quence des lettres dans la langue fran\u00e7aise avec Python peut s&rsquo;av\u00e9rer compliqu\u00e9 si on ne sait pas par o\u00f9 commencer. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Nous allons voir dans cet article comment proc\u00e9der \u00e0 partir d&rsquo;un fichier texte contenant tous les mots de la langue fran\u00e7aise.<\/p>\n\n\n\n<!--more-->\n\n\n\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_85 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 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/www.mathweb.fr\/euclide\/2021\/02\/16\/calculer-la-frequence-des-lettres-dans-la-langue-francaise-avec-python\/#Calculer_la_frequence_des_lettres_dans_la_langue_francaise_avec_Python_le_fichier\" >Calculer la fr\u00e9quence des lettres dans la langue fran\u00e7aise avec Python: le fichier<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/www.mathweb.fr\/euclide\/2021\/02\/16\/calculer-la-frequence-des-lettres-dans-la-langue-francaise-avec-python\/#Le_programme_Python\" >Le programme Python<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/www.mathweb.fr\/euclide\/2021\/02\/16\/calculer-la-frequence-des-lettres-dans-la-langue-francaise-avec-python\/#Resultats\" >R\u00e9sultats<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/www.mathweb.fr\/euclide\/2021\/02\/16\/calculer-la-frequence-des-lettres-dans-la-langue-francaise-avec-python\/#Calculer_la_frequence_des_lettres_dans_la_langue_francaise_avec_Python_a_quoi_cela_peut_servir\" >Calculer la fr\u00e9quence des lettres dans la langue fran\u00e7aise avec Python: \u00e0 quoi cela peut servir?<\/a><\/li><\/ul><\/nav><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Calculer_la_frequence_des_lettres_dans_la_langue_francaise_avec_Python_le_fichier\"><\/span>Calculer la fr\u00e9quence des lettres dans la langue fran\u00e7aise avec Python: le fichier<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Je suis parti du fichier t\u00e9l\u00e9chargeable sur le site <a href=\"https:\/\/www.freelang.com\/dictionnaire\/dic-francais.php\" target=\"_blank\" rel=\"noreferrer noopener\">https:\/\/www.freelang.com\/dictionnaire\/dic-francais.php<\/a>, en le modifiant un peu (car il y avait quelques anomalies).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Une fois le fichier t\u00e9l\u00e9charg\u00e9 et \u00e9pur\u00e9, l&rsquo;objectif est de le lire et de compter toutes les occurrences des lettres en stockant les r\u00e9sultats dans un dictionnaire. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Pour cela, il faut faire attention \u00e0:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>supprimer les \u00ab\u00a0\\n\u00a0\u00bb en fin de lignes;<\/li><li>supprimer les espaces;<\/li><li>transformer les caract\u00e8res accentu\u00e9s en caract\u00e8res non accentu\u00e9s (en utilisant par exemple le module <em>unidecode<\/em> et sa fonction \u00e9ponyme);<\/li><li>transformer les minuscules en majuscules<\/li><\/ul>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Le_programme_Python\"><\/span>Le programme Python<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Afin de mieux visualiser les r\u00e9sultats, j&rsquo;ai opt\u00e9 pour la construction d&rsquo;un histogramme:<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"640\" height=\"480\" src=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2021\/02\/frequences_lettres_triee.png\" alt=\"fr\u00e9quence lettres langue fran\u00e7aise Python\" class=\"wp-image-5808\" srcset=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2021\/02\/frequences_lettres_triee.png 640w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2021\/02\/frequences_lettres_triee-300x225.png 300w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2021\/02\/frequences_lettres_triee-600x450.png 600w\" sizes=\"auto, (max-width: 640px) 100vw, 640px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Le programme Python, joint avec le fichiers texte, est disponible pour les abonn\u00e9\u00b7e\u00b7s de mathweb.fr ci-dessous :<\/p>\n\n\n\n<div class=\"wp-block-file aligncenter um_article\"><a href=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2021\/02\/Frequences-lettres.zip\">Fr\u00e9quences lettres<\/a><a href=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2021\/02\/Frequences-lettres.zip\" class=\"wp-block-file__button\" download>T\u00e9l\u00e9charger<\/a><\/div>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Resultats\"><\/span>R\u00e9sultats<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Le programme Python donne alors les fr\u00e9quences suivantes:<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\"> A : 7.87%\n B : 1.56%\n C : 4.18%\n D : 2.41%\n E : 16.32%\n F : 1.4%\n G : 1.72%\n H : 1.22%\n I : 8.82%\n J : 0.24%\n K : 0.11%\n L : 4.32%\n M : 3.1%\n N : 7.51%\n O : 5.92%\n P : 2.89%\n Q : 0.62%\n R : 8.78%\n S : 6.85%\n T : 7.36%\n U : 4.5%\n V : 1.39%\n W : 0.04%\n X : 0.43%\n Y : 0.34%\n Z : 0.1%<\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Et quand on demande au programme de trier dans l&rsquo;ordre d\u00e9croissant, cela donne:<\/p>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\" data-enlighter-theme=\"dracula\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"26\" data-enlighter-title=\"\" data-enlighter-group=\"\">for c in sorted(alphabet.items() , key = lambda t: t[1] , reverse = True):\n    frequences[c[0]] = alphabet[c[0]] \/ nb_lettres\n  \nfor key,values in frequences.items():\n    print('{} : {}%'.format(key,round(values*100,2)))<\/pre>\n\n\n\n<pre class=\"wp-block-preformatted\"> E : 16.32%\n I : 8.82%\n R : 8.78%\n A : 7.87%\n N : 7.51%\n T : 7.36%\n S : 6.85%\n O : 5.92%\n U : 4.5%\n L : 4.32%\n C : 4.18%\n M : 3.1%\n P : 2.89%\n D : 2.41%\n G : 1.72%\n B : 1.56%\n F : 1.4%\n V : 1.39%\n H : 1.22%\n Q : 0.62%\n X : 0.43%\n Y : 0.34%\n J : 0.24%\n K : 0.11%\n Z : 0.1%\n W : 0.04%<\/pre>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"640\" height=\"480\" src=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2021\/02\/frequences_lettres_triee_croissant.png\" alt=\"fr\u00e9quence lettres langue fran\u00e7aise Python\" class=\"wp-image-5813\" srcset=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2021\/02\/frequences_lettres_triee_croissant.png 640w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2021\/02\/frequences_lettres_triee_croissant-300x225.png 300w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2021\/02\/frequences_lettres_triee_croissant-600x450.png 600w\" sizes=\"auto, (max-width: 640px) 100vw, 640px\" \/><\/figure><\/div>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Calculer_la_frequence_des_lettres_dans_la_langue_francaise_avec_Python_a_quoi_cela_peut_servir\"><\/span>Calculer la fr\u00e9quence des lettres dans la langue fran\u00e7aise avec Python: \u00e0 quoi cela peut servir?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Certaines techniques de cryptographie s&rsquo;appuient sur les fr\u00e9quences des lettres dans le langage consid\u00e9r\u00e9 pour d\u00e9coder un message.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Cela est valable si le syst\u00e8me de codage est bien entendu ind\u00e9pendant de la position des lettres dans le message (par exemple, si le syst\u00e8me de codage transforme toujours le \u00ab\u00a0A\u00a0\u00bb en \u00ab\u00a0T\u00a0\u00bb). Mais n&rsquo;\u00e9tant pas du tout un sp\u00e9cialiste de la cryptographie, je ne peux en dire davantage.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">La seule chose que je peux dire c&rsquo;est que ce genre de syst\u00e8me de codage n&rsquo;est pas du tout optimal. En effet, on peut deviner \u00e0 l&rsquo;aide des fr\u00e9quences les diverses substitutions. Avec un tel syst\u00e8me, le mot \u00ab\u00a0abracadabra\u00a0\u00bb serait transform\u00e9 par exemple en \u00ab\u00a0kxNkBkOkxNk\u00a0\u00bb (j&rsquo;ai ici utilis\u00e9 un <a href=\"https:\/\/www.mathweb.fr\/euclide\/2018\/08\/19\/chiffrement-affine-en-python\/\" target=\"_blank\" rel=\"noreferrer noopener\">chiffrement affine<\/a>). On voit alors que la lettre \u00ab\u00a0k\u00a0\u00bb appara\u00eet souvent (sa fr\u00e9quence d&rsquo;apparition est \u00e9lev\u00e9e par rapport \u00e0 celle des autres lettres), donc elle doit repr\u00e9senter une des premi\u00e8res lettres (\u00ab\u00a0E\u00a0\u00bb, \u00ab\u00a0I\u00a0\u00bb, \u00ab\u00a0R\u00a0\u00bb, \u00ab\u00a0A\u00a0\u00bb).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Cela dit, cette logique ne fonctionne pas pour \u00ab\u00a0hurluberlu\u00a0\u00bb (que j&rsquo;ai chiffr\u00e9 en \u00ab\u00a0VBPrBxjPrB\u00a0\u00bb avec un chiffrement affine). Mais le \u00ab\u00a0U\u00a0\u00bb appara\u00eet tout de m\u00eame parmi les premi\u00e8res lettres (9\u00e8me position sur 26).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u00c0 l&rsquo;aide des fr\u00e9quences, on peut donc craquer le code et d\u00e9chiffrer le message. C&rsquo;est aussi la raison pour laquelle les chiffrements de ce type ne sont pas utilis\u00e9s si l&rsquo;on souhaite assurer une s\u00e9curit\u00e9 optimale au chiffrement.  <\/p>\n","protected":false},"excerpt":{"rendered":"<p>Calculer la fr\u00e9quence des lettres dans la langue fran\u00e7aise avec Python peut s&rsquo;av\u00e9rer compliqu\u00e9 si on ne sait pas par o\u00f9 commencer. Nous allons voir dans cet article comment proc\u00e9der \u00e0 partir d&rsquo;un fichier texte contenant tous les mots de la langue fran\u00e7aise.<\/p>\n","protected":false},"author":1,"featured_media":5807,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5],"tags":[129,259,260],"class_list":["post-5806","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-python","tag-dictionnaire","tag-frequence","tag-histogramme"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.1 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Calculer la fr\u00e9quence des lettres dans la langue fran\u00e7aise avec Python<\/title>\n<meta name=\"description\" content=\"Calculer la fr\u00e9quence des lettres dans la langue fran\u00e7aise avec Python peut s&#039;av\u00e9rer compliqu\u00e9 si on ne sait pas par o\u00f9 commencer...\" \/>\n<meta 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