{"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&#8217;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&#8217;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_84 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&#8217;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 &#8220;\\n&#8221; 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&#8217;ai opt\u00e9 pour la construction d&#8217;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&#8217;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&#8217;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 &#8220;A&#8221; en &#8220;T&#8221;). Mais n&#8217;\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&#8217;est que ce genre de syst\u00e8me de codage n&#8217;est pas du tout optimal. En effet, on peut deviner \u00e0 l&#8217;aide des fr\u00e9quences les diverses substitutions. Avec un tel syst\u00e8me, le mot &#8220;abracadabra&#8221; serait transform\u00e9 par exemple en &#8220;kxNkBkOkxNk&#8221; (j&#8217;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 &#8220;k&#8221; appara\u00eet souvent (sa fr\u00e9quence d&#8217;apparition est \u00e9lev\u00e9e par rapport \u00e0 celle des autres lettres), donc elle doit repr\u00e9senter une des premi\u00e8res lettres (&#8220;E&#8221;, &#8220;I&#8221;, &#8220;R&#8221;, &#8220;A&#8221;).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Cela dit, cette logique ne fonctionne pas pour &#8220;hurluberlu&#8221; (que j&#8217;ai chiffr\u00e9 en &#8220;VBPrBxjPrB&#8221; avec un chiffrement affine). Mais le &#8220;U&#8221; 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&#8217;aide des fr\u00e9quences, on peut donc craquer le code et d\u00e9chiffrer le message. C&#8217;est aussi la raison pour laquelle les chiffrements de ce type ne sont pas utilis\u00e9s si l&#8217;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&#8217;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&#8217;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 v27.7 - 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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