{"id":187,"date":"2008-07-23T20:47:08","date_gmt":"2008-07-23T18:47:08","guid":{"rendered":"http:\/\/wordpress.callac.online\/index.php\/le-paquet-pro-graphes\/"},"modified":"2023-10-14T20:12:22","modified_gmt":"2023-10-14T18:12:22","slug":"le-paquet-pro-graphes","status":"publish","type":"page","link":"https:\/\/wordpress.callac.online\/index.php\/edition-mathematique\/professor\/les-paquets-de-professor-sty-2\/le-paquet-pro-graphes\/","title":{"rendered":"Le paquet pro-graphes"},"content":{"rendered":"

Cet outil a pour but de faciliter la r\u00e9daction de documents sur les graphes<\/strong>.<\/p>\n

Il permettra de cr\u00e9er :
\n– des graphes probabilistes ;
\n– des graphes orient\u00e9s ou non, pond\u00e9r\u00e9s ou non ;
\n– des graphes color\u00e9s ;
\n– le code latex de la matrice associ\u00e9 ou de celle-ci \u00e0 la puissance n ;
\n– un tableau des degr\u00e9s des sommets avec l’application des th\u00e9or\u00e8mes d’Euler ;
\n– le tableau correspondant \u00e0 l’algorithme de Dijkstra.<\/p>\n

Lors de la cr\u00e9ation des graphes, on pourra si besoin repositionner les sommets pour am\u00e9liorer sa lisibilit\u00e9.<\/p>\n

Dans le pr\u00e9ambule<\/h2>\n
\n

On rajoute ceci :<\/p>\n

\\usepackage[xcas]{pro-graphes}<\/code><\/p>\n

pro-grapheproba<\/h2>\n
\n

Cet environnement sert \u00e0 construire un graphe probabiliste.<\/p>\n

\\begin{pro-grapheproba}{1}\n[\"A\",\"B\"],\n[\n[\"$@dfrac{1}{4}$\",\"$@dfrac{3}{4}$\"],\n[\"$@dfrac{7}{9}$\",\"$@dfrac{2}{9}$\"]\n],\n[\n[\"titre-gauche\",\"Graphe probabiliste\"]\n]\n\\end{pro-grapheproba}<\/pre>\n
On obtient :<\/p>\n
\"graphe1-2.jpg\"<\/p>\n

\nNB : le code source correspondant est enregistr\u00e9 dans le fichier : <\/em><\/span><\/p>\n
nomfichier_grapheprob i.mp, la valeur i \u00e9tant donn\u00e9e en argument.<\/em>
\n<\/span><\/p>\n
pro-tableg<\/h2>\n
\n
Cet environnement sert \u00e0 construire le code latex de la matrice associ\u00e9e.<\/p>\n
\\begin{pro-tableg}{1}\n[\"M\"],\n[\n[1,2,3],\n[4,5,6],\n[7,8,9]\n]\n\\end{pro-tableg}<\/pre>\n
On obtient :<\/p>\n
\"tableg.jpg\"<\/p>\n

\nNB : le code source correspondant est enregistr\u00e9 dans le fichier : <\/em><\/span><\/p>\n
nomfichier_tableg i.tex, la valeur i \u00e9tant donn\u00e9e en argument.<\/em>
\n<\/span><\/p>\n
pro-tablegp<\/h2>\n
\n
Cet environnement sert \u00e0 construire le code latex de la matrice associ\u00e9e \u00e9lev\u00e9e \u00e0 la puissance n.<\/p>\n
\\begin{pro-tablegp}{1}\n[\"M\"],\n[\n[1,2,3],\n[4,5,6],\n[7,8,9]\n],\n3\n\\end{pro-tablegp}<\/pre>\n
On obtient :<\/p>\n
\"tablegp.jpg\"<\/p>\n

\nNB : le code source correspondant est enregistr\u00e9 dans le fichier : <\/em><\/span><\/p>\n
nomfichier_tablegp i.tex, la valeur i \u00e9tant donn\u00e9e en argument.<\/em>
\n<\/span><\/p>\n
pro-graphedessin<\/h2>\n
\n
Cet environnement sert \u00e0 construire un graphe.<\/p>\n
Par d\u00e9faut, le graphe est non orient\u00e9 et non pond\u00e9r\u00e9. On utilise la partie haute de la matrice comme information.<\/p>\n
Les ar\u00eates sont dessin\u00e9es par des segments.<\/p>\n
\\begin{pro-graphedessin}{1}\n[\"A\",\"B\",\"C\",\"D\"],\n[\n[0,1,0,1],\n[1,0,1,1],\n[0,1,0,1],\n[1,1,1,0]\n],\n[\n[\"titre-gauche\",\"Graphe par defaut (non oriente, non pondere)\"]\n]\n\\end{pro-graphedessin}<\/pre>\n
On obtient :<\/p>\n
\"graphe2-2.jpg\"<\/p>\n

\nNB : le code source correspondant est enregistr\u00e9 dans le fichier : <\/em><\/span><\/p>\n
nomfichier_graphedessin i.mp, la valeur i \u00e9tant donn\u00e9e en argument.<\/em>
\n<\/span><\/p>\n
pro-greuler<\/h2>\n
\n
Cet environnement sert \u00e0 construire le tableau des degr\u00e9s des sommets ainsi que l’application des th\u00e9or\u00e8mes d’Euler.<\/p>\n
\\begin{pro-greuler}{1}\n[\"A\",\"B\",\"C\",\"D\"],\n[\n[0,1,0,1],\n[1,0,1,1],\n[0,1,0,1],\n[1,1,1,0]\n]\n\\end{pro-greuler}<\/pre>\n
On obtient :<\/p>\n
\"greuler.jpg\"<\/p>\n

\nNB : le code source correspondant est enregistr\u00e9 dans le fichier : <\/em><\/span><\/p>\n
nomfichier_greuler i.tex, la valeur i \u00e9tant donn\u00e9e en argument.<\/em>
\n<\/span><\/p>\n
Exemple de graphe color\u00e9<\/h2>\n
\n
\\begin{pro-graphedessin}{2}\n[\"A\",\"B\",\"C\",\"D\"],\n[\n[0,1,0,1],\n[1,0,1,1],\n[0,1,0,1],\n[1,1,1,0]\n],\n[\n[\"titre-gauche\",\"Graphe colorie\"],\n[\"graphe-colorie\",[\"rouge\",\"jaune\",\"rouge\",\"bleu\"]]\n]\n\\end{pro-graphedessin}<\/pre>\n
On obtient :<\/p>\n
\"graphe3-2.jpg\"<\/p>\n
Exemple de graphe pond\u00e9r\u00e9<\/h2>\n
\n
\\begin{pro-graphedessin}{3}\n[\"A\",\"B\",\"C\",\"D\",\"E\",\"G\",\"F\"],\n[\n[0,5,7,0,0,0,0],\n[5,0,0,8,15,6,0],\n[7,0,0,10,15,0,0],\n[0,8,10,0,0,10,20],\n[0,15,15,0,0,0,5],\n[0,6,0,10,0,0,0],\n[0,0,0,20,5,0,0]\n],\n[\n[\"titre-gauche\",\"Graphe pondere\"],\n[\"type-graphe\",[\"pondere\"]]\n]\n\\end{pro-graphedessin}<\/pre>\n
On obtient :<\/p>\n
\"graphe4-2.jpg\"<\/p>\n
pro-dijkstra<\/h2>\n
\n
Cet environnement sert \u00e0 construire le tableau correspondant \u00e0 l’application de l’algorithme de Dijkstra.<\/p>\n
\\begin{pro-dijkstra}{1}\n[\"A\",\"B\",\"C\",\"D\",\"E\",\"G\",\"F\"],\n[\n[0,5,7,0,0,0,0],\n[5,0,0,8,15,6,0],\n[7,0,0,10,15,0,0],\n[0,8,10,0,0,10,20],\n[0,15,15,0,0,0,5],\n[0,6,0,10,0,0,0],\n[0,0,0,20,5,0,0]\n]\n\\end{pro-dijkstra}<\/pre>\n
On obtient :<\/p>\n
\"diljkstra.jpg\"<\/p>\n

\nNB : le code source correspondant est enregistr\u00e9 dans le fichier : <\/em><\/span><\/p>\n
nomfichier_dijkstra i.tex, la valeur i \u00e9tant donn\u00e9e en argument.<\/em>
\n<\/span><\/p>\n
Exemple de graphe orient\u00e9<\/h2>\n
\n
\\begin{pro-graphedessin}{4}\n[\"A\",\"B\",\"C\",\"D\",\"E\"],\n[\n[1,1,0,1,0],\n[0,1,1,1,1],\n[0,1,1,0,0],\n[1,1,0,1,1],\n[1,0,0,1,1]\n],\n[\n[\"titre-gauche\",\"Graphe oriente\"],\n[\"type-graphe\",[\"oriente\"]]\n]\n\\end{pro-graphedessin}<\/pre>\n
On obtient :<\/p>\n
\"graphe5-2.jpg\"<\/p>\n
Exemple de graphe orient\u00e9 pond\u00e9r\u00e9<\/h2>\n
\n
\\begin{pro-graphedessin}{5}\n[\"A\",\"B\",\"C\",\"D\",\"E\",\"F\"],\n[\n[2,1,0,2,0,3],\n[0,0,0,3,1,0],\n[0,5,0,0,0,1],\n[0,1,0,0,7,0],\n[6,1,0,3,1,0],\n[4,0,0,2,0,0]\n],\n[\n[\"titre-gauche\",\"Graphe oriente pondere\"],\n[\"type-graphe\",[\"oriente\",\"pondere\"]]\n]\n\\end{pro-graphedessin}<\/pre>\n
On obtient :<\/p>\n
\"graphe6-2.jpg\"<\/p>\n
Repositionnement des n\u0153uds<\/h2>\n
\n
Dans l’exemple suivant, les n\u0153uds du graphe sont mal plac\u00e9s :<\/p>\n
\\begin{pro-graphedessin}{6}\n[\"A\",\"B\",\"C\",\"D\",\"E\",\"F\"],\n[\n[0,0,0,0,4,0],\n[2,0,0,0,0,3],\n[0,9,0,2,0,6],\n[9,0,2,0,0,3],\n[0,0,0,4,0,0],\n[6,3,6,0,0,0]\n],\n[\n[\"titre-gauche\",\"Graphe oriente pondere\"],\n[\"type-graphe\",[\"oriente\",\"pondere\"]]\n]\n\\end{pro-graphedessin}<\/pre>\n
On obtient :<\/p>\n
\"graphe7.jpg\"<\/p>\n
On peut alors rajouter l’option de positionnement pour am\u00e9liorer le dessin :<\/p>\n
\\begin{pro-graphedessin}{7}\n[\"A\",\"B\",\"C\",\"D\",\"E\",\"F\"],\n[\n[0,0,0,0,4,0],\n[2,0,0,0,0,3],\n[0,9,0,2,0,6],\n[9,0,2,0,0,3],\n[0,0,0,4,0,0],\n[6,3,6,0,0,0]\n],\n[\n[\"titre-gauche\",\"Graphe oriente pondere\"],\n[\"type-graphe\",[\"oriente\",\"pondere\"]],\n[\"position-noeuds\",[[-1,2],[4,3],[4,-2],[0,-3],[-3,-1],[2,0]]]\n]\n\\end{pro-graphedessin}<\/pre>\n
On obtient :<\/p>\n
\"graphe8.jpg\"<\/p>\n
Echelle des graphes<\/h2>\n
\n
On pourra modifier l’\u00e9chelle d’un graphe en ajoutant l’option \u00ab\u00a0echelle\u00a0\u00bb comme dans l’exemple suivant :<\/p>\n
[\"echelle\",0.75]<\/code><\/p>\n","protected":false},"excerpt":{"rendered":"
Cet outil a pour but de faciliter la r\u00e9daction de documents sur les graphes. Il permettra de cr\u00e9er : – des graphes probabilistes ; – des graphes orient\u00e9s ou non,…<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":2247,"menu_order":4,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-187","page","type-page","status-publish","hentry"],"yoast_head":"\nLe paquet pro-graphes - Maths & Num\u00e9rique<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/wordpress.callac.online\/index.php\/edition-mathematique\/professor\/les-paquets-de-professor-sty-2\/le-paquet-pro-graphes\/\" \/>\n<meta property=\"og:locale\" content=\"fr_FR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Le paquet pro-graphes - Maths & Num\u00e9rique\" \/>\n<meta property=\"og:description\" content=\"Cet outil a pour but de faciliter la r\u00e9daction de documents sur les graphes. 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