{"id":627,"date":"2019-11-13T17:04:00","date_gmt":"2019-11-13T13:04:00","guid":{"rendered":"https:\/\/iremi.univ-reunion.fr\/?p=627"},"modified":"2025-07-25T13:25:44","modified_gmt":"2025-07-25T09:25:44","slug":"reseaux-de-petri","status":"publish","type":"post","link":"https:\/\/iremi.univ-reunion.fr\/?p=627","title":{"rendered":"R\u00e9seaux de Petri"},"content":{"rendered":"\n<p>Dans un r\u00e9seau de Petri, il y a des places (o\u00f9 on place des jetons) et des transitions (par lesquelles les jetons transitent). Par exemple, avec ce r\u00e9seau de Petri (en haut de page) :<\/p>\n\n\n\n<div data-wp-interactive=\"core\/file\" class=\"wp-block-file\"><object data-wp-bind--hidden=\"!state.hasPdfPreview\" hidden class=\"wp-block-file__embed\" data=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2019\/11\/doubleur1.pdf\" type=\"application\/pdf\" style=\"width:100%;height:620px\" aria-label=\"Contenu embarqu\u00e9 doubleur1.\"><\/object><a id=\"wp-block-file--media-e536f991-f9ac-4aea-92d1-4314e93ed1de\" href=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2019\/11\/doubleur1.pdf\">doubleur1<\/a><a href=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2019\/11\/doubleur1.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-e536f991-f9ac-4aea-92d1-4314e93ed1de\">T\u00e9l\u00e9charger<\/a><\/div>\n\n\n\n<p>On voit deux transitions (l&rsquo;une en haut, l&rsquo;autre en bas) et chacune des deux ne peut se d\u00e9clencher que s&rsquo;il y a au moins un jeton en amont. En partant de<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"720\" height=\"281\" src=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2019\/11\/add1.jpg\" alt=\"\" class=\"wp-image-724\" srcset=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2019\/11\/add1.jpg 720w, https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2019\/11\/add1-300x117.jpg 300w\" sizes=\"auto, (max-width: 720px) 100vw, 720px\" \/><\/figure>\n\n\n\n<p>on fait \u00e9voluer le r\u00e9seau de Petri tant qu&rsquo;on peut, et lorsqu&rsquo;aucune des deux transitions ne peut plus \u00eatre d\u00e9clench\u00e9e, on a :<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"720\" height=\"273\" src=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2019\/11\/add3.jpg\" alt=\"\" class=\"wp-image-725\" srcset=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2019\/11\/add3.jpg 720w, https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2019\/11\/add3-300x114.jpg 300w\" sizes=\"auto, (max-width: 720px) 100vw, 720px\" \/><\/figure>\n\n\n\n<p>On constate que le r\u00e9seau de Petri ach\u00e8ve son calcul avec 5 jetons dans la place de droite, alors qu&rsquo;il y avait en tout 5 jetons dans les places de gauche : il s&rsquo;agit d&rsquo;un r\u00e9seau de Petri additionneur.<\/p>\n\n\n\n<p>En fait, un r\u00e9seau de Petri m\u00e8ne en quelque sorte un calcul. Pour trouver lequel, on peut faire tourner jusqu&rsquo;\u00e0 son arr\u00eat (lorsqu&rsquo;aucune transition n&rsquo;est d\u00e9clenchable) le r\u00e9seau de Petri, et noter les \u00e9tats initial et final comme ceci (pour le r\u00e9seau de Petri ci-dessus) :<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td><strong><em>haut<\/em><\/strong><\/td><td><strong><em>bas<\/em><\/strong><\/td><td><strong><em>droite<\/em><\/strong><\/td><\/tr><tr><td>3<\/td><td>2<\/td><td>5<\/td><\/tr><tr><td>2<\/td><td>3<\/td><td>5<\/td><\/tr><tr><td>5<\/td><td>3<\/td><td>8<\/td><\/tr><tr><td>0<\/td><td>2<\/td><td>2<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Ce r\u00e9seau de Petri (celui du haut) calcule simultan\u00e9ment la diff\u00e9rence et le minimum de deux nombres entiers :<\/p>\n\n\n\n<div data-wp-interactive=\"core\/file\" class=\"wp-block-file\"><object data-wp-bind--hidden=\"!state.hasPdfPreview\" hidden class=\"wp-block-file__embed\" data=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2019\/11\/soustractionminmystere.pdf\" type=\"application\/pdf\" style=\"width:100%;height:520px\" aria-label=\"Contenu embarqu\u00e9 soustractionminmystere.\"><\/object><a id=\"wp-block-file--media-9e8feb69-0ea8-4325-80ba-140f0fb8472e\" href=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2019\/11\/soustractionminmystere.pdf\">soustractionminmystere<\/a><a href=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2019\/11\/soustractionminmystere.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-9e8feb69-0ea8-4325-80ba-140f0fb8472e\">T\u00e9l\u00e9charger<\/a><\/div>\n\n\n\n<p>Par exemple, avec 5 et 2 :<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"720\" height=\"371\" src=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2019\/11\/soust1-1.jpg\" alt=\"\" class=\"wp-image-730\" srcset=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2019\/11\/soust1-1.jpg 720w, https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2019\/11\/soust1-1-300x155.jpg 300w\" sizes=\"auto, (max-width: 720px) 100vw, 720px\" \/><\/figure>\n\n\n\n<p>il calcule 5-2 (\u00e0 gauche) et le minimum de 5 et 2 (\u00e0 droite) :<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"720\" height=\"369\" src=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2019\/11\/soust2.jpg\" alt=\"\" class=\"wp-image-731\" srcset=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2019\/11\/soust2.jpg 720w, https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2019\/11\/soust2-300x154.jpg 300w\" sizes=\"auto, (max-width: 720px) 100vw, 720px\" \/><\/figure>\n\n\n\n<p>En fait, un r\u00e9seau de Petri peut calculer toute fonction <em>sous-lin\u00e9aire<\/em> (inf\u00e9rieure ou \u00e9gale \u00e0 une fonction  affine) comme la racine carr\u00e9e ou le logarithme.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Cr\u00e9ation de r\u00e9seaux de Petri<\/h2>\n\n\n\n<p>Lorsque le temps l&rsquo;a permis, des \u00e9l\u00e8ves ont invent\u00e9 leur propre r\u00e9seau de Petri. C&rsquo;est une activit\u00e9 tr\u00e8s populaire surtout en 6<sup>e<\/sup>, comme par exemple :<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"720\" height=\"480\" src=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2019\/11\/DSC_0397.jpg\" alt=\"\" class=\"wp-image-1271\" srcset=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2019\/11\/DSC_0397.jpg 720w, https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2019\/11\/DSC_0397-300x200.jpg 300w\" sizes=\"auto, (max-width: 720px) 100vw, 720px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">R\u00e9seaux de Petri \u00e0 arcs inhibiteurs<\/h2>\n\n\n\n<p>En ajoutant des arcs inhibiteurs (repr\u00e9sent\u00e9s par des ronds : la pr\u00e9sence d&rsquo;au moins un jeton en amont de l&rsquo;arc inhibiteur emp\u00eache la transition de se d\u00e9clencher, m\u00eame s&rsquo;il y a suffisamment de jetons en amont de celle-ci), on peut calculer tout ce qui est calculable avec un tel r\u00e9seau de Petri.<\/p>\n\n\n\n<p>Un th\u00e9or\u00e8me dit qu&rsquo;avec 2 arcs inhibiteurs, on peut calculer toute fonction calculable avec un r\u00e9seau de Petri. Avec les r\u00e9seaux de Petri \u00e0 un arc inhibiteurs, on dispose donc d&rsquo;une puissance de calcul qui couvre plus que les fonctions sous-lin\u00e9aires et moins que les fonctions calculables. On ne sait pas quelles sont ces fonctions. Voici un multiplicateur \u00e0 deux arcs inhibiteurs :<\/p>\n\n\n\n<p><\/p>\n\n\n\n<div data-wp-interactive=\"core\/file\" class=\"wp-block-file\"><object data-wp-bind--hidden=\"!state.hasPdfPreview\" hidden class=\"wp-block-file__embed\" data=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2019\/11\/multiplication2.pdf\" type=\"application\/pdf\" style=\"width:100%;height:520px\" aria-label=\"Contenu embarqu\u00e9 multiplication2.\"><\/object><a id=\"wp-block-file--media-2516e247-317d-40ea-9196-166fddadbcd3\" href=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2019\/11\/multiplication2.pdf\">multiplication2<\/a><a href=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2019\/11\/multiplication2.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-2516e247-317d-40ea-9196-166fddadbcd3\">T\u00e9l\u00e9charger<\/a><\/div>\n\n\n\n<p>Voici un exemple d&rsquo;utilisation de ce r\u00e9seau de Petri (pour v\u00e9rifier que 3\u00d72=6) :<\/p>\n\n\n\n<div data-wp-interactive=\"core\/file\" class=\"wp-block-file\"><object data-wp-bind--hidden=\"!state.hasPdfPreview\" hidden class=\"wp-block-file__embed\" data=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2019\/11\/multiplicationPetri.pdf\" type=\"application\/pdf\" style=\"width:100%;height:430px\" aria-label=\"Contenu embarqu\u00e9 multiplicationPetri.\"><\/object><a id=\"wp-block-file--media-0e5d82b7-c9ed-4b61-9865-41f1055e0bb6\" href=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2019\/11\/multiplicationPetri.pdf\">multiplicationPetri<\/a><a href=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2019\/11\/multiplicationPetri.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-0e5d82b7-c9ed-4b61-9865-41f1055e0bb6\">T\u00e9l\u00e9charger<\/a><\/div>\n\n\n\n<p>Peut-on faire un r\u00e9seau de Petri multiplicateur avec un seul arc inhibiteur ? En tout cas, si on va jusqu&rsquo;\u00e0 trois arcs inhibiteur, on peut calculer tout ce qui est calculable, comme la division euclidienne :<\/p>\n\n\n\n<div data-wp-interactive=\"core\/file\" class=\"wp-block-file\"><object data-wp-bind--hidden=\"!state.hasPdfPreview\" hidden class=\"wp-block-file__embed\" data=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2019\/11\/divisionPetri-1.pdf\" type=\"application\/pdf\" style=\"width:100%;height:520px\" aria-label=\"Contenu embarqu\u00e9 divisionPetri.\"><\/object><a id=\"wp-block-file--media-1c8a5054-8443-4284-8a8a-889f0433fb1b\" href=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2019\/11\/divisionPetri-1.pdf\">divisionPetri<\/a><a href=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2019\/11\/divisionPetri-1.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-1c8a5054-8443-4284-8a8a-889f0433fb1b\">T\u00e9l\u00e9charger<\/a><\/div>\n\n\n\n<p>Voici un exemple d&rsquo;utilisation de ce r\u00e9seau de Petri, pour diviser 5 par 2 :<\/p>\n\n\n\n<div data-wp-interactive=\"core\/file\" class=\"wp-block-file\"><object data-wp-bind--hidden=\"!state.hasPdfPreview\" hidden class=\"wp-block-file__embed\" data=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2019\/11\/cinq_sur_deux.pdf\" type=\"application\/pdf\" style=\"width:100%;height:430px\" aria-label=\"Contenu embarqu\u00e9 cinq_sur_deux.\"><\/object><a id=\"wp-block-file--media-972a4484-3103-4641-86df-39c3a7651ef8\" href=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2019\/11\/cinq_sur_deux.pdf\">cinq_sur_deux<\/a><a href=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2019\/11\/cinq_sur_deux.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-972a4484-3103-4641-86df-39c3a7651ef8\">T\u00e9l\u00e9charger<\/a><\/div>\n\n\n\n<p>ou un calcul de PGCD :<\/p>\n\n\n\n<div data-wp-interactive=\"core\/file\" class=\"wp-block-file\"><object data-wp-bind--hidden=\"!state.hasPdfPreview\" hidden class=\"wp-block-file__embed\" data=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2019\/11\/petripgcd1.pdf\" type=\"application\/pdf\" style=\"width:100%;height:950px\" aria-label=\"Contenu embarqu\u00e9 petripgcd1.\"><\/object><a id=\"wp-block-file--media-3dd4a8ae-8c49-469d-95a2-08da4c1b6965\" href=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2019\/11\/petripgcd1.pdf\">petripgcd1<\/a><a href=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2019\/11\/petripgcd1.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-3dd4a8ae-8c49-469d-95a2-08da4c1b6965\">T\u00e9l\u00e9charger<\/a><\/div>\n\n\n\n<p>Ce r\u00e9seau de Petri est une repr\u00e9sentation graphique de l&rsquo;algorithme d&rsquo;Euclide, \u00e0 6 arcs inhibiteurs. Voici la preuve par Petri du fait que 5 et 3 sont premiers entre eux (\u00e0 la fin il ne reste qu&rsquo;un jeton l\u00e0 o\u00f9 initialement il y en avait 5) :<\/p>\n\n\n\n<div data-wp-interactive=\"core\/file\" class=\"wp-block-file\"><object data-wp-bind--hidden=\"!state.hasPdfPreview\" hidden class=\"wp-block-file__embed\" data=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2019\/11\/euclidedemo.pdf\" type=\"application\/pdf\" style=\"width:100%;height:430px\" aria-label=\"Contenu embarqu\u00e9 euclidedemo.\"><\/object><a id=\"wp-block-file--media-23e69ec5-0c74-40b6-8aaa-5c5f205f07ec\" href=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2019\/11\/euclidedemo.pdf\">euclidedemo<\/a><a href=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2019\/11\/euclidedemo.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-23e69ec5-0c74-40b6-8aaa-5c5f205f07ec\">T\u00e9l\u00e9charger<\/a><\/div>\n\n\n\n<h2 class=\"wp-block-heading\">Jeux sur r\u00e9seaux de Petri<\/h2>\n\n\n\n<p>Les r\u00e9seaux de Petri permettent de mod\u00e9liser des jeux de Nim, comme par exemple le jeu de Fort Boyard : <\/p>\n\n\n\n<div data-wp-interactive=\"core\/file\" class=\"wp-block-file\"><object data-wp-bind--hidden=\"!state.hasPdfPreview\" hidden class=\"wp-block-file__embed\" data=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2019\/11\/petriNim.pdf\" type=\"application\/pdf\" style=\"width:100%;height:520px\" aria-label=\"Contenu embarqu\u00e9 petriNim.\"><\/object><a id=\"wp-block-file--media-1899457f-3dd4-45c1-8127-e4aa8a076cc0\" href=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2019\/11\/petriNim.pdf\">petriNim<\/a><a href=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2019\/11\/petriNim.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-1899457f-3dd4-45c1-8127-e4aa8a076cc0\">T\u00e9l\u00e9charger<\/a><\/div>\n\n\n\n<p>ou d&rsquo;autres, comme ce r\u00e9seau de Petri invent\u00e9 pour servir de plateau de jeu :<\/p>\n\n\n\n<div data-wp-interactive=\"core\/file\" class=\"wp-block-file\"><object data-wp-bind--hidden=\"!state.hasPdfPreview\" hidden class=\"wp-block-file__embed\" data=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2019\/11\/jeupetri.pdf\" type=\"application\/pdf\" style=\"width:100%;height:930px\" aria-label=\"Contenu embarqu\u00e9 jeupetri.\"><\/object><a id=\"wp-block-file--media-98dbb70a-12ce-4e35-b073-a696132b72dc\" href=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2019\/11\/jeupetri.pdf\">jeupetri<\/a><a href=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2019\/11\/jeupetri.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-98dbb70a-12ce-4e35-b073-a696132b72dc\">T\u00e9l\u00e9charger<\/a><\/div>\n\n\n\n<p>D&rsquo;autres exemples (y compris un compteur binaire) sont pr\u00e9sents ici :<\/p>\n\n\n\n<div data-wp-interactive=\"core\/file\" class=\"wp-block-file\"><object data-wp-bind--hidden=\"!state.hasPdfPreview\" hidden class=\"wp-block-file__embed\" data=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2019\/11\/petrigames1.pdf\" type=\"application\/pdf\" style=\"width:100%;height:780px\" aria-label=\"Contenu embarqu\u00e9 petrigames1.\"><\/object><a id=\"wp-block-file--media-d640251b-d191-47db-98e4-80c0317c660f\" href=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2019\/11\/petrigames1.pdf\">petrigames1<\/a><a href=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2019\/11\/petrigames1.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-d640251b-d191-47db-98e4-80c0317c660f\">T\u00e9l\u00e9charger<\/a><\/div>\n\n\n\n<h2 class=\"wp-block-heading\">R\u00e9seaux de Petri et \u00e9cologie<\/h2>\n\n\n\n<p>Les r\u00e9seaux de Petri permettent aussi de mod\u00e9liser les interactions entre populations, comme ce mod\u00e8le proie-pr\u00e9dateur discret :<\/p>\n\n\n\n<div data-wp-interactive=\"core\/file\" class=\"wp-block-file\"><object data-wp-bind--hidden=\"!state.hasPdfPreview\" hidden class=\"wp-block-file__embed\" data=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2019\/11\/lapinsrenards.pdf\" type=\"application\/pdf\" style=\"width:100%;height:200px\" aria-label=\"Contenu embarqu\u00e9 lapinsrenards.\"><\/object><a id=\"wp-block-file--media-616832a9-2c19-4021-b50e-22ec634bbe21\" href=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2019\/11\/lapinsrenards.pdf\">lapinsrenards<\/a><a href=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2019\/11\/lapinsrenards.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-616832a9-2c19-4021-b50e-22ec634bbe21\">T\u00e9l\u00e9charger<\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Dans un r\u00e9seau de Petri, il y a des places (o\u00f9 on place des jetons) et des transitions (par lesquelles les jetons transitent). Par exemple, avec ce r\u00e9seau de Petri (en haut de page) : On voit deux transitions (l&rsquo;une en haut, l&rsquo;autre en bas) et chacune des deux ne peut se d\u00e9clencher que s&rsquo;il [&hellip;]<\/p>\n","protected":false},"author":6,"featured_media":1073,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[12],"tags":[30,31,47],"coauthors":[54],"class_list":["post-627","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-jeux-mathematiques","tag-cycle-3","tag-cycle-4","tag-mathnipulez"],"_links":{"self":[{"href":"https:\/\/iremi.univ-reunion.fr\/index.php?rest_route=\/wp\/v2\/posts\/627","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/iremi.univ-reunion.fr\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/iremi.univ-reunion.fr\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/iremi.univ-reunion.fr\/index.php?rest_route=\/wp\/v2\/users\/6"}],"replies":[{"embeddable":true,"href":"https:\/\/iremi.univ-reunion.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=627"}],"version-history":[{"count":12,"href":"https:\/\/iremi.univ-reunion.fr\/index.php?rest_route=\/wp\/v2\/posts\/627\/revisions"}],"predecessor-version":[{"id":1272,"href":"https:\/\/iremi.univ-reunion.fr\/index.php?rest_route=\/wp\/v2\/posts\/627\/revisions\/1272"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/iremi.univ-reunion.fr\/index.php?rest_route=\/wp\/v2\/media\/1073"}],"wp:attachment":[{"href":"https:\/\/iremi.univ-reunion.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=627"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/iremi.univ-reunion.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=627"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/iremi.univ-reunion.fr\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=627"},{"taxonomy":"author","embeddable":true,"href":"https:\/\/iremi.univ-reunion.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fcoauthors&post=627"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}