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 <!DOCTYPE html>
 <html lang="fr">
 <head>
-    <meta charset="UTF-8">
-    <meta name="viewport" content="width=device-width, initial-scale=1.0">
-    <title>Mariam M-0 | Solution Mathématique</title>
-    <link href="https://cdn.jsdelivr.net/npm/tailwindcss@2.2.19/dist/tailwind.min.css" rel="stylesheet">
-    <!-- Optimized MathJax Configuration -->
-    <script>
-        window.MathJax = {
-            tex: {
-                inlineMath: [['$', '$']],
-                displayMath: [['$$', '$$']],
-                processEscapes: true,
-                packages: ['base', 'ams']
-            },
-            options: {
-                enableMenu: false,
-                messageStyle: 'none'
-            },
-            startup: {
-                pageReady: () => {
-                    console.log('MathJax is fully loaded and ready.');
-                    window.mathJaxReady = true; // Signal that MathJax is ready
-                    // On pourrait appeler une fonction ici pour traiter du contenu initial si nécessaire
-                }
-            }
-        };
-    </script>
-    <script src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js" id="MathJax-script" async></script>
-    <script src="https://cdn.jsdelivr.net/npm/marked/lib/marked.umd.min.js"></script>
-    <style>
-        @import url('https://fonts.googleapis.com/css2?family=Space+Grotesk:wght@400;700&display=swap');
-        body {
-            font-family: 'Space Grotesk', sans-serif;
-        }
-        .uploadArea {
-            background: #f3f4f6;
-            border: 2px dashed #d1d5db;
-            transition: border-color 0.2s ease;
-        }
-        .uploadArea:hover {
-            border-color: #3b82f6;
-        }
-        .blue-button {
-            background: #3b82f6;
-            transition: background-color 0.2s ease;
         }
-        .blue-button:hover {
-            background: #2563eb;
-        }
-        .loader {
-            width: 48px;
-            height: 48px;
-            border: 3px solid #3b82f6;
-            border-bottom-color: transparent;
-            border-radius: 50%;
-            display: inline-block;
-            animation: rotation 1s linear infinite;
-        }
-        @keyframes rotation {
-            0% { transform: rotate(0deg); }
-            100% { transform: rotate(360deg); }
-        }
-        .thought-box {
-            transition: max-height 0.3s ease-out;
-            max-height: 0;
-            overflow: hidden;
-        }
-        .thought-box.open {
-            max-height: 500px;
-        }
-        #thoughtsContent, #answerContent {
-            max-height: 500px;
-            overflow-y: auto;
-            scroll-behavior: smooth;
-            white-space: pre-wrap; /* Gérer les espaces et les sauts de ligne */
-        }
-        .preview-image {
-            max-width: 300px;
-            max-height: 300px;
-            object-fit: contain;
-        }
-        .timestamp {
-            color: #3b82f6;
-            font-size: 0.9em;
-            margin-left: 8px;
-        }
-    </style>
 </head>
 <body class="p-4">
-    <div class="max-w-4xl mx-auto">
-        <div class="p-6">
-            <div class="text-center mb-8">
-                <h1 class="text-4xl font-bold text-blue-600">Mariam M-0</h1>
-                <p class="text-gray-600">Solution Mathématique/Physique/Chimie Intelligente</p>
             </div>
-            <form id="problemForm" class="space-y-6">
-                <div class="uploadArea p-8 text-center relative">
-                    <input type="file" id="imageInput" accept="image/*" class="absolute inset-0 w-full h-full opacity-0 cursor-pointer">
-                    <div class="space-y-3">
-                        <div class="w-16 h-16 mx-auto border-2 border-blue-400 rounded-full flex items-center justify-center">
-                            <svg class="w-8 h-8 text-blue-400" fill="none" stroke="currentColor" viewBox="0 0 24 24">
-                                <path stroke-linecap="round" stroke-linejoin="round" stroke-width="2" d="M4 16l4.586-4.586a2 2 0 012.828 0L16 16m-2-2l1.586-1.586a2 2 0 012.828 0L20 14m-6-6h.01M6 20h12a2 2 0 002-2V6a2 2 0 00-2-2H6a2 2 0 00-2 2v12a2 2 0 002 2z" />
-                            </svg>
-                        </div>
-                        <p class="text-gray-700 font-medium">Déposez votre image ici</p>
-                        <p class="text-gray-500 text-sm">ou cliquez pour sélectionner</p>
-                    </div>
-                </div>
-                <div id="imagePreview" class="hidden text-center">
-                    <img id="previewImage" class="preview-image mx-auto" alt="Prévisualisation">
-                </div>
-                <button type="submit" class="blue-button w-full py-3 text-white font-medium rounded-lg">
-                    Résoudre le problème
-                </button>
-            </form>
-            <div id="loader" class="hidden mt-8 text-center">
-                <span class="loader"></span>
-                <p class="mt-4 text-gray-600">Analyse en cours...</p>
-            </div>
-            <div id="solution" class="hidden mt-8 space-y-6">
-                <div class="border-t pt-4">
-                    <button id="thoughtsToggle" class="w-full flex justify-between items-center p-2">
-                        <span class="font-medium text-gray-700">Processus de Réflexion</span>
-                        <span id="timestamp" class="timestamp"></span>
-                    </button>
-                    <div id="thoughtsBox" class="thought-box">
-                        <div id="thoughtsContent" class="p-4 text-gray-600"></div>
-                    </div>
-                </div>
-                <div class="border-t pt-6">
-                    <h3 class="text-xl font-bold text-gray-800 mb-4">Solution</h3>
-                    <div id="answerContent" class="text-gray-700"></div>
-                </div>
-            </div>
         </div>
-    </div>
-    <script>
-        document.addEventListener('DOMContentLoaded', () => {
-            const form = document.getElementById('problemForm');
-            const imageInput = document.getElementById('imageInput');
-            const loader = document.getElementById('loader');
-            const solution = document.getElementById('solution');
-            const thoughtsContent = document.getElementById('thoughtsContent');
-            const answerContent = document.getElementById('answerContent');
-            const thoughtsToggle = document.getElementById('thoughtsToggle');
-            const thoughtsBox = document.getElementById('thoughtsBox');
-            const imagePreview = document.getElementById('imagePreview');
-            const previewImage = document.getElementById('previewImage');
-            const timestamp = document.getElementById('timestamp');
-            let startTime = null;
-            let timerInterval = null;
-            let thoughtsBuffer = '';
-            let answerBuffer = '';
-            const updateTimestamp = () => {
-                if (startTime) {
-                    timestamp.textContent = `${Math.floor((Date.now() - startTime) / 1000)}s`;
-                }
-            };
-            const startTimer = () => {
-                startTime = Date.now();
-                timerInterval = setInterval(updateTimestamp, 1000);
-                updateTimestamp();
-            };
-            const stopTimer = () => {
-                clearInterval(timerInterval);
-                startTime = null;
-                timestamp.textContent = '';
-            };
-            const handleFileSelect = file => {
-                if (!file) return;
-                const reader = new FileReader();
-                reader.onload = e => {
-                    previewImage.src = e.target.result;
-                    imagePreview.classList.remove('hidden');
-                };
-                reader.readAsDataURL(file);
-            };
-            thoughtsToggle.addEventListener('click', () => {
-                thoughtsBox.classList.toggle('open');
-            });
-            imageInput.addEventListener('change', e => handleFileSelect(e.target.files[0]));
-            const dropZone = document.querySelector('.uploadArea');
-            dropZone.addEventListener('dragover', e => {
-                e.preventDefault();
-                dropZone.classList.add('border-blue-400');
-            });
-            dropZone.addEventListener('dragleave', e => {
-                e.preventDefault();
-                dropZone.classList.remove('border-blue-400');
-            });
-            dropZone.addEventListener('drop', e => {
-                e.preventDefault();
-                dropZone.classList.remove('border-blue-400');
-                handleFileSelect(e.dataTransfer.files[0]);
-            });
-            const typesetAnswerIfReady = async () => {
-                if (window.mathJaxReady) {
-                    MathJax.startup.document.elements = [document.getElementById('answerContent')];
-                    await MathJax.typesetPromise();
-                    answerContent.scrollTop = answerContent.scrollHeight;
-                } else {
-                    setTimeout(typesetAnswerIfReady, 200);
-                }
-            };
-            // Configuration de marked pour gérer les sauts de ligne
-            marked.setOptions({
-              breaks: true, // Interpréter les sauts de ligne simples comme des <br>
-            });
-            form.addEventListener('submit', async e => {
-                e.preventDefault();
-                const file = imageInput.files[0];
-                if (!file) {
-                    alert('Veuillez sélectionner une image.');
-                    return;
                 }
-                startTimer();
-                loader.classList.remove('hidden');
-                solution.classList.add('hidden');
-                thoughtsContent.innerHTML = '';
-                answerContent.innerHTML = '';
-                thoughtsBuffer = '';
-                answerBuffer = '';
-                thoughtsBox.classList.add('open');
-                const formData = new FormData();
-                formData.append('image', file);
-                try {
-                    let currentMode = null;
-                    const response = await fetch('/solve', {
-                        method: 'POST',
-                        body: formData
-                    });
-                    const reader = response.body.getReader();
-                    const decoder = new TextDecoder();
-                    let buffer = '';
-                    const processChunk = async (chunk) => {
-                        buffer += decoder.decode(chunk, { stream: true });
-                        const lines = buffer.split('\n\n');
-                        buffer = lines.pop();
-                        for (const line of lines) {
-                            if (!line.startsWith('data:')) continue;
-                            const data = JSON.parse(line.slice(5));
-                            if (data.mode) {
-                                currentMode = data.mode;
-                                loader.classList.add('hidden');
-                                solution.classList.remove('hidden');
-                            }
-                            if (data.content) {
-                                if (currentMode === 'thinking') {
-                                    thoughtsBuffer += data.content;
-                                } else if (currentMode === 'answering') {
-                                    answerBuffer += data.content;
-                                }
-                            }
-                        }
-                        // Mettre à jour le contenu visible à chaque chunk reçu
-                        thoughtsContent.innerHTML = marked.parse(thoughtsBuffer);
-                        answerContent.innerHTML = marked.parse(answerBuffer);
-                        await typesetAnswerIfReady();
-                    };
-                    while (true) {
-                        const { done, value } = await reader.read();
-                        if (done) {
-                            // Traiter le contenu restant dans le buffer à la fin du stream
-                            if (buffer) {
-                                const data = JSON.parse(buffer.slice(5));
-                                if (data.content) {
-                                    if (currentMode === 'thinking') {
-                                        thoughtsBuffer += data.content;
-                                    } else if (currentMode === 'answering') {
-                                        answerBuffer += data.content;
-                                    }
-                                }
-                            }
-                            // Mettre à jour le contenu visible une dernière fois à la fin du stream
-                            thoughtsContent.innerHTML = marked.parse(thoughtsBuffer);
-                            answerContent.innerHTML = marked.parse(answerBuffer);
-                            await typesetAnswerIfReady();
-                            break;
-                        }
-                        await processChunk(value);
-                    }
-                    stopTimer();
-                } catch (error) {
-                    console.error('Erreur:', error);
-                    alert('Une erreur est survenue.');
-                    loader.classList.add('hidden');
-                    stopTimer();
                 }
-            });
-        });
-    </script>
 </body>
-</html>

 <!DOCTYPE html>
 <html lang="fr">
 <head>
+  <meta charset="UTF-8">
+  <meta name="viewport" content="width=device-width, initial-scale=1.0">
+  <title>Mariam M-0 | Solution Mathématique</title>
+  <!-- Tailwind CSS (version 2.2.19 utilisée ici, à mettre à jour si besoin) -->
+  <link href="https://cdn.jsdelivr.net/npm/[email protected]/dist/tailwind.min.css" rel="stylesheet">
+  <!-- Configuration optimisée de MathJax avec support étendu LaTeX -->
+  <script>
+    window.MathJax = {
+      tex: {
+        inlineMath: [['$', '$']],
+        displayMath: [['$$', '$$']],
+        processEscapes: true,
+        // Chargement automatique de commandes supplémentaires (ex. environnements de tableaux)
+        packages: {'[+]': ['autoload','ams']}
+      },
+      options: {
+        enableMenu: false,
+        messageStyle: 'none'
+      },
+      startup: {
+        pageReady: () => {
+          console.log('MathJax est complètement chargé.');
+          window.mathJaxReady = true;
         }
+      }
+    };
+  </script>
+  <script src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js" id="MathJax-script" async></script>
+  <script src="https://cdn.jsdelivr.net/npm/marked/lib/marked.umd.min.js"></script>
+  <style>
+    @import url('https://fonts.googleapis.com/css2?family=Space+Grotesk:wght@400;700&display=swap');
+    body {
+      font-family: 'Space Grotesk', sans-serif;
+    }
+    .uploadArea {
+      background: #f3f4f6;
+      border: 2px dashed #d1d5db;
+      transition: border-color 0.2s ease;
+    }
+    .uploadArea:hover {
+      border-color: #3b82f6;
+    }
+    .blue-button {
+      background: #3b82f6;
+      transition: background-color 0.2s ease;
+    }
+    .blue-button:hover {
+      background: #2563eb;
+    }
+    .loader {
+      width: 48px;
+      height: 48px;
+      border: 3px solid #3b82f6;
+      border-bottom-color: transparent;
+      border-radius: 50%;
+      display: inline-block;
+      animation: rotation 1s linear infinite;
+    }
+    @keyframes rotation {
+      0% { transform: rotate(0deg); }
+      100% { transform: rotate(360deg); }
+    }
+    .thought-box {
+      transition: max-height 0.3s ease-out;
+      max-height: 0;
+      overflow: hidden;
+    }
+    .thought-box.open {
+      max-height: 500px;
+    }
+    #thoughtsContent, #answerContent {
+      max-height: 500px;
+      overflow-y: auto;
+      scroll-behavior: smooth;
+      white-space: pre-wrap;
+    }
+    .preview-image {
+      max-width: 300px;
+      max-height: 300px;
+      object-fit: contain;
+    }
+    .timestamp {
+      color: #3b82f6;
+      font-size: 0.9em;
+      margin-left: 8px;
+    }
+    /* Styles supplémentaires pour une meilleure présentation des tableaux */
+    table {
+      border-collapse: collapse;
+      width: 100%;
+      margin-bottom: 1rem;
+    }
+    th, td {
+      border: 1px solid #d1d5db;
+      padding: 0.5rem;
+      text-align: left;
+    }
+    th {
+      background-color: #f3f4f6;
+      font-weight: 600;
+    }
+    /* Pour un rendu responsive, ajouter éventuellement : */
+    .table-responsive {
+      overflow-x: auto;
+    }
+  </style>
 </head>
 <body class="p-4">
+  <div class="max-w-4xl mx-auto">
+    <header class="p-6 text-center mb-8">
+      <h1 class="text-4xl font-bold text-blue-600">Mariam M-0</h1>
+      <p class="text-gray-600">Solution Mathématique/Physique/Chimie Intelligente</p>
+    </header>
+    <main>
+      <form id="problemForm" class="space-y-6" novalidate>
+        <!-- Zone de dépôt et sélection d'image -->
+        <div class="uploadArea p-8 text-center relative" aria-label="Zone de dépôt d'image">
+          <input type="file" id="imageInput" accept="image/*" class="absolute inset-0 w-full h-full opacity-0 cursor-pointer" aria-label="Choisir une image">
+          <div class="space-y-3">
+            <div class="w-16 h-16 mx-auto border-2 border-blue-400 rounded-full flex items-center justify-center">
+              <svg class="w-8 h-8 text-blue-400" fill="none" stroke="currentColor" viewBox="0 0 24 24" aria-hidden="true">
+                <path stroke-linecap="round" stroke-linejoin="round" stroke-width="2"
+                  d="M4 16l4.586-4.586a2 2 0 012.828 0L16 16m-2-2l1.586-1.586a2 2 0 012.828 0L20 14m-6-6h.01M6 20h12a2 2 0 002-2V6a2 2 0 00-2-2H6a2 2 0 00-2 2v12a2 2 0 002 2z" />
+              </svg>
             </div>
+            <p class="text-gray-700 font-medium">Déposez votre image ici</p>
+            <p class="text-gray-500 text-sm">ou cliquez pour sélectionner</p>
+          </div>
+        </div>
+        <!-- Aperçu de l'image -->
+        <div id="imagePreview" class="hidden text-center">
+          <img id="previewImage" class="preview-image mx-auto" alt="Prévisualisation de l'image sélectionnée">
+        </div>
+        <button type="submit" class="blue-button w-full py-3 text-white font-medium rounded-lg">
+          Résoudre le problème
+        </button>
+      </form>
+      <!-- Loader d'analyse -->
+      <div id="loader" class="hidden mt-8 text-center">
+        <span class="loader"></span>
+        <p class="mt-4 text-gray-600">Analyse en cours...</p>
+      </div>
+      <!-- Affichage de la solution -->
+      <section id="solution" class="hidden mt-8 space-y-6">
+        <div class="border-t pt-4">
+          <button id="thoughtsToggle" type="button" class="w-full flex justify-between items-center p-2">
+            <span class="font-medium text-gray-700">Processus de Réflexion</span>
+            <span id="timestamp" class="timestamp"></span>
+          </button>
+          <div id="thoughtsBox" class="thought-box">
+            <div id="thoughtsContent" class="p-4 text-gray-600"></div>
+          </div>
         </div>
+        <div class="border-t pt-6">
+          <h3 class="text-xl font-bold text-gray-800 mb-4">Solution</h3>
+          <!-- Enveloppement d'éventuels tableaux dans une div responsive -->
+          <div id="answerContent" class="text-gray-700 table-responsive"></div>
+        </div>
+      </section>
+    </main>
+  </div>
+  <script>
+    document.addEventListener('DOMContentLoaded', () => {
+      // Récupération des éléments DOM
+      const form = document.getElementById('problemForm');
+      const imageInput = document.getElementById('imageInput');
+      const loader = document.getElementById('loader');
+      const solutionSection = document.getElementById('solution');
+      const thoughtsContent = document.getElementById('thoughtsContent');
+      const answerContent = document.getElementById('answerContent');
+      const thoughtsToggle = document.getElementById('thoughtsToggle');
+      const thoughtsBox = document.getElementById('thoughtsBox');
+      const imagePreview = document.getElementById('imagePreview');
+      const previewImage = document.getElementById('previewImage');
+      const timestamp = document.getElementById('timestamp');
+      let startTime = null;
+      let timerInterval = null;
+      let thoughtsBuffer = '';
+      let answerBuffer = '';
+      let currentMode = null;
+      // Mise à jour de l'affichage du temps écoulé
+      const updateTimestamp = () => {
+        if (startTime) {
+          const seconds = Math.floor((Date.now() - startTime) / 1000);
+          timestamp.textContent = `${seconds}s`;
+        }
+      };
+      const startTimer = () => {
+        startTime = Date.now();
+        timerInterval = setInterval(updateTimestamp, 1000);
+        updateTimestamp();
+      };
+      const stopTimer = () => {
+        clearInterval(timerInterval);
+        startTime = null;
+        timestamp.textContent = '';
+      };
+      // Gestion de la sélection ou du dépôt de l'image
+      const handleFileSelect = file => {
+        if (!file) return;
+        const reader = new FileReader();
+        reader.onload = e => {
+          previewImage.src = e.target.result;
+          imagePreview.classList.remove('hidden');
+        };
+        reader.readAsDataURL(file);
+      };
+      // Toggle pour afficher/cacher le processus de réflexion
+      thoughtsToggle.addEventListener('click', () => {
+        thoughtsBox.classList.toggle('open');
+      });
+      imageInput.addEventListener('change', e => handleFileSelect(e.target.files[0]));
+      // Gestion des événements de glisser-déposer
+      const dropZone = document.querySelector('.uploadArea');
+      dropZone.addEventListener('dragover', e => {
+        e.preventDefault();
+        dropZone.classList.add('border-blue-400');
+      });
+      dropZone.addEventListener('dragleave', e => {
+        e.preventDefault();
+        dropZone.classList.remove('border-blue-400');
+      });
+      dropZone.addEventListener('drop', e => {
+        e.preventDefault();
+        dropZone.classList.remove('border-blue-400');
+        handleFileSelect(e.dataTransfer.files[0]);
+      });
+      // Fonction pour relancer le rendu MathJax dès que le contenu de la réponse est mis à jour
+      const typesetAnswerIfReady = async () => {
+        if (window.mathJaxReady) {
+          MathJax.startup.document.elements = [document.getElementById('answerContent')];
+          await MathJax.typesetPromise();
+          answerContent.scrollTop = answerContent.scrollHeight;
+        } else {
+          setTimeout(typesetAnswerIfReady, 200);
+        }
+      };
+      // Configuration de marked avec support du mode GFM (pour les tableaux) et interprétation des sauts de ligne
+      marked.setOptions({
+        gfm: true,
+        breaks: true
+      });
+      // Soumission du formulaire
+      form.addEventListener('submit', async e => {
+        e.preventDefault();
+        const file = imageInput.files[0];
+        if (!file) {
+          alert('Veuillez sélectionner une image.');
+          return;
+        }
+        // Initialisation de l'affichage et des variables
+        startTimer();
+        loader.classList.remove('hidden');
+        solutionSection.classList.add('hidden');
+        thoughtsContent.innerHTML = '';
+        answerContent.innerHTML = '';
+        thoughtsBuffer = '';
+        answerBuffer = '';
+        currentMode = null;
+        thoughtsBox.classList.add('open');
+        const formData = new FormData();
+        formData.append('image', file);
+        try {
+          // Envoi de la requête au serveur
+          const response = await fetch('/solve', {
+            method: 'POST',
+            body: formData
+          });
+          const reader = response.body.getReader();
+          const decoder = new TextDecoder();
+          let buffer = '';
+          // Traitement d'un chunk de données
+          const processChunk = async chunk => {
+            buffer += decoder.decode(chunk, { stream: true });
+            const lines = buffer.split('\n\n');
+            buffer = lines.pop(); // Conserver la dernière ligne incomplète
+            for (const line of lines) {
+              if (!line.startsWith('data:')) continue;
+              const data = JSON.parse(line.slice(5));
+              if (data.mode) {
+                currentMode = data.mode;
+                loader.classList.add('hidden');
+                solutionSection.classList.remove('hidden');
+              }
+              if (data.content) {
+                if (currentMode === 'thinking') {
+                  thoughtsBuffer += data.content;
+                } else if (currentMode === 'answering') {
+                  answerBuffer += data.content;
                 }
+              }
+            }
+            // Mise à jour de l'affichage en temps réel
+            thoughtsContent.innerHTML = marked.parse(thoughtsBuffer);
+            answerContent.innerHTML = marked.parse(answerBuffer);
+            await typesetAnswerIfReady();
+          };
+          // Lecture du flux de réponse
+          while (true) {
+            const { done, value } = await reader.read();
+            if (done) {
+              // Traitement du contenu restant dans le buffer
+              if (buffer) {
+                const data = JSON.parse(buffer.slice(5));
+                if (data.content) {
+                  if (currentMode === 'thinking') {
+                    thoughtsBuffer += data.content;
+                  } else if (currentMode === 'answering') {
+                    answerBuffer += data.content;
+                  }
                 }
+              }
+              thoughtsContent.innerHTML = marked.parse(thoughtsBuffer);
+              answerContent.innerHTML = marked.parse(answerBuffer);
+              await typesetAnswerIfReady();
+              break;
+            }
+            await processChunk(value);
+          }
+          stopTimer();
+        } catch (error) {
+          console.error('Erreur:', error);
+          alert('Une erreur est survenue.');
+          loader.classList.add('hidden');
+          stopTimer();
+        }
+      });
+    });
+  </script>
 </body>
+</html>