Update app.py

app.py

@@ -24,6 +24,71 @@ anthropic = Anthropic(
 MAX_REQUESTS_PER_DAY = 25
 request_history = deque(maxlen=1000)
 
+def get_difficulty_parameters(difficulty_level):
+    """Return specific parameters and constraints based on difficulty level"""
+    parameters = {
+        1: {  # Very Easy
+            "description": "very easy, suitable for beginners",
+            "constraints": [
+                "Use only basic concepts and straightforward calculations",
+                "Break complex problems into smaller, guided steps",
+                "Provide hints within the question when needed",
+                "Use simple numbers and avoid complex algebraic expressions"
+            ],
+            "example_style": "Similar to standard homework problems",
+            "model": "claude-3-sonnet-20240229"
+        },
+        2: {  # Easy
+            "description": "easy, but requiring some thought",
+            "constraints": [
+                "Use basic concepts with minor complications",
+                "Include two-step problems",
+                "Minimal guidance provided",
+                "Use moderately complex numbers or expressions"
+            ],
+            "example_style": "Similar to quiz questions",
+            "model": "claude-3-sonnet-20240229"
+        },
+        3: {  # Intermediate
+            "description": "intermediate difficulty, testing deeper understanding",
+            "constraints": [
+                "Combine 2-3 related concepts",
+                "Include some non-obvious solution paths",
+                "Require multi-step reasoning",
+                "Use moderate algebraic complexity"
+            ],
+            "example_style": "Similar to midterm exam questions",
+            "model": "claude-3-sonnet-20240229"
+        },
+        4: {  # Difficult
+            "description": "challenging, requiring strong mathematical maturity",
+            "constraints": [
+                "Combine multiple concepts creatively",
+                "Require insight and deep understanding",
+                "Include non-standard approaches",
+                "Use sophisticated mathematical reasoning"
+            ],
+            "example_style": "Similar to final exam questions",
+            "model": "claude-3-opus-20240229"
+        },
+        5: {  # Very Difficult
+            "description": "very challenging, testing mastery and creativity at a graduate level",
+            "constraints": [
+                "Create novel applications of theoretical concepts",
+                "Require graduate-level mathematical reasoning",
+                "Combine multiple advanced topics in unexpected ways",
+                "Demand creative problem-solving approaches",
+                "Include rigorous proof construction",
+                "Require synthesis across mathematical domains",
+                "Test deep theoretical understanding"
+            ],
+            "example_style": "Similar to graduate qualifying exams or advanced competition problems",
+            "model": "claude-3-opus-20240229"
+        }
+    }
+    
+    return parameters.get(difficulty_level)
+
 def create_latex_document(content, questions_only=False):
     """Create a complete LaTeX document"""
     try:
@@ -96,7 +161,7 @@ def validate_question_counts(computation, proof, application):
         return False, "Please enter valid numbers"
 
 def generate_test(subject, difficulty, computation_count, proof_count, application_count):
-    """Generate a math test"""
+    """Generate a math test with enhanced difficulty scaling"""
     try:
         # Validate inputs
         is_valid, error_message = validate_question_counts(
@@ -136,31 +201,76 @@ def generate_test(subject, difficulty, computation_count, proof_count, applicati
             ["application"] * int(application_count)
         )
         
-        difficulty_descriptions = {
-            1: "very easy",
-            2: "easy",
-            3: "intermediate difficulty",
-            4: "difficult",
-            5: "very difficult"
-        }
+        difficulty_params = get_difficulty_parameters(difficulty)
         
-        system_prompt = f"""You will write math exam questions. Follow these requirements EXACTLY:
-        1. Write exactly 3 university-level questions focusing on these specific topics: {', '.join(selected_topics)}
-        2. Include the following question types in this exact order:
-           {', '.join(question_types)}
-        3. Make all questions {difficulty_descriptions[difficulty]} difficulty
-        4. For LaTeX math formatting:
-           - Use $ for simple inline math
-           - For equations and solution steps, use $$ on separate lines
-           - For multi-step solutions, put each step on its own line in $$ $$
-           - DO NOT use \\begin{{aligned}} or any other environments
-        5. Number each question as 1), 2), 3)
-        6. Include detailed solutions after each question
-        7. Keep formatting simple and clear"""
+        # Enhanced prompt for difficulty level 5
+        if difficulty == 5:
+            system_prompt = f"""You are an expert mathematics professor creating graduate-level exam questions.
+
+STRICT REQUIREMENTS:
+1. Write exactly 3 graduate-level questions on {subject} with these specific characteristics:
+   - Question Types (in order): {', '.join(question_types)}
+   - Topics to cover: {', '.join(selected_topics)}
+
+2. Advanced Difficulty Requirements:
+   These questions must be suitable for PhD qualifying exams or advanced competitions.
+   MUST include:
+   - Novel applications of theoretical concepts
+   - Graduate-level mathematical reasoning
+   - Unexpected connections between different areas of {subject}
+   - Creative problem-solving approaches
+   - Rigorous proof requirements where applicable
+   
+   Follow these specific constraints:
+   {chr(10).join(f'   - {c}' for c in difficulty_params['constraints'])}
+
+3. Style Reference:
+   Questions should be {difficulty_params['example_style']}
+
+4. Each question MUST:
+   - Bridge multiple mathematical domains
+   - Require deep theoretical understanding
+   - Test mastery of advanced concepts
+   - Demand innovative solution approaches
+
+5. For LaTeX formatting:
+   - Use $ for inline math
+   - Use $$ on separate lines for equations and solutions
+   - Put each solution step on its own line in $$ $$
+   - DO NOT use \\begin{{aligned}} or similar environments
+
+6. Number questions as 1), 2), 3)
+7. Include detailed solutions with thorough explanations of advanced concepts used
+8. Maintain clear, precise formatting"""
+        else:
+            system_prompt = f"""You are an expert mathematics professor creating {difficulty_params['description']} exam questions.
+
+STRICT REQUIREMENTS:
+1. Write exactly 3 university-level questions on {subject} with these specific characteristics:
+   - Question Types (in order): {', '.join(question_types)}
+   - Topics to cover: {', '.join(selected_topics)}
+
+2. Difficulty Level Guidelines:
+   {difficulty_params['description'].upper()}
+   Follow these specific constraints:
+   {chr(10).join(f'   - {c}' for c in difficulty_params['constraints'])}
+
+3. Style Reference:
+   Questions should be {difficulty_params['example_style']}
+
+4. For LaTeX formatting:
+   - Use $ for inline math
+   - Use $$ on separate lines for equations and solutions
+   - Put each solution step on its own line in $$ $$
+   - DO NOT use \\begin{{aligned}} or similar environments
+
+5. Number questions as 1), 2), 3)
+6. Include detailed solutions
+7. Maintain clear formatting"""
         
         logger.debug("Sending request to Anthropic API")
         message = anthropic.messages.create(
-            model="claude-3-opus-20240229",
+            model=difficulty_params['model'],
             max_tokens=1500,
             temperature=0.7,
             messages=[{
@@ -195,7 +305,7 @@ def generate_test(subject, difficulty, computation_count, proof_count, applicati
 # Create Gradio interface
 with gr.Blocks() as interface:
     gr.Markdown("# Advanced Mathematics Test Generator")
-    gr.Markdown("""Generates unique university-level mathematics exam questions with solutions using Claude 3 Opus.
+    gr.Markdown("""Generates unique university-level mathematics exam questions with solutions using Claude 3.
     Each test features different topics and difficulty levels. Limited to 25 requests per day.""")
     
     with gr.Row():
@@ -223,7 +333,7 @@ with gr.Blocks() as interface:
                 step=1,
                 value=3,
                 label="Difficulty Level",
-                info="1: Easy, 3: Moderate, 5: Difficult"
+                info="1: Very Easy, 2: Easy, 3: Moderate, 4: Difficult, 5: Very Difficult"
             )
     
     with gr.Row():