DDx: Dynamic Diagnosis System for Mathematical Problem Solving

DDx (Dynamic Diagnosis) is an intelligent, iterative problem-solving system inspired by the critical-thinking process seen in House M.D.. It is designed to break down complex mathematical problems into manageable phases, leveraging multiple agents to collaboratively solve and refine solutions.

🚀 Features

• Phased Problem Solving: DDx splits problem-solving into six logical phases:

  1. Understanding: Decipher the problem statement and identify goals.
  2. Decomposition: Break the problem into smaller, solvable components.
  3. Planning: Create a strategy to solve the subproblems.
  4. Execution: Solve each component systematically.
  5. Verification: Validate the solutions against the original problem.
  6. Compilation: Combine results into a cohesive final answer.

• Interactive Agents: Mimics the dynamic interaction of "House" (critical guide) and "Team" (problem solvers) to iteratively improve solutions.

• Tool Integration: Leverages symbolic computation (e.g., SymPy) for mathematical operations during the execution phase.

• Verbose Debugging: Option to enable detailed output for tracking agent reasoning and decision-making.

🧠 How It Works

1. Input a Problem: Provide a complex mathematical or symbolic problem to DDx.
2. Iterative Problem-Solving:
   • The "House" agent oversees the process, iteratively questioning and refining the solution.
   • The "Team" agent generates outputs for each phase.
3. Tools & Execution: Utilize computational tools like SymPy for precise calculations.
4. Verification & Refinement: Validate and refine solutions until the "House" agent is satisfied.
5. Final Answer: Output a fully solved and explained solution.

🔨 How to use?

Ensure you have OPENAI_API_KEY in the environment and the API is just one function.

from ddx_ai import DDx

DDx("<question>", verbose=False)

📄 Example Usage

Input Problem

Nondimensionalize the polynomial: [ P(x) = a_1 x^{25} + a_2 x + a_3 ] into the form: [ \epsilon y^{25} + y + 1 ] Express (\epsilon) as a function of (a_1), (a_2), and (a_3).

Output

1. Understanding Phase:

   • Identify the goal: Transform the polynomial into the specified nondimensional form.
   • Extract key coefficients: (a_1), (a_2), (a_3).

2. Decomposition Phase:

   • Break the problem into:
     • Variable scaling ((L)) to make (y^1) coefficient equal to 1.
     • Normalizing the constant term to 1.
     • Calculating (\epsilon).

3. Execution Phase:

   • Perform substitutions: (x = L y), where (L = \frac{1}{a_2}).
   • Solve for (\epsilon = \frac{a_1 a_3^{24}}{a_2^{25}}).

4. Verification Phase:

   • Substitute back into the polynomial to ensure it matches the desired form.

5. Compilation Phase:

   • Final answer: [ \boxed{\epsilon = \frac{a_1 a_3^{24}}{a_2^{25}}} ]

💡 Key Design Principles

1. Iterative Refinement:
   • Mimics real-world diagnostic processes to refine solutions through critical questioning.
2. Dynamic Interactions:
   • Encourages agents to think critically, ensuring high-quality solutions.
3. Phased Approach:
   • Logical segmentation for tackling complex problems methodically.