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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?

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.