Symbolic Algebra MCP Server

Instructions

Args:
    expr_key: The key of the expression (previously introduced) to differentiate.
    var_name: The name of the variable to differentiate with respect to.
    order: The order of differentiation (default is 1 for first derivative).

Example:
    # Introduce a variable
    intro("x", [Assumption.REAL], [])

    # Create an expression to differentiate: x^3
    expr_key = introduce_expression("x**3")

    # First derivative
    first_deriv = differentiate_expression(expr_key, "x")
    # Returns 3x²

    # Second derivative
    second_deriv = differentiate_expression(expr_key, "x", 2)
    # Returns 6x

Returns:
    A key for the differentiated expression.

Implementation Reference

• server.py:1026-1077 (handler)

  The core handler function for the 'differentiate_expression' MCP tool. It retrieves a stored SymPy expression by key, differentiates it with respect to a specified variable and order using sympy.diff, stores the result in the global expressions dictionary with a new key, and returns that key. The @mcp.tool() decorator registers this function as an MCP tool.

  @mcp.tool()
  def differentiate_expression(expr_key: str, var_name: str, order: int = 1) -> str:
      """Differentiates an expression with respect to a variable using SymPy's diff function.
  
      Args:
          expr_key: The key of the expression (previously introduced) to differentiate.
          var_name: The name of the variable to differentiate with respect to.
          order: The order of differentiation (default is 1 for first derivative).
  
      Example:
          # Introduce a variable
          intro("x", [Assumption.REAL], [])
  
          # Create an expression to differentiate: x^3
          expr_key = introduce_expression("x**3")
  
          # First derivative
          first_deriv = differentiate_expression(expr_key, "x")
          # Returns 3x²
  
          # Second derivative
          second_deriv = differentiate_expression(expr_key, "x", 2)
          # Returns 6x
  
      Returns:
          A key for the differentiated expression.
      """
      global expression_counter
  
      if expr_key not in expressions:
          return f"Error: Expression with key '{expr_key}' not found."
  
      if var_name not in local_vars:
          return f"Error: Variable '{var_name}' not found. Please introduce it first."
  
      if order < 1:
          return "Error: Order of differentiation must be at least 1."
  
      try:
          expr = expressions[expr_key]
          var = local_vars[var_name]
  
          result = diff(expr, var, order)
  
          result_key = f"expr_{expression_counter}"
          expressions[result_key] = result
          expression_counter += 1
  
          return result_key
      except Exception as e:
          return f"Error during differentiation: {str(e)}"