Symbolic Algebra MCP Server

Instructions

Args:
    scalar_field_key: The key of the scalar field expression.

Example:
    # First create a coordinate system
    create_coordinate_system("R")

    # Create a scalar field f = x^2 + y^2 + z^2
    scalar_field = introduce_expression("R_x**2 + R_y**2 + R_z**2")

    # Calculate gradient
    grad_result = calculate_gradient(scalar_field)
    # Returns (2x, 2y, 2z)

Returns:
    A key for the gradient vector field expression.

Implementation Reference

• server.py:1270-1309 (handler)

  The core handler implementation for the 'calculate_gradient' MCP tool. It retrieves a scalar field expression by key, computes its gradient using SymPy's vector.gradient function (which requires a coordinate system context from prior tool calls), stores the resulting vector field with a generated key, and returns that key. The @mcp.tool() decorator registers it as an MCP tool.

  @mcp.tool()
  def calculate_gradient(scalar_field_key: str) -> str:
      """Calculates the gradient of a scalar field using SymPy's gradient function.
  
      Args:
          scalar_field_key: The key of the scalar field expression.
  
      Example:
          # First create a coordinate system
          create_coordinate_system("R")
  
          # Create a scalar field f = x^2 + y^2 + z^2
          scalar_field = introduce_expression("R_x**2 + R_y**2 + R_z**2")
  
          # Calculate gradient
          grad_result = calculate_gradient(scalar_field)
          # Returns (2x, 2y, 2z)
  
      Returns:
          A key for the gradient vector field expression.
      """
      global expression_counter
  
      if scalar_field_key not in expressions:
          return f"Error: Scalar field with key '{scalar_field_key}' not found."
  
      try:
          scalar_field = expressions[scalar_field_key]
  
          # Calculate gradient
          grad_result = gradient(scalar_field)
  
          # Store the result
          result_key = f"vector_{expression_counter}"
          expressions[result_key] = grad_result
          expression_counter += 1
  
          return result_key
      except Exception as e:
          return f"Error calculating gradient: {str(e)}"

• server.py:1270-1270 (registration)

  The @mcp.tool() decorator registers the calculate_gradient function as an MCP tool.

  @mcp.tool()

• tests/test_calculus.py:215-235 (handler)

  Unit test demonstrating usage of calculate_gradient tool.

  def test_calculate_gradient(self):
      # Create coordinate system
      create_coordinate_system("R")
  
      # Introduce variables
      intro("x", [Assumption.REAL], [])
      intro("y", [Assumption.REAL], [])
      intro("z", [Assumption.REAL], [])
  
      # Create a simple scalar field
      scalar_field_key = introduce_expression("x**2 + y**2 + z**2")
  
      # Calculate gradient
      grad_key = calculate_gradient(scalar_field_key)
  
      # Check if gradient calculation was successful
      if "error" not in grad_key.lower():
          assert grad_key.startswith("vector_")
      else:
          assert False, f"Failed to calculate gradient: {grad_key}"