Symbolic Algebra MCP Server

Instructions

Implementation Reference

• server.py:1186-1226 (handler)

  The core handler function for the 'calculate_curl' MCP tool. It retrieves a stored vector field by key, computes its curl using SymPy's vector.curl function, stores the resulting vector field expression with a new auto-generated key in the global 'expressions' dictionary, and returns that key. The @mcp.tool() decorator registers this function as an MCP tool.
  @mcp.tool() def calculate_curl(vector_field_key: str) -> str: """Calculates the curl of a vector field using SymPy's curl function. Args: vector_field_key: The key of the vector field expression. Example: # First create a coordinate system create_coordinate_system("R") # Create a vector field F = (y, -x, 0) vector_field = create_vector_field("R", "R_y", "-R_x", "0") # Calculate curl curl_result = calculate_curl(vector_field) # Returns (0, 0, -2) Returns: A key for the curl expression. """ global expression_counter if vector_field_key not in expressions: return f"Error: Vector field with key '{vector_field_key}' not found." try: vector_field = expressions[vector_field_key] # Calculate curl curl_result = curl(vector_field) # Store the result result_key = f"vector_{expression_counter}" expressions[result_key] = curl_result expression_counter += 1 return result_key except Exception as e: return f"Error calculating curl: {str(e)}"
• server.py:1080-1131 (helper)

  Helper tool to create a SymPy 3D coordinate system (CoordSys3D), required before creating vector fields for curl computation.
  def create_coordinate_system(name: str, coord_names: Optional[List[str]] = None) -> str: """Creates a 3D coordinate system for vector calculus operations. Args: name: The name for the coordinate system. coord_names: Optional list of coordinate names (3 names for x, y, z). If not provided, defaults to [name+'_x', name+'_y', name+'_z']. Example: # Create a coordinate system coord_sys = create_coordinate_system("R") # Creates a coordinate system R with coordinates R_x, R_y, R_z # Create a coordinate system with custom coordinate names coord_sys = create_coordinate_system("C", ["rho", "phi", "z"]) Returns: The name of the created coordinate system. """ if name in coordinate_systems: return f"Warning: Overwriting existing coordinate system '{name}'." try: if coord_names and len(coord_names) != 3: return "Error: coord_names must contain exactly 3 names for x, y, z coordinates." if coord_names: # Create a CoordSys3D with custom coordinate names cs = CoordSys3D(name, variable_names=coord_names) else: # Create a CoordSys3D with default coordinate naming cs = CoordSys3D(name) coordinate_systems[name] = cs # Add the coordinate system to the expressions dict to make it accessible # in expressions through parsing expressions[name] = cs # Add the coordinate variables to local_vars for easier access for i, base_vector in enumerate(cs.base_vectors()): vector_name = ( f"{name}_{['x', 'y', 'z'][i]}" if not coord_names else f"{name}_{coord_names[i]}" ) local_vars[vector_name] = base_vector return name except Exception as e: return f"Error creating coordinate system: {str(e)}"
• server.py:1133-1184 (helper)

  Helper tool to create a vector field expression in a coordinate system by parsing string components and combining with base vectors, prerequisite for calculate_curl.
  @mcp.tool() def create_vector_field( coord_sys_name: str, component_x: str, component_y: str, component_z: str ) -> str: """Creates a vector field in the specified coordinate system. Args: coord_sys_name: The name of the coordinate system to use. component_x: String expression for the x-component of the vector field. component_y: String expression for the y-component of the vector field. component_z: String expression for the z-component of the vector field. Example: # First create a coordinate system create_coordinate_system("R") # Create a vector field F = (y, -x, z) vector_field = create_vector_field("R", "R_y", "-R_x", "R_z") Returns: A key for the vector field expression. """ global expression_counter if coord_sys_name not in coordinate_systems: return f"Error: Coordinate system '{coord_sys_name}' not found. Create it first using create_coordinate_system." try: cs = coordinate_systems[coord_sys_name] # Parse the component expressions parse_dict = {**local_vars, **functions, coord_sys_name: cs} x_comp = parse_expr(component_x, local_dict=parse_dict) y_comp = parse_expr(component_y, local_dict=parse_dict) z_comp = parse_expr(component_z, local_dict=parse_dict) # Create the vector field vector_field = ( x_comp * cs.base_vectors()[0] + y_comp * cs.base_vectors()[1] + z_comp * cs.base_vectors()[2] ) # Store the vector field result_key = f"vector_{expression_counter}" expressions[result_key] = vector_field expression_counter += 1 return result_key except Exception as e: return f"Error creating vector field: {str(e)}"
• server.py:1186-1226 (registration)

  The @mcp.tool() decorator on calculate_curl registers it in the FastMCP server instance 'mcp'.
  @mcp.tool() def calculate_curl(vector_field_key: str) -> str: """Calculates the curl of a vector field using SymPy's curl function. Args: vector_field_key: The key of the vector field expression. Example: # First create a coordinate system create_coordinate_system("R") # Create a vector field F = (y, -x, 0) vector_field = create_vector_field("R", "R_y", "-R_x", "0") # Calculate curl curl_result = calculate_curl(vector_field) # Returns (0, 0, -2) Returns: A key for the curl expression. """ global expression_counter if vector_field_key not in expressions: return f"Error: Vector field with key '{vector_field_key}' not found." try: vector_field = expressions[vector_field_key] # Calculate curl curl_result = curl(vector_field) # Store the result result_key = f"vector_{expression_counter}" expressions[result_key] = curl_result expression_counter += 1 return result_key except Exception as e: return f"Error calculating curl: {str(e)}"