sympy_mcp_calculus_operation

Instructions

Implementation Reference

• fmcp/sympy_mcp/core/calculus.py:14-109 (handler)

  Handler function implementing the core logic for the 'sympy_mcp_calculus_operation' tool, supporting diff, integrate, limit, and series operations using SymPy.

  def calculus_operation(
      operation: CalculusOperation,
      expr: str,
      sym: Optional[str] = None,
      # diff parameters
      n: int = 1,
      # integrate parameters
      lower: Optional[Union[int, float, str]] = None,
      upper: Optional[Union[int, float, str]] = None,
      # limit parameters
      point: Union[int, float, str] = 0,
      direction: Literal["+", "-"] = "+",
      # series parameters
      series_n: int = 6,
  ) -> str:
      """
      Unified interface for calculus operations.
  
      Args:
          operation: The calculus operation to perform. One of:
              - 'diff': Differentiate the expression
              - 'integrate': Integrate the expression
              - 'limit': Compute the limit of the expression
              - 'series': Compute the series expansion of the expression
          expr: The expression to process as a string
          sym: The symbol to differentiate/integrate with respect to, or the variable for limits/series
          n: Order of derivative for 'diff' or order of series expansion for 'series' (default: 1 for 'diff', 6 for 'series')
          lower: Lower limit for definite integral (only for 'integrate')
          upper: Upper limit for definite integral (only for 'integrate')
          point: The point to approach for 'limit' or about which to expand for 'series' (default: 0)
          direction: Direction to approach from for 'limit' ('+' or '-', default: '+')
  
      Returns:
          str: The result of the operation as a string
  
      Examples:
          >>> calculus_operation('diff', 'x**2 + 2*x + 1', 'x')
          '2*x + 2'
          >>> calculus_operation('integrate', '2*x + 2', 'x')
          'x**2 + 2*x'
          >>> calculus_operation('limit', 'sin(x)/x', 'x', point=0)
          '1'
          >>> calculus_operation('series', 'exp(x)', 'x', point=0, n=3)
          '1 + x + x**2/2 + O(x**3)'
      """
      # Convert string to SymPy expression
      expr_obj = sympify(expr)
  
      # Convert symbol string to Symbol if provided
      sym_obj = sympify(sym) if sym is not None else None
  
      if operation == "diff":
          # Handle differentiation
          if sym_obj is None:
              raise ValueError("Symbol must be provided for differentiation")
          return str(_diff(expr_obj, sym_obj, n))
  
      elif operation == "integrate":
          # Handle integration
          if sym_obj is None:
              raise ValueError("Symbol must be provided for integration")
  
          # Check for definite integral
          if lower is not None or upper is not None:
              # Definite integral
              lower_val = sympify(lower) if isinstance(lower, str) else lower
              upper_val = sympify(upper) if isinstance(upper, str) else upper
              return str(_integrate(expr_obj, (sym_obj, lower_val, upper_val)))
          else:
              # Indefinite integral
              return str(_integrate(expr_obj, sym_obj))
  
      elif operation == "limit":
          # Handle limits
          if sym_obj is None:
              raise ValueError("Symbol must be provided for limit")
  
          # Convert point to SymPy expression if it's a string
          point_val = sympify(point) if isinstance(point, str) else point
  
          return str(_limit(expr_obj, sym_obj, point_val, direction))
  
      elif operation == "series":
          # Handle series expansion
          if sym_obj is None:
              raise ValueError("Symbol must be provided for series expansion")
  
          # Convert point to SymPy expression if it's a string
          point_val = sympify(point) if isinstance(point, str) else point
  
          return str(_series(expr_obj, sym_obj, point_val, series_n).removeO())
  
      else:
          valid_ops = get_args(CalculusOperation)
          raise ValueError(f"Invalid operation. Must be one of: {valid_ops}")

• fmcp/sympy_mcp/server.py:18-21 (registration)

  Registration of the calculus_operation handler as the 'sympy_mcp_calculus_operation' tool in the FastMCP server.

  sympy_mcp.tool(
      calculus_operation,
      description="Do calculus operations like diff, integrate, limit, series",
  )

• fmcp/sympy_mcp/core/calculus.py:1-11 (schema)

  Type definitions used for input schema validation, including CalculusOperation literal types and parameter annotations in the handler.

  from typing import Optional, Literal, get_args, Union
  from sympy import (
      sympify,
      diff as _diff,
      integrate as _integrate,
      limit as _limit,
      series as _series,
  )
  
  # Define operation types for type hints
  CalculusOperation = Literal["diff", "integrate", "limit", "series"]