Fermat MCP

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"] 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}")