from typing import Optional, Dict, List, Tuple, Union

class Expression:
    @staticmethod
    def parse(s: str) -> "Expression": ...
    @staticmethod
    def symbol(name: str) -> "Expression": ...
    @staticmethod
    def num(n: int) -> "Expression": ...
    @staticmethod
    def float(f: float) -> "Expression": ...

    def simplify(self) -> "Expression": ...
    def expand(self) -> "Expression": ...
    def derivative(self, var: str) -> "Expression": ...
    def diff(self, var: str) -> "Expression": ...
    def integrate(self, var: str) -> "Expression": ...
    def limit(self, var: str, value: float) -> "LimitResult": ...
    def solve(self, var: str) -> List["Expression"]: ...
    def series(self, var: str, point: float, order: int) -> "Expression": ...
    def evaluate(self, bindings: Dict[str, float]) -> float: ...
    def to_latex(self) -> str: ...
    def to_code(self, language: str) -> str: ...
    def variables(self) -> List[str]: ...
    def substitute(self, var: str, replacement: "Expression") -> "Expression": ...
    def replace(self, pattern: str, replacement: str) -> "Expression": ...
    def check_dimensions(self, context: Dict[str, str]) -> str: ...
    def laplace(self, t_var: str, s_var: str) -> Optional["Expression"]: ...
    def fourier(self, t_var: str, omega_var: str) -> Optional["Expression"]: ...

    def __add__(self, other: "Expression") -> "Expression": ...
    def __radd__(self, other: object) -> "Expression": ...
    def __sub__(self, other: "Expression") -> "Expression": ...
    def __mul__(self, other: "Expression") -> "Expression": ...
    def __rmul__(self, other: object) -> "Expression": ...
    def __truediv__(self, other: "Expression") -> "Expression": ...
    def __neg__(self) -> "Expression": ...
    def __pow__(self, exp: "Expression") -> "Expression": ...
    def __str__(self) -> str: ...
    def __repr__(self) -> str: ...

class LimitResult:
    @property
    def value(self) -> Optional["Expression"]: ...
    @property
    def is_finite(self) -> bool: ...
    @property
    def description(self) -> str: ...
    def __str__(self) -> str: ...
    def __repr__(self) -> str: ...

def S(names: str) -> Union["Expression", Tuple["Expression", ...]]: ...
def E(s: str) -> "Expression": ...
def N(n: int) -> "Expression": ...
def is_prime(n: int) -> bool: ...
def factorize(n: int) -> List[Tuple[int, int]]: ...
def gcd(a: int, b: int) -> int: ...
def fibonacci(n: int) -> int: ...