from types import NotImplementedType
from typing import Literal
from typing_extensions import Self

from sympy.core import Basic

class OmegaPower(Basic):
    def __new__(cls, a, b) -> Self: ...
    @property
    def exp(self) -> Basic: ...
    @property
    def mult(self) -> Basic: ...
    def __eq__(self, other) -> bool: ...
    def __hash__(self) -> int: ...
    def __lt__(self, other) -> bool: ...

class Ordinal(Basic):
    def __new__(cls, *terms) -> Self: ...
    @property
    def terms(self) -> tuple[Basic, ...]: ...
    @property
    def leading_term(self) -> Basic: ...
    @property
    def trailing_term(self) -> Basic: ...
    @property
    def is_successor_ordinal(self) -> Literal[False]: ...
    @property
    def is_limit_ordinal(self) -> bool: ...
    @property
    def degree(self): ...
    @classmethod
    def convert(cls, integer_value) -> OrdinalZero | Ordinal: ...
    def __eq__(self, other) -> bool: ...
    def __hash__(self) -> int: ...
    def __lt__(self, other) -> bool: ...
    def __le__(self, other) -> bool: ...
    def __gt__(self, other) -> bool: ...
    def __ge__(self, other) -> bool: ...

    __repr__ = ...
    def __add__(self, other) -> NotImplementedType | Self | Ordinal: ...
    def __radd__(self, other) -> NotImplementedType | OrdinalZero | Ordinal: ...
    def __mul__(self, other) -> NotImplementedType | OrdinalZero | Ordinal: ...
    def __rmul__(self, other) -> NotImplementedType | OrdinalZero | Ordinal: ...
    def __pow__(self, other) -> NotImplementedType | Ordinal: ...

class OrdinalZero(Ordinal): ...

class OrdinalOmega(Ordinal):
    def __new__(cls) -> Self: ...
    @property
    def terms(self) -> tuple[OmegaPower]: ...

ord0 = ...
omega = ...
