from collections.abc import Generator
from typing import Any, Callable, Literal, NoReturn
from typing_extensions import Self

from sympy.core.basic import Basic
from sympy.core.symbol import Symbol
from sympy.polys.domains.gaussiandomains import GaussianIntegerRing, GaussianRationalField
from sympy.polys.orderings import LexOrder
from sympy.utilities import public

__all__ = ["Options"]

class Option:
    option: str | None = ...
    is_Flag = ...
    requires: list[str] = ...
    excludes: list[str] = ...
    after: list[str] = ...
    before: list[str] = ...
    @classmethod
    def default(cls) -> None: ...
    @classmethod
    def preprocess(cls, option) -> None: ...
    @classmethod
    def postprocess(cls, options) -> None: ...

class Flag(Option):
    is_Flag = ...

class BooleanOption(Option):
    @classmethod
    def preprocess(cls, value) -> bool: ...

class OptionType(type):
    def __init__(cls, *args, **kwargs) -> None: ...

@public
class Options(dict):
    __order__ = ...
    __options__: dict[str, type[Option]] = ...
    def __init__(self, gens, args, flags=..., strict=...) -> None: ...
    def clone(self, updates=...) -> Self: ...
    def __setattr__(self, attr, value) -> None: ...
    @property
    def args(self) -> dict[Any, Any]: ...
    @property
    def options(self) -> dict[Any, Any]: ...
    @property
    def flags(self) -> dict[Any, Any]: ...

class Expand(BooleanOption, metaclass=OptionType):
    option = ...
    requires: list[str] = ...
    excludes: list[str] = ...
    @classmethod
    def default(cls) -> Literal[True]: ...

class Gens(Option, metaclass=OptionType):
    option = ...
    requires: list[str] = ...
    excludes: list[str] = ...
    @classmethod
    def default(cls) -> tuple[()]: ...
    @classmethod
    def preprocess(cls, gens) -> tuple[Basic, ...]: ...

class Wrt(Option, metaclass=OptionType):
    option = ...
    requires: list[str] = ...
    excludes: list[str] = ...
    _re_split = ...
    @classmethod
    def preprocess(cls, wrt) -> list[str] | list[Any] | list[str | Any]: ...

class Sort(Option, metaclass=OptionType):
    option = ...
    requires: list[str] = ...
    excludes: list[str] = ...
    @classmethod
    def default(cls) -> list[Any]: ...
    @classmethod
    def preprocess(cls, sort) -> list[str]: ...

class Order(Option, metaclass=OptionType):
    option = ...
    requires: list[str] = ...
    excludes: list[str] = ...
    @classmethod
    def default(cls) -> LexOrder: ...
    @classmethod
    def preprocess(cls, order) -> Callable[..., Any] | LexOrder: ...

class Field(BooleanOption, metaclass=OptionType):
    option = ...
    requires: list[str] = ...
    excludes = ...

class Greedy(BooleanOption, metaclass=OptionType):
    option = ...
    requires: list[str] = ...
    excludes = ...

class Composite(BooleanOption, metaclass=OptionType):
    option = ...
    @classmethod
    def default(cls) -> None: ...

    requires: list[str] = ...
    excludes = ...

class Domain(Option, metaclass=OptionType):
    option = ...
    requires: list[str] = ...
    excludes = ...
    after = ...
    _re_realfield = ...
    _re_complexfield = ...
    _re_finitefield = ...
    _re_polynomial = ...
    _re_fraction = ...
    _re_algebraic = ...
    @classmethod
    def preprocess(cls, domain) -> Any | GaussianIntegerRing | GaussianRationalField: ...
    @classmethod
    def postprocess(cls, options) -> None: ...

class Split(BooleanOption, metaclass=OptionType):
    option = ...
    requires: list[str] = ...
    excludes = ...
    @classmethod
    def postprocess(cls, options) -> None: ...

class Gaussian(BooleanOption, metaclass=OptionType):
    option = ...
    requires: list[str] = ...
    excludes = ...
    @classmethod
    def postprocess(cls, options) -> None: ...

class Extension(Option, metaclass=OptionType):
    option = ...
    requires: list[str] = ...
    excludes = ...
    @classmethod
    def preprocess(cls, extension) -> bool | set[Any] | None: ...
    @classmethod
    def postprocess(cls, options) -> None: ...

class Modulus(Option, metaclass=OptionType):
    option = ...
    requires: list[str] = ...
    excludes = ...
    @classmethod
    def preprocess(cls, modulus) -> int: ...
    @classmethod
    def postprocess(cls, options) -> None: ...

class Symmetric(BooleanOption, metaclass=OptionType):
    option = ...
    requires = ...
    excludes = ...

class Strict(BooleanOption, metaclass=OptionType):
    option = ...
    @classmethod
    def default(cls) -> Literal[True]: ...

class Auto(BooleanOption, Flag, metaclass=OptionType):
    option = ...
    after = ...
    @classmethod
    def default(cls) -> Literal[True]: ...
    @classmethod
    def postprocess(cls, options) -> None: ...

class Frac(BooleanOption, Flag, metaclass=OptionType):
    option = ...
    @classmethod
    def default(cls) -> Literal[False]: ...

class Formal(BooleanOption, Flag, metaclass=OptionType):
    option = ...
    @classmethod
    def default(cls) -> Literal[False]: ...

class Polys(BooleanOption, Flag, metaclass=OptionType):
    option = ...

class Include(BooleanOption, Flag, metaclass=OptionType):
    option = ...
    @classmethod
    def default(cls) -> Literal[False]: ...

class All(BooleanOption, Flag, metaclass=OptionType):
    option = ...
    @classmethod
    def default(cls) -> Literal[False]: ...

class Gen(Flag, metaclass=OptionType):
    option = ...
    @classmethod
    def default(cls) -> Literal[0]: ...
    @classmethod
    def preprocess(cls, gen) -> Basic | int: ...

class Series(BooleanOption, Flag, metaclass=OptionType):
    option = ...
    @classmethod
    def default(cls) -> Literal[False]: ...

class Symbols(Flag, metaclass=OptionType):
    option = ...
    @classmethod
    def default(cls) -> Generator[Symbol | Any, Any, NoReturn]: ...
    @classmethod
    def preprocess(cls, symbols): ...

class Method(Flag, metaclass=OptionType):
    option = ...
    @classmethod
    def preprocess(cls, method) -> str: ...

def build_options(gens, args=...) -> Any: ...
def allowed_flags(args, flags) -> None: ...
def set_defaults(options, **defaults) -> dict[Any, Any]: ...