from collections.abc import Generator
from typing import Any, Literal, NoReturn

from sympy.utilities.decorator import public

def is_rat(c) -> Any | Literal[True]: ...
def is_int(c) -> Any | Literal[True]: ...
def get_num_denom(c) -> tuple[Any, Any]: ...
@public
def extract_fundamental_discriminant(a) -> tuple[dict[Any, Any], dict[int, int]] | tuple[dict[Any, Any], dict[Any, Any]]: ...
@public
class AlgIntPowers:
    def __init__(self, T, modulus=...) -> None: ...
    def red(self, exp): ...
    def __rmod__(self, other): ...
    def compute_up_through(self, e) -> None: ...
    def get(self, e) -> list[int] | list[Any]: ...
    def __getitem__(self, item) -> list[int] | list[Any]: ...

@public
def coeff_search(m, R) -> Generator[Any, Any, NoReturn]: ...
def supplement_a_subspace(M): ...
@public
def isolate(alg, eps=..., fast=...) -> tuple[Any, Any]: ...