from typing import Any

from sympy.core.numbers import Integer
from sympy.polys.domains.groundtypes import _GMPYInteger
from sympy.polys.domains.integerring import IntegerRing

class GMPYIntegerRing(IntegerRing):
    dtype = _GMPYInteger
    zero: _GMPYInteger
    one: _GMPYInteger
    tp: type[_GMPYInteger]
    alias = ...
    def __init__(self) -> None: ...
    def to_sympy(self, a) -> Integer: ...
    def from_sympy(self, a) -> _GMPYInteger: ...
    def from_FF_python(K1, a, K0) -> _GMPYInteger: ...
    def from_ZZ_python(K1, a, K0) -> _GMPYInteger: ...
    def from_QQ(K1, a, K0) -> _GMPYInteger | None: ...
    def from_QQ_python(K1, a, K0) -> _GMPYInteger | None: ...
    def from_FF_gmpy(K1, a, K0): ...
    def from_ZZ_gmpy(K1, a, K0): ...
    def from_QQ_gmpy(K1, a, K0) -> None: ...
    def from_RealField(K1, a, K0) -> _GMPYInteger | None: ...
    def from_GaussianIntegerRing(K1, a, K0) -> None: ...
    def gcdex(self, a, b) -> tuple[Any, Any, Any]: ...
    def gcd(self, a, b): ...
    def lcm(self, a, b): ...
    def sqrt(self, a) -> int: ...
    def factorial(self, a) -> int: ...