from typing import Any
from typing_extensions import Self

from sympy import Complement, ConditionSet, FiniteSet, Intersection
from sympy.core import Basic
from sympy.sets.sets import Set, Union

class ImplicitRegion(Basic):
    def __new__(cls, variables, equation) -> Self: ...
    @property
    def variables(self) -> Basic: ...
    @property
    def equation(self) -> Basic: ...
    @property
    def degree(self) -> Any: ...
    def regular_point(self) -> tuple[Any] | tuple[Any, Any] | tuple[int, int, Any] | type[list[Any]]: ...
    def singular_points(self) -> FiniteSet | Set | Intersection | Union | Complement | ConditionSet: ...
    def multiplicity(self, point) -> Any: ...
    def rational_parametrization(
        self, parameters=..., reg_point=...
    ) -> tuple[Basic] | tuple[Any, Any] | tuple[Any, Any, Any]: ...

def conic_coeff(variables, equation) -> tuple[Any, Any, Any, Any, Any, Any]: ...