from typing import Any

from sympy.series.order import Order
from sympy.utilities import public

@public
def swinnerton_dyer_poly(n, x=..., polys=...) -> Any: ...
@public
def cyclotomic_poly(n, x=..., polys=...): ...
@public
def symmetric_poly(n, *gens, polys=...) -> Any | Order: ...
@public
def random_poly(x, n, inf, sup, domain=..., polys=...) -> Any: ...
@public
def interpolating_poly(n, x, X=..., Y=...) -> Order: ...
def fateman_poly_F_1(n) -> tuple[Any, Any, Any]: ...
def dmp_fateman_poly_F_1(
    n, K
) -> tuple[Any | list[Any] | list[list[Any]], Any | list[Any] | list[list[Any]], list[list[Any]] | Any | list[Any]]: ...
def fateman_poly_F_2(n) -> tuple[Any, Any, Any]: ...
def dmp_fateman_poly_F_2(
    n, K
) -> tuple[Any | list[Any] | list[list[Any]], Any | list[Any] | list[list[Any]], Any | list[list[Any]]]: ...
def fateman_poly_F_3(n) -> tuple[Any, Any, Any]: ...
def dmp_fateman_poly_F_3(
    n, K
) -> tuple[Any | list[Any] | list[list[Any]], Any | list[Any] | list[list[Any]], Any | list[list[Any]]]: ...
def f_polys() -> tuple[Any, Any, Any, Any, Any, Any, Any]: ...
def w_polys() -> tuple[Any, Any]: ...
