from typing import Any

from sympy.core.basic import Basic
from sympy.core.symbol import Dummy
from sympy.functions.elementary.piecewise import Piecewise

def components(f, x) -> set[Any]: ...

_symbols_cache: dict[str, list[Dummy]] = ...

def heurisch_wrapper(
    f, x, rewrite=..., hints=..., mappings=..., retries=..., degree_offset=..., unnecessary_permutations=..., _try_heurisch=...
) -> Basic | Piecewise: ...

class BesselTable:
    def __init__(self) -> None: ...
    def diffs(self, f, n, z) -> tuple[Any, Any] | None: ...
    def has(self, f) -> bool: ...

_bessel_table = ...

class DiffCache:
    def __init__(self, x) -> None: ...
    def get_diff(self, f): ...

def heurisch(
    f, x, rewrite=..., hints=..., mappings=..., retries=..., degree_offset=..., unnecessary_permutations=..., _try_heurisch=...
): ...