from typing import Any, Literal, LiteralString

class GaloisGroupException(Exception):
    ...


class ResolventException(GaloisGroupException):
    ...


class Resolvent:
    def __init__(self, F, X, s) -> None:
        ...
    
    def get_prec(self, M, target=...) -> int | Any:
        ...
    
    def approximate_roots_of_poly(self, T, target=...) -> list[Any]:
        ...
    
    @staticmethod
    def round_mpf(a) -> int | Any:
        ...
    
    def round_roots_to_integers_for_poly(self, T) -> dict[int, int | Any]:
        ...
    
    def eval_for_poly(self, T, find_integer_root=...) -> tuple[list[Any], int | Any | None, int | None]:
        ...
    


def wrap(text, width=...) -> LiteralString | Literal['']:
    ...

def s_vars(n) -> Any:
    ...

def sparse_symmetrize_resolvent_coeffs(F, X, s, verbose=...) -> tuple[list[Any], list[Any]]:
    ...

def define_resolvents() -> dict[tuple[Literal[4], Literal[0]] | tuple[Literal[4], Literal[1]] | tuple[Literal[5], Literal[1]] | tuple[Literal[6], Literal[1]] | tuple[Literal[6], Literal[2]], Any]:
    ...

def generate_lambda_lookup(verbose=..., trial_run=...) -> str:
    ...

def get_resolvent_by_lookup(T, number) -> list[Any]:
    ...

if __name__ == "__main__":
    verbose = ...
    trial_run = ...
    table = ...
