from typing import Any, Literal, Self
from sympy.core.numbers import Integer, Rational
from sympy.liealgebras.cartan_type import Standard_Cartan
from sympy.matrices import Matrix

class TypeF(Standard_Cartan):
    def __new__(cls, n) -> Self:
        ...
    
    def dimension(self) -> Literal[4]:
        ...
    
    def basic_root(self, i, j):
        ...
    
    def simple_root(self, i) -> list[int] | list[Rational | Any | Integer] | None:
        ...
    
    def positive_roots(self) -> dict[Any, Any]:
        ...
    
    def roots(self) -> Literal[48]:
        ...
    
    def cartan_matrix(self) -> Matrix:
        ...
    
    def basis(self) -> Literal[52]:
        ...
    
    def dynkin_diagram(self) -> str:
        ...
    


