Pyupgrade to Python 3.9 (#4718)

* Pyupgrade to Python 3.9

* updating DIRECTORY.md

Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>

arithmetic_analysis/in_static_equilibrium.py

@@ -1,14 +1,14 @@
 """
 Checks if a system of forces is in static equilibrium.
 """
-from typing import List
+from __future__ import annotations
 
 from numpy import array, cos, cross, ndarray, radians, sin
 
 
 def polar_force(
     magnitude: float, angle: float, radian_mode: bool = False
-) -> List[float]:
+) -> list[float]:
     """
     Resolves force along rectangular components.
     (force, angle) => (force_x, force_y)

arithmetic_analysis/lu_decomposition.py

@@ -3,12 +3,12 @@
 Reference:
 - https://en.wikipedia.org/wiki/LU_decomposition
 """
-from typing import Tuple
+from __future__ import annotations
 
 import numpy as np
 
 
-def lower_upper_decomposition(table: np.ndarray) -> Tuple[np.ndarray, np.ndarray]:
+def lower_upper_decomposition(table: np.ndarray) -> tuple[np.ndarray, np.ndarray]:
     """Lower-Upper (LU) Decomposition
 
     Example:

arithmetic_analysis/newton_forward_interpolation.py

@@ -1,7 +1,7 @@
 # https://www.geeksforgeeks.org/newton-forward-backward-interpolation/
+from __future__ import annotations
 
 import math
-from typing import List
 
 
 # for calculating u value
@@ -22,7 +22,7 @@ def ucal(u: float, p: int) -> float:
 
 def main() -> None:
     n = int(input("enter the numbers of values: "))
-    y: List[List[float]] = []
+    y: list[list[float]] = []
     for i in range(n):
         y.append([])
     for i in range(n):

arithmetic_analysis/newton_raphson.py

@@ -2,15 +2,16 @@
 # Author: Syed Haseeb Shah (github.com/QuantumNovice)
 # The Newton-Raphson method (also known as Newton's method) is a way to
 # quickly find a good approximation for the root of a real-valued function
+from __future__ import annotations
+
 from decimal import Decimal
 from math import *  # noqa: F401, F403
-from typing import Union
 
 from sympy import diff
 
 
 def newton_raphson(
-    func: str, a: Union[float, Decimal], precision: float = 10 ** -10
+    func: str, a: float | Decimal, precision: float = 10 ** -10
 ) -> float:
     """Finds root from the point 'a' onwards by Newton-Raphson method
     >>> newton_raphson("sin(x)", 2)