Delete arithmetic_analysis/ directory and relocate its contents (#10824)

* Remove eval from arithmetic_analysis/newton_raphson.py

* Relocate contents of arithmetic_analysis/

Delete the arithmetic_analysis/ directory and relocate its files because
the purpose of the directory was always ill-defined. "Arithmetic
analysis" isn't a field of math, and the directory's files contained
algorithms for linear algebra, numerical analysis, and physics.

Relocated the directory's linear algebra algorithms to linear_algebra/,
its numerical analysis algorithms to a new subdirectory called
maths/numerical_analysis/, and its single physics algorithm to physics/.

* updating DIRECTORY.md

---------

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

maths/numerical_analysis/newton_method.py

@@ -0,0 +1,54 @@
+"""Newton's Method."""
+
+# Newton's Method - https://en.wikipedia.org/wiki/Newton%27s_method
+from collections.abc import Callable
+
+RealFunc = Callable[[float], float]  # type alias for a real -> real function
+
+
+# function is the f(x) and derivative is the f'(x)
+def newton(
+    function: RealFunc,
+    derivative: RealFunc,
+    starting_int: int,
+) -> float:
+    """
+    >>> newton(lambda x: x ** 3 - 2 * x - 5, lambda x: 3 * x ** 2 - 2, 3)
+    2.0945514815423474
+    >>> newton(lambda x: x ** 3 - 1, lambda x: 3 * x ** 2, -2)
+    1.0
+    >>> newton(lambda x: x ** 3 - 1, lambda x: 3 * x ** 2, -4)
+    1.0000000000000102
+    >>> import math
+    >>> newton(math.sin, math.cos, 1)
+    0.0
+    >>> newton(math.sin, math.cos, 2)
+    3.141592653589793
+    >>> newton(math.cos, lambda x: -math.sin(x), 2)
+    1.5707963267948966
+    >>> newton(math.cos, lambda x: -math.sin(x), 0)
+    Traceback (most recent call last):
+        ...
+    ZeroDivisionError: Could not find root
+    """
+    prev_guess = float(starting_int)
+    while True:
+        try:
+            next_guess = prev_guess - function(prev_guess) / derivative(prev_guess)
+        except ZeroDivisionError:
+            raise ZeroDivisionError("Could not find root") from None
+        if abs(prev_guess - next_guess) < 10**-5:
+            return next_guess
+        prev_guess = next_guess
+
+
+def f(x: float) -> float:
+    return (x**3) - (2 * x) - 5
+
+
+def f1(x: float) -> float:
+    return 3 * (x**2) - 2
+
+
+if __name__ == "__main__":
+    print(newton(f, f1, 3))