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/bisection.py

@@ -0,0 +1,55 @@
+from collections.abc import Callable
+
+
+def bisection(function: Callable[[float], float], a: float, b: float) -> float:
+    """
+    finds where function becomes 0 in [a,b] using bolzano
+    >>> bisection(lambda x: x ** 3 - 1, -5, 5)
+    1.0000000149011612
+    >>> bisection(lambda x: x ** 3 - 1, 2, 1000)
+    Traceback (most recent call last):
+        ...
+    ValueError: could not find root in given interval.
+    >>> bisection(lambda x: x ** 2 - 4 * x + 3, 0, 2)
+    1.0
+    >>> bisection(lambda x: x ** 2 - 4 * x + 3, 2, 4)
+    3.0
+    >>> bisection(lambda x: x ** 2 - 4 * x + 3, 4, 1000)
+    Traceback (most recent call last):
+        ...
+    ValueError: could not find root in given interval.
+    """
+    start: float = a
+    end: float = b
+    if function(a) == 0:  # one of the a or b is a root for the function
+        return a
+    elif function(b) == 0:
+        return b
+    elif (
+        function(a) * function(b) > 0
+    ):  # if none of these are root and they are both positive or negative,
+        # then this algorithm can't find the root
+        raise ValueError("could not find root in given interval.")
+    else:
+        mid: float = start + (end - start) / 2.0
+        while abs(start - mid) > 10**-7:  # until precisely equals to 10^-7
+            if function(mid) == 0:
+                return mid
+            elif function(mid) * function(start) < 0:
+                end = mid
+            else:
+                start = mid
+            mid = start + (end - start) / 2.0
+        return mid
+
+
+def f(x: float) -> float:
+    return x**3 - 2 * x - 5
+
+
+if __name__ == "__main__":
+    print(bisection(f, 1, 1000))
+
+    import doctest
+
+    doctest.testmod()