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>

physics/in_static_equilibrium.py

@@ -0,0 +1,94 @@
+"""
+Checks if a system of forces is in static equilibrium.
+"""
+from __future__ import annotations
+
+from numpy import array, cos, cross, float64, radians, sin
+from numpy.typing import NDArray
+
+
+def polar_force(
+    magnitude: float, angle: float, radian_mode: bool = False
+) -> list[float]:
+    """
+    Resolves force along rectangular components.
+    (force, angle) => (force_x, force_y)
+    >>> import math
+    >>> force = polar_force(10, 45)
+    >>> math.isclose(force[0], 7.071067811865477)
+    True
+    >>> math.isclose(force[1], 7.0710678118654755)
+    True
+    >>> force = polar_force(10, 3.14, radian_mode=True)
+    >>> math.isclose(force[0], -9.999987317275396)
+    True
+    >>> math.isclose(force[1], 0.01592652916486828)
+    True
+    """
+    if radian_mode:
+        return [magnitude * cos(angle), magnitude * sin(angle)]
+    return [magnitude * cos(radians(angle)), magnitude * sin(radians(angle))]
+
+
+def in_static_equilibrium(
+    forces: NDArray[float64], location: NDArray[float64], eps: float = 10**-1
+) -> bool:
+    """
+    Check if a system is in equilibrium.
+    It takes two numpy.array objects.
+    forces ==>  [
+                        [force1_x, force1_y],
+                        [force2_x, force2_y],
+                        ....]
+    location ==>  [
+                        [x1, y1],
+                        [x2, y2],
+                        ....]
+    >>> force = array([[1, 1], [-1, 2]])
+    >>> location = array([[1, 0], [10, 0]])
+    >>> in_static_equilibrium(force, location)
+    False
+    """
+    # summation of moments is zero
+    moments: NDArray[float64] = cross(location, forces)
+    sum_moments: float = sum(moments)
+    return abs(sum_moments) < eps
+
+
+if __name__ == "__main__":
+    # Test to check if it works
+    forces = array(
+        [
+            polar_force(718.4, 180 - 30),
+            polar_force(879.54, 45),
+            polar_force(100, -90),
+        ]
+    )
+
+    location: NDArray[float64] = array([[0, 0], [0, 0], [0, 0]])
+
+    assert in_static_equilibrium(forces, location)
+
+    # Problem 1 in image_data/2D_problems.jpg
+    forces = array(
+        [
+            polar_force(30 * 9.81, 15),
+            polar_force(215, 180 - 45),
+            polar_force(264, 90 - 30),
+        ]
+    )
+
+    location = array([[0, 0], [0, 0], [0, 0]])
+
+    assert in_static_equilibrium(forces, location)
+
+    # Problem in image_data/2D_problems_1.jpg
+    forces = array([[0, -2000], [0, -1200], [0, 15600], [0, -12400]])
+
+    location = array([[0, 0], [6, 0], [10, 0], [12, 0]])
+
+    assert in_static_equilibrium(forces, location)
+
+    import doctest
+
+    doctest.testmod()