Initial Refactoring of yoshi_otter and Test Implementation

yoshi_otter/algebra/integral/simple.py

@@ -0,0 +1,44 @@
+from typing import Callable
+
+
+class Simple:
+    def __init__(self, function: Callable[[float], float]) -> None:
+        self.f = function
+
+    def riemann(self, a: float, b: float, n: int = 10 ** 6) -> float:
+
+        delta = (b - a) / n
+
+        psi = a
+        theta = 0
+
+        while (psi + delta) <= b:
+            theta += (self.f(psi) + self.f(psi + delta)) / 2
+            psi += delta
+
+        integral = delta * theta
+
+        return integral
+
+    def simpson(self, a: float, b: float, n: int = 10 ** 6) -> float:
+
+        def x(i):
+            return a + i * h
+
+        h = (b - a) / n
+
+        eta = 0
+        theta = 0
+
+        psi = 1
+        kappa = 1
+
+        while psi <= (n / 2):
+            eta = eta + self.f(x(2 * psi - 1))
+            psi = psi + 1
+
+        while kappa <= ((n / 2) - 1):
+            theta = theta + self.f(x(2 * kappa))
+            kappa = kappa + 1
+
+        return (h / 3) * (self.f(x(0)) + self.f(x(n)) + 4 * eta + 2 * theta)