Feat: Add tp5

ex5.py

@@ -0,0 +1,31 @@
+
+class Point:
+    def __init__(self, x: float, y: float):
+        self.x = x
+        self.y = y
+
+
+def interpolation_lagrange(points: list[Point], x: float) -> float:
+    interpolation: float = 0.
+    n = len(points)
+    for i in range(n):
+        term: float = 1. # 0.0 will always give 0, it's a product ! So lets put 1
+        # Lagrange L(x)
+        for k in range(n):
+            if k != i:
+                term *= ((x - points[k].x) / (points[i].x - points[k].x))
+        # interpolation with a piece of Lagrange (y_i)
+        interpolation += term * points[i].y
+
+    return interpolation
+
+
+def interpolation_newton(points: list[Point], x: float) -> float:
+    interpolation = 0. # alpha sum
+    n = len(points)
+    for i in range(n):
+        a_i = 1.
+        for k in range(n-1):
+            a_i *= (points[k+1].y - points[k].y) / (points[k+1].x - points[k].x)
+
+    return interpolation