def lagrange_polynom(points, j):
    nom = ""
    dem = 1
    xj = points[j][0]
    for u in range(len(points)):
        if u == j:
            continue
        nom += f"(x - {points[u][0]})"
        dem *= xj - points[u][0]
    return (nom, dem)

def interpolate_lagrange(points):
    n = len(points)
    poly = ""
    for i in range(n):
        (lagrange, dem) = lagrange_polynom(points, i)
        poly += f" + {points[i][1]*dem}*{lagrange}"
    return poly

def test():
    points = [[1,2], [3,5], [4,-1]]
    print(f"polynom via lagrange: {interpolate_lagrange(points)}")