"""
Exercise 9.6 from "A primer on..."
Create a subclass of the class to 
represent a point using polar coordinates.

"""

import numpy as np

class Point:
    def __init__(self, x, y):
        self.x, self.y = x, y

    def __str__(self):
        return f'({self.x}, {self.y})' 

class PolarPoint(Point):
    def __init__(self, r, theta):
        self.r = r
        self.theta = theta
        x = r * np.cos(theta)
        y = r * np.sin(theta)
        super().__init__(x, y)

    def __str__(self):
        return super().__str__() + f', ({self.r}, {self.theta})'


def test_PolarPoint():
    #create one instance of the class and
    # verify that all attributes have expected values:
    tol = 1e-8
    pp = PolarPoint(1, np.pi)
    #expected values:
    x, y, r, theta = -1, 0, 1, np.pi
    max_error = max(abs(pp.x - x), abs(pp.y - y), abs(pp.r - r), abs(pp.theta - theta))
    assert max_error < tol


if __name__ == "__main__":
    #call the test function
    test_PolarPoint()   

    #example code to demonstrate class use:
    p = PolarPoint(1, np.pi)
    print(p)