import unittest


class Point:

    def __init__(self, x, y, a, b):
        self.a = a
        self.b = b
        self.x = x
        self.y = y

        if self.x is None and self.y is None:
            return

        if self.y**2 != self.x**3 + a * x + b:
            raise ValueError('({}, {}) is not on the curve'.format(x, y))

    def __eq__(self, other):
        return self.x == other.x and self.y == other.y \
            and self.a == other.a and self.b == other.b

    def __ne__(self, other):
        # this should be the inverse of the == operator
        return self.x != other.x or self.y != other.y \
            or self.a != other.a or self.b != other.b

    def __repr__(self):
        if self.x is None:
            return 'Point(infinity)'
        else:
            return 'Point({},{})_{}_{}'.format(self.x, self.y, self.a, self.b)

    def __add__(self, other):
        if self.a != other.a or self.b != other.b:
            raise TypeError('Points {}, {} are not on the same curve'.format
                            (self, other))

        if self.x is None:
            return other
        if other.x is None:
            return self

        # Case 1: self.x == other.x, self.y != other.y
        # Result is point at infinity
        if self.x == other.x and self.y != other.y:
            return self.__class__(None, None, self.a, self.b)

        # Case 2: self.x ≠ other.x
        # Formula (x3,y3)==(x1,y1)+(x2,y2)
        # s=(y2-y1)/(x2-x1)
        # x3=s**2-x1-x2
        # y3=s*(x1-x3)-y1
        if self.x != other.x:
            s = (other.y-self.y)/(other.x-self.x)
            x = s**2-self.x-other.x
            y = s*(self.x-x)-self.y
            return self.__class__(x, y, self.a, self.b)

        # Case 3: self == other
        # Formula (x3,y3)=(x1,y1)+(x1,y1)
        # s=(3*x1**2+a)/(2*y1)
        # x3=s**2-2*x1
        # y3=s*(x1-x3)-y1

        s = (3*self.x**2+self.a)/(2*self.y)
        x = s**2-2*self.x
        y = s*(self.x-x)-self.y

        return self.__class__(x, y, self.a, self.b)


class PointTest(unittest.TestCase):

    def test_ne(self):
        a = Point(x=3, y=-7, a=5, b=7)
        b = Point(x=18, y=77, a=5, b=7)
        self.assertTrue(a != b)
        self.assertFalse(a != a)

    def test_add0(self):
        a = Point(x=None, y=None, a=5, b=7)
        b = Point(x=2, y=5, a=5, b=7)
        c = Point(x=2, y=-5, a=5, b=7)
        self.assertEqual(a + b, b)
        self.assertEqual(b + a, b)
        self.assertEqual(b + c, a)

    def test_add1(self):
        a = Point(x=3, y=7, a=5, b=7)
        b = Point(x=-1, y=-1, a=5, b=7)
        self.assertEqual(a + b, Point(x=2, y=-5, a=5, b=7))

    def test_add2(self):
        a = Point(x=-1, y=-1, a=5, b=7)
        self.assertEqual(a + a, Point(x=18, y=77, a=5, b=7))


unittest.main()