Point.py

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):
        return not (self == other)
    
    def __add__(self, other):
        if self.a != other.a or self.b != other.b:
            raise TypeError('Point {}, {} are not on the same curve'.formet(self, other))
        
        if self.x is None:
            return other
        
        if other.x is None:
            return self
        
        if self.x == other.x and self.y != other.y:
            return self.__class__(None, None, self.a, self.b)
        
        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)
        
        if self == other:
            s = (3 * self.x**2 + self.a)
            x = s**2 + 2 * self.x
            y = s * (self.x - x) - self.y
            return self.__class__(x, y, self.a, self.b)
        
        if self == other and self.y == 0 * self.x:
            return self.__class__(None, None, self.a, self.b)
        
    def __str__(self):
        return "Point(" + str(self.x) + "," +str(self.y) + ")_" + str(self.a) + "_" + str(self.b)