def __init__(self, x, y):

self.x = x

self.y = y

def add(self, other, curve, mod):

if self.x == float("inf") and self.y == float("inf") and other.x == float("inf") and other.y == float("inf"):

return (float("inf"), float("inf"))

elif self.x == float("inf") and self.y == float("inf"):

return other

elif other.x == float("inf") and other.y == float("inf"):

return self

point1_curve = self.check_curve(self.x, self.y, curve[0], curve[1], mod)

point2_curve = self.check_curve(other.x, other.y, curve[0], curve[1], mod)

if not point1_curve or not point2_curve:

return "One point is not on the curve"

elif (self.x == other.x) and (self.y == other.y):

d_up = 3 * self.x ** 2 + curve[0]

d_low = 2 * self.y

elif self.x == other.x:

return (float('inf'), float('inf'))

else:

#(y2 - y1),(x2 - x1)

d_up = other.y - self.y

d_low = other.x - self.x

d_low_mi = gmpy.invert(d_low, mod)

lmb = (d_up * d_low_mi) % mod

fin_x = (lmb ** 2 - other.x - self.x) % mod

fin_y = (lmb * (self.x - fin_x) - self.y) % mod

return Point(fin_x, fin_y)

def check_curve(self, x, y, a, b, mod):

# Equation: y^2 = x^3 + ax + b

first_side = y ** 2

second_side = x ** 3 + a * x + b