def edwardsadd(P1,P2):
  x1,y1 = P1
  x2,y2 = P2
  x3 = (x1*y2+y1*x2)/(one+d*x1*y1*x2*y2)
  y3 = (y1*y2-x1*x2)/(one-d*x1*y1*x2*y2)
  return x3,y3

# example:
one = 1
d = -300
P1 = (0.8,-0.043188945044921672046)
P2 = (-0.4,0.130930734141595428759)

print edwardsadd(P1,P2)
# output: (0.26691902067523626, 0.20374230558087345)
print edwardsadd(P2,P1)
# output: (0.26691902067523626, 0.20374230558087345)

def F(p):
  # caveat: caller must ensure that p is prime
  class F:
    def __init__(self,x):
      self.int = x % p
    def __str__(self):
      return str(self.int)
    __repr__ = __str__
    def __eq__(a,b):
      return a.int == b.int
    def __ne__(a,b):
      return a.int != b.int
    def __add__(a,b):
      return F(a.int + b.int)
    def __sub__(a,b):
      return F(a.int - b.int)
    def __mul__(a,b):
      return F(a.int * b.int)
    def __div__(a,b):
      # caveat: caller must ensure that b is nonzero
      return a*F(pow(b.int,p-2,p))
  return F

# example:
F1009 = F(1009)
d = F1009(-11)
one = F1009(1)

P1 = (F1009(7),F1009(415))
P2 = (F1009(23),F1009(487))

print edwardsadd(P1,P2)
# output: (944, 175)
print edwardsadd(P2,P1)
# output: (944, 175)