# point tripling over characteristics three field not getting proper result

import time p=(3^151)

```
F1.<x>=GF(3)[]
F.<a>=GF(3^151,'a',modulus=x^151+2*x^2+1);F.modulus();F
A=1;A
B=(0x1fc4865afe00a9216b0b5fd32c6300c4bed0707ae4072a03e55299f157b);B
E = EllipticCurve(F, (0,A,0,0,B));E
P = E.random_point();#P
Q = E.random_point();#Q
print "\n point1 =",P# P.xy()
print "\n point2 =",Q #Q.xy()
x1 = P[0]
y1 = P[1]
x2 = Q[0]
y2 = Q[1]
#x31=((y1^6)*(A^2*(x1^3+B)^2)^(-1))
#x32=((A*x1^3)*((x1+B)^(-1)))
#X3=(x31-x32);X3
#y31=((y1^9)*((A^3*(x1^3+B)^3))^(-1));y31
#y32=((y1^3)*((x1^3+B)^(-1)));y32
#Y3=(y31-y32)
X3=F(((x1^3+B)^3-(B*x1^3))*((x1+B)^2)^(-1));X3
Y3=F(((y1^9)-((y1^3)*(x1^3+B)^2)*((x1+B)^3)^(-1)));Y3
R=E(X3,Y3);R
#print "\n H = P + Q has the components:\n
```

after executing the code the error is point are not on the curve. I have written the equation for x3 and y3 by different ways.

Please edit your post to format the code: select the code and press the

`101010`

button. Also, what is the source of these formulae?Paper: Efficient Arithmetic on Elliptic Curves over Fields of Characteristics three

You can vote on answers using the arrows on the left of them, and accept an answer by clicking the checkmark below the arrows; please do this (in general).