# point addition on elliptic curve

I have the following code where I want to add a 4-torsion point given by
`P=[15+36*B, 27*a*(a^2-4*B-5)]`

with `B^2=-2`

and `a^4-5*a^2-32=0`

and `Q=[r,s]`

on my elliptic curve `E`

as given below:

```
E=EllipticCurve([-3267,45630])
k.<B>=NumberField(x^2-2)
k.<a>=NumberField(x^4-5*x^2-32)
kr.<r>=FunctionField(k);
krS.<S>=kr[]
R.<s>=krS.quo(S^2-(r^3-3267*r+45630))
P=E(R)(15+36*B, 27*a*(a^2-4*B-5))
Q=E(R)(r,s)
P+Q
```

but it keeps giving error such as :

```
TypeError: unsupported operand parent(s) for '-': 'Number Field in a with defining polynomial x^4 - 5*x^2 - 32' and 'Number Field in B with defining polynomial x^2 - 2'
```

Can someone please advise me what is wrong in my coding.

I am not sure if this is appropriate but I think @nbruin perhaps knows how to answer this because you helped me in this kind of question before and it was so helpful.