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.
