Getting the trace polynomial
Dear all,
I am using sagemath to get the trace polynomial from a given reciprocal polynomial of even degree. The process is described nicely on the documentation. I am not allowed to post a link. See below for a concrete example.
However, the algorithm returns a triple (Q,R,q). For further calculations, I need to take out just the polynomial Q. Here is an example
pol.<x> = PolynomialRing(Rationals()) sage: u = x^6 +1; u1=u.trace_polynomial()
The algorithm returns u1=(x3−3∗x,1,1) (in my examples, I know that R=q=1 always). How can I get the first component of u1?
Edit: Simply take u1[0] as suggested below by another user.
How can we resolve this problem? I am sorry if my question is too trivial. Thank you very much!
Best wishes, Tung