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Question: Decomposition fields of polynomials and generator of a cyclic Galois group.

Question:Decomposition fields of polynomials and generator of a cyclic Galois group.

petit loup 40 Maple 2017
polynomial galois
July 23 2018
0

Hi all. I have two questions about polynomials over Q.

i) Let f,g be polynomials over Q. How to show (with Maple) that the decomposition field of f is included in the decomposition field of g?

ii) Let f be a polynomial of degree n  over Q with Galois group C_n, the cyclic group of order n. Then, there is a polynomial P with coefficients in Q, of degree n-1, s.t. the iteration: u0=some root of f, u_{k+1}=P(u_k) gives all the roots of f; how to find P (with Maple)?

Thanks in advance.
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