Deciding the nilpotency of the Galois group by computing elements in the centre
نویسندگان
چکیده
We present a new algorithm for computing the centre of the Galois group of a given polynomial f ∈ Q[x] along with its action on the set of roots of f , without previously computing the group. We show that every element in the centre is representable by a family of polynomials in Q[x]. For computing such polynomials, we use quadratic Newton-lifting and truncated expressions of the roots of f over a p-adic number field. As an application we give a method for deciding the nilpotency of the Galois group. If f is irreducible with nilpotent Galois group, an algorithm for computing it is proposed.
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عنوان ژورنال:
- Math. Comput.
دوره 73 شماره
صفحات -
تاریخ انتشار 2004