We describe an algorithm which, forf∈Q[x] , determinesgandh∈Q[x] forming non-trivial decompositions,g○h, so thatf|g○h, when such exist.
Introduction. The following theorem linking polynomials, Galois group actions, and subfields, motivates our algorithm:.
Bibliographic details on Ideal Decompositions and Subfields.
May 10, 2021 · In this paper, we show that the decomposition group of a cyclotomic ring of arbitrary conductor may be utilised in order to significantly ...
Mar 26, 2016 · 1 Answer 1 ... OK, so here are the details. The decomposition law in cyclotomic extensions tells you that a prime p coprime to m splits completely ...
A pair g,h of polynomials of degree strictly smaller than that of f, such that f(x)|g(h(x)) is called an ideal decomposition. In the context of field extensions ...
Apr 29, 2016 · It means a decomposition of the ideal (p) as a product of prime ideals in the ring of integers of R. For a reference see, for example, math.
An algorithm for solving the principal ideal problem with subfields
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The principal ideal principal (PIP) is the problem of deciding whether a given ideal of a number field is principal and, if it is, of finding a generator.
Idea 2: Compute the remainder modulo prime ideals. Let. O ⊂ K(t) be a ring with max. ideal P. Then O is a good ring if: Fi (x,t) ∈ O[x]. The image of f (t) ...
May 26, 2021 · In this paper, we show that the decomposition group of a cyclotomic ring of arbitrary conductor may be utilised in order to significantly ...