COMPUTING NORMAL INTEGRAL BASES OF ABELIAN NUMBER FIELDS

Computing automorphisms of abelian number fields

Let L = Q(α) be an abelian number field of degree n. Most algorithms for computing the lattice of subfields of L require the computation of all the conjugates of α. This is usually achieved by factoring the minimal polynomial mα(x) of α over L. In practice, the existing algorithms for factoring polynomials over algebraic number fields can handle only problems of moderate size. In this paper we ...

Construction of Self-Dual Integral Normal Bases in Abelian Extensions of Finite and Local Fields

Let F/E be a finite Galois extension of fields with abelian Galois group Γ. A self-dual normal basis for F/E is a normal basis with the additional property that TrF/E(g(x), h(x)) = δg,h for g, h ∈ Γ. Bayer-Fluckiger and Lenstra have shown that when char(E) 6= 2, then F admits a self-dual normal basis if and only if [F : E] is odd. If F/E is an extension of finite fields and char(E) = 2, then F ...

Finding Normal Integral Bases of Cyclic Number Fields of Prime Degree

Computing all power integral bases in orders of totally real cyclic sextic number fields

An algorithm is given for determining all power integral bases in orders of totally real cyclic sextic number fields. The orders considered are in most cases the maximal orders of the fields. The corresponding index form equation is reduced to a relative Thue equation of degree 3 over the quadratic subfield and to some inhomogeneous Thue equations of degree 3 over the rationals. At the end of t...

Integral Bases for Number Fields Arising from Circulant Matrices

In this paper we compute integral bases for some algebraic number fields. Mathematics Subject Classification: 11R04, 11R09, 11S15