On sextic integral bases using relative quadratic extention

On integral bases in relative quadratic extensions

Let F be an algebraic number field and E a quadratic extension with E = F(√μ). We describe a minimal set of elements for generating the integral elements oE of E as an oF module. A consequence of this theoretical result is an algorithm for constructing such a set. The construction yields a simple procedure for computing an integral basis of E as well. In the last section, we present examples of...

Power integral bases in sextic fields with a cubic subfield

In the present paper we give an algorithm to compute generators of power integral bases having ”small” coordinates in an integral basis in sextic fields containing a cubic subfield. As an application of the method, we give a sufficient condition for infinite parametric families of number fields of this type to have power integral basis. To illustrate the statement we construct parametric famili...

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...

Calculating Power Integral Bases by Solving Relative Thue Equations

In our recent paper I. Gaál: Calculating “small” solutions of relative Thue equations, J. Experiment. Math. (to appear) we gave an efficient algorithm to calculate “small” solutions of relative Thue equations (where “small” means an upper bound of type 10500 for the sizes of solutions). Here we apply this algorithm to calculating power integral bases in sextic fields with an imaginary quadratic...

Friction Analysis Based on Integral Quadratic Constraints