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We describe an efficient algorithm to calculate generators of power integralbases in composites of totally real fields with imaginary quadratic fields. Weshow that the calculation can be reduced to solving index form equations in theoriginal totally real fields.  We illustrate our method by investigating monogenity in the infiniteparametric family of imaginary quadratic extensions of the simplest quarticfields.

Monogenity in totally real extensions of imaginary quadratic fields with an application to simplest quartic fields