Calculating Generators of Power Integral Bases in Sextic Fields with a Quadratic Subfield: The General Case

In some previous works we gave algorithms for determining generators of power integral basis in sextic fields with a quadratic subfield, under certain restrictions. The purpose of the present paper is to extend those methods to the general case, when the relative integral basis of the sextic field over the quadratic subfield is of general form. This raises several technical difficulties, which we consider here.