Solving Index Form Equation in Fields of Degree 9 with Cubic Subfields

摘要

We describe an efficient algorithm for solving index form equatons in number fields of degree 9 which are composites of cubic fields with coprime discriminants. We develop the algorithm in detail for the case of complex cubic fields, but the main steps of the procedure are also applicable for other cases. Our most important tool is the main theorem of a recent paper of Gaal (1998a),