Solving index form equations in fields of degree 9 with cubic subfields
This paper gives a detailed description of an effective algorithm for solving index form equations in number fields of degree 9, which are composites of complex cubic fields with coprime discriminants. In view of a recent result by the author [Can. Math. Bull. 41, 158-165 (1998; Zbl 0951.11012)], the index form equation may be reduced to cubic relative Thue equations over the cubic subfields. The most difficult computational task is to solve these Thue equations. The main purpose of the paper is to show that the present approach is much more effective than the direct method, which reduces the index form equation to unit equations over the normal closure of the degree 9 field. At the end of the paper, the author describes his computational experience with three explicit examples.
scientific article; zbMATH DE number 1513057
scientific article