Mathematics of Computation

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ISSN 1088-6842(e) ISSN 0025-5718(p)

Computing all power integral bases in orders of totally real cyclic sextic number fields

Author(s): István Gaál.
Journal: Math. Comp. 65 (1996), 801-822.
MSC (1991): Primary 11Y50; Secondary 11Y40, 11D57
MathSciNet review: 1333313
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Abstract: 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 the paper, numerical examples are given.

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