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On the resolution of relative Thue equations

2001; American Mathematical Society; Volume: 71; Issue: 237 Linguagem: Inglês

10.1090/s0025-5718-01-01329-1

1088-6842

István Gaál, Michael Pohst,

Polynomial and algebraic computation

An efficient algorithm is given for the resolution of relative Thue equations. The essential improvement is the application of an appropriate version of Wildanger's enumeration procedure based on the ellipsoid method of Fincke and Pohst. Recently relative Thue equations have gained an important application, e.g., in computing power integral bases in algebraic number fields. The presented methods can surely be used to speed up those algorithms. The method is illustrated by numerical examples.