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Displaying similar documents to “Euclid's algorithm in algebraic function fields, II”

A computer algorithm for finding new euclidean number fields

Roland Quême (1998)

Journal de théorie des nombres de Bordeaux

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This article describes a computer algorithm which exhibits a sufficient condition for a number field to be euclidean for the norm. In the survey [3] p 405, Franz Lemmermeyer pointed out that 743 number fields where known (march 1994) to be euclidean (the first one, ℚ , discovered by Euclid, three centuries B.C.!). In the first months of 1997, we found more than 1200 new euclidean number fields of degree 4, 5 and 6 with a computer algorithm involving classical lattice properties of the...