A computer algorithm for finding new euclidean number fields
Roland Quême · Journal de Théorie des Nombres de Bordeaux · 1998
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 embedding of the degree n field 𝐊 into ℝ n and the structure of the unit group of 𝐊 . This articles ends with a generalization of the method for the determination of rings of S -integers of number fields euclidean for the norm and for the study of the inhomogeneous minimum of the norm form. Our results are in accordance with known results.