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Mathematics of Computation

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Enumeration of quartic fields of small discriminant

Authors: Johannes Buchmann, David Ford and Michael Pohst
Journal: Math. Comp. 61 (1993), 873-879
MSC: Primary 11R16; Secondary 11R32, 11R80
MathSciNet review: 1176706
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Abstract: With the mixed-type case now completed, all algebraic number fields of degree 4 with absolute discriminant $ < {10^6}$ have been enumerated. Methods from the totally real and totally complex cases were used without major modification. Isomorphism of fields was determined by a method similar to one of Lenstra. The $ {T_2}$ criterion of Pohst was applied to reduce the number of redundant examples.

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Article copyright: © Copyright 1993 American Mathematical Society