The computation of the fundamental unit of totally complex quartic orders

Buchmann, Johannes

doi:10.1090/S0025-5718-1987-0866097-1

The computation of the fundamental unit of totally complex quartic orders

Author: Johannes Buchmann
Journal: Math. Comp. 48 (1987), 39-54
MSC: Primary 11Y40; Secondary 11R16
DOI: https://doi.org/10.1090/S0025-5718-1987-0866097-1
MathSciNet review: 866097
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Abstract: We describe an efficient algorithm for the computation of the regulator and a fundamental unit of an arbitrary totally complex quartic order. We analyze its complexity and we present tables with computational results for the orders ${\mathbf{Z}}{[^4}\sqrt { - d} ]$ , $1 \leqslant d \leqslant 500$ .

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