The Computation of the Fundamental Unit of Totally Complex Quartic Orders
Johannes A Buchmann · Mathematics of Computation · 1987
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 ${\mathbf {Z}}{[^4}\sqrt { - d} ]$, $1 \leqslant d \leqslant 500$.