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arXiv · 1911.12453

On parameters of orders of quartic fields and essential pairs -- extended version

Samuel A. Hambleton·Randy Yee
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Abstract

Classes of pairs of ternary quadratic forms parametrize quartic rings by a result of Bhargava. We give an algorithm for finding a pair of ternary quadratic forms that parametrize a given order of a quartic field. We examine a new technique, essential pairs, for obtaining parameters of orders of quartic fields from a number field database. Essential pairs for maximal orders of quartic fields are very common and provide a simple means of obtaining an integral basis for the ring of integers.

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Samuel A. Hambleton, Randy Yee. 2019-11-27. On parameters of orders of quartic fields and essential pairs -- extended version. https://arxiv.org/abs/1911.12453

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