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arXiv · 1606.01053

Splitting quaternion algebras over quadratic number fields

Péter Kutas
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Abstract

We propose an algorithm for finding zero divisors in quaternion algebras over quadratic number fields, or equivalently, solving homogeneous quadratic equations in three variables over $\mathbb{Q}(\sqrt{d})$ where $d$ is a square-free integer. The algorithm is randomized and runs in polynomial time if one is allowed to call oracles for factoring integers.

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Péter Kutas. 2016-06-03. Splitting quaternion algebras over quadratic number fields. https://arxiv.org/abs/1606.01053

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