Splitting quaternion algebras over quadratic number fields. (September 2019) - Kutas, Péter
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 Q ( 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.