Splitting quaternion algebras over quadratic number fields

06/03/2016

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by   Péter Kutas, et al.

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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 deterministic and runs in polynomial time if one is allowed to call oracles for factoring integers and polynomials over finite fields.